Levels in 156Gd studied in the (n, γ) reaction

Nuclear Physics A380 (1982) 189-260 © North-Holland Publishing Company

LEVELS IN ' s6Gd STUDIED IN THE (a, ~y) REACTION A. BÂCKLIN*, G. HEDIN, B. FOGELBERG and M. SARACENO The Studsvik Science Researcch Laboratory, Studsvik, Nykôping, Sweden.

R.C. GREENWOOD and C.W . REICH Idaho National Engineering Laboratory, EG & G Idaho, Inc., Idaho Falls, Idaho 83415, USA** H.R . KOCH***, H.A . BARDER, H.D . BREITIG**** and O.W.B . SCHULT**" Technische Universität München, München, Germany and Danish Atomic Energy Commission, Research Establishment Ris,I, Roskilde, Denmark and

K. SCHRECKENBACH*****, T. VON EGIDY and W. MAMPE***** Technische UniversitätMünchen, München, Gernrany Received 7 July 1981 (Revised 13 November 1981) Abslrad: Levels up to 2.3 MeV in 1ssGd have been studied using the (n, y) reaction . Energies and intensities of low-energy y-rays and electrons emitted after thermal neutron capture have been measured with a curved-crystal spectrometer, Ge(Li) detectors and a magnetic electron spec trometer . High-energy (primary) y-rays and electrons have been measured with Ge(Li) detectors and a magnetic spectrometer . The high-energy y-ray spectrum has also been measured in thermal neutron capture in 2 keV resonance neutron capture. The neutron separation energy in 13sGd was measured as S = 8535 .8 t0.5 keV. About 600 transitions were observed of which ^-50°k could be placed in a level scheme containing more than SO levels up to 2.3 MeV excitation energy . 42 of these levels were grouped into 15 excited bands. In addition to the ß-band at 1050 keV we observe 0+ bands at 1168, 1715 and 1851 keV. Other positive-parity bands are: 1+ bands at 1966, 2027 and 2187 keV; 2+ bands at 1154 (y-band) and 1828 keV; and 4+ banda at 1511 and 1861 keV. Negative-parity bands are observed at 1243 keV (1 -), 1366 keV (0-), 1780 keV (2 -) and 2045 keV (4 -). Reduced E2 and EO transition probabilities have been derived for many transitions. The ground band, the ß- and y-bands and the 0+ band at 1168 keV have been included in a phenomenological four-band mixing calculation, which reproduces well the experimental energies and E2 transition probabilities. The lowest three negative-parity (octupole) bands of which the 0- and the 1- bands are very strongly mixed, were included in a Coriolis-coupling analysis, which reproduces well the observed energies . The El transition probabilities to the ground band are also well reproduced, while those * Present address: Tandem Accelerator Laboratory, Box 533, Uppsala, Sweden . ** Work supported by the US Department of Energy under DOE Contract no . DE-AC07-76ID0 1570. *** Present address: Institut für Kernphysik, Kernforschungsanlage Jülich, 517 Jülich, Germany. **** Present address: Zentrum für Klinische Grundlagen-Forschung, Universität Ulm, 73 Ulm, Germany. ***"* Present address: Institut Laue-Langevin, 38042 Grenoble Cedex, France . 189 May 1982

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from the higher-lying 0+ bands to the octupole bands are not reproduced . Absolute and relative transition probabilities have been compared with predictions of the IBA model and the pairingplus-quadrupole model. Both models reproduce well the E2 transitions from the y-band, while strong disagreements are found for the E2 transitions from the ß-band. The IBA model predicts part of the decay features of the higher lying 22, 4 ; and 2; bands. E

NUCLEAR REACTIONS 'ssGd(n, y)'S6Gd, E=thermal and averaged-resonance ; measured E I E«, I« . ~S6Gd deduced levels, J, a, ICC, B(A), neutron binding energy. Ge(Li) detectors, curved-crystal spectrometer, magnetic electron-spectrometers . Enriched targets.

1. Introdnction The lowest excitations in even deformed nuclei, generally quadrupole and octupole vibrations, have been fairly extensively studied during the last decades. At higher energies, where two-quasiparticle states and two-phonon vibrational states are expected, our knowledge is still fragmentary. A unique opportunity for obtaining a fairly complete picture of the levels with spin I ~ 6 in even deformed tssGd ts'Gd nuclei up to ~2 MeV is offered by the (n, y) reaction on and . These two nuclei have the extremely high capture cross sections of 61 000 b and 255 000 b, respectively r), which permits a variety of high-resolution spectrometers to be used for detection of the prompt electromagnetic transitions . Both nuclei have a groundstate spin of i-, thus permitting transitions from levels with I ~ 6 to be detected . In a joint project involving y-ray spectroscopy at Ris~l/München and Idaho and conversion-electron spectroscopy at Studsvik and München, these (n, y) reactions tseGd tseGd have been used to obtain information on the level structure of and . rseGd, z-s) Preliminary results on refs . and the work on 'se ed, ref. 6), have been published earlier. iseGd The low-energy level structure of has been extensively studied 1) under a tseEu variety of different experimental conditions, including: the ß-decay of rseTb [refs.'-")], the EC decay of [refs.'s-24)], charged particle induced transfer zs-Z8), s° reactions the (d, d') reaction z9), the (a, 2ny) reaction .3'), and Coulomb sz-sa excitation ) . In addition, several earlier studies of the (n, y) reaction exist, both s9-aa) as .ae) . with thermal neutrons and with resonance neutrons 2. Experiment 2.1 . GAMMA-RAY MEASUREMENTS

2.1 .1 . The curved-crystal y-spectrometer at Risk (Denmark) . The low-energy

y)rseGd y-ray spectrum following the reaction 1ssGd(na  was measured with the a') curved crystal spectrometer operated by the München group at the Risk reactor. rssGd oxide a FWHM of 2.6 s of arc Using a source of 18 mg of 99% enriched

A. Bâcklin et al. / issGd

19 1

-6 was obtained corresponding to an energy resolution of dE = 1.1 x 10 Ez,. (dE and E,, in keV) in the 5th-order reflection . The spectrum was scanned from 31 keV to 2 .4 MeV. The time of measurement at one angular position was 1 min for energies larger than 67 keV in the first-order reflection . At lower energies the time of measurement was reduced to 15 s. The crystal angle was changed in steps of 1 second

of arc. as) . As the crystal The K X-rays of Gd were used for the energy calibration spectrometer intensities are affected by energy-dependent uncertainties [y-ray 6)] we absorption in the source, diffraction power of the crystal and other effects have adjusted the intensities of the Risk measurement through multiplication with numbers which vary smoothly with the energy, so that, for the stronger lines, the resultant intensities agree with those determined in the Ge(Li) measurement. 2.1 .2. The Ge(Li) detector systems at Idaho 2.1 .2 .1 . Thermal-neutro n capture y-rays . Gamma-ray spectra following capture a'ssGd target were studied at the thermal-neutron capture of thermal neutrons in y-ray measurements facility at the materials testing reactor. This facility used an external neutron beam and target arrangement; with a maximum flux of 6 x 10 6 -z neutrons cm ~ s-' at the target position . This facility and the experimental techniques used to measure the y-ray spectra to obtain energies and intensities are described in ref. 49). The high-energy primary y-rays were measured with the two y)'saGd 6), reaction Ge(Li) detectors used in the companion work on the's'Gd(n, i.e ., the 5.8 cmz x 4 mm planar detector and the 12 cm3 coaxial detector . The targets consisted of either 3.2 or 9.0 mg of' ss Gdz03 enriched to 94 .4% in'ss Gd . The low-energy y-ray spectrum was also measured with the same Ge(Li) detectors 6), used in ref. i.e ., the 2 .3 cmz x 6 mm and the 6.4 cm z x 8 mm planar detectors, both of which have an energy resolution of ^-1 .0 keV FWHM at 100 keV and ^-1.7 keV FWHM at 1 MeV. Samples of enriched 'ss Gdz03 with masses ranging from 1 .4 to 5.8 mg were used as targets. Details of the energy calibration and y-ray spectral analysis procedures are given 6.49) . in refs . 2.1 .2 .2 . 2 keV neutron capture y-rays . The spectrum of primary y-rays resulting 'ssGd was measured using the Sc-filtered 2 keV from 2 keV neutron capture in neutron beam facility at the materials testing reactor, Idaho. The use of this facility a9.so) . A 5 cm 3 in neutron capture y-ray spectroscopy has been discussed in refs . coaxial Ge(Li) detector was used to detect the capture y-rays produced in the -z target. The 2 keV neutron flux obtained at this facility, -~-2 x 106 neutrons cm ~ s-', coupled with the low 2 keV neutron capture cross sections (typically, a few b or less) require large targets (a few grams or larger) to be used in order to obtain 'ssGdz03 (enriched to high-quality y-ray spectra . The 1 .7 g target of enriched 'ssGd) 74 .5% in used in this study was barely adequate and provided us with averaged capture data of only moderate quality, in terms of counting statistics and signal-to-background ratio.

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2 .2 . CONVERSION-ELECTRON MEASUREMENTS

2.2.1. The electron spectrometer at Studsvik. The conversion-electron spectrum was measured with the vrJ2 spectrometer at Studsvik sl) . The sources were of the voltage gradient type consisting of 20 strips 2 mm wide covering a total area of 4 x 4 cmZ. Doubly enriched material was usedt containing 98.73 % 'SSGd and 0.23 ts'Gd . The sources were made by electroplating gadolinium nitrate in acetone on 3 mg/cmZ aluminium backing. Because of the large capture cross section, a large density of lines should be observable in the spectrum . It was therefore necessary to work with the highest possible resolution . The spectrometer was adjusted to give a momentum resolution of 0.16% (FWHM) and the source thickness was chosen so that its contribution to the line width was at most 25% .Below 100 keV the line width slowly increased to about 0.3% at 40 keV due to field imperfections. Four different source thicknesses were employed ranging from 0.02 to 1 .4 mg/cmZ . The spectrum was recorded from 35 keV to 2.3 MeV electron energy, in total about 10 000 "points" were registered . The stability of the gas-filled detector system and the neutron beam monitor system was continuously checked and found to be within 5% . A part of the spectrum is shown in fig. 1 . Altogether the spectrum contained over 400 detectable lines associated with about 340 transitions. A special run to obtain good statistics was made of the L-group of the 111 .94 keV line. We obtained an intensity ratio Lt/LtI = 4 .7 f 0.8. A special computer program HELP was developed sZ) in order to make possible the resolution of the often very complicated line structures . Weak lines often had to be resolved from neighbouring much stronger lines which, in spite of the comparatively thin sources used, generally showed a non-negligible low-energy tail . Therefore the line profile had to be given very accurately. No combination of simple mathematical functions, such as, e .g., a gaussian for the line and an exponential for the tail, was found to reproduce the line shape well enough . We therefore preferred to describe the line shape numerically, i.e., in terms of a co-ordinate table of about 30 points . This table was obtained manually for a number of strong isolated lines and fed into the computer, which, for each line group to be resolved, first determined the standard line shape by interpolating between the given shapes . Only two parameters per line, i .e., height and position, were then fitted'by the least-squares program . Above a few-hundred keV, where the K/L ratios for the lowest multipole orders are very similar, and little additional information could be extracted from L subshell ratios, the intensities and positions of L and M + N + O lines were calculated using the corresponding K-line intensity and subtracted from the experimental data before the fitting procedure. t Purchased from Reaktorzentrum, Seibersdorf, Vienna .

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In the region below 1 MeV, where the resolution of the crystal diffraction spectrometer was superior to that of the or"l2 spectrometer, the accuracy of the fitted conversion-electron intensities for weak unresolved lines could be improved by inputting to the computer the positions of the K-lines as calculated from the energies obtained by the crystal diffraction spectrometer, leaving only the peak heights to be fitted . An example of the output from the HELP program is shown in fig. 2. 2.2.2. The conversion-electron spectrometer at München. The conversion-electron spectrum corresponding to the high energy primary transitions following issGd(n~, 1s6Gd was measured with the ß-spectrometer ss-ss) at the FRM reactor y) near München. The target consisted of enriched 1ssGdZ03 with 1.1% ls'GdZ03 impurity. Fabrication of the target was accomplished by depositing 10 mg/cm2 of the oxide onto a 1 x 8 cmZ backing of 1 mg/cmZ Al foil, covering it with a 0.2 mg/cm Z Al foil and pressing it with a pressure of 3000 kg/cmZ. Energies up to 8500 keV were scanned four times in steps of dp/p = 5 x 10 -4 and 5 min counting time per step. The resolution was dBp/Bp = 0.25% for 7 MeV electrons. The electron lines were fitted with a computer program. 3. Results 3 .1 . LOW-ENERGY TRANSITIONS

3.1 .1. Gamma rays . The low-energy y-ray measurements resulted in two independent sets of y-ray energies in the region 0 .089-2 .5 MeV, one being obtained with the bent-crystal spectrometer and the other with the Ge(Li) systems. For all transitions up to -~-1 MeV, where the two sets of data could be compared, excellent agreement was found. The results of the y-ray and conversion electron measurements are summarized in table A1 in the appendix . Up to -~-1 MeV the bent crystal data are superior both as regards sensitivity and resolution, but above that energy the Ge(Li) data become increasingly competitive. The data given in table A1 are those of the bent-crystal spectrometer up to 1 .2 MeV, with the intensities adjusted to the results of the Ge(Li) measurement as described in subsect. 2.1.1. In the region 1 .2-1.5 MeV both the energies and the intensities have been obtained as averages of the two data sets. Above 1 .5 MeV the Ge(Li) data are definitely superior to the bent crystal data . They also agree well with the data of ref. a4), which in this energy region were found to match the sensitivity of the conversion electron measurements better than the present y-ray data . The energies and intensities of y-rays above 1 .5 MeV given in table A1 are those of ref. °~). 3.1 .2. Conversion electrons. The low-energy conversion electron data are presented in the appendix, table A1. As mentioned in sect . 2 the energy values obtained in the y-ray measurements were generally more accurate than those obtained in

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the electron measurements . Therefore, for the conversion-electron data, only the electron intensities are given in table A1, except for the transitions, for which only conversion electrons were observed . Energy calibration was made at the bent crystal value of the 1040 .43 keV line for lines below 1 .3 MeV. A slight change of the spectrometer constant was noted, probably due to source thickness effects. Above 1 .3 MeV the electron spectrometer was energy-calibrated at the present Ge(Li) detector values for the energies of the 1682 .2 and 1965 .2 keV transitions . The transition energies deduced from the conversion electron lines generally agreed with the y-ray energies within the expected deviation, normally one or a few parts in 104. The electron intensities were normalized on the 296.53 keV, pure E2 transition . In view of possible source thickness effects the normalization constant was checked at a number of lines at higher energies with expected pure multipolarity, i.e., the 987.92, 1187 .14, 1230 .68, 1242 .47 and 1277.43 keV E1 transitions and the 1079 .24 keV E2 transition . Agreement was found within 10% .Theoretical converse) sion coefficients were interpolated from ref. up to 1550 keV and above that s'). ref. The multipolarity characters suggested by the conversion energy from coefficients are given to the right in table Al . It is interesting to note that above -~-1 .2 MeV the conversion electron measurement is more sensitive than the available y-ray experiments. 3 .2 . HIGH-ENERGY TRANSITIONS

3.2.1. Primary transitions following thermal-neutron capture 3 .2 .1.1 . Gamma rays. The energies and relative intensities of the primary y-rays measured using the Ge(Li) detector systems in Idaho are summarized in the appendix, table A2. From these data, a neutron separation energy of 8535 .8 t 0.5 keV is obtained for 1s6Gd. The relative intensities of the primary y-rays were converted to an absolute scale by using the absolute intensities of some of the strongest conversion lines (see below) . This procedure involved the assumption that the 5661 .6, 6033 .8, 6429.4, 6481 .7 and 7287 .7 keV transitions are pure E1 transitions and the use of the sa). theoretical conversion coefficients of Trusov issGd results primarily from a The thermal-neutron capture cross section of single compound-nucleus resonance, with an energy of 0 .0268 eV and I~ = 2-. Thus, primary dipole transitions following thermal-neutron capture will populate final states with spin values of 1, 2 and 3. It is thus reasonable to suggest that the spins of final states observed to be populated following such capture are limited to one of these three values . Because of the large statistical fluctuations in the intensities of the primary y-rays to states of the same parity which are expected to occur, and in fact are observed to occur (table A2), following thermal-neutron capture, the ability to make definitive parity assignments on the basis of these data

A. Bäcklin ct ai. / i3sGd

197

alone is severely limited. At best, it might be considered reasonable to assume that the strongest primary y-ray transitions have E1 multipolarity . Combination of these primary y-ray intensities with the internal-conversion data discussed in subsect. 3.2.1 .2 below does, however, provide unique multipolarity assignments. 3 .2.1.2. Conversion electrons. Energies and intensities of the high-energy electrons measured with the München spectrometer are shown in table A2 of the appendix. The conversion-electron energies were calibrated at the corresponding y-ray energies of the following lines: K 1040 .43, K 1129.41, K 1682.2, K 6033 .8 and K 7287 .7 keV. The electron intensities were corrected for burn-up of the target in the neutron flux of 4 x lO IZ n/cm 2 ~ s. Conversion-electron lines below 4 .5 MeV measured with the München specas) trometer have been published elsewhere . The absolute intensity calibration of the low-energy lines could thereby be extended to the transitions above 4.5 MeV with an accuracy of about 8% . 3.2.2. Primary transitions following capture of 2 keV neutrons. The energies and relative intensities of the primary y-rays resulting from 2 keV neutron capture, obtained with the Ge(Li) detector system in Idaho, are summarized in the appendix, table A3 . For 2 keV neutron capture in issGd, the neutron energy is still sufficiently low that s-wave capture predominates . Thus, compound-nucleus states with I~ =l and 2- are principally populated in this capture reaction, and primary dipole transitions will occur to final states with spin values of 0, 1, 2 and 3. The finite spread in the neutron energy distribution (---0.7 keV FWHM) ensures that the neutron-capture spectra result from an average over many compound-nucleus states in is6Gd [approximately 400 such states, assuming an average s-wave level spacing of 1 .8 eV, ref. s9 )]. This degree of averaging in this spectrum is sufficient to discriminate between primary El and M1 transitions on the basis of their intensity. issGd with I =1 and Additional discrimination is possible between finai states in 2 and those with I = 0 and 3 because the former states may be populated by dipole transitions from compound-nucleus states with either spin value, whereas the latter may be populated by dipole transitions from compound-nucleus states with only one spin value. For 2 keV neutron capture this leads to primary transitions to final states with 1=1 and 2 which are a factor -~-2.0 greater than those to final states with I = 0 and 3 [ref. e°)]. Thus, in a plot of the reduced primary y-ray intensities, I,,EY3, against the transition (or level) energy, the El transitions should be expected to fall along two distinct, essentially horizontal lines. Such a plot is shown in fig. 3, which shows that this expected behaviour is approximately true. It is thus possible to use this behaviour to distinguish between the spin alternatives 0 or 3 and 1 or 2. Negative-parity states are populated from the capture state either by M1 transitions after s-wave neutron capture or by El transitions after p-wave capture. It can be seen in fig. 3 that the resulting intensities fall below the stronger E1 intensities to the positive-parity states . The dashed lines in the diagram differ by a factor of two

A . Bücklin et al. / iscGd

19 8

0

500

1000 LEVEL

1500 ENERGY

2000

(keV)

Fig. 3. The reduced intensities I,.Ey3 of primary y-rays observed in the capture of 2 keV average resonance neutrons by issGd plotted as a function of the energy of the final level. Rings indicate primary y-rays to positive-parity states, squares those to negative-parity states . The numbers indicate known spin values . The dashed curves have been fitted approximately to the points with the only constraint that they differ by a factor of 2.0 (see text).

and have been adjusted roughly to fit those transitions leading to states with known I~ values . The fact that the curves deviate from an E;, dependence is probably due to the tail of the E1 giant resonance extending down into this energy region as). Comparison of these 2 keV neutron capture data with the averaged neutron capture data for the tssGd(n, y) reaction inferred by Bollinger and Thomas as) from measurements with a natural Gd target show satisfactory agreement, with no,major discrepancies evident. This gives us added confidence that, despite the relatively moderate quality of the 2 keV neutron capture spectrum obtained in the present work and the use of a natural Gd target by Bollinger and Thomas as), these two sets of averaged capture results can be used to provide reliable spin and parity assignments in tssGd . 4. Level scheme 4.1 . GENERAL PROCEDURE

Normally, the task of constructing a level scheme involving of the order of 500 transitions distributed between 0.1-2 .3 MeV is extremely difficult if extensive coincidence information is not available. The absence of any coincidence information in the present work was to some extent compensated for by the existence of complementary information on some transitions and levels .

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One of the main tools for deducing the levels from low-energy transition data "62), which calculated levels from was the energy combination program NUCLEV 61 transition energies and the energies of known levels . Since the probability for obtaining accidental combinations, in spite of the high energy accuracy of the present data, is in general very high, almost no level suggested by the program was taken to be true unless otherwise supported. Such support was available from zs-sz) charged particle reaction data and from the data on primary transitions as as) given in the present work and in ref. . As discussed above, the intensities of the primary transitions carry information on the spin and parity of the levels populated. Other strong support for the existence of several of the levels was obtained from 1s6Eu ll .la) radioactive decay, where for the decay, we utilized mainly refs . and, lss.f.b zs) for the decay, we used mainly ref. . Both of those decay schemes are very complex, each containing about 100 lines, not all of which have been placed in a level scheme . When transitions from a level candidate suggested by the NiJCLEV program showed the same intensity ratios in the (n, y) spectrum and in a radioactive decay, this was taken as strong support for the existence of the level. Further support for the levels was obtained from intensity considerations . From bs) empirical intensity curves one may with some confidence predict the feeding of a missing member of a rotational band (cf. fig. 4 and below) . Furthermore, members of the same rotational band generally exhibit similar decay patterns, which helps in identifying new members of the band .

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Fig. 4 . Relative population of bands in the reaction issGd (nw, y)iseGd as a function of the energy of the band head . In order to facilitate the comparison between bands the energy spacings between the levels in e band have been kept fixed according to the scale shown in the figure . Curves have been fitted to the OZ, 2i and 4i bands (full lines) and these "standard" profiles have then been used to roughly predict the population of band members of other bands (dashed lines) .

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In the early phase of this work only the first members of the OZ (ß-vibrational), 2i (y-vibrational), Oi and 11 (octupole) banddi' were known from radioactive decay work ~-1~ ' 18), (n, y) work 391 ) and inelastic deuteron scattering 29 ). Also the 4+ and 5+ states of the 4 i band were well known. The first results of the present work 2), together with concurrent radioactive decay work s) established the 03 band . The present level scheme was constructed as follows. From energy combinations between the very strongest E2 and E1 transitions we deduced the positions of: the 2 i and OZ bands" up through the 4+ states ; the seven negative-parity states with spins from 1 through 5 between 1242 and 1539 keV; and the first three members of the second excited K~ = 0+ band (03) at 1168 .21 keV. In addition, the 4+ and 5+ states at 1510 .5 and 1622 .5 keV, the 1851 .8 and 1934 .3 keV, 3- states seen in the 1ss.Lb decay ls.zo)~ and the 1965 .9 keV state seen in the 1ssEu decay la) were verified . These states, together with three states at 1506 .8,1771 .0 and 1916.35 keV, which were uniquely established from both primary y-rays and energy combinations, were taken as known levels in the first run with the NUCLEV program with all unplaced transitions below 1.1 MeV. From this run seven new levels between 1 .5 and 2.0 MeV, which could be supported by other evidence, were established. These additional levels were included among the known levels in the second computer run. This latter run suggested many additional states, and no further run was made since, with few exceptions, all strong and medium-intensity lines had by then been placed in the level scheme . The main part of the level scheme is given in fig. 5, which includes all the levels that could be grouped into rotational bands containing at least two members. Additional levels are given in table 1 . 4 .2 . THE GROUND-STATE (Oi) BANDt

The ground-state band up to the 14+ level is known from (a, 2ny) and Coulomb excitation experiments 30-35) . In the present experiment the transitions within the band up to the 6+ ~4+ were easily identified from their large intensities. The expected population for the 8 + level is so small (of the order of 5 units on the intensity scale of table Al) that the 8+ -> 6+ transition cannot be identified from the present data without additional information. The transition energies 380.2 keV obtained in the (a, 2ny) reaction 3~ and 380.6 keV obtained in Coulomb excitation 3s) suggest that the 380.381 keV transition observed by us is this transition, in agreement with the recently obtained value of 380.35 keV [ref. 31 )]. This proposal is supported by the observed intensity of 3 .3 units and the conversion coefficient, which corresponds to an E2 transition . t The bands are labelled according to their relative position in the level scheme . For example, the sernnd K~ =0` band is labelled 02.

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1s6Gd

20 1

TABLE 1

Levels in 1ssGd for which no definite K-assignment can be made') Initial level energy (keV) 1934 .20 `) (5)

1934 .33 ~ (4)

Final level

Transitions

I~

K~

energy (keV)

K, I~

energy (keV)

I,.

2-

2

88 .97 1154 .12 1247 .96 1258 .04 1242 .44 1276 .11 1319 .71 1366 .42 88 .97 288.18 1154 .12 1247 .96 1355 .38 1258 .04 1242 .44 1276 .11 1319 .71 0 58 .97 1242 .44 1366 .42 288.18 1247 .96 1355 .38 1506 .81 1408 .05 1462 .27 1622 .48 88 .97 288 .18 1154 .12 0 88 .97 1049 .50 1129 .40 1168 .21 1258 .04 1715 .16 1771 .04

Oh 2+ 21,2+ 21,3+ 03,2 +

1845 .5 780.23 686.33 676.14 691 .68 658 .31 614.49 567.68 1845 .5 1646 .2 780.23 686.33 578.94 676.14 691.68 658.31 614.49 1946 .1 1857 .5 709.90 585.80 (1676 .87) 717.09 609.65 458.24 556.69 502.90 342.57 2014 .4 1815 .7 949.17 2204 .9 2116 .5 `) 1156 .0 `) 1076 .0 `) 1037 .4 °) 947.5 `) 490.32 434.46

16 29 3.1 2.7 3.6 4 .7 51 27 43 37 26 4.9 5 .0 1 .1 2.5 2.1 1 .9 33 .6 48 22 3 .1 <10 37 8.5 4.8 1 .5 1 .5 0.30 27 4.2 24 11 .2 1 .47 1 .61 4.4 42 3.6 3 .2 3.1

3-

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2205 .50 °)

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0

(11), 1 (11), 311, 2(Ol), 1Ol, 2+ 0~, 4+ 21, 2+ 21, 3+ 2~,4 + 03,2 + (11), 1(11), 311, 2Ol, 0+ Ol, 2+ (11), 1(Ol), 1Ol, 4+ 21,3 + 21, 4+ 21, S+ (11), 503, 4+ 4~, 5 + Oh 2+ Oh 4+ 21, 2+ Ol, 0+ Ol, 2+ OZ, 0+ 0 2 , 2+ 03, 0' 03, 2+ 0,, 0+ 04, 2+

Multipolarity

El El E1 E2 Ml Ml M1+E2 El El El El El E2 Ml Ml El El Ml Ml+E2 (E1) El E1 El E2, Ml (El) (El) (El) (El) E1 E1 (El) (El) (El) (El) (El) E1 E1

') These levels are not shown in the level diagram, fig. 5. b) Tentative assignment, see text . `) The level is supported by data obtained in the decay of 1s6Tb , ref. z3). °) The level is supported by data obtained in the decay of ~ssEu, ref.'4) . q The transition could not be observed in the present experiment . The data are taken from the decay of 1ssEu, ref. 14). The intensities were normalized to the scale of table A1 of the appendix using the intensity of the 2204 .9 keV transition .

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1ssGd

TAHLE 2

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03

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Energy (keV)

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1049 .46 1040 .43 1009 .53

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1169 .09 1174 .22

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ea) where l1x is the atomic factor for EO conversion . The values in parentheses indicate the error in percent. ~9 Relative values as calculated with IBA-1 [ref. )]. Normalization was made on the . value for the OZ2+ -~ 012+ transition ~ Pairing-plus-quadrupole mode1 89). a) B(E2 ; OZO+-~ 0 1 2+) was obtained from the band-mixing calculations, see sect . 5. 3s) `) B(E2 ; Oz2+ -> 010+) was taken from ref. . The 1040 keV y-transition was taken as le) pure E2, ref. . ~) B(E2 ; OZ4+-~ 012+) was obtained from the 4+-" 2+ intraband transition assuming the 3~) same value of Qo as in the ground-state band . The OZ4+ -" 014+ y-transition was assumed to be pure E2 . The error given includes only the experimental error in the electron and y-intensities. ~ B(E2 ; 030+ -+012+) was obtained from the band-mixing calculations, see sect . 5. 3a) . The E2 percentage in the 032' -~ 0, 2+ n) B(E2 ; 032+ -~ 012+) was obtained from ref. transition was taken es (12 .6±zé)%,ref.'") . ') B(E2 ; 034+-~ 014+) was obtained from the 4+-> 2+ intraband transition assuming the 37) same value of Qo as in the ground-state band . The 034+ -> 014+ y-transition was assumed to be 100% E2 .

4.3 . THE 0+ BAND

(OZ)

AT 1049 keV

tseEu [refs. The 0 + and 2 + states of this band are well known from the decay of tS6Tb . [refs.'~Za)] '-l ')] and the 2 + and 4 + members are populated in the decay of The ß-vibrational character of this band is inferred from its observation in the av) se) (d, d') reaction and in Coulomb excitation . This interpretation is supported probabilities by the fairly large values of the reduced EO as given in table 2. The E2 decay of this band is treated in sect . 5. 3t) The 6 + level of the band has recently been observed at 1540 .3 keV. In the present experiment the population of this level is expected to be only about 20 of the intensity units of table A1 and transitions from this state are not observed .

A. Bäcklin et al. / iseGd

20 3

4 .4 . THE 2+ BAND (2 i) AT 1154 keV

1s6Tb The first three members of this band are known from the decay of [refs.'e-za)], and its collective character (y-vibration) is established by Coulomb se) of excitation the 2+ state and the excitation of the 2+ and 4+ states in the (d, d') s9) reaction . These states were also strongly populated in the (n, y) reaction and observed to decay through strong E2 transitions to the ground-state band . Two other strong E2 transitions with about the expected intensities form a combination suggesting the 5+ state at 1506 .8 keV. Strong support is obtained from the fact that a K, I~ = 2, 5+ state has been observed at 1508 keV in both the (d, p) and ze) (d, t) reactions . The level is probably fed also in the 156Th decay, since a weak zs) transition is observed at 921 .9 keV. (The expected stronger 1219 keV transition is probably masked by the 1222 keV transition between the 1510 keV and 288 keV levels, whose intensity is about 200 times stronger than that expected for the 1219 keV transition .) The 6+ level of this band has recently been observed at 1643 .8 keV [ref . 31 )] . In the present experiment we expect a population of about 30 units, with a predominant decay to the 0, 6+ level. A transition with an intensity of the right order of magnitude and no alternative position in the level scheme is observed at 1060 .1 keV, thereby tentatively suggesting an energy of 1644 .8 t 0.4 keV for the 6+ state . 4.5 . THE 0+ BAND (03) AT 1168 keV As has been reported earlier z) a second excited 0+ band, at 1168 keV, is observed in the (n, y) reaction . Further support for the band is obtained from peaks at the appropriate energies in the (d, p) and (d, t) reactions 2a) ; and two members of the band are observed in the 1s6Eu decay' -1') and the 156Th decay 18-Za) . In the recent (a, 2ny) experiment 31) the 6+ level of the band was suggested by a transition at 1180 .9 keV leading to the 6+ level of the ground-state band. In the present experiment this transition is masked by the very strong 1180 .4 keV transition . A weak transition observed at 303.96 keV could possibly be the 6+ -> 4+ intraband transition . The decay of this band is different from that of the OZ band . The reduced EO transition probabilities to the ground-state band are significantly weaker than those from the OZ band, (ef. table 2) . The E2 transition rates are treated in sect . 5. 4.6 . THE 0- AND 1 - BANDS AT 1242 AND 1366 keV The strongest E1 transitions in table A1 were found to combine into two states at 1242 .52 and 1366 .42 keV, whose decay modes required 1 - assignments. Similarly, two 3- states at 1276 .11 and 1538 .83 keV and a 5- state at 1408 .05 keV could be deduced from energy combinations . Transitions corresponding to the 1242, 1276 and 1366 keV levels are observed in the average resonance capture

204

A . Bäcklin et al.

Gd

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A. Bäcklin et aL

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work as) . The 1242, 1276 and 1408 keV levels are identified in the (d, t) ze) and (d, d') z9) reactions as members of an octupole vibrational band. Peaks corresponding to the 1366 and 1538 keV levels have also been observed in those reactions. Furthermore, the 1- and 3- levels have been observed in radioactive decay la.zs) . In addition to these levels we might expect 2- and 4- states in this energy region . The two strongest remaining E1 transitions may be placed ending at the 2+ and 4+ levels of the ground-state band, thus defining a 2- level at 1319 .65 keV and a 4- level at 1468 .55 keV. The existence of these levels is supported by radioactive decay data la .z3) and by the observation of a primary M1 or E2 transition to a level at 1319 keV (tables A2 and A3 in the appendix). From the Coriolis-mixing calculations, sect . 6, the second S- level is predicted to occur at 1803 keV. It is expected to decay to the 4+ and 6+ states in the ground-state band with E1 transitions with an intensity of the order of 40 units of table Al . We have not been able to locate this state and it is likely that at least one of the two expected transitions coincides with a stronger transition placed elsewhere in the level scheme . We have also looked for the lowest 7- state, but this is expected to have a population of the order of only 15 units of table Al, so it should be very difficult to observe in the present experiment [it was recently observed at 1638 keV in the (a, 2ny) reaction sl )]. As seen in fig. 5 the level spacings of the negative-parity states are irregular, indicating strong mixing among the odd-spin states . The grouping of these negativeparity bands shown in fig. 5 is based on the Coriolis-mixing analysis (see sect. 6) and is done for convenience only. The odd-spin states are highly mixed and K is not a very good quantum number for them . This is indicated in fig. 5 by including the K quantum numbers in parentheses. 4 .7 . THE 4+ BAND (4i) AT 1510 keV

Levels at 1510 and 1622 keV, with I~ = 4+ and 5+, respectively, are well known from studies of the 156Th decay la-z4). They are also populated in the (n, y) reaction and decay mainly to the ground-state band and the 21 band. The fact that we find no candidate for a lower-lying 3+ state with a population of the expected order of magnitude implies K= 4. A 3+ state in the appropriate energy region would also have been observed in the resonance capture study. Most of the transitions to the 2 i band are probably mixed M1 +E2 transitions, but the 414+ ~ 212+ and 414+ ~ 2 13+ transitions are mainly E2 (cf. table Al). Their intensity ratio deviates by a factor of 4 from the Alaga value, suggesting K-impurities . We expect the 6+ member of this band about 134 keV above the 5+ state. The transitions to the ground-state band are not expected to be strong enough to be observed, but the intraband transitions should be detectable . The only combination we find reasonably close to the expected energy consists of the 131 .112 and 243 .047 keV transitions corresponding to a 4, 6+ energy of 1753 .59 keV. The

A . Bücklin et al. / 1seGd

209

probability of finding an accidental combination of two transitions to the lower band members within an energy interval of 10 keV from the calculated position can be estimated to be only about 4% .Further support for this level is obtained from the fact that the branching ratios appear reasonable (see below) . These observations are in agreement with the recent (~, 2ny) experiment 3t) . From the present data the ratio Qô/(gx - gR) Z could be determined both from the E2/M1 mixing ratio of the 4, 5+ ~ 4, 4+ transition and from the branching ratio of the intraband transitions from the 4, 6+ level. As shown in table 3 the two values are consistent . By combining this information with the value of the magnetic moment ,u = 3.12 t 0.20 fcN, as given in ref. t9), the parameters gx and gn are obtained as gx = 0.88 t 0.10 and gR = 0.38 f 0.07 . The latter value agrees well with values observed for the corresponding quantity for the ground-state band 19 .65) and with the theoretical values calculated by Prior et al. 66) . As discussed in refs. 1 9 31 ) the value of gx indicates that the 4, 4+ state has a large component of the two-proton state (~+[413], z+[411])a~, which is predicted 6') at 1 .6 MeV. TABLE 3 Values of Qô/(gx - gx) Z for the 4+ band at 1510 .54 keV Method

Qô (8x - SR

Ll/Lll ratio of the 41 5'-> 414+ transition branching ratio from the 41 6 + level (Alaga rule) average

178 f 37 182 f 30 180 f 25

This band is most likely closely similar in character to the lowest 4+ band, at 6 1380 keV [ref. )], in the neighbouring doubly even isotope, 15gGd. In 158Gd, it was suggested 6) that this lowest 4+ band contains an appreciable mixture of the two-neutron state {z- [523], z [521]}4. The question of possible mixing between these two-proton and two-neutron states in the lowest 4+ band of 156Gd is an open question at present. Our deduced gx value is not inconsistent with a sizeable (up to ^-20%)admixture of this two-neutron state, but the experimental uncertainties are presently sufficiently large that no definite conclusions regarding the presence of a two-neutron component in the 4+ band can be drawn. 4.8 . THE K = 0 + BAND (0;) AT 1715 keV

The average resonance capture data, table A3, suggest a O+ or 3+ level at 1714 .6 t 0.5 keV. At 1715 .06 t 0.30 keV we observe a conversion line, for which our upper limit of the y-intensity implies a K-conversion coefficient corresponding to multipolarities equal to or higher than M2. Since such transitions from a level at this high energy are not a likely decay mode, we assign the 1715 .06 keV transition

21 0

A. Bäcklin et al. / iseGd

as an EO transition . Another transition with a K-conversion coefficient corresponding to a multipolarity of M2 or larger is found at 547 .20 keV. These two possible EO transitions combine with the .ground state and the 0+ state at 1168 .21 keV suggesting a 0+ level at about 1715 .2 keV, which agrees closely with the energies suggested for the K~ = 0+ or 3+ level in the average resonance capture experiments. In view of the extremely small probability of obtaining an accidental combination of two of the possible EO transitions with I~ = 0+ states we suggest an IK ~ = 00+ level at 1715 .2 keV. Further support for the level is obtained from three additional de-exciting transitions to low-spin states, see fig. 5 . The expected 1626.2 keV transition to the 2+ level in the Oi band is contained in the complex electron line at 1627 .98 keV. The work by Siddiqi et al. 44) shows a line at 1625 .5 keV, which is likely to be the 040+ ~ 012+ transition . The 2+ level of the band can be expected at about 1800 keV and should be populated with about 150 intensity units of table Al, cf. fig. 4. The only two candidates with I~ = 2+ inferred from the average capture data and the low-energy combinations are found at 1771 .04 and 1827 .78 keV. Of these only the former exhibits decay properties similar to those of the 0+ state, and we therefore assign it as the 04, 2+ state. Support for this assignment is provided by the fact that both the 1715 and 1771 keV states are populated in the 156Eu decay via the 2205 .50 keV level (see below) . The 4+ member of the band can be expected at about 1900 keV. Its decay should, if analogous to that of the 2+ level, proceed mainly via an M1 transition of the order of 70 units of intensity to the 4+ member of the Oi band. The 1605 .20 keV transition is the only likely candidate, since thé 1628 and 1646 keV transitions are too weak and are also placed in other positions in the level scheme (see below) . All three band members suggested are supported by peaks observed in the (d, t) zs) reaction . The band decays preferentially via M1 transitions to the Oi band. The 0+ state, which cannot decay via M1 transitions to the Oi band, strongly prefers E1 decay to the 1- state at 1242 keV. Other members of this negative-parity band also receive transitions from the 2+ state, while the corresponding transitions from the 4+ state are masked. For all members of the band dI = 0 transitions to the 0+ band at 1168 keV are observed. 4.9 . THE 2 - BAND (2 i) AT 1780 keV

The decay of 156Th populates a level at 1852 keV [ref. ss)] which decays preferentially to the 2+ , 3+ and 4+ members of the 2i band and to the 2+ and 4+ members of the Oi band. These transitions are found with the same intensity ratios in the (n, y) reaction, and we conclude from their E1 multipolarity that the 1851.7 keV 29) and level has I~ = 3-. The existence of this 3- state is supported by (d, d') data to some extent by single-neutron transfer reaction data 28)..The resonance averaged

A. Bäcklin et al. / iseGd

211

capture spectrum contains a transition corresponding to a level at 1850 .7 keV. It is not clear if this transition leads to this 3 - level or to the 0+ level at 1851 .23 keV (see below) . The branching ratios to the 2i band are compatible with K = 2, which is also the case for the branching to the Oi band, as observed in the decay of 1 s 6Tb, ref. z3) (the intensity of the 3- ~ 4+ transition being below our detection limit) . If there is a 2- state associated with this 3 - state, it should have a population of about 150 units in table Al . In the NUCLEV output we find only one level candidate in the appropriate energy region with that large a population, namely one at 1780 .38 keV. It decays, as does the 3- level, preferentially to the 21 band, with a branching in good agreement with the Alaga value for K; = 2. This level is further supported by four additional combinations involving K~ = 0+ and 0- bands, and by its observation in the (d, t) reaction 2s) . The 626.28 keV transition to the 2+ member of the 2i band is observed also in the 'S6Tb decay zs), implying that the 1780 .38 keV level is fed in this decay (the expected 532.42 keV transition from the 2- state to the 3+ member of the 2i band is masked by the 500 times stronger 534.3 keV transition). The 4- member of this band can be expected at about 1950 keV and should be populated strongly enough to be observed . Inspecting the region t70 keV around the expected energy, we observe three possible candidates for 4- levels, at 1952 .30, 1965 .05 and 1995 .47 keV. The latter is not likely to belong to the presently discussed band, since its decay pattern is considerably different from those of the 2- and 3- states . The candidates at 1952 .30 and 1965 .05 keV have several similar properties in that they both have the expected population in the (n, y) reaction and in the' S`Tb decay, and they both decay strongly to the 2i band. The following arguments favour the 1952.30 keV level as being the 4- member of this 2- band: (i) the E1 branching to the 2i band is in good agreement with the Alaga values for a K = 2 band, whereas that of the 1965 .05 keV level is not. (Since this behaviour is found for the 2- and 3- states, we may expect it to hold also for the 4- state.) (ü) we can place a transition as the 2, 4- ~ 2, 2- intraband transition from the 1952 .30 keV state, but not from the 1965 .05 keV state. From the intensity of the 171 .86 keV, 4- -> 2~ transition we can calculate retardation factors of about 104 for the E1 transitions to the 2i band . These represent rather fast transitions. The lack of an intraband transition from the 1965.05 keV level would imply even faster E1 transitions, which seems less likely . From the energies of the 2-, 3 - and 4- band members the first two coefficients of the I(I + 1) expansion of the rotational energy can be calculated. From these, the 5 - level of the band is predicted at 2086 keV. Its population is expected to be about 10 units in table Al . The energy region 2055-2095 keV was searched for combinations with the 21 band . Only one possible combination was found, corresponding to a level energy of 2066 .70 keV. Since the intensities of the involved transitions agree well with those expected, we tentatively assign this level as the 2, 5- state.

21 2

A. Bâcklin et aL / iseGd

4.10. THE K=2+ BAND (2Z) AT 1828 keV

The primary y-rays from the resonance averaged capture reaction yield a level with I~ =1 + or 2+ at 1827 .6 t 0.5 keV. At 1828.78 keV we find a combination of -s 8 transitions, which has a probability of the order of only 10 of occurring by chance within 1 keV of a given energy. The level decays with strong E2 transitions to the OZ and 2i bands and the branching ratios agree with the Alaga values for a K, I~ = 2, 2+ level. A level at 1827 keV was observed in the d, d') reaction z9) and assigned as a 1- state. If the latter assignment is correct the level is a close doublet, with the 1 - level too weakly populated in the (n, y) reaction to be revealed in this experiment. Additional support for a K, I~ = 2, 2+ assignment for the 1827 .78 keV level is obtained from the fact that no associated 1+ state, although it should have been easily observed, could be found and from the considerable EO admixture indicated by the large conversion coefficient of the di = 0 transition to the 2+ member of the 2i band . Inspecting the energy range where we expect the 3+ member of the band, we find at 1916 .35 keV a combination of 9 transitions, which, in the particular run with the NUCLEV program, had about a 5% probability of occurring by accident within an interval of 100 keV. Further support for this state is obtained from a 6622.7 keV primary y-ray, suggesting a level at 1915 .0 t 0.4 keV. As demonstrated in fig. 3 its intensity is clearly too large to correspond to I~ = 3 +. The large intensity is understandable if one assumes the 6622 .7 keV line to consist of a doublet leading partly to the 3+ state and. partly to a 1+ or 2+ state. As discussed below there is evidence for a 2+ state at 1914 .76 keV, which explains both the excess intensity and the poor energy agreement of the primary transition . The decay mode of the 3+ level is similar to that of the 2+ level, with strong E2 transitions to the OZ and 2i bands and an EO admixture in the transition to the 3+ member of the 2i band . The E2 branching ratios agree with the Alaga values for a K, I = 2, 3 state. The population of the 4+ member of the band can be expected to be about 40 units in table A1 and should be observed at about 2030 keV. We expect it to decay mainly via an Ml transition to the 4+ state in the Oi band. In the region 17401 50 keV only the 1732 .2 keV transition has the appropriate multipolarity and intensity, and it has no better alternative position in the level scheme . Support for this level is given by the fit of the 665 .48 keV transition to the 4+ member of the 2 i band. Further, this transition contains a strong EO component. At least some of this EO intensity may, however, be placed between the 0+ states at 1715 .16 and 1049 .50 keV, but considering the lack of EO transitions between other members of these K~ = 0+ bands, this placement seems less likely. Below 1 MeV, only four transitions were observed to have conversion coefficients large enough to definitely indicate an EO admixture. The fact that three of these have been placed as di = 0 transitions to the 2 i band strongly supports the existence of the band suggested.

A. Bäckün et al.

/ iseGd

21 3

No transitions from the 5 + state of the band are expected to be strong enough to be detected in the présent experiment. 4.11. THE K = 0+ BAND (Os) AT 1851 keV

As discussed in subsect. 4.10 the large intensity of the 6622.7 keV primary y-ray is compatible only with the existence of an unresolved doublet consisting of a 1 + or 2+ state in addition to the 3 + state at --1915 keV. Close to the established 3 + state at 1916 .35 keV, at 1914 .76 keV, we find a combination of 8 transitions as indicated in fig. 5 (a few additional transitions, which are likely to combine by accident, are not shown) . The relatively large number of combining transitions, together with the indication from the strength of the primary transition, is considered to be sufficient evidence to definitely establish the level, which, according to the decay mode, must be 2 + . The population of the level is about 90 units (table Al), and we therefore expect no difficulties in observing possible 1 + and 3 + states associated with the level, if they exist. The fact that, in spite of a careful search, we do not observe any candidates for such states in the appropriate energy regions indicates K = 0 for the 1914 .76 keV level. The strong Ml decay to the ground-state band also suggests a low K quantum number. The only candidate for a 0 + state in the region 1.8-1 .9 MeV is observed at 1851 .23 keV, where four transitions combine with low-spin states and a primary y-ray indicates a level with I~ = 0 + or 3 + . The decay mode is compatible with what can be expected for a 0 + state associated with the 2 + state at 1914.76 keV, i.e. medium strong El transitions to the 1 - states at 1242 and 1366 keV and possibly an E2 transition to the 2 + level in the ground-state band. In addition, a conversion line fits well to the ground state; the fact that no y-ray has been observed at this energy suggests an EO multipolarity. The 4 + state of the band can be expected around 2060 keV. At 2055.9 keV a number of E1 transitions combine with members of the negative-parity bands around 1 .3 MeV. Also an Ml or E2 transition with about the expected intensity may be placed to the 4 + state of the ground-state band, but the energy fit is rather poor and the state must be considered as tentative. 4.12. THE 4+ BAND (4Z) AT 1861 keV

Almost all strong transitions were straightforwardly placed in the level scheme in the early stage of this work . At the end of that phase a few strong transitions still remained unplaced, among these the 350.45 keV transition, which is the strongest Ml transition below 1 MeV. Its intensity is so large that it cannot for population reasons be placed higher than about 2 MeV (cf. fig. 4). Furthermore,

214

A. Bticklin et al. / issGd

such a strong line at so low an energy is likely to depopulate a state which does not have many decay branches to the already established states . The most plausible interpretation of this is the presence of K-forbiddenness, and it is therefore natural to look for combinations between the 350.45 keV transition and the lowest bands with the highest K quantum numbers. Indeed, the 350 .45 keV transition combines with the medium strong 238 .52 keV transition and the two lowest levels in the K = 4 + band at 1510 keV. The probability for a given transition to combine by accident with any transition in this energy region with an intensity of, say, greater than 1 unit in table A1 is of the order of 10 -3 . In view of this small random probability and the above discussion, it seems natural to suggest a level at 1861 .00 keV. The spin must be 3+, 4+ or 5+. Unfortunately the multipolarity of the 238 .52 keV line could not be determined, since the K-conversion line is masked by the M-line of the strong 199.21 keV transition . However, in view of the discussion above and the fact that no transitions to the 2 i band were observed, I~ = 4 + or 5 + are the most likely alternatives . Inspection of the appropriate energy region above the 1861 keV level for possible higher members of the band, defined by combinations with the 4 i band at 1510 keV, reveals only one candidate, at 1962 keV, defined by transitions to the 4+, 5+ and 6 + states of the 4 i band . Further support for this band is obtained from a transition which fits as an intraband transition . The population is about that expected, and we accordingly consider the level as rather firmly established. The decay mode is compatible with I~ = 5+, which supports the K = 4+ assignment to the band. This assignment is also supported by the branching ratios, which, assuming all transitions to be M1, agree well with the Alaga values for transitions from a K = 4 band, but not with the corresponding values for K = 3 or 5 bands. Additional support for the K~ =4 + assignment is obtained from the Ml component in the 451 .48 keV transition to the 41, 4+ level, which excludes an I~ = 6 + assignment for the 1962 keV level, and from the fact that no primary transition to the 1861 keV level is observed in the resonance averaged capture spectrum, which excludes an I~ = 3 + assignment for this level. A similar K~ =4 + band was observed 6) in'seGd at 1920 keV. After the {z+ [413], z +[411]}x~ two-proton state, which most probably constitutes a large part of the 41 band at 1510 keV, the next lowest-lying 4 + bands expected in is6Gd are the two-neutron states {z+ [642], z +[651]}x* and {z-[523], i-[521]}x", which are expected e') to occur at ~2.0 and ^-2.3 MeV, respectively . By analogy with the presumably similar situation e) in iseGd, where the second 4+ band was found to be the two-neutron state {i-[523], i_[521]}a ", we suggest that the 1861 keV band in is6Gd consists largely, if not entirely, of this same two-neutron state . Evidence supporting this suggestion is provided by the is'Gd (d, t) reaction spectrum zs), in which peaks with approximately the cross sections expected for the 4+ and 5 + members of this band are observed near these energies . The extent to which the two 4+ bands in is6Gd are mutually mixed is not presently clear. The available evidence is consistent with the assumption that they, to a considerable

A. Bäcklin et al. / iseGd

21 5

part, are two-quasiparticle states, but the 4 i band also shows collective properties, cf. subsect. 7.1 . 1 below. The preferential decay of the 4Z band to the 4 ; band, similar to that observed 6) in 'SgGd, may suggest some mixing of these two bands. 4.13 . THE K = 1 +(1 i ) BAND AT 1966 keV

In the decay of iseEu four strong transitions combine, suggesting a 1+ or 2+ level at 1965 .5 keV l4). The same transitions are observed with the same relative intensity ratios in the (n, y) reaction . Further support for the level is obtained from the average resonance capture y-rays, table A3. The multipolarities of the de-exciting transitions, the log ft value, 7.2, of the feeding ß-transition from the 0+ ground state of iseEu, and the absence of a transition to the 3+ state in the 2 i band are compatible only with I~ = 1+. Possible candidates for the associated 2+ state are found at 2003 .76 and 2054 .15 keV. Considering the energies, and especially the decay modes, we assign the former state as the 2+ member of this band. The existence of this level is inferred from a primary transition in the resonance capture reaction, table A3, and from the combination of four of the stronger transitions in the 0.7-0 .9 MeV region . We suggest that the 3~ level of the band occurs at 2070 .30 keV, where the primary y rays from averaged resonance capture indicate a 0+ or 3+ state, and six transitions with the expected total intensity combine with levels in the bands to which such a 3 + state would be expected to decay. The energy region between 2130 keV and 2200 keV was searched for a candidate for a 4+ member of the band and several possible energies were found. In fig. 5 we have indicated as a very tentative level the most likely candidate, based mainly on the decay mode. The total de-exciting intensity for this possible state is somewhat smaller than expected, but this may be explained as due to the fact that possible transitions to the ground-state band are too weak to be observed . The relative reduced Ml transition probabilities from this band to the 21 band agree well with the Alaga values for K = 1 . The E1 branching ratios to the (0)- and (1)- bands, however, are not compatible with the Alaga values for any K-value. This may possibly be explained as a result of the strong mixing of the two negative-parity bands rather than from a K-impurity in the 1 + band. 4 .14 . THE K =1 + BAND

(12)

AT 2027 keV

Inspection of table A1 reveals two energy regions above 1.5 MeV, where strong Ml (or possible Ml) transitions are observed . In addition to the group around 1.65 MeV, associated with the K~ = 0+ band at 1715 keV, we observe another group around 1 .8-2 .0 MeV. As shown in fig. 5, six of the strongest M1 (+E2)

216

A . Bäcklin et al. / ~S6Gd

transitions combine with the Oi band defining possible levels at 2027 .1, 2054.2 and 2106 .6 keV. The probability of obtaining one such combination by accident can be estimated to be of the order of 20%,but the probability of obtaining two or three combinations by accident is very small. The existence of all three states suggested is supported by primary transitions observed in the resonance averaged capture spectrum . The lowest of the states is also observed in the decay of is6Eu [ref. ia)]. Only rather weak transitions may be placed to other bands, i.e., the 03 band, the (0,)- and 1 ~ bands. The transitions to these bands from the 1+ state were too weak to be observed here but were found in the iseEu decay ".'a) . The strong resemblance of the decay modes of the levels and the relative population of the levels indicate that these levels are likely to be members of the same rotational band, especially since no other candidates for such members are available. The decay mode of the levels is compatible only with K~ =1+. The 4+ level of the band should also be populated strongly enough to be observed, with about 60 units of table Al . It can be expected in the region 2150-2200 keV. Assuming that, by analogy with the 2+ state, the main part of the intensity is concentrated in the di = 0 transition to the 0i band, there remains only one possible transition, at 1902 .7 keV, that could define a level in the expected energy region . This suggests that the 4+ state has an energy of 2190.2 keV. The de-excitation intensity is, however, somewhat lower than expected, although the missing intensity may be contained in E2 transitions to the 2+ and 6+ levels of the 0i band, which are below the detection limit; and the level must therefore be considered as very tentative. The relative reduced Ml transition probabilities from the 1+ state are in good agreement with the Alaga values for K=1 . 4.15 . THE 4 - BAND (4 i) AT 2045 keV

It is well known that the strongest branch of the beta decay of 1S~Tb feeds a 4level in iseGd at 2045 keV, which is depopulated mainly by the two strong 544.3 and 422.4 keV E1 transitions feeding the 4+ band at 1510.54 keV [ref. Za )]. These two transitions are observed with the same intensity ratio in the (n, y) reaction, implying that the 2045 keV level is populated in this reaction . The branching ratio corresponds well with the Alaga value for K = 4, but deviates strongly if one assumes K = 3. The K= 4 assignment is also supported by the fact that in spite of a careful search, we observe no state with the properties expected for a corresponding 3- state. The NLJCLEV program yields only one level candidate, at 2116.40 keV, above the 4- state with the properties expected for the 5- state. We judge that the probability that the suggested level is obtained by accidental combinations of transitions with approximately the expected total, as well as relative, intensities

A. Bâcklin et al.

/ iseGd

21 7

feeding the expected levels, is vanishingly small, especially since no other level candidate was found with decay properties of any similarity to those expected . The I~ = 6~ band member is expected in the region around 2200 keV. The most likely candidate is found at 2195 .20 keV, but, in view of the weak intensity expected, we cannot overlook the possibility that one or more of the transitions from the real 6- state is masked by stronger transitions, and the suggested state must accordingly be considered as very tentative. The relative reduced transition probabilities indicate no strong admixtures of K = 3 or 5 in the states . It is interesting to note the strongly preferential decay to the K= 4i band : the next strongest transitions, leading to the 2i band, although only once K-forbidden, are weaker on the average by a factor 103. A K~ = 4- band was observed s) in isaGd at 1636 keV. On the basis of the (d, p) cross sections it was assigned as the two-neutron state {z- [521], i+[642]}4-. Since this band shows the same decay pattern as the band observed in is6Gd, we suggest that the two bands are due to the same configuration. (13) AT 2187 keV In the decay of issEu a level at about 2186.7 keV is deduced both from energy combinations and coincidence relations''l4). The strongest of the transitions depopulating this state are observed also in the (n, y) reaction with essentially unaltered intensity ratios, implying that the state is also populated in this reaction. This conclusion is supported by the observation of a feeding primary transition . The conversion coeffcients of the transitions to the 0; band observed in the present work indicate Ml or E2 multipolarities. The conversion coefficients obtained by combining the data of refs.''ll) yield M1 multipolarities, which, in view of the cleaner conditions of the decay scheme studies, should be considered as more reliable . The level must therefore be I~ =1+. The associated 2+ state can be expected to have a population larger than 70 units in table A1 and should be observed in the resonance averaged capture spectrum . There is only one NUCLEV level candidate, at 2216.8 keV, available within 100 keV of the expected energy range, which corresponds to these expectations. It decays as expected to the Oi band and the (1)- band. The 3+ state should also be observed in both the averaged resonance capture and the low-energy spectrum (population about 60 units in table A1). Only one energy, 2270 keV, fulfills these requirements . However, a primary transition is observed in the thermal capture spectrum, which indicates a 1+, 2+ or 3+ state at 2256 keV. The low-energy transitions that may be placed as depopulating a level at this energy are not as strong as expected, but this level cannot be neglected as a candidate for the 13, 3+ state. The 2270 keV level is therefore indicated as tentative in the level diagram. 4 .16 . THE K =1 + BAND

A. Bücklin et al. / rssGd

21 8

4.17. NEGATIVE-PARITY STATES IN THE REGION 1930 TO 2205 keV

In addition to the bands discussed above we observe candidates for about fifteen levels in the region 1.9-2 .3 MeV, mostly with a negative parity . They cannot be ordered in bands. The levels we consider as best established are given in table 1 and are discussed in the following. An I~ = 3 - level at 1934 keV is well established in the decay of 156Th through the combination of eleven transitions z3) . Ten of these transitions are found in this work with an energy agreement 0.1 keV or better with the energies of ref. Zs) . The level is also supported by a primary transition and by the transfer-reaction data za). There is a severe difficulty with this seemingly well-established level, however. This is illustrated in table 4, which gives the intensity ratio I,,(n, y)/I,. (Tb decay) for the transitions involved. It is seen that this ratio (which should be constant) varies strongly, suggesting the following possibilities: (i) no level exists here ; (ü) only a minority of the transitions should be placed here ; or (üi) the level consists of a close doublet. Alternative (i) is extremely unlikely since the probability of 11 transitions in the Tb decay combining by chance is vanishingly small. Alternative (ü) is not very likely either, since only three, or at most four, transitions have the same intensity ratios to within the errors, and it therefore implies an accidental fit TABLE 4 Relative intensities of transitions de-exciting the close doublet level 1934 .20 (2 -) and 1934 .33 (3 -)

Transition energy (keV)

Multipolarity

1845 .5 1646 .2 780.23 686.33 578 .94 676.14 691 .68 658.31 614.49 567.68

E1 El E1 El El E2 Ml Ml Ml+E2

Ke li ac 0,, 2+ 0,, 4' 21, 2+ 21 , 3~ 21, 4+ 03, 2' (1 1), 1(1 1), 31,, 2(0,), 1-

I,.(n,

Y) °)

60 (8) 37 (8) 55 (5) 8.0 (19) 5.0 (8) 3.7 (21) 6.0 (10) 6.8 (11) 53 (5) 27 (5)

lY('ssTb) `,)

h~ s'~Tb)Iv

13 .0 (4) 4.58 (9) 11 .7 (4) 3.15 (9) 7.7 (4) 7 .0 (7) 1 .46 (11) 5 .5 (20) 1 .41 (6) 3 .5 (10) 0.31 (13) 12 .3 (24) 0 .73 (15) 8.3 (18) 0.63 (15) 10.8 (18) 0.56 (10) 95 (11) 0.09 (22) 294 (22)

343 (8) 37 (8) 26 (10) 4.9 (15) 5.0 (8) 1.1 (15) 2.5 (15) 2.0 (20) 1.9 (10) --0

') Numbers in parentheses give errors in percent. za) . b) Ref. The intensities are obtained from the following formulas (see also text):

K I2 = K-k (1-ki)~I-ki,

K (I_ki),rki, I3=I_ K_k

I-ki iz° K-k ,

2-

is=i -

16 (25) ~0 29 (10) 3.1 (20) -0 2 .7 (25) 3 .6 (15) 4.7 (20) 51 (5) 27 (5)

1-ki Ki-I = K-k , K _K

where I = intensity observed in the (n, y) reaction, i = intensity observed in Tb decay. Indexes 2, 3: Intensity from spin 2, 3 level. k = intensity ratio I3 li3 = 3.3 as determined from the average of the 1646 and 579 keV transitions, K = intensity ratio IZ /i~ = 294 as determined from the 568 keV transition .

A. Bäcklin tt al. / 1s6Gd

21 9

of as many as seven transitions in the Tb decay. This is most unlikely and, since the intensity ratio does not vary in a completely random way but depends on the band to which the transition proceeds, we are inclined to suggest that the 1934 keV state consists of a close doublet. Some support for this suggestion is obtained from the energy values, for which the combinations with the 2 i band give 1934 .35 t 0.05, 1934 .29 t 0.10 and 1934 .32 t 0.04 keV, while the combinations with the 1 1 2 and (0 1)1 - levels, which are associated with a completely different intensity ratio, give 1934 .20 t 0 .07 and 1934 .11 t 0.06 keV. These two groups of energy values are

significantly different. The 1934 .33 keV level has to be a 3 - state, since it decays via E1 transitions to 2+, 3+ and 4+ states . The 1934 .20-keV state must be 1 - or 2- (from its Ml decay) and 2-, 3- or possibly 4- (from its E1 decay), yielding 2- as the only consistent assignment . This 2- state should not decay to 4+ states with observable intensities, and the 1646 and 579 keV transitions to the O1, 4+ and 2 1, 4+ states, respectively, should therefore have the same intensity ratio I,.(n, y)/I,.(Tb), which is also the case (cf. table 4) . In order to calculate how the observed gamma intensities are shared between the levels, one more ratio must be known. For this we assume that the 568 keV transition proceeds entirely from the 2- state. This may not be exactly true, but the ratio I,.(n, y)/I,.(Tb) for this transition is so much larger than the corresponding ratio for the other transitions, that its exact value has little influence on the calculated intensities except for the 568 keV transition itself, cf . table 4, footnote ~. The resulting intensities from the two levels are given in table 4, column 7 . Obviously these intensities are based on the assumption that the assumed placement of the 568 keV transition is correct. However, almost the same intensity values are obtained if the calculations instead are based on the ratio I,.(n, y)/I,,(Tb) for the 614 keV transition . Both the 3- state at 1934 .33 keV and the 2- state at 1934 .20 keV are populated strongly enough to permit the observation of additional states of the corresponding rotational band(s). As discussed below, the region 1850-2050 keV contains two possible 4- states, of which the one at 1952 .30 keV is likely to belong to the 2band at 1780 .38 keV. The remaining state is at 1965 .05 keV. It is obtained from eight energy wmbinations (two of which had to be removed due to inconsistent multipolarities) and is strongly supported by the fact that the two strongest transiz3) tions are also observed in the 156Th decay with the same intensity ratio. From energy combinations between the 20 E1 transitions in the region 1 .52 .3 MeV and the ground-state band several candidates for I~ = 1 - and 3- statesare suggested. The level candidate at 1946 .3 keV in table 1 has been obtained in 1s6Eu that way. It is supported by the observation of an I = 1 level in the decay of la) with a similar mode of de-excitation . The E1 multipolarities of the transitions to the ground-state band imply I? = 1 - for the level. Other candidates for I~ = 1 - levels are observed at 1952 .30 keV and 2205 .50 keV. The latter state is observed in the resonance averaged capture

22 0

A. Bâcklin et al. / iseGd

reaction as). The existence of both states is supported by the fact that they have been observed with a similar decay mode in the decay of 'seEu [ref. '°)]. In the decay of 'ss.hb a 3- state at 2103 .49 keV as) is fairly strongly populated. The three strongest of the ten transitions observed in the decay are observed with approximately the same intensity ratio in the (n, y) reaction . The other transitions are either too weak to be observed or are masked by stronger transitions. It is difficult to group the levels discussed in this section into rotational bands. Considering the populating intensities and modes of depopulation, one is inclined to suggest that the 1934 .20 keV, 2- state, the 1934.33 keV, 3- state and the 1965 .05 keV, 4- state are members of the same band. The level energies of the band would then be strongly distorted as compared to a regular band structure, but this could possibly be explained as due to influence from other negative-parity states, which are frequent in this energy region (cf. fig. 5 and table 1). The same argument may possibly be used to explain the fact that the log ft values of the EC transitions feeding the two states then would differ more than expected for members of the same band . The transition probabilities from these three states give no clear answer regarding their respective K-values . The transition probabilities from the I = 2- state at 1934 .20 keV agree best with K = 2, while those from the 1934.33 keV, 3- state fall between those for the K = 2 and K= 3 values. The relative intensities of the transitions to the ground-state band agree best with K = 0 or 2 . Also for the 4states the relative transition probabilities to the 21 band lie between the values corresponding to K = 2 and 3 . The population of both the 2- and the 3- states is large enough to make the observation of an associated 1- state, if it exists, highly probable . No such state could be observed in the expected energy region, which indicates K = 2 for the 2state and K , 2 for the 3- state. These assignments are supported by the fact that the reduced E1 transition probabilities to the Oi band are significantly smaller than those to the 2 i band, which may indicate K-forbiddenness for the former . The relative reduced transition probabilities for the 1- level at 1946 .3 keV are compatible with K= 0. This, however, does not necessarily mean that this state is predominantly K = 0, since this agreement may be due to an admixed K = 0 amplitude. A possible 2- level associated with this 1 - level is not likely to be easily identified since it can be expected to decay observably only to one level (012+). The 3 - level at 2103 .29 keV is not likely to be associated with the same band as the 1946 .3 keV, 1- level . The preferential decay to the 2 i band and the fact that we have not been able to find a 1- state with the appropriate population and mode of decay indicate K> 1 for this state. The 2- state at 1934 keV could possibly be the head of the band involving this state, but its energy is rather far from an expected undisturbed position, and it is populated about twice as strongly as expected, so one may tentatively suggest the 2103 keV state to be the head of a K = 3- band .

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221

A careful search was made for further members of the band containing the 1level at 2205 keV. A candidate for a 3- level was found at 2291 .69 keV, which shows the expected decay mode and population strength . The level may be identical with the 3- level observed at 2297 keV in the (d, t) reaction ze) . No 2- level with a decay mode similar to those of the 1 - and 3- states was discovered in the region 2.1-2 .4 MeV. This may be taken as an indication of K = 0 for the band. On the other hand, the decay mode of the even-spin states may be different from that of the odd-spin states, which would make it very difficult to identify the 2- state in this experiment. The branching ratios of the transitions to the 0+ band at 1715 keV agree well with those expected for a pure K = 0 band . On the other hand, the ground-state band transitions do not seem to conform to this assignment, and the K = 0 assignment for this band must therefore be considered as very tentative. 5. The miring of the Oi, 0?, 03 and 2i bands

It is well known from earlier radioactivi ty studies 1" 12,17,23) of 156 Gd that the E2 transition probabilities from the O2, ß-vibrational band and the 2i, y-vibrational band to the ground-state band deviate strongly from the Alaga-rule predictions, which suggests that the bands are mixed. The E2-transition data for the y-rays connecting the y-vibrational and ground-state bands are conveniently summarized by the "Mikhailov plot" ea) shown in fig. 6. The experimental values on which this plot is based are summarized in table 5. The straight line shown in fig. 6 represeftts

Fig . 6 . "Mikhailov plot" of the reduced transition probabilities of the y-ray transitions from the yvibrational band to the ground-state band in iseGd . The data points are labelled by the spin of the initial state. The straight line represents a least-squares fit to the experimental points .

A. Bncklin ct al. / ls°Gd

222

B(E2) values for the transitions from the OZ, Initial state K,I;

212+ 21 3+ 214+ 215+ O20' 022+ 024+ 03 0+ 032+ 034+

Final state Kf7f

010+ 012+ 014+ 012+ 0,4+ 012+ 014+ 014+ 016' 012+ 010+ 012+ 014+ 012+ 014+ 016+ 012+ 010+ 012+ 014+ 012+ 014+ 01 6+

Transition energy (keV)

1154 .19 1065 .15 865 .80 1159 .04 959.86 1266 .38 1067 .19 1218 .67 922.33 960.55 1129 .41 1040 .43 841 .20 1208 .90 1009 .53 713,07 1079,24 1257,99 1169,09 969.86 1373 .17 1174,22 877.56

TABLE S

03 and 2i bands to the Oi ground-state band in 1ssGd B(E2; K;I; ~ Kell)[e 2 x 10-so tea]

exp')

mixing talc

2.22 (11) °) 3.55 (19) °) 0.32 (3) °'~ (3 .64 (17)) ~) (2 .8 (6)) ~) 0.78 (9) ~ 4.6 (5) ~ 2.95 (30) ~ 4.1 (4) ~

2.25 3.61 0.43 3.65 2.85 0.82 4.34 2 .56 3.97 3.9 0.36 1.60 1 .82 0.58 1.66 1 .27 1.8 0.15 0.13 2.10 0.18 0.069 4.27

0.316 (18) °) 1.64 (16) ~) 1 .81 (17) ~) 0.61 (7) ~ 1.40 (13) ~~) 0.91 (14) ~ 0.154(14) °) 0.084±ô:ôiv ~' t) 2.10 (25) a) 0.15(4) ~ 2.3 (2) s'') 3.7 (3) ~

theory b)

1 .86 3.04 0.20 3.26 1.75 0.87 3.6 2.54 2.32 0.95 0.16 0.22 0.58 0.22 0.13 0.64

2.9 4.4 0,88 4,3 3.2 1,4 3.6 3.3 4.0 1,15 0.39 3.2 6.7 0.13 4.1 5.1

') The quantity given in parentheses is the uncertainty in the last figure . q IBA-1 [ref .' 9)] . The calculations were made with the codes PHINT and FBEM se) with the input parameter values (in MeV) EPS = 0,05698, ELL = 0.01476, QQ = -0 .03079, PAIR = 0, E2SD = -E2DD=1. The B(E2) values were normalized at B(E2 ; 012+-X0 10+)=0.93 c2 " b2, ref. 3~) . ~ Pairing-plus-quadrupole model ss). 3s) °) From Coulomb excitation . °) The branching ratio (2 12+-~ 014+)/(212+-~ 012+) observed in the present work is almost twice as large as the corresponding ratio as observed in radioactive decay la.2a) and Coulomb excitation 3s), which indicates that the 865.8 keV transition observed by us is a close doublet. ~) The transition was assumed to be pure E2 . The listed B(E2) value was obtained from the measured B(E2) ratio as described in the text (sect. 5) . °) Value obtained from the branching ratio of the interband and intraband transitions, as described in the text (sect. 5) . 13) . The y-ray transition was assumed b) The 022+ -> 012+ transition is 97 .2±i i°~ E2 according to ref . to be pure E2 . ') From B(F.1; 01 0+-~ 022+) =1 .58 x 10 -2 e2 ~ b2, ref. 3s), and the branching ratio obtained in the present work . ~) The y-ray was assumed to be pure E2. ls) ~`) The 032+-~ 01 2+ transition is 12 .6±z :é °k E2 according to ref . .

A. Bâcklin ct al.

/ 1s6Gd

223

the result of a least-squares fit of the experimental data to a function of the form' t )t

which is expected to describe them if a simple two-band mixing picture is applicable . The values obtained for the parameters Mt and Mz from this analysis are Mtf= 0.365 t 0.005 e ~ b ,

-Mzf = 0.0072 t 0.0007 e ~ b .

From these, we obtain for the band-mixing parameter, z the value z,. = 0.043t0 .004 . The fit is good, having a reduced Xz value of 0.75 . Asimilar treatment can be made for the transition probabilities from the ß-band to'tz'i') to the ground-state band, and it has been shown that for this band the transition probabilities to the ground-state band are not adequately reproduced by a two-band mixing calculation . A further step may be taken by considering also mixing between the ß-band and the y-band . With this three-band mixing approach it has been possible to describe the relative E2 transition probabilities from the y-band to the ground-state band fairly well tz ), while the transition rates from the ß-band are still not adequately reproduced t°.t'). The proximity of the 03 band to the ß- and y-vibrational bands suggests that this band should also be considered in any realistic mixing analysis of their y-ray transition probabilities . Accordingly, following the procedure described in ref. 6), we have carried out a four-band mixing calculation involving the Oi, O2, 03 and 2 i bands. The energy matrix was constructed using off-diagonal elements of the 6'69''0) form (IK, a'~H ct ~~IK, a)=(K, a'~h olK, a)[I(I+1)-Kz] between bands with dK = 0, and (I2, a'~H cs~~IO, a)=(2, a~hzl0, a)[2(I-1)I(I+1)(I+2)]t~z between bands with ~dK~ = 2. The number a is used to label the different bands. The diagonal elements were calculated from the formula' s ) E(K,I)= EK+A[I(I+1)-Kz] +B[I(I+1)-Kz]z

The reduced E2 transition probabilities are given by the expression B(E2 ;I->I')=I . ~ a(I,K,a)a(l',K',a')(IK2K'-K~I'K') rc.~ ~.x' 0)~]t/zlz ~ x(K', a'IM'(E2)IK, a)[1+~5(K, 0)-S(K', t Refs. 68'' 1) differ in the sign used for M2.

(2)

22 4

A. Bäcklin et al.

/ 136Gd

where the a, a' are the admixed amplitudes (obtained from diagonalization of the energy matrix) of the various bands in the initial and final states, respectively, and the (M'(E2)) are the E2 matrix elements between the respective unmixed bands. For the intraband E2 transitions, the matrix element (M'(E2)) is related to the corresponding intrinsic quadrupole moment, Qo(a) (expressed in b), by the relation l~z (K, a~M'(E2)~K, a)= eQo(a) \16~rl The experimental B(E2) values are given in table 5. For the 2+ states, they have been taken from the results of a recent Coulomb-excitation measurement 3a) . For the 3 + member of the y-vibrational band, only the ratio of the B(E2) values of the de-exciting transitions is available. We have derived the "absolute" B(E2) values for the individual y-ray transitions from this measured ratio and a suitable normalization obtained from the "Mikhailov plot" (cf. fig. 1). For the 4+ levels and the 5 + level, intraband transitions with dl = -2 are observed in addition to the interband transitions. From the respective interband to intraband intensity ratios, absolute B(E2) values were derived for the interband transitions assuming those of the intraband transitions could be reliably calculated using the formula for rotational E2 transitions . During the mixing analysis it was found that, because of the mixing among the 4+ states, the B (E2) values of these intraband transitions were somewhat lower than those of "pure" rotational E2 transitions. This reduction in the intraband B(E2) values was found to be ^-5%, -r2% and ^-13%,respectively, for the 2 14+, OZ4+ and 034+ states . These reductions were taken into account in obtaining the experimental B (E2) values listed in table 5. Since, in the four-band mixing analysis discussed here, the 21 5+ state is not mixed, no reduction was made in the calculated B(E2) value of its de-exciting rotational transition . For purposes of simplicity, it was assumed that the intrinsic quadrupole moments of the excited bands were all equal to that of the ground-state band. We have taken this latter value from ref. 3'), where the value Qô = 46 .56 bZ is reported . We have also assumed that the three E2 matrix elements between the excited bands are all zero . While done partly for simplicity in the analysis, this assumption was motivated primarily by the desire to see to what extent the available data could be described without invoking non-zero values for these quantities . The various parameters were adjusted until a reasonable fit to the level energies and B(E2) values was obtained. The B(E2) values resulting from this analysis are summarized in table 5 . The parameters (he,c) and (M'(E2)) are given, in matrix form, in table 6 and the energy parameters of the unperturbed bands are given in table 7 . In the analysis the signs of all the E2 matrix elements, (M'(E2)), were taken to be positive, and the signs of the matrix elements, (hnK), were then chosen so as to give the proper type of interference in the overall E2 transition amplitudes . In comparing the parameters deduced from this analysis with those obtained e) for l'SGd, it is found that the signs of the parameters (hvx) are the same for both

A. B&klin ct al. /'seGd

225

TABLE 6 Matrix elements (hex ) and (M'(E2)) used in the four-bandmixing calculation

(h ex ) (keV)

(M'(E2)) (e " b)

Oi OZ 03 2i

Oi

Oz

Os

2i

°) 0.19 0.093 0.24

-0 .68 °) 0 0

-3 .7 +0.8 °) 0

-1 .40 +0 .53 +1,25 °)

°) The diagonal elements in the E2 matrix were all set equal to 2.15 e " b [ref. 3')]. The diagonal elements in the energy matrix were obtained from the parameters given in table 7. nuclides, except for those which involve the "ß-vibrational" band (i .e ., the OZ band tseGd 1saGd) in and the 03 band in . The interband E2 matrix elements, (M'(E2)), tseGd are generally similar in the two isotopes, although in they are systematically larger . The calculated B(E2) values are compared with experiment in table 5 . The agreement between calculation and experiment is generally quite good . The analysis also gives an insight into the make-up of the amplitudes for the various E2 transitions [cf. eq . (2)] . For example, it shows that the E2 branching of both the OZ and 03 bands is strongly influenced by admixtures from the y-vibrational band . In some instances the contribution to the transition amplitude from the y-band admixture is equal to or larger than that from the admixture of the ground-state band (the one that is considered in the simple two-band mixing treatment) . The calculation appears to underpredict the strength of the 034+ -> 0 14+ transition . However, it is le) known that the 2+ -> 2+ transition between these bands has a large M1 component. TABLE 7 Rotational parameters °) for the 0i, OZ , 03 and 2i bands in 'seed

Band Oi OZ 03 2;

exp fitted q exp fitted ~ exp fitted ~ exp fitted n)

A (keV)

B (eV)

A4 (eV)

15 .01 14 .96 13 .70 13 .77 15 .09 15 .21 15 .89 16 .13

-30.0 -10.7 -64.5 -58.7 -19.2 -79.2 -63.1 -51.0

-15.8 +0 .27

°) Cf . eq . (1). Values used to calculate the input energies for the four-band mixing analysis .

A . Bäcklin et al. / iseGd

226

It is reasonable to suppose that a similar situation exists for the 4+ -~ 4+ transition as well (a direct measurement of the E2 content of this transition would be of interest) . Since the B(E2) value for this transition was obtained assuming that the y-ray was pure E2, this discrepancy between calculation and experiment is not unexpected, and this transition was not considered in the final fit. In the analysis, the energies of all the states with I , 5 were considered ; and the parameter adjustments were continued until all these energies were fitted "exactly" (i.e., to within a few tenths of a keV) . For the 0;, OZ and 2i bands, as indicated in table 7, the B and A4 parameters used to generate the input level energies are smaller than those of the observed (band-mixed) levels . However, these B-values, although smaller, are nonetheless still rather large, and that for the 03 band is even considerably larger in the input spectrum than in the actual spectrum . Further, the predicted energies of the 6+ members of the excited bands differ significantly (several tens of keV) from the values measured in a recent (a, 2ny) experiment 31) . Some of these problems can be resolved simply by choosing a different parametrization for the input energies . For example, using a VMI parametrization (involving the parameters ~o and C) of the input energies, we have achieved quite good fits to the level energies through spin 6 for the O1 and OZ bands. The problems with the 03 and 2i bands, although somewhat reduced, still remain . The predicted 6+ energies of these two bands can be brought into better agreement with experiment if the magnitude of the coupling matrix element, (hnK), between these bands is significantly (-r20%)reduced. However, this worsens the agreement for the 4+ states, in addition to adversely affecting the calculated B(E2) values of the transitions from both bands. One explanation of these observations is that the energies of the excited bands are affected by the coupling to other, higher-lying bands, which has been neglected in the present analysis. The question of whether there exist non-zero interband E2 matrix elements between the OZ, 03 and 2i bands could not be answered in this work. No transitions were observed between the 2i and the OZ bands. The upper limit estimated for the intensity of the 214+ -> Oz2+ transition corresponds to B(E2 ; 2 14+ ~ Oz2+) < O.le z ~bz. This limit is more than an order of magnitude larger than the value predicted by e.g. the IBA model (see below) . Two transitions, having energies of 164.464 and 332.867 keV could be placed with a good energy accuracy between + the 034+ state and the Oz4 and Oz2+ states, respectively (see fig. Sa). If these transitions are assumed to be pure E2, their respective B(E2) values are inferred to be ~--0 .59 z ~ bz and ~-0.041 bz. However, the assumption of pure E2 is transitions: The 034+ -~ Oz4+ transition may, in addition to E2, uncertain for both proceed through an Ml transition . The 332.867 keV line should be pure E2 if it contains only the 034+ -> Oz2+ transition . However, its conversion coefficient is compatible with Ml rather than E2, which indicates that the 332.867 keV transition is a doublet with the M1 part situated elsewhere in the level scheme. e

e z ~

A. Biicklin et al. / issGd

227

6. Corlolls mixing of the octapole-vibrsüonal bands We have carried out a Coriolis-mixing analysis of the level energies and E1transition-probability data for the octupole-vibrational states in iseGd . We have included only the lowest-lying K~ = 0-, 1- and 2- bands in this analysis . Neglect of the KA = 3- octupole band should not seriously affect any of the important conclusions to be drawn. Our failure to identify this band in this experiment indicates that it must lie above 1 .9 MeV; and the "reasonable" value (-~-12 keV) of the inertial parameter of the 2- band (to which the 3- band will couple directly) suggests that its coupling is rather weak. The procedure used in this analysis follows closely that employed earlier in treating Coriolis mixing among the octupole bands in l'zYb [ref. 'z)] and issGd [ref. e )]. 6.1 . LEVEL ENERGIES

The Coriolis matrix elements have the form 6 ''z .'3)

where

(I, K+1~H~~I, K) _ -A,~x+i[(1+Sxo)(I -K)(I +K+1)] l~ z ,

The two matrix elements, Axx+i, together with the unperturbed energies of the three band heads and the inertial parameters, A [cf. eq . (1)], of the three bands were treated as adjustable parameters and were varied to yield good agreement between the calculated and observed level energies up through I = 5. The resulting level energies and Kadmixtures are summarized in table 8. Also included in the table are the values of the various parameters used to calculate these quantities . The fit to the experimental level energies is rather good, although somewhat worse than was the case in issGd [ref. e )] . There, however, the three bands were more widely separated than in issGd and the overall level shifts due to the mixing were thus smaller. [The 5- states associated with the 0- and 1- bands in iseGd, for example, were shifted by -~-0.2 MeV by the Coriolis mixing.] Because of the close spacing of the unperturbed K~ = 0 - and 1 - bands and the strength of the coupling, the odd-spin band members are predicted to be highly mixed (cf. table 8). For these states, K is not even approximately a good quantum number, as mentioned in subsect. 4.6 above. Using a reasonable value of 11 keV for the parameter (hz /2~)cor, we obtain from our analysis the following values for the matrix elements (K + 1 ~J+ ~K) : These values are somewhat smaller than the theoretically calculated values of

A. Bâcklin et al. / issGd

22 8

Neergikrd and Vogel'3) for these.quantities, which are 3.12 and 2.83, respectively . The agreement between our empirical values and the theoretically calculated ones tsaGd . is somewhat worse for ts6Gd than was found 6) to be the case for 6.2. El TRANSTITON PROBABILITIES

We observe several E1 transitions from the lowest octupole bands to the groundstate band . In addition, a number of E1 transitions are observed from the Oâ and OS bands to the octupole bands (see fig. Sa) . For all these cases, the reduced E1 transition probabilities can be expressed in the form e) B(E1 ; I ~ l') _ (O~~~M~(E1 ; 0)~0~) Z~ao(IOlO~l'0)+~at (IK1 t 1~I'K t 1)Z~ Z ,

(3)

where Z = ((K t 1)~~~M~(E1 ; tl)~K~)/(O~~~M~(El ; 0)~0~) . Here, ao and al represent the admixed amplitudes of K = 0 and 1, respectively, in the octupole state (cf. table 8) . The K~ = 0+ states are assumed to be pure, i.e., the effect of possible admixed configurations in these states is neglected. This seems to be a reasonable supposition, at least for the ground-state band, in view of the TwsLe 8 Admixed amplitudes and energy parameters obtained in the Coriolis-mixing calculation for the octupole bands in tssGd I 1 1 2 2 3 3 3 4 4 5 5 5

Admixed amplitude

Level energy (keV) exp

talc

K=0

K=1

K=2

1242 .5 1366 .4 1319 .7 1780 .4 1276 .1 1538 .8 1851 .8 1468 .6 1952 .3 1408 .1

1243 .1 1363 .4 1316.7 1778 .7 1281 .2 1541 .0 1853 .7 1469 .4 1952 .1 1405 .4 1803 .4 2079 .7

0.500 0.866

0.658 0.746 0.103

0.866 -0.500 0.997 0.076 0.779 -0.614 -0.128 0.988 0.155 0.746 -0 .626 -0 .228

0.076 -0 .997 0 .076 -0 .111 0.991 0.155 -0 .988 0 .105 -0 .227 0.968

1273 .2 10.74

1333 .3 11 .55

1776.0 11 .75

(2066.7) °)

Parameters of the unperturbed bands Band-head energy (keV) Inertial parameter A (keV) Matrix elements A,~,r+i (keV)

') Tentative assignment .

0.623 0.781 0.040

26 .05

17 .41

A. Bâcklin et al. / iseGd

22 9

smallness of the admixed amplitudes as determined from the band-mixing calculation (sect. 5) . In the above expressions for the reduced E1 matrix elements, the initial- and final-state K-values appear at the right and the left, respectively . Thus, if the de-excitation of a Coriolis-mixed octupole state is being treated, K =1 in the above expression and the lower sign is used, while, if the feeding of such a state is being described, K = 0 and the upper sign is used . The B(El) ratio data can be analyzed using eq. (3) to obtain values of the parameter Z From the analysis of the E1 branching between the octupole states and the ground-state band, we find that all of the branching ratios are consistent with a single Z-value (see table 9). The fact that these data are all consistent with a single value of Z tends to support the results of the Coriolis-mixing calculation, since the mixing amplitudes, ax, used in the E1 analysis were derived from these calculations . The fact that Z is small is consistent with observations in other strongly deformed nuclei 6"3a " 'z .~a), The mean life of the 1276 .11 keV, 3- state has recently been measured ss) to be 0.11 t 0.03 ps. From this value, together with the El branching data summarized in table 9 and the admixed amplitudes derived from the Coriolis-mixing analysis (table 8), we obtain the following values of the E1 matrix elements :

For purposes of comparison, the values obtained e) for these two quantities in issGd are 10.3e x 10 -is cm and -0.448e x -is 10 cm, respectively . Although the ~dK~ =1 matrix elements are significantly different in these two nuclides, it is interesting to note that the matrix elements with dK = 0 are essentially identical. In table 9 are given values of Z derived from branching ratios of transitions from the Oâ and OS bands to the octupole states . (Both values of Z derived from each ratio are given.) It is seen that no consistent set of values of Z is obtained for either of the two 0+ bands. This is in marked contrast with the situation involving the octupoes and the ground-state band . Although the reasons for the erratic behaviour of the E1 branching of the 04 and OS bands are not clear, it seems plausible that mixing of other configurations into these bands may have an important influence on the E1 transition probabilities . 7. Discussion Altogether 15 excited bands with K quantum numbers ranging from 0 to 4 were observed at energies up to 2.2 MeV. The sensitivity of the present experiments was such that we believe that we have detected essentially all bands with K ~ 5 with band heads below ~1 .9 MeV. Six of the fifteen bands were observed in the recent (a, 2n) experiment s') up to spins of 8-14 units. They are all within ^-1 .2 MeV

A. Bücklin etal. / tseGd

23 0

TnHt.E 9 Relative reduced El transition probabilities and deduced values of the ratios of the reduced El matrix elements Z for transitions between the mixed octupole states and the Oi, Oâ and Os bands in tssGd

Experimental B(El)') ratio

Transition ratio

(l l -" OtO+) /(ltl -.Ot2 +) (l tt3i0 t2+)/(l t3 -~Ot4+) (1t5--" Ot4+) /(1t5--~Ot6 +) K; __ (Ot) - band : (O t3 î0 t0+)/(O t l--~Ot 2+) (O t3- -~ Ot2+)/(Ot3--+Ot4+)

.

Alaga value

Zq

0.81(9)~ 1.34 (9) 1.13 (17) a) 1.34(12)

2.0 1 .33 1 .20

-0 .068(16) -0 .117 (18) -0 .082 (32) -0 .105(20)

0.428 (33) 0.606 (51)

0.50 0.75

-0 .063 (31) -0 .067 (27)

weighted average °) :

-0 .078 (10)

K;'=04 band : (0a0+ -~ l tl )/(OaO+-.Otl )

3.68 (26)

(Oa2+-~ l tl ) /(Oa2+ i lt3-)

0.101 (13)

(Oa2+ -+ 1 t 1-) /(Oa2+-~ O t 1-)

0.33 (5)

(Oa2+ -~ l t3 )/(Oa2+ -~Otl -)

3.2 (3)

0.45 (2) 16 (4) 0.27 (2) 2.8 (3) 0 .003 (50) 2.4 (2) -1 .34 (2) 1 .7 (2)

K; =05 band : (OsO +-.l t l ) /(OsO+-~Otl )

0.38(23)

(Os2+-~ Otl )/(OsO+ ~ Ot 3-)

1 .84 (36)

0.67

(Os2+ -' lt l )/(Os2+ -~ l t3-)

0.50 (15)

0.25

(Os2+-~ l t )/(Os2+-.Otl )

0.77 (24)

(O s2+ -" lt3- )/(Os2+-.Ot3 -)

2 .8 (6)

0.25

8 0.02± 3 -1 .31 (43) 0.28 (7) 2.63 (27) -0.03 (6) +z -6-so -0 .28 (13) 4.2 (10) 0.33 (5) 6.7 (50)

°) The number in parentheses denotes the uncertainty in the last figure (or figures) of the associated value. q For definition, see text. For the transitions from the 04, Os bands both solutions are given. `) The 1153 .6 keV, El transition coincides with the 1154 .2 keV, E2 transition ; and its intensity value obtained in the present work is thus uncertain. The intensity ratio given in the table is obtained from ref . ta). °) Ref zs). `) The value deduced from the ratio (1t3--~Ot2+)/(1t3--~Ot4+) as obtained from the present data was not included in the calculation of the average since that obtained from ref . za) was considered to be more reliable due to the lower line density in the latter spectrum .

A . Bäcklin ct al. / 1sbGd

23 1

of the yrast line, while the remaining nine bands identified here have their band heads 1 .7-2 .2 MeV from the yrast line . Thus the (a, 2n) reactions and the (n, y) reaction are seen to complement each other in that they tend to cover different regions in the energy-spin space . In the following we will discuss some of the bands with a special emphasis on their collective properties. The particle character of some of the bands has been discussed in sect . 4. 7 .1 . POSTTIVE-PARITY BANDS

7.1.1. Even-spin bands. In addition to the well-known K = 2i y-vibrational band,

we observe four excited 0+ bands, one 2+ band and two 4+ bands. The two lowest 0+ bands, the OZ band at 1050 keV and the 03 band at 1168 keV, decay to the ground-state band via, on the average, enhanced E2 transitions, cf. table 5 . The two bands differ in two respects : (i) The E2 matrix element with the ground-state band (table 6) is twice as large for the OZ band as for the 03 band, the latter corresponding to E2 transition probabilities smaller than one Weisskopf unit. ['The large values of B(E2; 032+-> 01 4+) and B(E2; 034+ ~ 016+), corresponding to -~-4 and ~-8 W.u., respectively (see table 5) are essentially due to the mixing between the 03 band and the ground-state band .] (ü) The EO transition probabilities from the OZ band are large, see table 2, while those from the 03 band are at least an order of magnitude smaller. The classification of the OZ band as a ß-band is therefore obvious, while the origin of the 03 band cannot be inferred from the present data. All the other bands with even spin appear in the region where the two-phonon quadrupole vibrational bands can be expected and it is interesting to make a qualitative comparison between the decay modes expected for the latter and those shown by the experimentally observed bands. None of the 03, Oâ or Os bands seems to correspond to the simple picture of a 2y or a 2ß band, i.e., a band at about twice the energy as the corresponding one-phonon band, which decays to the one-phonon band in a way similar to the decay of the latter to the ground band. The 03 band has much too low an energy and the decay modes of the 04 and OS bands differ strongly from those expected . The 2Z band and the 4i band, on the other hand, exhibit features that can be expected for the ß + y band and the 4+ 2y band, respectively. The 22 band decays with strong E2 transitions to the OZ ß-band and with E2+EO transitions to the 2i y-band (cf. table 10). The similarity between the latter mode of decay and that of the ß-band is conspicuous and may indicate that both are d1V~ =1 transitions. The weak E2 decay from the 22 band to the ground-state band is in accord with this. For the 2 2 2+~ 21 2+ transition we observe a value of X = e2R°p2(EO)/B(E2) -~ 1 .2, assuming the y-transition to be 30% E2 for reasons given in table 10 . This value

A. Bâcklin et al. / 1ssGd

23 2

TABLE 10

Ratios of reduced E2 and EO transition probabilities from the 22 band Ratio B(E2 ; 222+ -~ 020+) B(E2; 222+ ~ 022+) B(E2 ; 223+-~ 024+ )

B(E2 : 222+ -~ 020+ ) B(E2; 222+ ~ 022+) B(E2 ; 223+ -~ 014+) B(E2 ; 223+ -+024+ ) B(E2 ; 222' i 213+) B(E2 ; 223+ -~ 215+) B(E2 ; 222+ -~ 212+)

Exp value `)

IBA n)

0.9 t0.3

0.56

0.7f0 .3`)

0.57

0.7±â :i

1.3

<0 .014

4 x 10 -°

<0 .02

4 x 10 -`

<0 .08

3 x 10 -°

2.1t0 .3

0.25

1 .4±ôa

0.17

-1 .0 °)

»1

°) E2 and EO percentages were deduced from the data of table Al in the appendix . q IBA-1. $ee text and comments to table 5. `) A part of the 786.95 keV line is probably El and placed elsewhere in the scheme . °) The y-transition was assumed to be 30% E2 . As judged from the conversion coefficients of other transitions between the two K° _ 2+ bands, the uncertainty in this E2 percentage is not likely to change the ratio given more than a factor of 3 up or down .

is comparable in magnitude to the corresponding value for the 022 + --> 0,2 + transition, which has X = 0.55 . The 4 i band decays preferentially via E2 transitions to the 2 i y-band, as one would expect for the 2y band (cf. table 11) . Furthermore, the reduced transition probabilities of these E2 transitions are approximately of the same magnitude as those de-exciting the y-band . However, the low excitation energy of this 4+ band indicates that this band may, in addition to a 2y part, also have other components' s''6) and subsect. 4.7 above. 7 .1 .1.1. Comparison with the interacting boson model. The interacting boson model (IBA) ") has been successful in predicting systematic trends for low-lying collective states in even nuclei over vast mass regions 'a) , tseGd can be taken as

A. Biicklin et al. / 1ssGd

233

TABLE 11

Reduced E2 transition probabilities from the 4i band Initial state KIA

Final state KIA

Transition energy (keV)

414+ ~

012+ 01 4+ 016+ OZ2+ OZ4+ 21 2+ 213+ 214+

1421 .44 1222 .36 926 .26 381.13 212.74 356.43 262.58 155.16

415+ n)

014+

1334 .5

213+ 214+ 215+ 414+

374.43 267.09 115.67 111 .94

B(E2)

[e Z " bZ x 10-4 ]

exp')

theory b)

0.10 (8) 0.33 (14) a) 0.28 (11) 2.9 (6) 0.68 (20) `) 82(5) 178 (6)) 130 (7) °)

4 x 10 -s 1 x 10 -4 1 x 10 -s 0.02 0.08 480 315 134

1 .2 (50) ~)

3 x 10-°

10(25) ~230 k) 3l0(25)) 1.54 x 30` (4) n)

280 360 220

°) The number given in parentheses indicates the error in percent. IBA-1 . See text and comments to table 5. `) The half-life of the level was taken as 0.190 t 0.006 ns, ref. 19) . a) The E2 percentage was taken as 65 .8 t7.8, ref. i°). `) The E2 percentage wes taken as 19 .4 t 2 .3, ref. Z~. r) The E2 percentage was taken as 100% . The upper limit of the conversion coefficient, table 2, corresponds to X9696 E2 . ~ The E2 percentage was taken as 18 .7 t 1 .0, ref. Z~ . h) The reduced transition probabilities are calculated from the assumption that Q° has the same value as for the ground-state band s~) . The 111.94 keV intraband transition was taken as 7.5 t 1 .0~ E2, cf . table Al . ') The conversion coefficient, table Al, corresponds to 67±s9 °~ E2 . i) The 1037 .93 keV transition could not be observed in the present work since it falls between two stronger lines. The energy and intensity (15 units in the scale of table Al) of the 415+ -~ 016+ transition was taken from ref. zs) . A pure E2 transition was assumed. k) The transition is assumed to be pure E2 . ~) The transition is assumed to be (4 .5 f 0 .7)°~ E2, ref. a°).

an example of a nucleus near the SU(3) limit (axially symmetric rotors)' 9). Recently the IBA-1 model has been used st) to predict energy levels and y-ray branching ratios for the bands observed 31) in ts6Gd in the (tx, 2ny) reaction . With a few exceptions, good agreement was obtained for the ß- and y-bands and the two lowest octupole bands. The present work considerably extends the information on transition probabilities 3t) over that given in ref. and it is of interest to extend the comparison with the

23 4

A. Bücklin et al. / "6Gd

IBA model accordingly. The IBA-1 codes PHINT and FBEM se) were employedt, using the same set of input parameters as that used in the earlier calculation 31) [see also table 5, footnote b)] . The calculated E2 transition probabilities from the y- and ß-bands are compared with the experimental data in table 5. The transition probabilities from the y-band are generally well reproduced, while those from the ß-band in several cases deviate strongly from the experimental values . A similar deviation, although somewhat less pronounced, was obtained in a recent IBA-1 calculation for the 2+ states sa) [here an additional parameter in the E2 operator was adjusted in order to reproduce exactly the experimental value of B(E2 ; 212+ i 010+)]. This deviation is not likely to be explained only as due to the admixture of the 03 band into the ß-band since the mixing calculations, sect. 5, indicate that this only weakly influences the E2 transition probabilities from the latter . Also the relative magnitudes of the EO transition probabilities from the ß-band to the ground band were calculated . They were found to be very nearly constant, in accordance with the experimental values (table 2). The "anomalous" 03 band cannot be reproduced within the IBA model employed here. This band may possibly be associated with the subshell closure at Z = 64, which may induce additional modes of excitation's). Work is underway to include these in the IBA model through the introduction of additional bosons' s ). In addition to the ß- and y-vibrational-like states the IBA predicts higher lying collective states with characteristics similar to two-phonon quadrupole vibrations 8~. Such states are predicted at 1 .92 MeV (0+), 2 .10 MeV (0+), 2.02 MeV (2+) and 2.24 MeV (4+). They are all expected to decay with enhanced E2 transitions to the corresponding one-phonon states s). The first 4+ band is observed at an energy of more than 0 .7 MeV below the predicted value, which indicates that also other degrees of freedom than those considered in the IBA calculation must be of importance for this band . It is however interesting to compare the predicted B (E2) values with those observed for the 4+ band, see table 11 . With one or two exceptions, the transition probabilities to the y-band, which are expected to be the strongest, are predicted with the correct order of magnitude . If also a g-boson is included in the IBA's), the energy of the band can be lowered and the reproduction of the B(E2) values is improved'6). The second K~ = 2+ band is predicted by the IBA-1 within 0.2 MeV from the experimentally observed 2Z band . Ratios of reduced transition probabilities from the 22 band are given in table 10. The IBA reproduces well the ratios involving transitions to the same band (first three entries) and predicts the ratios involving transitions to the ground-state band (next three entries) to be small, as observed . The last four entries all involve E2 transitions to the y-band . Here the IBA predictions are seen to deviate from the observed values in away that suggests t We are indebted to Dr . O. Scholten for providing calculations and codes.

A . Bäcklin et al. / ~SeGd

23 5

that the present IBA calculation predicts the E2 transition rates from the 2Z band to the y-band an order of magnitude too small. The observed Oâ and OS bands occur not far from the region where the second and third excited 0+ bands should be expected according to the IBA. The experimental data allowed extraction of only a few ratios of reduced E2 and EO probabilities, which are given in table 12 . The second excited 0+ band predicted by the IBA shows some qualitative features similar to those observed for the Oâ band. However, the data are too scarce to draw any definite conclusions regarding the nature of the Oâ and OS bands. In summary, we find that the IBA-1 model in the version used here successfully predicts the properties of the y-band but not those of the ß-band . At higher energies, however, the agreement with experiment varies from good prediction of the qualitative properties of the 2 z band to the completely missing prediction of the existence of the 03 band . 7.1 .1 .2. Comparison with the pairing-plus-quadrupole model. The pairing-plusquadrupole model of Kumar and Baranger ei'8z) has earlier been applied to iSeGd, ref. 8s) . The predictions for the E2 transition probabilities from the y-band, table 5, are rather similar to those of the IBA, and agree fairly well with the experimental data. The E2 transitions from the ß-band, however, deviate considerably from the observed values, often in the opposite direction to the deviation of the IBA values . The EO transition probabilities between the ß-band and the ground-state band are predicted to be constant, as observed, although a factor of two too large (table 2). Gupta et al. 8s) obtained a second excited 0+ band at 2.28 MeV. It is not clear from theE2 branching ratios given intable 12 whetherthis bandcan be identified withany of the observed Oâ or OS bands. 7.1.2. Odd-spin bands. Three closely spaced K~ =1+ bands are observed near 2 MeV. Their modes of decay show some differences. The 1 i band decays mainly via El transitions to the low-lying octupole bands and Ml (+E2) transitions to the y-band . The lZ and 13 bands, on the other hand, prefer M1 decay to the groundstate band with weaker E1 transitions to the octupole states. It is not possible from the present data to make definite conclusions about the character of these states. However, the conspicuous El decay especially of the 1 ; state suggests that a two-phonon octupole state may be involved . Other 1 + states expected are two-particle states, the three lowest of which have been predicted at 1.6, 2.0 and 2.4 MeV, respectively 6') . Pyatov and coworkers have calculated 1+ states in even deformed nuclei as obtained with a residual interaction consisting of a pairing part and a spin-spin interaction part 84'85). Three states are obtained, at 2.06, 2.09 and 2.15 MeV, all of which have a collective nature (mainly neutron configurations). Two of the states are predicted to decay with strong M1 transitions (0.1-0 .3 s.p.u.) to the ground-state band . One may compare these transition rates with those we can calculate from our experimental E1/Ml branching ratios, if we assume the El transitions to have

23 6

A. Bäcklin et al. /' S6 Gd TABLE 12 Ratios of reduced E2 and EO transition probabilities from the 0; and OS bands

Ratio

Exp value

a)

c)

4 x 10-q

10-s

0.06

0.93

0.031

23

((1 .6 f 0.3) x 10-2) a)

4 x 10-q

10-s

1 .5 t 0.3

4.3

20

0.03

0.17t0.05

4.3

20

0.03

3 x 10-q

10-e

0.020 t 0.004 B(E2 ; OgO+ -~ 022+) B(E2 ; OqO+ -~ 212+) B(E2 ; OgO+- +0~2+) B(E2 ; OqO+ -~ 02 2+) e2Rgp2(E0; OgO+~ 010+ ) B(E2 ; OqO+ -~012+)

Theory

(1 .2t0 .2) d)

(0 .23 f 0.13) °)

') IBA-1, second excited 0+ band . IBA-1, third excited 0+ band . " s9). ~ Pairing-plus-quadrupole model, second excited 0' band a3 positions of the transitions placed to the OZ band are uncertain. a) The b)

a reduced transition probability of the same order of magnitude as those de-exciting the one-phonon octupole states (cf. sect . 6). For the 1 1 1 + and 1 3 1 + states we then obtain M1 transition probabilities about two orders of magnitude weaker than those predicted, while the l Z l + state could be a possible candidate for a spin-spin state. A collective K~ =1 + level is obtained in the IBA model if neutron- and protonbased bosons are treated separately (IBA-2) [ref. e°)] . From the presently available data no conclusions can be made regarding the existence of such a state, which ao.s~)]. should occur at 2 .05 MeV [refs . 7.2 . NEGATIVE-PARITY BANDS

Altogether about 20 levels with negative parity were identified in the region 1 .2-2 .2 MeV. Twelve of these could be ordered into the four bands shown in fig. 5, which have been discussed in sects. 4 and 5. The missing K~ = 3 - octupole band, which is predicted at 1 .84 MeV [ref . 'a)], could not be identified among the candidates that occur close to 2.0 MeV (table 1). Several two-quasiparticle states e') five bands with K~ = 3 - are are expected to occur in this energy region : in ref. predicted in the energy region 2.0-2 .3 MeV. Also, states formed as two-phonon quadrupole plus octupole vibrational states may occur at these energies . The seeming lack of prominent features of the negative-parity states made it difficult

A . Bäcklin et aJ.

/ l ' 6 Gd

237

to identify any band structure in this energy region and may indicate a strong mixing of the states. The El decay of the 0~ and 1~ octupole vibrational states has been compared in ref. a') with the predictions of the IBA-1 . An f-boson was included in the calculation and good agreement was found with experiment. This calculation also yields ratios of B(El) values from the 2i band, which are compared with the experimental data in table 13 . One observes a good agreement between the predicted and the experimental values for transitions from the 2 - and 4 - levels of the band, while for transitions from the 3 - level strong deviations occur. An estimate of the absolute E1 transition probabilities from the 2 t4 - state may be obtained with the aid of the 4 - -> 2 - intraband E2 transition. Assuming the same value of Qo as for the ground-state band s') we obtain B(El ; 2 t4 - -> 2,4 +) =1.7e 2 x TABLE 13 Ratio 2 1 2 -> 2 1 3+ 2 1 2 -. 2 1 2+ 2 1 2 - 10x 2+ i 212-- 212+ + 2 1 2 -. 0 1 2 2 1 2- .2 1 2 + 2 1 3 -~ 2 14 + 2 1 3 -~ 2 1 2 + 213- i 213 + 213--. 212+ 2 1 3 -. Ox 2 + 2 1 3 -. 2 1 2 + 21 3 -.Ox4 + 2 1 3 -. Ox 2 + 213- i 012+ 2 1 3 - 12 1 2 + 21 3 -. 0 1 4 + 21 3 - -. 0 1 2 + 21 4 -. 2 1 3 + 2 1 4 -~ 2 1 4 + 2 1 4 -~ 2 1 5 + 2 1 4 - -.2 1 4 + 2 1 4 -~ 0 1 4 + 2 1 4 -~ 2 1 4 +

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23 8

A. B&klin et al. / 1seGd

10-a° cm z and B(E2 ; 214- ~ 0,4+) < 0.06e Z x 10 -s° cmZ. The first of these values corresponds to an E1 matrix element (2+ ~M'(E1 ; 0)~2 -) = 2.9e x 10-1s cm, a value intermediate between the matrix elements for the El decay from the 0i and 1 i bands to the ground band . 8. Sammary A detailed study of the level scheme of 156Gd has been made using the (n, y) reaction with both thermal and 2 keV neutrons. Fifteen excited rotational bands have been established and we believe that essentially all bands below ~1.9 MeV with K , 5 have been observed . A large number of relative and absolute reduced transition probabilities have been obtained, from which we can draw some conclusions, especially regarding the collective properties of the states . The lowest positive-parity bands are mixed. A phenomenological mixing analysis including the ground-state band, the ß- and y-bands and the 0+ band at 1168 keV reproduces well the experimentally obtained E2 transition probabilities between these states . Of the higher bands, the 2+ band at 1828 keV and the 4+ band at 1511 keV show some features similar to those expected for two-phonon vibrational states, but especially for the 4+ state, other components, such as the {i +[411], i+[413]}x+ two-proton state, are important. The 0- and 1- octupole bands are very strongly mixed. A Coriolis-coupling calculation including also the 2- octupole band reproduces well the energies and the E1 transition rates to the ground-state band. The E2 transition probabilities from five of the lowest positive-parity bands have been compared with predictions of the IBA model and the pairing-plus-quadrupole model. Both models reproduce well the decay of the y-band, but are unable to predict the decay of the ß-band . Some of the decay properties of the 22, 4i and 2 i bands are reasonably well predicted by the IBA model, while others are not. We wish to thank Drs. P.O . Tj~dm and B. Elbek for communicating their transfer reaction data . We are grateful to Dr. O. Scholten for valuable aid with the IBA calculations and for helpful discussions, and to Prof . F. Iachello for stimulating discussions. We also wish to thank Dr. N.I. Pyatov for communicating results. Appendix Transitions observed in the reaction 155 Gd(n, y)

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TABLE A3 issGd(n, y) ; priatary y-ray energies and intensities, 2 keV neutron capture Gamma-ray energy (keV) 8537 .4 8448.8 7488.8 7408 .4 7383 .E 7368 .5 7289 .9 7279.1 7261 .3 7254.3 ~ 7216.8 6823 .0 6766 .9 6730 .0 6710 .0 6687 .0 6678 .E q 6622 .7 6572 .0 6550 .8 6533 .7 6511 .4 6489 .2 6483 .1 6467 .8 6455 .E q 6431 .5 6419 .2 b) 6390.7 6380 .0 6348 .3 6320.0 6267 .4 ~ 6236.4 6214 .5 6176 .0 6170.3 6155 .5 6134.9 q 6031 .3 6003 .E 5963 .E 5948.4 5939.8 5892 .9 5886 .1 5819 .3

Error (keV)

Relative gamma-ray intensity

0.7 0.5 0.7 0 .5 0 .5 0.5 0 .5 0.5 0 .9 1 .3 0.9 0 .7 0 .5 0 .7 0 .5 0.7 1 .1 0 .5 0 .6 0 .8 0 .5 0 .6 0 .7 0 .8 0 .9 1 .0 0.8 1 .2 0.6 0 .7 0.5 1 .1 1 .3 0.5 0 .6 1 .4 1 .3 0.8 1 .1 1 .0 0.7 0.6 1 .9 0.7 0.8 1 .0 1 .1

45.4 100 17.9 45 .9 43 .E <56.4 24 .4 35 .4 <11 .8 5 .1 9 .7 20 .4 28 .4 14 .5 30 .2 15 .7 8 .0 38 .0 25 .8 13 .4 21 .5 20 .E 23 .2 20 .E 12 .5 11 .3 12 .5 11 .1 20 .E 14 .5 32 .0 15 .5 12 .2 39.8 17 .9 15 .7 19 .E 17 .0 16.7 12 .7 20.4 23 .3 10 .1 21 .4 30.2 23 .9 17 .1

Error

10 7 15 10 10 12 12 25 40 25 25 15 20 12 20 30 10 12 20 15 15 15 20 20 25 25 25 15 25 12 25 30 12 20 30 30 20 25 25 20 15 50 15 15 40 30

IY E3Y 7 .3 16 .6 4 .3 11 .2 10 .9 <14 .1 6.3 9 .1 <3 .1 1 .4 2 .6 6 .5 9 .1 4.8 10.0 5 .3 2 .7 13 .1 9 .1 4 .8 7 .7 7.5 8 .5 7 .6 4 .6 4 .2 4 .7 4 .2 7 .9 5 .6 12 .5 6 .1 4 .9 16 .4 7 .4 6 .6 8 .3 7 .3 7 .3 5 .8 9 .4 10 .9 4 .8 10 .2 14 .8 11 .7 8 .7

Level energy (keV) 0 .3 88 .9 1048 .9 1129 .3 1154 .1 1169 .2 1247 .8 1258 .E 1276 .3 1283 .4 q 1320 .8 1714 .E 1770 .8 1807 .E 1827 .E 1850 .7 1859 .1 q 1915 .0 1965 .7 1986 .9 2003 .9 2026 .3 2048 .4 2054 .E 2069 .9 2082 .1 ~ 2106 .2 2118 .4 2147 .0 2157 .7 2189 .4 2217 .E 2270 .2 q 2301 .2 2323 .1 2361 .E 2367 .4 2382 .2 2402 .8 q 2506 .4 2534 .1 2574 .0 2589 .3 2597 .9 2644 .8 2651 .5 2718 .4

Error (keV) 0.4 0 .4 0 .5 0 .3 0 .4 0 .4 0 .3 0 .8 1 .2 0 .8 0 .5 0 .5 0 .7 0 .5 0 .6 1 .0 0 .4 0 .5 0 .7 0 .5 0 .5 0 .6 0 .7 0 .8 0 .9 0 .7 1 .1 0 .6 0 .8 0 .4 1 .0 1 .2 0.4 0 .7 1 .4 1 .2 0 .7 1 .0 0 .9 0 .6 0 .6 1 .9 0 .6 0.7 0.9 1 .1

Level spin and Parity `) 0+ 2+ 0+ 2+ 2+ 0+ 3' 2+ 320+ 2+ 2+ (3 - ) 2+ +3 + 1+ 2+ 1+ 2+ 3+ 3+

1 + +T 2+ 3+

258

A.

issGd Biicklin et al. /

T.4BLE A3 Gamma-ray energy (keV) 5813 .8 5801 .9 5564 .5 5551 .4 5539 .3 5430 .5 5415 .6 5380 .3 5045 .0 `)

Error (keV)

Relative gamma-ray intensity

1.4 0.9 0.9 0.7 0.9 1 .0 0.8 0.9 0.8

12 .7 15 .3 16 .1 30 .1 15 .9 15 .6 21 .0 18 .7 21 .7

(cont.)

Error

_I, E',3,

Level energy (keV)

Error (keV)

30 20 25 20 25 25 20 25 25

6.4 7.9 9.3 17 .6 9.4 9.8 13 .2 12 .0 16 .8

2723.8 2735 .8 2973 .1 2986 .3 2998 .4 3107 .2 3122 .1 3157 .4 3492 .6

1.4 0.8 0.9 0.6 0.9 0.9 0.7 0 .9 0 .8

Level spin and parity')

From all information as given in the level scheme . Questionable line and level.

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