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Yrast cascades in even-mass Ce isotopes
ll.E.1:3.A[
Nuclear Physics AZ25 (1974) 1- 15; @ Not to
North-Holland Publishing Co., Amsterdam
be reproduced by photoprint or microfilm without written permission from the publisher
YRAST CASCADES
IN EVEN-MASS
W. DEHNHARDT,
Ce ISOTOPES
S. J. MILLSt, M. MULLER-VEGGIAN, U. NEUMANN, G. POGGItt, B. POVH and P. TARASrt I. Physikalische Institut der Universitiit Heidelberg, Germany and Max-Planck-Institut fir Kernphysik, Heidelberg, Germany Received 22 February
D. PELTE,
1974
Abstract: The
isotopes 130*132*134*136Ce are investigated by means of the reactions 118~120~122~124Sn(160,4n) at bombarding energies between 68 and 76 MeV. From lifetime measurements a reduction of the collective behaviour is observed with increasing neutron number. Yrast cascades of rotational structure are identified up to angular momenta J= 16+ or I= lg+ in 13’3~13%134Ce. Th ese cascades show a strong “back-bending” effect. In 13%e no such simple yrast cascade could be found. NUCLEAR REACTIONS 11**120*1~. 124Sn(160, 4ny), E = 68-76 MeV; measured Er, I,(@, 1/1/coin. 130*132.134*136Ce d e d uced levels, J, T+. Enriched targets.
E
1. Introduction
The low lying energy levels of many even-A nuclei can be grouped into rotational bands. Their excitation energies follow approximately the simple rule E = (h2/20) 1(1-f- 1). At high angular momenta (I NNlOh-- 16h), however, some of these nuclei show a characteristic departure from the rotational behaviour. This phenomenon is commonly labelled the “back-bending” effect. In the region of the “back-bending” one observes a sudden increase of the moment of inertia 8 with increasing angular momentum. Although this behaviour is not too surprising and was even predicted ‘) before it was observed experimentally, the detailed mechanism and why it occurs only in a selective group of nuclei is still not understood completely. A review of the theoretical interpretations is given in a publication by Johnson and Szymanski “). The strongest changes in the moment of inertia have been observed 3, “) in the rare earth nuclei ls8Er and 166Yb and in the nucleus r3’Ce. The latter nucleus appears particularly interesting with respect to the possible theoretical interpretations “). This is related to the fact that the Fermi levels of protons and neutrons are near the h+ shell model state with the protons having a small angular momentum projection t On leave from National Physical Research Laboratory, CSIR, Pretoria, South Africa. tt On leave from University of Florence, Italy. ttt On leave from Universite de Montreal, Canada. 1 June
1974
2
W. DEHNHARDT et at.
$2 and%he neutrons a large St if the nuclear deformation is positive. If the deformation is negative, the role of protons and neutrons is reversed. In this paper we describe the results of an experimental study of the nuclei 130S132r1343136Ce.These nuclei were inyestiga~ed earlier by Ward eit a!. 5), who identified low excited levels wliich were interpreted as members of rotational bands. Part of the results that are described in the present paper were published already elsewhere *). The Ce isotopes are situated near the closed neutron shell n = 82 and one expects a decrease in the collective behaviour with increasing neutron number. This can be deduced from the positions of ,the first excited 2” states which are shifted towards higher excitation energies if neutrons are added. The level schemes of 13oy132*1349‘36Ce are displayed in fig. 1. This figure comprises the information
m91
?
i.
,
-L._ 4091
13’
Ce
Ce
0’
ISOTOPES
Fig. 1. Level schemes in 130, 132*r3**136Ce.
which was known “) prior to our study and also the results of the present investigation. A more direct measure of the collectivity, however, is the E2 strengths of the ytransitions between the low lying states. In sect. 2 we give the necessary information on the experimental procedures and in sect. 3 we describe the measurement of the lifetimes of levels in the four Ce isotopes. A detailed report on the level structures observed in 130,132,134Ce is given in subsect. 4.i. The nucleus 13%e behaves in many respects differently from the other three Ce isotopes. Subsect. 4.2 of this paper is reserved for the report of the properties of levels in 136Ce. A summary of the observed phenomena in the even-A Ce isotopes is given in sect. 5.
2. Experimental procedure The Ce isotopes were populated by the reactions 118~120~122~‘24Sn(160,4n) 130,132T134,136Ce. The 160 beam was accelerated by the MP tandem Van de Graaff generator of the Max-Planck-Institut fur Kernphysik, Heidelberg. The beam energies varied between 68 and 76 MeV. The current of the charge state 7+ was of the order of 15 nA. The targets consisted of isotopically enriched (99 %) Sn material and were 200-500 pg/cm2 thick. For the lifetime measurement the Sn was evaporated onto 1 mg/cm’ gold foils. In the other experiments the target backing consisted of a 150 mg/cm2 thick Pb foil. The deexcitation y-rays were detected with Ge(Li) detectors which had an active volume of 60 cm3. The Ge(Li) detectors could be rotated around the target centre and their front faces had a distance of 7 cm from the target. In all runs except in the lifetime measurements 3 Ge(Li) detectors were used, two of which were positioned at fixed angles 55” and 125” with respect to the beam. The positioning of the detectors was checked with 6oCo and 152Eu sources which were centred in target position. Departures of less than 9 % from the isotropic y-ray angular distributions were found and corrections made. The sources were also used to determine the relative detection efficiencies of the Ge(Li) detectors for the various y-ray energies and to obtain an absolute energy calibration. From the measured nonlinearities and energy resolution (2.5 keV for 1.33 MeV) the error in the energy of y-ray lines is estimated to be 0.15 %. The data consisted of y-singles spectra, y-y coincidence spectra and y-ray angular distributions. In order to determine angular distributions the movable detector was rotated around the target in 15” steps from 0” to 135” while the fixed detectors served as monitor detectors. In the coincidence runs, coincident events were registered between the movable detector and either one of the fixed detectors. The signals from the detectors were processed in conventional ORTEC electronics and stored either in a 4096 channel pulse height analyzer or in an on-line computer. The resulting y-ray spectra were analyzed with a peak fitting program assuming a Gaussian line shape for the photo peaks and a smooth background.
et al.
W. DEHNHARDT
3. Lifetime measurements From the excitation energies and the expected enhancements of the E2 transition strengths in deformed nuclei it is estimated that the lifetimes of the low lying states in the even-A Ce isotopes are of the order of 1 to 500 ps. In this range the proper method of lifetime determination is the recoil distance method. This technique makes use of the Doppler shift of y-rays emitted from a moving source in order to measure the number of recoiling nuclei that decay within a certain distance. This method was used in this laboratory to measure the lifetimes of states in the Ba and Xe isotopes “). We refer to @is paper “) for more details on the experimental method and analysis. Ref. “) also includes a summary of the necessary corrections that have to be taken into account in order to deduce the lifetimes. The y-rays were detected with one Ge(Li) crystal, positioned at 0” with respect to the beam and at a 10 cm distance from the target. A y-ray spectrum obtained from the 12oSn(160, 4n)13’C!e “Osn(‘so,4”l’32Ce 6+--l+
4+-Z+
2+-o+
I
Unshifted
2*-o+ >
300
6+-1*
4*-Z+ 100
8+-6+
500
600
8*-6+ 800
mo
ENERGY
Fig. 2. Gamma-ray
spectra observed at 0” and different plunger settings following 120Sn(160, 4n)13Ve.
i keVl
the reaction
4’-2+
l<
--f-4
------A
----___ --___j_ i
6*-4’
~&-~.-.._.-I. ...__.___.__. ._ __.__._~_ _. ijj i / /
I//,
8 /
: lD0
200 TiME OF FLIGHT
300 AFTER
400
REACmW
Fig. 3. Decay curves of the four lowest excited states in ‘%Ze.
500 msec)
6
W. DEHNHARDT
et d.
reaction is shown in fig. 2. The vertical lines connect the peaks that correspond to the decay in flight and the decay in the stopper at various distances of the stopper. The largest distance in this figure is 3.8 mm. In some runs, however, the distance was as large as 8.5 cm. In this case the detector was positioned at 90” and faced only the stopper. The target itself was not seen by the detector because of a lead shield. In this way states with very long lifetimes z > 30 ns could be identified. The experimentally measured decay of the four lowest levels of the rotational band in 13’Ce is presented in fig. 3. As deduced in ref. “) a decay curve is given as the ratio between the intensity of the “stopped” peak and the intensity of the sum of “stopped” and “flight” peaks. The analysis of the decay of a particular state is complicated by the lifetimes of the higher lying rotational levels which decay to the state and by the population via side feedings. In the analysis of the decay curves the time structure of the population from higher rotational levels was taken into account by the direct measurement of the decay from the next higher rotational level whereas the side feedings were treated as unknown exponential decays with time constants that had to be determined by the decay curve of the state under investigation. The intensities of these different feeding processes were taken from the experimentally determined y-ray intensities. The fits that are obtained by this procedure are plotted in fig. 3. The decay curves of the most energetic transitions in the rotational cascades and therefore presumably the fastest ones contained a component with a decay constant that varied between 6 ps for 13’Ce and 17 ps for 13%e. These decay times are much slower than is expected for intraband transitions and were interpreted by Diamond et al. ‘) as the feeding times. The feeding time is the time the y-decay process needs to reach the upper members of the ground-state band after the evaporation of the last neutron. The side feeding, on the other hand, contained in general two components: one with a lifetime varying from 30 to 350 ps; the second with a long lifetime of greater than 5000 ps. At least part of the last component, however, may also arise from contaminations in the y-ray spectra. The large variations in the decay constants of the side feedings are not understood. It is, however, interesting to note that the side feedings are slower than the direct feeding through the yrast cascade. The lifetimes of the low lying states and the feeding times are listed in table 1. The lifetime of the 2+ state in 13%!e could not be extracted because of the nearby 548 keV line from 197A~. The last column of table 1 shows the enhancements of the E2 transitions in Weisskopf units “). These values are corrected for the electron conversion “). It is evident that the enhancements become smaller with increasing neutron number. Furthermore the ratios B(E2,4+ --+2+)/B(E2,2+ -+ O+) indicate that ’ 3‘, 132Ce behave like permanently deformed nuclei whereas 134Ce falls into a transitional region. A very long lifetime z > 30 ns of a level at 2.990 MeV in 136Ce was observed by the method that was described earlier in this section. This result will be discussed in more detail in subsect. 4.2.
mice
130,132,134*
7
TABLE1 Transition energies, lifetimes and transition Nucleus
130Ce
2++0+ 4+ -+2” 6’+4+ 8+ -+ 6+
253.9 456.6 613.9 729.9
22X3&19 7.8&2.3 2.451.2 < 1.0 6.0+2.0
0.319f0.02 0.52 &to.15 0.39 rto.20
81.6+6 132.9&39 99.6+50
2+ -to+ 4+-+2* 6+ -+4+ 8+ +6+
325.4 532.2 682.4 786.8
67.9&9.5 4.213.7 l.l&O.S < 1.0 11.0+2.0
0.320&0.05 0.446&0.18 0.49410.36
80.1112 111.7+45 123.8190
2++0+ 4+ +2* 6+ -+4+ 8+-+6+
409.1 639.5 814.4 948.0
35.5k8.0 6.552.7 < 1.0
0.197fto.04 0.117~0.08
feeding-time 134Ce
feeding-time 13We feeding-time
in J30, I329134S‘%e
Transition
feeding-time lazCe
probabilities
48.3&-11 X%6&12
14.013.0 2+ -to+ 4+ -+2+
552.1 762.3
9.442.5 17.oIfi5.0
0.034&0.008
8.1 f2
4. Level structures r3%I!e were investigated by means The properties of levels in the nuclei 130~13231343 of their y-decay. The formation of the compound nuclei by bombardment with heavy ions and the subsequent successive evaporation of neutrons leave the final nuclei in excited states that have high spin values and strong alignments. In our case it can be estimated from the statistical model lo) that the residual Ce isotopes are formed on the average with states having a spin of I = 18+ at a bombarding energy of 76 MeV. The average excitation energies before y-emission are 5.0, 9.0, 12.5 and 15.5 MeV for 130CIe 13’Ce ’ 34Ce and ’ 3‘Ce, respectively. The &excitation proceeds then by y-emission’prefer~~tialIy through states that have m~um angular momentum at minimum excitation energy (yrast states), This behaviour of the deexcitation mechanism produces y-ray spectra which consist of isolated lines situated on a broad y-ray background. The order in which the y-transitions follow each other was established by the following criteria: (i) Each of the y-rays proposed to be a member of a cascade is in coincidence with all the other members. (ii) The relative intensities of the y-transitions in the singles spectra show a gradual decrease with increasing excitation energy. This feature is consistent with the statistical picture ’ “) of the deexcitation process.
8
W. DEHNHARDT
et al.
(iii) In the coincidence spectra the relative intensities of all transitions following a gate transition are equal within statistics- while those transitions preceding a gate transition have the same intensities as in the singles spectra. A coincidence y-ray spectrum observed in the 122Sn(‘60, 4n) 134Ce reaction is shown in fig. 4. During the analysis it was found that some of the peaks are actually doublets or belong to the (160, 5n) reaction. This complicated the analysis. The ambiguities, however, could be removed by proper gate settings. (iv) The relative excitations of levels measured at increasing bombarding energies become gradually stronger for higher excitation energies. This is again to be expected from the statistical nature lo) of the population mechanism. The results of this measurement are displayed for all four Ce isotopes in fig. 5. Within the error limits the change of the relative intensities with increasing bombarding energy can be reproduced by straight lines. The lines are labelled in fig. 5 either by the corresponding y-ray energies or by the spin sequence if this could be established (see later). The level schemes that are extracted in this way are presented in fig. 1. The isosopes ’ 3‘a132,134Ce behave very similarly whereas 13%e displays different properties. The discussion of this nucleus is therefore postponed to subsect. 4.2. 600/
t
h-
/ + 409.1 639.5
948.0
908.5
+ 724.6
o+
I
500
i
ENERGY
Fig. 4. Gamma-gamma 4.1. THE NUCLEI
+
1000
I keV 1
coincidence spectrum following the reaction 122Sn(160, 4n)134Ce.
130*132.134Ce
The dominant y-ray lines measured in 13’S1323134Ce belong to only one cascade in each of these nuclei. The intensities of the y-transitions normalized to the last transi-
9 13’Ce
ie 70
i3
is
‘3”Ce
'34Ce
I
i
68 70 72 7L 76
BOMBARDING Fig. 5. Excitation fictions
ENERGY ( MeVV) OFlevels in 130*m* 134*f 36Ce.
tion are listed in table ,2 together with their energies. The angular distributions of the y-rays show a positive anisotropy. The coefficients of the expansion in terms of even Legendre polynomials to fourth order are listed in table 2. The values of these coe~cjents correspond to a stretched E2 cascade starting at a nearly aligned state with an angular momen~m of f = 18’. The theoretical predictions ‘I) for this cascade are uz/ao= 0.384 and ah/a0= - 0.137assuming complete initial alignment. These values include a correction I2 ) due to the finite size of the detector. The spins of the states in the cascades deduced from this analysis are shown in fig. 1. It seems that the states in the cascades can be interpreted as members of rotational bands.
W. DEHNHARDT
10
et al.
TABLE 2 Transition
energies,
relative intensities
Transition
and angular
E#eV)
distribution
Relative intensity
coefficients
in I308 132*134Ce
Angular distribution coefficients
“WA0
-AlAo
130Ce
2+0 4+2 6+4 8-+6 IO-+8 12 3 10 14412 16 -+ 14
253.9 456.6 613.9 729.9 756.8 503.4 549.7 693.7
100 loo&5 99&4 58f4 35&S 17&S 13&3 854
0.4010.01 0.32+0.01 0.25&0.02 0.30&0.03 0.38 stO.02 0.37&-0.04 0.37&0.10 0.3250.04
0.18~0.02 0.14&0.01 0.1440.03 0.11&0.04 0.19&0.03 0.06&0.05 0.10*0.14 0.20 AO.06
132Ce
2+0 4+2 6-+4 8+6 lo-t8 12 + 10
325.4 532.2 682.4 786.8 827.7 569.7
100 9014 67+3 47+3 30&3 23&4
0.32f0.02 0.33&0.02 0,35&0.03 0.38kO.03 0.43 10.04 0.3510.04
0.07&0,03 0.03 kO.03 0.04&0.03 0.03 jzo.04 0.07&0.05 0.01 hO.05
14+12 16 -z- 14 18 +- 16
512.2 698.6 823.4
2015 16&3 11+3
“) 0.39&0.04 0.29kO.08
“) 0.03&0.05 0.12+0.10
409.1 639.5 814.4 948.0 908.5 464.3 724.6 817.9 397.0
100 90$5 54,t6 4815 26&4 22f4 19”4 8f2 2146
0.3orto.03 0.31 kO.03 0.33+0.01 0.30*0.03 0.34kO.06 0.3390.05 0.2910.05 0.49f0.05 -0.10~0.03
O.lOf0.04 0.07,1;0.03 0.09f0.02 0.09&0.04 0.09&0.08 0.16&0.07 0.04&0.06 0.07$20.06 0.03&0.04
134Ce
2+0 4-+2 6+4 8+6 10 + 12 3 14 --f 16 --t I+8
“) Contaminated
s IO 12 14
by the 511 keV annihilation line.
Fig. 6 displays the positions of the excitation energies versus 1(1-l- 1). One observes a sudden change in the slopes near angular momentum I = 10’. This will be further discussed in sect. 5. The relative population ofthe cascade states decreases with increasing excitation energy. Abrupt changes in the population are observed for some levels particularly for the 1= S4 levels in 132y134Ce and the I = 6” level in 13’%e. It is plausible to try and find other transitions than those already ident~ed that feed these levels. In the case of the nucleus I3 “Ce a second y-transition populating the I = 8 + state could be ideutified that seems to account completely for the extra intensity of the 8+ -+ 6’ transition. It has an energy of 0.397 MeV. The angular distribution of the corresponding y-ray has small negative anisotropy (table 2). From the measured coeflicients of the Legendre expansion it may be concluded that the 0.397 MeV transition i.s not of an E2 nature but probably of an El or Ml nature. This could indicate the existence
I30,132,134,
IS”&
Fig. 6. Plot of the level excitation energy as a function Off@+ f >.
of a second I = 8 state near the excitation energy where a sudden change in the moment of inertia is observed, The attempt to follow this new cascade to higher excitation energies was not successful. A few single transitions were also found that seem to feed the I= 4+ and f = 6* states. Their intensities, however, were too small for a further analysis. 4.2. THE NUCLEUS 13%e
As pointed out already, the nucleus ’ 3‘Ce shows a behaviour that differs from the other Ce isotopes. The differences are twofold: (i) at least four cascades were populated in the 124Sn(160, 4~)‘~~ Ce reaction; (ii) The angular ~str~butio~s of the y-rays belonging to a cascade are not of a stretched E2 type. The energy levels in I3 %e that are deduced from the identified y-cascades are displayed in fig. 1. The level sequence 2.215, 1.314, 0.552, 0 MeV was found already by Ward et al. “) and was interpreted as the ground state rotational band. However, as previously stated in sect. 3, the lifetime of the 2.990 MeV state that feeds this sequence is found to be longer than 30 ns. This is an uncommonly long lifetime if one assumes that the five Ievels are members of a rotational band. The transition strength is smaller than 10m3 W.U. as compared to the enhancements of more than 80 W.U. that are observed for the rotational bands in the other Ce isotopes (table 1). Correspondingly the anisotropies of the y-ray angular distributions are very small (table 3)
W. DEHNHARDT
et al.
130.132.134,
i36Ce
13
due to the deorientation effect in the 2.990 MeV state. Another cascade could be identified that depopulates the 2.990 MeV state. This cascade, too, consists of ytransitions which have small and positive anisotropies‘in their angular distributions (table 3). Because of its long lifetime, transitions feeding the 2.990 MeV state were not observed. In view of these results we believe that a definite spin assignment for the states of these two cascades cannot be given. A third sequence of states that are connected by subsequent y-transitions could be identified up to an excitation energy of 5.557 MeV. This sequence consists of nine states of which the last three are the same as those of the two former cascades. The expansion coefficients of the y-ray angular distributions are listed in table 3. One observes both positive and negative anisotropies. The negative anisotropies can be explained only by an El or Ml nature of the corresponding y-transition if the initial state is aligned. However, it is not possible to reproduce all the measured anisotropies by assuming an initially aligned state and a cascade with Ii = Ii_1 +A where /z can be 1 or 2. The assumption of a Gaussian sub-state population of the initial state fails likewise. It is found that the experimentally measured negative anisotropies remain too strong when the positive anisotropies are reproduced. If this cascade in 13%e corresponds to the yrast cascades that were observed in I309132,134Ce it must be concluded that it is of a very different nature. In 13’Ce a fourth sequence of states was found which are connected by y-rays but which have no y-ray in common with the other three cascades. It is, therefore, impossible to deduce the absolute excitation energies and this level sequence is not shown in fig. 1. Table 3, however, contains the y-transition energies and the expansion coefficients of the corresponding angular distributions. The anisotropies are found to be positive or negative. No attempt was made to deduce spin assignment. 5. Summary and conclusions At low excitation energies the isotopes 130Y132,134,136Ceare characterized by a decrease in the collective behaviour with increasing neutron number. This can be deduced from the level structures and from the enhancements of the E2 transitions between the low lying states. In view of a simple model one may interpret 130S132Ce as being permanently deformed at small excitations. These two nuclei and 134Ce are found to have level sequences with angular momenta that are characteristic of the ground state rotational bands. From the corresponding excitation energies, however, it can be concluded that a strong variation of the moments of inertia occurs in these bands. In fig. 7 the moments of inertia 0 are plotted against the rotational frequencies o. This plot demonstrates the “back-bending” effect in the ground state bands of the three Ce isotopes. At small excitation energies the addition of neutrons causes a reduction in the moments of inertia. In the region of the “back-bending” the interpolated values of 8 are very similar in each of the isotopes and nearly reach the rigid rotor value. At still higher angular momenta fig. 7 indicates that the moments of
14
W. DEHNHARDT
I
,
1
0.1
02
et al.
I
93 VlU12
I MeV21
Fig. 7. Plot of the nuclear moments of inertia 0 as a function of the angular frequency CU.The rigid rotor values are calculated for o = 0.
inertia become smaller with increasing rotational frequencies. This “down-bending” has been observed “) otherwise only in “‘Er and 16’Yb. Nevertheless, the moments of inertia are, at high angular momenta, within 30 ‘A of their rigid rotor values. This result is also found in other nuclei where yrast cascades could be established and is independent of the presence of the “back-bending” effect. One may conclude, therefore, that the yrast states at high excitation energy are of a similar nature in different nuclei although these nuclei can behave quite differently at low excitations. In this respect the identification of rotational like yrast states at high excitation energies in nuclei that are not collective at low excitations would be rather interesting. Unfortunately our attempt to locate such yrast states in i3’%e was not successful. The reason for this failure is not obvious but might be related to the neutron closure of the h, sub-shell. The significance of the h, sub-shell in producing the observed phenomena would probably be better understood if the properties of 124,1261“sCe were known. These nuclei should be producible with the (160, 4n) reactions at slightly higher bombarding energies. The only information on the structure of the Ce isotopes at excitation energies where single y-transitions are no longer resolved comes from the feeding times. The results of this experiment show that the feeding times become longer when the Ce isotopes approach the closed neutron shell n = 82. This tendency was also observed in other nuclei by Diamond et al. and Newton et al. ‘). Two other points are important in discussing the significance of the feeding times. Firstly the initial excitation energies in the Ce isotopes vary, as has already been pointed out in sect. 4. The experimental evidence for this fact comes from the sizeable yield of the 124Sn(160, 5n) 135Ce reaction at 76 MeV bombarding energy and from the relatively weak population of the I = 16+ state in 13’Ce. Secondly the strong “back-bending” effects in the Ce isotopes result in traps for the y-decay through the yrast cascade. For example
the 12+ + IO+ transition in 134Ce is estimated to be 12 ps assuming the same enhancement factor as for the 2+ + O+ transition. It is evident that the values quoted in table 1 are only upper limits of the feeding times with large uncertainties. For these reasons it seems unjustified to deduce information about the structure of the high excitation regions from the feeding times. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
B. R. Mottelson and J. G. Valatin, Phys. Rev. Lett. 5 (1960) 511 A. Johnson and Z. Szymanski, Phys. Rep. 7C (1973) 181 H. Beuscher, W. F. Davidson, R. M. Lieder and C. Mayer-Biiricke, Phys. Left, 40B (1972) 449 P. Taras, W. Dehnhardt, S. J. Mills, M. Veggian, J. C. Merdinger, U. Neumann and B. Povh, Phys. Lett. 41B (1972) 295 D. Ward, R. M. Diamond and F. S. Stephens, Nucl. Phys. All7 (1968) 309 W. Kutschera, W. Dehnhardt, 0. C. Kistner, P. Kump. B. Povh and E-I.J. Sann, Phys. Rev. C5 (1972) 1958 R. M. Diamond, F. S. Stephens, W. H. Kelly and E. Ward, Phys. Rev. Lett. 22 (1969) 546; J. 0. Newton, F. S. Stephens and R. M. Diamond, Nucl. Phys. A210 (1973) 19 C. M. Lederer, J. M. Hollander and I. Perlman, Tables of Isotopes (Wiley, New York, 1967) A. Bohr and B. R. Mottelson, Nuclear structure, vol. I (Benjamin, New York, 1969) p. 389 S. JBgare, Nucl. Phys. A95 (1967) 481 W. G. Winn and D. G. Sarantites, Nucl. Instr. 66 (1968) 61 D. D. Watson and I. Harris, Nucl. Data A3 (1967) 25
Nuclear Physics AZ25 (1974) 1- 15; @ Not to
North-Holland Publishing Co., Amsterdam
be reproduced by photoprint or microfilm without written permission from the publisher
YRAST CASCADES
IN EVEN-MASS
W. DEHNHARDT,
Ce ISOTOPES
S. J. MILLSt, M. MULLER-VEGGIAN, U. NEUMANN, G. POGGItt, B. POVH and P. TARASrt I. Physikalische Institut der Universitiit Heidelberg, Germany and Max-Planck-Institut fir Kernphysik, Heidelberg, Germany Received 22 February
D. PELTE,
1974
Abstract: The
isotopes 130*132*134*136Ce are investigated by means of the reactions 118~120~122~124Sn(160,4n) at bombarding energies between 68 and 76 MeV. From lifetime measurements a reduction of the collective behaviour is observed with increasing neutron number. Yrast cascades of rotational structure are identified up to angular momenta J= 16+ or I= lg+ in 13’3~13%134Ce. Th ese cascades show a strong “back-bending” effect. In 13%e no such simple yrast cascade could be found. NUCLEAR REACTIONS 11**120*1~. 124Sn(160, 4ny), E = 68-76 MeV; measured Er, I,(@, 1/1/coin. 130*132.134*136Ce d e d uced levels, J, T+. Enriched targets.
E
1. Introduction
The low lying energy levels of many even-A nuclei can be grouped into rotational bands. Their excitation energies follow approximately the simple rule E = (h2/20) 1(1-f- 1). At high angular momenta (I NNlOh-- 16h), however, some of these nuclei show a characteristic departure from the rotational behaviour. This phenomenon is commonly labelled the “back-bending” effect. In the region of the “back-bending” one observes a sudden increase of the moment of inertia 8 with increasing angular momentum. Although this behaviour is not too surprising and was even predicted ‘) before it was observed experimentally, the detailed mechanism and why it occurs only in a selective group of nuclei is still not understood completely. A review of the theoretical interpretations is given in a publication by Johnson and Szymanski “). The strongest changes in the moment of inertia have been observed 3, “) in the rare earth nuclei ls8Er and 166Yb and in the nucleus r3’Ce. The latter nucleus appears particularly interesting with respect to the possible theoretical interpretations “). This is related to the fact that the Fermi levels of protons and neutrons are near the h+ shell model state with the protons having a small angular momentum projection t On leave from National Physical Research Laboratory, CSIR, Pretoria, South Africa. tt On leave from University of Florence, Italy. ttt On leave from Universite de Montreal, Canada. 1 June
1974
2
W. DEHNHARDT et at.
$2 and%he neutrons a large St if the nuclear deformation is positive. If the deformation is negative, the role of protons and neutrons is reversed. In this paper we describe the results of an experimental study of the nuclei 130S132r1343136Ce.These nuclei were inyestiga~ed earlier by Ward eit a!. 5), who identified low excited levels wliich were interpreted as members of rotational bands. Part of the results that are described in the present paper were published already elsewhere *). The Ce isotopes are situated near the closed neutron shell n = 82 and one expects a decrease in the collective behaviour with increasing neutron number. This can be deduced from the positions of ,the first excited 2” states which are shifted towards higher excitation energies if neutrons are added. The level schemes of 13oy132*1349‘36Ce are displayed in fig. 1. This figure comprises the information
m91
?
i.
,
-L._ 4091
13’
Ce
Ce
0’
ISOTOPES
Fig. 1. Level schemes in 130, 132*r3**136Ce.
which was known “) prior to our study and also the results of the present investigation. A more direct measure of the collectivity, however, is the E2 strengths of the ytransitions between the low lying states. In sect. 2 we give the necessary information on the experimental procedures and in sect. 3 we describe the measurement of the lifetimes of levels in the four Ce isotopes. A detailed report on the level structures observed in 130,132,134Ce is given in subsect. 4.i. The nucleus 13%e behaves in many respects differently from the other three Ce isotopes. Subsect. 4.2 of this paper is reserved for the report of the properties of levels in 136Ce. A summary of the observed phenomena in the even-A Ce isotopes is given in sect. 5.
2. Experimental procedure The Ce isotopes were populated by the reactions 118~120~122~‘24Sn(160,4n) 130,132T134,136Ce. The 160 beam was accelerated by the MP tandem Van de Graaff generator of the Max-Planck-Institut fur Kernphysik, Heidelberg. The beam energies varied between 68 and 76 MeV. The current of the charge state 7+ was of the order of 15 nA. The targets consisted of isotopically enriched (99 %) Sn material and were 200-500 pg/cm2 thick. For the lifetime measurement the Sn was evaporated onto 1 mg/cm’ gold foils. In the other experiments the target backing consisted of a 150 mg/cm2 thick Pb foil. The deexcitation y-rays were detected with Ge(Li) detectors which had an active volume of 60 cm3. The Ge(Li) detectors could be rotated around the target centre and their front faces had a distance of 7 cm from the target. In all runs except in the lifetime measurements 3 Ge(Li) detectors were used, two of which were positioned at fixed angles 55” and 125” with respect to the beam. The positioning of the detectors was checked with 6oCo and 152Eu sources which were centred in target position. Departures of less than 9 % from the isotropic y-ray angular distributions were found and corrections made. The sources were also used to determine the relative detection efficiencies of the Ge(Li) detectors for the various y-ray energies and to obtain an absolute energy calibration. From the measured nonlinearities and energy resolution (2.5 keV for 1.33 MeV) the error in the energy of y-ray lines is estimated to be 0.15 %. The data consisted of y-singles spectra, y-y coincidence spectra and y-ray angular distributions. In order to determine angular distributions the movable detector was rotated around the target in 15” steps from 0” to 135” while the fixed detectors served as monitor detectors. In the coincidence runs, coincident events were registered between the movable detector and either one of the fixed detectors. The signals from the detectors were processed in conventional ORTEC electronics and stored either in a 4096 channel pulse height analyzer or in an on-line computer. The resulting y-ray spectra were analyzed with a peak fitting program assuming a Gaussian line shape for the photo peaks and a smooth background.
et al.
W. DEHNHARDT
3. Lifetime measurements From the excitation energies and the expected enhancements of the E2 transition strengths in deformed nuclei it is estimated that the lifetimes of the low lying states in the even-A Ce isotopes are of the order of 1 to 500 ps. In this range the proper method of lifetime determination is the recoil distance method. This technique makes use of the Doppler shift of y-rays emitted from a moving source in order to measure the number of recoiling nuclei that decay within a certain distance. This method was used in this laboratory to measure the lifetimes of states in the Ba and Xe isotopes “). We refer to @is paper “) for more details on the experimental method and analysis. Ref. “) also includes a summary of the necessary corrections that have to be taken into account in order to deduce the lifetimes. The y-rays were detected with one Ge(Li) crystal, positioned at 0” with respect to the beam and at a 10 cm distance from the target. A y-ray spectrum obtained from the 12oSn(160, 4n)13’C!e “Osn(‘so,4”l’32Ce 6+--l+
4+-Z+
2+-o+
I
Unshifted
2*-o+ >
300
6+-1*
4*-Z+ 100
8+-6+
500
600
8*-6+ 800
mo
ENERGY
Fig. 2. Gamma-ray
spectra observed at 0” and different plunger settings following 120Sn(160, 4n)13Ve.
i keVl
the reaction
4’-2+
l<
--f-4
------A
----___ --___j_ i
6*-4’
~&-~.-.._.-I. ...__.___.__. ._ __.__._~_ _. ijj i / /
I//,
8 /
: lD0
200 TiME OF FLIGHT
300 AFTER
400
REACmW
Fig. 3. Decay curves of the four lowest excited states in ‘%Ze.
500 msec)
6
W. DEHNHARDT
et d.
reaction is shown in fig. 2. The vertical lines connect the peaks that correspond to the decay in flight and the decay in the stopper at various distances of the stopper. The largest distance in this figure is 3.8 mm. In some runs, however, the distance was as large as 8.5 cm. In this case the detector was positioned at 90” and faced only the stopper. The target itself was not seen by the detector because of a lead shield. In this way states with very long lifetimes z > 30 ns could be identified. The experimentally measured decay of the four lowest levels of the rotational band in 13’Ce is presented in fig. 3. As deduced in ref. “) a decay curve is given as the ratio between the intensity of the “stopped” peak and the intensity of the sum of “stopped” and “flight” peaks. The analysis of the decay of a particular state is complicated by the lifetimes of the higher lying rotational levels which decay to the state and by the population via side feedings. In the analysis of the decay curves the time structure of the population from higher rotational levels was taken into account by the direct measurement of the decay from the next higher rotational level whereas the side feedings were treated as unknown exponential decays with time constants that had to be determined by the decay curve of the state under investigation. The intensities of these different feeding processes were taken from the experimentally determined y-ray intensities. The fits that are obtained by this procedure are plotted in fig. 3. The decay curves of the most energetic transitions in the rotational cascades and therefore presumably the fastest ones contained a component with a decay constant that varied between 6 ps for 13’Ce and 17 ps for 13%e. These decay times are much slower than is expected for intraband transitions and were interpreted by Diamond et al. ‘) as the feeding times. The feeding time is the time the y-decay process needs to reach the upper members of the ground-state band after the evaporation of the last neutron. The side feeding, on the other hand, contained in general two components: one with a lifetime varying from 30 to 350 ps; the second with a long lifetime of greater than 5000 ps. At least part of the last component, however, may also arise from contaminations in the y-ray spectra. The large variations in the decay constants of the side feedings are not understood. It is, however, interesting to note that the side feedings are slower than the direct feeding through the yrast cascade. The lifetimes of the low lying states and the feeding times are listed in table 1. The lifetime of the 2+ state in 13%!e could not be extracted because of the nearby 548 keV line from 197A~. The last column of table 1 shows the enhancements of the E2 transitions in Weisskopf units “). These values are corrected for the electron conversion “). It is evident that the enhancements become smaller with increasing neutron number. Furthermore the ratios B(E2,4+ --+2+)/B(E2,2+ -+ O+) indicate that ’ 3‘, 132Ce behave like permanently deformed nuclei whereas 134Ce falls into a transitional region. A very long lifetime z > 30 ns of a level at 2.990 MeV in 136Ce was observed by the method that was described earlier in this section. This result will be discussed in more detail in subsect. 4.2.
mice
130,132,134*
7
TABLE1 Transition energies, lifetimes and transition Nucleus
130Ce
2++0+ 4+ -+2” 6’+4+ 8+ -+ 6+
253.9 456.6 613.9 729.9
22X3&19 7.8&2.3 2.451.2 < 1.0 6.0+2.0
0.319f0.02 0.52 &to.15 0.39 rto.20
81.6+6 132.9&39 99.6+50
2+ -to+ 4+-+2* 6+ -+4+ 8+ +6+
325.4 532.2 682.4 786.8
67.9&9.5 4.213.7 l.l&O.S < 1.0 11.0+2.0
0.320&0.05 0.446&0.18 0.49410.36
80.1112 111.7+45 123.8190
2++0+ 4+ +2* 6+ -+4+ 8+-+6+
409.1 639.5 814.4 948.0
35.5k8.0 6.552.7 < 1.0
0.197fto.04 0.117~0.08
feeding-time 134Ce
feeding-time 13We feeding-time
in J30, I329134S‘%e
Transition
feeding-time lazCe
probabilities
48.3&-11 X%6&12
14.013.0 2+ -to+ 4+ -+2+
552.1 762.3
9.442.5 17.oIfi5.0
0.034&0.008
8.1 f2
4. Level structures r3%I!e were investigated by means The properties of levels in the nuclei 130~13231343 of their y-decay. The formation of the compound nuclei by bombardment with heavy ions and the subsequent successive evaporation of neutrons leave the final nuclei in excited states that have high spin values and strong alignments. In our case it can be estimated from the statistical model lo) that the residual Ce isotopes are formed on the average with states having a spin of I = 18+ at a bombarding energy of 76 MeV. The average excitation energies before y-emission are 5.0, 9.0, 12.5 and 15.5 MeV for 130CIe 13’Ce ’ 34Ce and ’ 3‘Ce, respectively. The &excitation proceeds then by y-emission’prefer~~tialIy through states that have m~um angular momentum at minimum excitation energy (yrast states), This behaviour of the deexcitation mechanism produces y-ray spectra which consist of isolated lines situated on a broad y-ray background. The order in which the y-transitions follow each other was established by the following criteria: (i) Each of the y-rays proposed to be a member of a cascade is in coincidence with all the other members. (ii) The relative intensities of the y-transitions in the singles spectra show a gradual decrease with increasing excitation energy. This feature is consistent with the statistical picture ’ “) of the deexcitation process.
8
W. DEHNHARDT
et al.
(iii) In the coincidence spectra the relative intensities of all transitions following a gate transition are equal within statistics- while those transitions preceding a gate transition have the same intensities as in the singles spectra. A coincidence y-ray spectrum observed in the 122Sn(‘60, 4n) 134Ce reaction is shown in fig. 4. During the analysis it was found that some of the peaks are actually doublets or belong to the (160, 5n) reaction. This complicated the analysis. The ambiguities, however, could be removed by proper gate settings. (iv) The relative excitations of levels measured at increasing bombarding energies become gradually stronger for higher excitation energies. This is again to be expected from the statistical nature lo) of the population mechanism. The results of this measurement are displayed for all four Ce isotopes in fig. 5. Within the error limits the change of the relative intensities with increasing bombarding energy can be reproduced by straight lines. The lines are labelled in fig. 5 either by the corresponding y-ray energies or by the spin sequence if this could be established (see later). The level schemes that are extracted in this way are presented in fig. 1. The isosopes ’ 3‘a132,134Ce behave very similarly whereas 13%e displays different properties. The discussion of this nucleus is therefore postponed to subsect. 4.2. 600/
t
h-
/ + 409.1 639.5
948.0
908.5
+ 724.6
o+
I
500
i
ENERGY
Fig. 4. Gamma-gamma 4.1. THE NUCLEI
+
1000
I keV 1
coincidence spectrum following the reaction 122Sn(160, 4n)134Ce.
130*132.134Ce
The dominant y-ray lines measured in 13’S1323134Ce belong to only one cascade in each of these nuclei. The intensities of the y-transitions normalized to the last transi-
9 13’Ce
ie 70
i3
is
‘3”Ce
'34Ce
I
i
68 70 72 7L 76
BOMBARDING Fig. 5. Excitation fictions
ENERGY ( MeVV) OFlevels in 130*m* 134*f 36Ce.
tion are listed in table ,2 together with their energies. The angular distributions of the y-rays show a positive anisotropy. The coefficients of the expansion in terms of even Legendre polynomials to fourth order are listed in table 2. The values of these coe~cjents correspond to a stretched E2 cascade starting at a nearly aligned state with an angular momen~m of f = 18’. The theoretical predictions ‘I) for this cascade are uz/ao= 0.384 and ah/a0= - 0.137assuming complete initial alignment. These values include a correction I2 ) due to the finite size of the detector. The spins of the states in the cascades deduced from this analysis are shown in fig. 1. It seems that the states in the cascades can be interpreted as members of rotational bands.
W. DEHNHARDT
10
et al.
TABLE 2 Transition
energies,
relative intensities
Transition
and angular
E#eV)
distribution
Relative intensity
coefficients
in I308 132*134Ce
Angular distribution coefficients
“WA0
-AlAo
130Ce
2+0 4+2 6+4 8-+6 IO-+8 12 3 10 14412 16 -+ 14
253.9 456.6 613.9 729.9 756.8 503.4 549.7 693.7
100 loo&5 99&4 58f4 35&S 17&S 13&3 854
0.4010.01 0.32+0.01 0.25&0.02 0.30&0.03 0.38 stO.02 0.37&-0.04 0.37&0.10 0.3250.04
0.18~0.02 0.14&0.01 0.1440.03 0.11&0.04 0.19&0.03 0.06&0.05 0.10*0.14 0.20 AO.06
132Ce
2+0 4+2 6-+4 8+6 lo-t8 12 + 10
325.4 532.2 682.4 786.8 827.7 569.7
100 9014 67+3 47+3 30&3 23&4
0.32f0.02 0.33&0.02 0,35&0.03 0.38kO.03 0.43 10.04 0.3510.04
0.07&0,03 0.03 kO.03 0.04&0.03 0.03 jzo.04 0.07&0.05 0.01 hO.05
14+12 16 -z- 14 18 +- 16
512.2 698.6 823.4
2015 16&3 11+3
“) 0.39&0.04 0.29kO.08
“) 0.03&0.05 0.12+0.10
409.1 639.5 814.4 948.0 908.5 464.3 724.6 817.9 397.0
100 90$5 54,t6 4815 26&4 22f4 19”4 8f2 2146
0.3orto.03 0.31 kO.03 0.33+0.01 0.30*0.03 0.34kO.06 0.3390.05 0.2910.05 0.49f0.05 -0.10~0.03
O.lOf0.04 0.07,1;0.03 0.09f0.02 0.09&0.04 0.09&0.08 0.16&0.07 0.04&0.06 0.07$20.06 0.03&0.04
134Ce
2+0 4-+2 6+4 8+6 10 + 12 3 14 --f 16 --t I+8
“) Contaminated
s IO 12 14
by the 511 keV annihilation line.
Fig. 6 displays the positions of the excitation energies versus 1(1-l- 1). One observes a sudden change in the slopes near angular momentum I = 10’. This will be further discussed in sect. 5. The relative population ofthe cascade states decreases with increasing excitation energy. Abrupt changes in the population are observed for some levels particularly for the 1= S4 levels in 132y134Ce and the I = 6” level in 13’%e. It is plausible to try and find other transitions than those already ident~ed that feed these levels. In the case of the nucleus I3 “Ce a second y-transition populating the I = 8 + state could be ideutified that seems to account completely for the extra intensity of the 8+ -+ 6’ transition. It has an energy of 0.397 MeV. The angular distribution of the corresponding y-ray has small negative anisotropy (table 2). From the measured coeflicients of the Legendre expansion it may be concluded that the 0.397 MeV transition i.s not of an E2 nature but probably of an El or Ml nature. This could indicate the existence
I30,132,134,
IS”&
Fig. 6. Plot of the level excitation energy as a function Off@+ f >.
of a second I = 8 state near the excitation energy where a sudden change in the moment of inertia is observed, The attempt to follow this new cascade to higher excitation energies was not successful. A few single transitions were also found that seem to feed the I= 4+ and f = 6* states. Their intensities, however, were too small for a further analysis. 4.2. THE NUCLEUS 13%e
As pointed out already, the nucleus ’ 3‘Ce shows a behaviour that differs from the other Ce isotopes. The differences are twofold: (i) at least four cascades were populated in the 124Sn(160, 4~)‘~~ Ce reaction; (ii) The angular ~str~butio~s of the y-rays belonging to a cascade are not of a stretched E2 type. The energy levels in I3 %e that are deduced from the identified y-cascades are displayed in fig. 1. The level sequence 2.215, 1.314, 0.552, 0 MeV was found already by Ward et al. “) and was interpreted as the ground state rotational band. However, as previously stated in sect. 3, the lifetime of the 2.990 MeV state that feeds this sequence is found to be longer than 30 ns. This is an uncommonly long lifetime if one assumes that the five Ievels are members of a rotational band. The transition strength is smaller than 10m3 W.U. as compared to the enhancements of more than 80 W.U. that are observed for the rotational bands in the other Ce isotopes (table 1). Correspondingly the anisotropies of the y-ray angular distributions are very small (table 3)
W. DEHNHARDT
et al.
130.132.134,
i36Ce
13
due to the deorientation effect in the 2.990 MeV state. Another cascade could be identified that depopulates the 2.990 MeV state. This cascade, too, consists of ytransitions which have small and positive anisotropies‘in their angular distributions (table 3). Because of its long lifetime, transitions feeding the 2.990 MeV state were not observed. In view of these results we believe that a definite spin assignment for the states of these two cascades cannot be given. A third sequence of states that are connected by subsequent y-transitions could be identified up to an excitation energy of 5.557 MeV. This sequence consists of nine states of which the last three are the same as those of the two former cascades. The expansion coefficients of the y-ray angular distributions are listed in table 3. One observes both positive and negative anisotropies. The negative anisotropies can be explained only by an El or Ml nature of the corresponding y-transition if the initial state is aligned. However, it is not possible to reproduce all the measured anisotropies by assuming an initially aligned state and a cascade with Ii = Ii_1 +A where /z can be 1 or 2. The assumption of a Gaussian sub-state population of the initial state fails likewise. It is found that the experimentally measured negative anisotropies remain too strong when the positive anisotropies are reproduced. If this cascade in 13%e corresponds to the yrast cascades that were observed in I309132,134Ce it must be concluded that it is of a very different nature. In 13’Ce a fourth sequence of states was found which are connected by y-rays but which have no y-ray in common with the other three cascades. It is, therefore, impossible to deduce the absolute excitation energies and this level sequence is not shown in fig. 1. Table 3, however, contains the y-transition energies and the expansion coefficients of the corresponding angular distributions. The anisotropies are found to be positive or negative. No attempt was made to deduce spin assignment. 5. Summary and conclusions At low excitation energies the isotopes 130Y132,134,136Ceare characterized by a decrease in the collective behaviour with increasing neutron number. This can be deduced from the level structures and from the enhancements of the E2 transitions between the low lying states. In view of a simple model one may interpret 130S132Ce as being permanently deformed at small excitations. These two nuclei and 134Ce are found to have level sequences with angular momenta that are characteristic of the ground state rotational bands. From the corresponding excitation energies, however, it can be concluded that a strong variation of the moments of inertia occurs in these bands. In fig. 7 the moments of inertia 0 are plotted against the rotational frequencies o. This plot demonstrates the “back-bending” effect in the ground state bands of the three Ce isotopes. At small excitation energies the addition of neutrons causes a reduction in the moments of inertia. In the region of the “back-bending” the interpolated values of 8 are very similar in each of the isotopes and nearly reach the rigid rotor value. At still higher angular momenta fig. 7 indicates that the moments of
14
W. DEHNHARDT
I
,
1
0.1
02
et al.
I
93 VlU12
I MeV21
Fig. 7. Plot of the nuclear moments of inertia 0 as a function of the angular frequency CU.The rigid rotor values are calculated for o = 0.
inertia become smaller with increasing rotational frequencies. This “down-bending” has been observed “) otherwise only in “‘Er and 16’Yb. Nevertheless, the moments of inertia are, at high angular momenta, within 30 ‘A of their rigid rotor values. This result is also found in other nuclei where yrast cascades could be established and is independent of the presence of the “back-bending” effect. One may conclude, therefore, that the yrast states at high excitation energy are of a similar nature in different nuclei although these nuclei can behave quite differently at low excitations. In this respect the identification of rotational like yrast states at high excitation energies in nuclei that are not collective at low excitations would be rather interesting. Unfortunately our attempt to locate such yrast states in i3’%e was not successful. The reason for this failure is not obvious but might be related to the neutron closure of the h, sub-shell. The significance of the h, sub-shell in producing the observed phenomena would probably be better understood if the properties of 124,1261“sCe were known. These nuclei should be producible with the (160, 4n) reactions at slightly higher bombarding energies. The only information on the structure of the Ce isotopes at excitation energies where single y-transitions are no longer resolved comes from the feeding times. The results of this experiment show that the feeding times become longer when the Ce isotopes approach the closed neutron shell n = 82. This tendency was also observed in other nuclei by Diamond et al. and Newton et al. ‘). Two other points are important in discussing the significance of the feeding times. Firstly the initial excitation energies in the Ce isotopes vary, as has already been pointed out in sect. 4. The experimental evidence for this fact comes from the sizeable yield of the 124Sn(160, 5n) 135Ce reaction at 76 MeV bombarding energy and from the relatively weak population of the I = 16+ state in 13’Ce. Secondly the strong “back-bending” effects in the Ce isotopes result in traps for the y-decay through the yrast cascade. For example
the 12+ + IO+ transition in 134Ce is estimated to be 12 ps assuming the same enhancement factor as for the 2+ + O+ transition. It is evident that the values quoted in table 1 are only upper limits of the feeding times with large uncertainties. For these reasons it seems unjustified to deduce information about the structure of the high excitation regions from the feeding times. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
B. R. Mottelson and J. G. Valatin, Phys. Rev. Lett. 5 (1960) 511 A. Johnson and Z. Szymanski, Phys. Rep. 7C (1973) 181 H. Beuscher, W. F. Davidson, R. M. Lieder and C. Mayer-Biiricke, Phys. Left, 40B (1972) 449 P. Taras, W. Dehnhardt, S. J. Mills, M. Veggian, J. C. Merdinger, U. Neumann and B. Povh, Phys. Lett. 41B (1972) 295 D. Ward, R. M. Diamond and F. S. Stephens, Nucl. Phys. All7 (1968) 309 W. Kutschera, W. Dehnhardt, 0. C. Kistner, P. Kump. B. Povh and E-I.J. Sann, Phys. Rev. C5 (1972) 1958 R. M. Diamond, F. S. Stephens, W. H. Kelly and E. Ward, Phys. Rev. Lett. 22 (1969) 546; J. 0. Newton, F. S. Stephens and R. M. Diamond, Nucl. Phys. A210 (1973) 19 C. M. Lederer, J. M. Hollander and I. Perlman, Tables of Isotopes (Wiley, New York, 1967) A. Bohr and B. R. Mottelson, Nuclear structure, vol. I (Benjamin, New York, 1969) p. 389 S. JBgare, Nucl. Phys. A95 (1967) 481 W. G. Winn and D. G. Sarantites, Nucl. Instr. 66 (1968) 61 D. D. Watson and I. Harris, Nucl. Data A3 (1967) 25