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Rotational bands and fast el transitions in 163Ho
Nuclear Physics Al90
(1912) 576-596;
@
North-Holland
Publishing
Not to be reproduced by photoprint ar microfilm without written permission
ROTATIONAL L. FUNKE,
Co., Amsterdam from the publisher
BANDS AND FAST El TRANSITIONS IN ‘63H~
K. H. KAUN,
Zentralinstitutfiir
P. KEMNITZ, Kernforschung, Received
H. SODAN
and
RossendorfiDresden,
11 April
G. WINTER DDR
1972
Abstract: The level scheme of the deformed odd-proton nucleus le3Ho has been investigated by inbeam and decay spectroscopic methods. Single y-ray spectra, conversion electron spectra, y-y coincidences and angular distributions of the y-rays were measured in the reaction rL3Dy(d 2ny) at a deuteron energy of about 13.5 MeV. Single y-ray spectra were also taken in the 16’Dy(p, ny) reaction with 6.7 MeV protons. Additional information on the 163H~ level scheme was obtained by re-investigating the y-radiation in the electron capture decay of 163Er. The proposed level scheme of re3Ho contains in addition to the ground state band $- [523] the rotational bands built on the intrinsic states 3’ [404], 3’ [411], )+ [41 l] and &- [541] (band heads at 439.94, 360.36, 297.88 and 471.25 keV, respectively). Further levels at 1113.5, 876.0 and 614.3 keV are interpreted as being mainly the quasiparticle excitations &- [532], 8’ [413] and possibly the ground state y-vibration, respectively. A comparison of the quasiparticle excitations in the Ho isotopes is performed on the basis of the Nilsson model including pairing corrections. Discontinuities in the rotational bands are described by Coriolis coupling effects. Several fast El interband transitions were observed in le3Ho. Some of them connect levels of the 4’ [411] band with the ground state band t-15231. The appearance of these K-forbidden transitions is explained by a weak mixing between states of the bands 4’ [411] and 4’ [404] caused by Coriolis interaction. NUCLEAR E
REACTIONS 163Dy(d, 2ny), Ed = 13.5 MeV; measured Er, Zr, I,,, EY, Zr. 163H~ deduced oCEr. or). 7-y coin., rb3Dy(p, ny), Ep = 6.7 MeV; measured levels, .I, n, cc, B(E1). Enriched target; Ge(Li) detectors. RADIOACTlVITY ‘63Er [from 164Er(Y, n)]; measured Eu, I?, y-y coin., 163H~ deduced levels, J, n. Enriched target: Ge(Li) detectors.
1. Introduction In the framework of a systematic study of the deformed odd-proton nuclei in the rare-earth region the nuclei 1ss*157Tb [ref. ‘)I, 161,163H~ [refs. “-“)I, r6’Tm [refs. 5, “)I, 171*173Lu [refs. ‘,“)I, and i “3 179Ta [ref. ‘)I were investigated by means of in-beam spectroscopic methods and in some cases also by decay measurements. In this paper our results on the 163H~ level scheme are given. Since 1957 an isomeric level lo) in 163H~ near 300 keV is known, which has been interpreted as the $‘[411] Nilsson state. In 1966 the levels of l‘j3Ho were studied [refs. 11,12)] in our laboratory in the electron capture (EC) decay of 163Er. AS a result of this investigation the quasiparticle excitations 3’ [4O4], 3’ [413] and -2- [532] were found at energies of 440, 876 and 1110 keV, respectively. The multipolarities of the two strongest transitions at 436 and 440 keV were determined by Babadjanov et al. 13) to be Ml (or E2) and El, respectively. 576
l’=Ho
ROTATIONAL
577
BANDS
In order to search for further quasiparticle states such as the orbitals sf [41 l] and ?-^ [541] expected ‘) at low energies and to study the rotational structure we investigated the y-radiation and conversion electrons in the reactions 163Dy(d, 2n) and 163Dy(p, n) as well as the y-radiation in the decay of 163Er. Very recently 14) we learned of an investigation of the 163Ho levels in the reaction 164Dy(p, 2n), but no detailed information was available. Preliminary results of our in-beam studies were presented previously 4S30). 2. Experimental procedures and results 2.1. IN-BEAM
EXPERIMENTS
The in-beam experiments were performed at the Rossendorf cyclotron U-120 with deuterons of 13.5 MeV and protons of 6.7 MeV. For the investigation of the y-radiation a 30 mgjcm2 thick dysprosium oxide target enriched to 93 % 163Dy has been used. Conversion electron measurements were carried out with an enriched 163Dy metallic target of 2 mg/cm2 thickness. Further details of the experimental arrangements are described in earlier publications 5S‘,I ‘).
I
b?
O~-.-~ LOO
600
800 CHANNEL
looolzco-----7ls---~~o
IL00
NUMBER
Fig. 1. In-beam y-ray spectrum recorded with a 0.4 cm3 Ge(Li) spectrometer during the bombardment of 163Dy with 13.5 MeV deuterons. The spectrum {a) has been taken without absorber, the spectra (b) and (c) with absorbers of 0.15 mm Cd+0.5 mm Cu. Most of the lines assigned to the reaction le3Dy(d, 2n)‘63Ho are marked by their energy value. Crosses indicate background lines.
578
L. FUNKE
et al.
TABLE 1 Gamma-rays
Ey (kev)
assigned
Ir Cdl3)
to re3Ho from the reactions
1, (P) Ir (d)
1 52.74 57.80 “) 59.25 62.48 80.16 84.45 87.71 97.03 100.04 112.4 122.14 123.52 131.44 135.72 136.17 142.62 144.41 154.40 158.27 159.38 “) 160.24 “) 163.61 165.14 168.0 173.38 175.7 181.59 183.5 187.76 192.74 195.53 197.51 204.87 220.85 222.27 223.54 229.57 232.86 239.6 254. I 263.0 “) 266.62 267.20 280.35 282.48 294.37 297.88
2
3
2ny) and lh3Dy(p,
1.oo 0.95 0.79 0.62 0.63 0.36 0.24 0.63 0.30 0.47 0.50 1.40 0.14 < 0.15 0.22 0.44 < 0.2 0.85 0.07 1.15 0.44 0.04 1.26 0.58 ” 0.1 < 0.05 0.28 0.27 0.49 < 0.1 0.40 1.oo 0.04 0.17 0.38 1.30 < 0.06 0.10
ny)
Assignment Ii, Kin + If, K,=
I tot
4
5
6
cz 10
z3 1.8 1.7 2.4 3.7 3.4 3.1 3.2 62.0 I 0.2 57.5 6.0 2.1 3.0 2.4 1.0 41.4 1.1 7.9 1.6 1.7 3.3 25.3 x2 1.9 0.7 14.7 S 0.5 12.6 8.0 2.4 4.0 6.4 20.3 8.5 6.2 2.8 2.5 0.6 1.0 11.0 13.0 3.8 3.1 7.4 8.9 1OOb)
Deduced spin value
‘e3Dy(d,
(20) 26 22 18 15.5 12.5 236 150 13.5 4.8 6.61 5.3) 1.7 84 1.2 8.7 2.91
0.03(l) 0.25(10) -0.06(7) 0.09(4) 0.17(6) 0.05(l) -0.25(15) -0.15(4)
I 3.6 43.5 ” 3 2.1 1.1 15.6 5 0.8 19.0 8.5 5.0 9.0 23.8 10.0 7.2 3.6 3.2 0.7
0.06(5)
0.02(4) 0.14(3) 0.14(6) 0.28(7) 0.04(9) _-0.24(17)
-0.05(2) 14.21 4.2) 3.2 8.0 9.5 131
0.09(14) 0.18(7) 0.08(3) 0.00 b)
7
‘=Ho
ROTATlONAL TABLE
E,(keV)
I,(dl3)
1, (P) $, Cd)
552.07 558.7 “) 568.5 “) 585.7 “) 588.0 590.4 611.6”) 614.6 622.5 652.5 “) 658.9 688.3 “)
80
. (
0.54 x 0.8 .: 0.1
7.6 3.0 2.0 4.0 3.2 3.0 5.7 4.0 4.7 3.7
Deduced spin value
1
4 i Gw
I 0.62 < 0.2 1.75 1.18 0.72 0.55
Xl
I ,Ot
Assignment
A2 Ii, 6
5 16.0 7.7 5.9 1.8
4” + h, KC’ 7
0.17(2) 0.13(5) 0.11(5) -0.06(5)
7.0 2.0 9.2 2.1 2.4
0.22(6)
high
< 0.1
4.0 4.0
5.8 2.5
0.27(5)
7 hYgh IOW low (8) (V)
O.lO(2) 0.18(15)
46.3 3.0 1.6 10.9 5.0 2.2 1.2 xl
0.08(4) O.ll(6) 0.24(24)
low 4.0 4.0
0.54
(‘$1
1.6 0.80
low low high
0.67 1.10
(3) low
4.0
1.25
low
5.7 4.0
1
-0.04(5) 0.03(5) 0.19(15) -0.30(15) O.OO(12) -0.06(10) O.Ol(5) -0.14(7)
3.7
=5
Column 1: The errors decimals certain.
0.07 0.10 0.19
15.0 7.3 5.6 1.6 6.9 2.0 8.9 2.1 2.4 2.9 5.6 2.4 2.2 46.0 2.9 1.6 10.8 5.0 2.2 1.2 Xl Z8
309.58 312.73 314.96 326.8 331.12 339.95 352.90 359.2 364.9 384.4 392.65 399.0 417.2 “) 431.16 434.45 436.1 439.94 452.00 465.9 469.0 478.0 514.5 “)
579
1 (continued)
4
3
2
1
BANDS
and smaller
than
of the energies are smaller than 0.1 keV 0.3 keV for the others. “) The assignment
for energies given with two to the nucleus 163H~ is not
Column 2: Gamma-ray intensities measured with deuterons of 13.5 MeV energy at an angle of 125” to the beam axis. The errors of intensity values are of the order of 5 to 30 y0 depending on the line strength. b, Normalization value. Column 3: Intensity ratio of the y-rays emitted in the reaction with 6.7 MeV protons and 13.5 MeV deuterons. “) Normalization. Column 4: Probable spin value deduced from the intensity ratio of column 3 (further comments see text). “) Normalization. Column 5: Total intensity values calculated with the y-ray intensities of column 2 and theoretical conversion coefficients. Column 6: Angular distribution coefficients according to the formula W(B) = l+AtPz(cos 0). The errors of the AZ coefficients are given in parentheses in units of the last decimal.
580
L. FUNKE
et al.
Single y-ray spectra were measured using germanium detectors of different volumes during the bombardment of the 163Dy target with 13.5 MeV deuterons or 6.1 MeV protons. As an example the spectrum with the highest resolution (0.5 keV for the 100.04 keV line) taken with a 0.4 cm3 Ge(Li) spectrometer in the deuteron reaction is plotted in fig. 1. The spectra taken with larger detectors have much better statistics especially at energies above 200 keV. Those lines ascribed to the reaction 163Dy(d, 2n) 163H~ are indicated by their energy values. Additional transitions assigned to either 162,163,164~~, 162,164H~ or 19F were marked by crosses. Most of these background transitions are caused by the reactions (d, d’) and (d, p) on 163Dy as well as by the (d, 2n) reaction on the neighbouring dysprosium isotopes. For the identification of these transitions targets enriched to more than 90 % 16’Dy or “j4Dy were also bombarded with deuterons or protons. In this way most of the observed y-ray transitions could be attributed to a certain nucleus. Several background transitions belong to the low-energy levels in the target nucleus ’ 63Dy excited by inelastic scattering of deuterons. The energies of these transitions have been measured very accurately by Schult et al. ’ “) in the (n, 7) reaction. Therefore these energies could be used as calibration standards. In table 1 a summary of the experimental data concerning the transitions assigned to 163H~ from the study of the reactions 163Dy(d, 2n) and ‘63Dy(p, n) is given. As the angular momentum transfer in the (d, 2n) reaction is higher than in the (p, n) reaction, high-spin states are excited much weaker in the (p, n) than in the (d, 2n) reaction. Thus from the y-ray intensity ratio of a transition in the (p, n) and (d, 2n) reaction given in column 3 of table 1 valuable conclusions to the spin of the state from which this transition arises can be drawn. However, this ratio depends also on the excitation mode of the initial state, quite similar to the cases discussed in refs. ‘, ‘). Nevertheless, the most probable spin values deduced from the intensity ratios Z,(p)/Z,(d) are g’iven in column 4 of table 1. These values (except for transitions de-exciting members of the $‘[404] band) were obtained using the spin dependence of the intensity ratios of the transitions within the well-established ground state band as normalization. Angular distribution measurements of the y-radiation have been performed to get additional information on the level scheme. For this purpose single y-ray spectra in the reaction with deuterons at angles of 18, 30, 45, 60, 75 and 90” to the beam axis were measured. As normalization, the intensity of the isomeric 297.9 keV transition has been used. Although in the (d, 2n) reaction the anisotropy is only a half of that in the (~1,2n) reaction [for comparison see table 1 of ref. “)I this information is valuable to check the proposed level scheme. The experimental A, values given in column 6 of table 1 support in a consistent way r6) the proposed level scheme. For the establishment of the level scheme extensive y-y coincidence experiments were performed in the reaction with deuterons. Two characteristic coincidence spectra are shown in fig. 2. The spectrum in coincidence with 100.0 keV offers mainly the transitions of the bands $- [523] and 3’ [404]. The second spectrum is typical for the
lc3Ho
-
“0 ; -
2 %
ROTATIONAL
BANDS
581
2’ 1~
Or
300 ENERGY
(k&j
Fig. 2. Two selected y-y coincidence spectra, taken with two germanium detectors of 14 and 27 cm3 volume. Transitions supposed to be in coincidence have their energy values given in keV. TABLE
Gamma-gamma
coincidences
observed
2
in the reaction
‘63Dy(d,
2n)163Ho
ET,l WV)
I+,, (keV) “)
100.0
122.1, 144.4, (158.3), 165.1, 187.8, 204.9, (220.8), 229.6, (239.6), 266.6, 309.6, (312.7), 331.1, 352.9, 392.6, (434.5), 452.0, 465.9, (478), (514), 552.1, 588.0, 590.4 100.0, 144.4, 165.1, 187.8, 204.9, 229.6, (239.6), 309.6, 352.9, 392.6, 434.5, 465.9,
122.1 123.5 132 136 144.4 158.3 181.6 192.7 197.5 220.8 223.5 282.5 431.2
“) Coincidences
(478), (622) (97.0), 158.3, 181.6, 197.5, 220.8, 282.5, 294.4, (223.5) (80.2), (84.5), 87.7, (97.0), (131), (136) 100.0, 122.1, 165.1, 187.8, 204.9, 222.2, 229.6, 154.4, 220.8, 282.5, 331.1, 354, 366, 431.2, 552 (123.5), 154.4, (181), 197.5, 282.5, 431.2 (112.4) 181.6, 282.5 123.5, 154.4, 158.3, 312.7, 326.8, 331.1, (399), (80), (131) 158.3, (181.6), 197.5, 220.8 97.0, (131), (136), 154.4, 158.3, 181.6, 197.5, 312.7, 315.0, 326.8, (359), (365), (384), 399.0, given
in parentheses
are weak
312.7
239.6,
352.9,
392.6, 434.5
431.2
220.8, (403)
or not very certain.
232.9,
(267),
282.5,
294.4,
582
et al.
L. FUNKE
de-excitation of the other bands. All coincidences The coincidence spectra were also quantitatively In order to get information on the multipolarity the conversion
electron
spectrum
observed are summarized in table 2. evaluated. of the intense 431.2 keV transition
has been measured ’
29i.9
,K392.6_?
in the deuteron
200
250
CHANNEL Fig. 3. Part of the in-beam special arrangement
using
’
1
I
150
reaction
50
300
31
NUMBER
conversion electron spectrum recorded with a silicon detector during the bombardment of r6aDy with 13.5 MeV deuterons.
in a
TABLE 3 Conversion
coefficients
(2,)
‘Y (rel.)
k (rel.)
266.6 291.9 309.6 312.7 315.0 392.6 431.2 439.9
13.0 100 “) 15.0 1.3 I 5.6 5.6 46.0 10.8
1.3 15.8 “)
and multipolarities
IL
c&c
‘*I.
(rel.)
(exp.) ‘)
(exp.)
10.8 “)
0.85 0.2 0.33 0.07
“) Normalization value. b, Errors are given in parentheses
of some transitions
0.10 (4) 0.158 “)
0.108 “)
0.030(15)
x 0.1
in units
0.035(15) 0.007(3) 0.007(4)
(0.002)
in 163H~ Multipolarity
(the%y )
0.07 0.155
(E2) (E3)
E2 E3
0.044
(E2)
W)
0.023 (E2) O.O063(El) 0.006 (El)
E2 El El
of the last decimal.
a Si(Li) detector of 50 mm2 x 2 mm in a special arrangement. A homogeneous magnetic field is applied to select the electrons from heavier charged particles and to reduce the y-ray background. At a distance of 20 cm between target and detector the transmission of the device was some percent for electrons of 200-400 keV. The complete electron spectrometer is described elsewhere “). A portion of the conversion electron spectrum is shown in fig. 3. Although the resolution is limited by the thick-
l’=Ho
ROTATIONAL
BANDS
583
ness of the target some essential information on transitions near 400 keV was obtained. The conversion electron intensities (related to the y-ray intensities by means of the well-known 297.9 keV E3 transition) and multipolarities of some transitions are given in table 3. The 431.2 keV transition was determined to have the multipolarity El. 2.2.
DECAY
EXPERIMENTS
The l’j3Er activity was produced by the (y, n) reaction on an erbium oxide target enriched to 65 % 164Er. A 100 mg target has been irradiated several times for 1 h at
VI i/
CHANNEL
5
NUMBER
z 5 I
CHANNEL NUMBER
Fig. 4. Gamma-ray spectra from the decay 163Er(EC)163Ho. (a) Single y-ray spectrum taken with a 18 cm’ germanium detector (absorber: 0.3 mm Cd). The lines assigned to the le3Er decay are marked by their energy values. (b) Selected parts of the y-y coincidence spectra taken with two germanium detectors of 18 and 22 cm3 volume.
the bremsstrahlung beam of the 30 MeV betatron of the Jena University. The irradiation technique is described elsewhere I’). Single y-ray spectra and y-y coincidence spectra were taken by means of germanium detectors of 18 and 22 cm3 volume. In order to find out the transitions decaying with the 163Er half-life three to four successive spectra were recorded. In every case an absorber between source and detector had to be used to reduce the very intense X-ray radiation caused by the strong allowed unhindered electron capture transition to the ’ 63Ho ground state. In fig. 4 the y-ray spectrum and a portion of the y-y coincidence measurements are shown. In addition to the transitions attributed to the 163Er decay the strongest transitions of the decay of * 61Er [ref. “)I and 167H~ [ref. ’ “)I as well as a few unidentified transitions having shorter or longer half-life were observed. The data concerning the transitions assigned to the 163Er decay are listed in table 4.
584
L FUNKE
et al.
TABLE 4 Gamma rays from the decay 163Er(EC)163Ho
Ey WV) 9
(80.5) 100.0 123.6 164.6 192.6 253.9 297.8 331.0 339.8 417.1 431.2 436.1 439.9 444.8 452.3 484.0 552.0 558.5 568.4 578.1 614.3 711.3 875.8 1013.6 1113.5 “) b, ‘) d,
(1) (2) (2) (2) (2) (1) (3) (2) (2) (2) (1) (1) (2) (2) (3) (3) (2) (2) (2) (1) (2) (2) (3) (3)
b, “)
b)
“) b, “)
I tot (per IO4 decays) a4 14.7 1.8 4.0 4.4 3.3 1008) 1.8 29 7.6 12.5 248 240 7.9 6.0 2.4 2.8 5.1 7.5 11.6
w 0.2 0.67 0.05
(8) (5) (5) (4) (5)
(1) (7) (9) (5) (5) (9) (6) (5) (7) (9) (8) (9)
29 (1) 10.7 (9)
b)
339.8,436.1
0.06 0.04 1.63 0.02 0.37 0.10 0.16 3.10 3.00 0.10 0.07 0.03 0.03 0.06 0.09 0.14 0.36 0.13 0.75 0.09 5.30 =gc)
(5)
60 (3) 7.5 (9) 426 (12)
Coincidence with
444.8 339.8,439.9 436.1 431.2
Normalization value. Not shown in the decay scheme. Taken from ref. II). Errors are given in brackets in units of the last decimal.
The very weak population of the excited states of 163H~ compared to that of the ground state is the reason why the coincidence experiments are of poor statistics. For instance the coincidence peaks 431.2-444.8 keV include only 5 to 10 events (see fig. 4b) but the coincidence relation is unambiguously certain because the background is very weak. 3. Construction of the level scheme 3.1. LEVELS
EXCITED
IN THE
REACTIONS
(d, 2n) AND
The level scheme of 163H~ obtained from fig. 5. The ground state band could very easily coincidence spectrum with 100.0 keV of fig. 2). but no clear coincidences have been observed state.
(p, n)
our in-beam experiments is shown in be followed up to spin y (see e.g. the They level was tentatively introduced because of the weak excitation of this
-Ho
ROTATIONAL
BANDS
585
586
L. FUNKE
et al.
From our former decay investigations ‘i) the position of the 5’ [404] single-particle level near 440 keV was known. The angular distribution of the 439.9 keV transition as well as its intensity ratio in the proton and deuteron induced reactions are similar to that of the 252.7 keV transition ‘) in i6iHo. Its assignment to the s’ state seems, therefore, to be certain. In addition the coincidence, excitation and angular distribution data and the comparison with the ’ 61Ho level scheme “) allow us to construct the band built on the $‘[404] state. The levels of this band de-populate by fast El interband transitions to the $- [523] ground state band. No intraband transitions were found, but in some cases the upper limit of their intensity values were estimated (see table 6). Additional to the strong transitions within the ground state band and weaker ones de-exciting the t’ [404] band several intense transitions were assigned to ’ 63Ho which could not readily be attributed to a certain band. The 297.0 keV transition de-excites the known lo) isomeric state _t’ [41 I]. A strong 431.16 keV transition with multipolarity El and the coincidence 100.0-331.1 keV suggests a 5’ level at 431.16 keV, but no band with K = 5 can be found on it. Otherwise several coincidences with the transitions at 33 1.1 and 43 1.2 keV were found as shown in fig. 2 and table 2. The 43 1.16 keV state can plausibly be explained as being the 3 member of the 4’ [411] band. An explanation of the intense K-forbidden transitions (AK = 3) from the 3 and 9 members of the f’ [41 l] band to the levels of the ground state band is given by a Coriolis coupling treatment in subsect. 4.3. The coincidence behaviour of the 123.52 keV transition is very similar to that of the 431.16 keV line. Therefore, this transition should also de-populate the 431.16 keV level. This assignment leads to a level at 307.64 keV being apparently the 3 member of the +‘[41 I] band. Support for a separation of only 9.8 keV between the 3 and 3 members is also obtained by transitions feeding these states from the lowest members of the bands +‘[411] and $- [541]. Using the coincidence data (table 2) and the information given in table 1 the states I+ 3 = even of the 4’ [411] band up to spin 9 and the states of the 4’ [41 l] band up to -‘+$ (tentatively -$?) were established quite similar “) to those in ’ 61Ho. The 552.07 keV transition de-populating the y member of the 3’ band is fixed by the coincidence with 100.0 keV but its intensity in the coincidence measurement is only a half of that in the single spectrum. This is consistent with the assumption of another transition at the same energy. The second 552.07 keV transition de-excites the 3 member of the 4’ [404] band. The levels I++ = odd of the 3;’ [411] band are supported to a certain extent by the coincidence measurement. Apparently, the 4 member de-excites also to the 3 member of the +’ [41 l] band. Since the intensity of this 3 state branches off to several transitions it is difficult to observe clear coincidences. The 84.45 keV transition were assigned between the 3 and 3 members of the +‘[411] band without contradictions to the experimental facts. The relative small separation of both these members compared to that in other nuclei 2, “) is explained by t h e C oriolis coupling with the members of the close-lying 3’ [41 l] band (see subsect. 4.2).
‘=Ho
ROTATIONAL
The rotational levels with the spin 8, Jg, J$ and y found on the basis of the coincidences data. Assuming of *61Ho [ref. ‘)I and ’ 67Tm [ref. “)I we looked for members of the +- [541] band and found transitions namely proper energy and intensity values, no strong ties in the (p, n) reaction. 3.2. DECAY
SCHEME
55-r
BANDS
of the &- [541] band were also this band to be similar to that the position of the $, 3 and 3 with the expected behaviour, coincidences and large intensi-
163Er(EC)163Ho
The decay scheme of 163Er to the ’ 63Ho levels is shown in fig. 6. The main features of this scheme have already been known from our former work “). Two levels ten‘gErsS(75 min) / 0.06
52
O.OL
70
_‘__
x-Vibr.
7/2+'lLOLl
7l2'
t:9:5
Y2* -
312'ILlll
3Q2.i 36O.L
3/2.
307.5 297.6
-m---
912-
7Kl5233
1.1 set
100-0 0
E,(keV)
99.8 I,&%)
:.a log ft
Fig. 6. Decay scheme of le3Er(EC) 163H~. The assignment of transitions marked by full dots is supported by the coincidence measurement. Energies are given in keV, total intensities per lo4 decays. The multipolarities of transitions are taken from ref. 13).
tatively introduced in ref. rl) were not confirmed. Additional information has been obtained on the population of members of the 4’ [411] band. As the transitions deexciting the 3 and 3 members of the 4’ band could not be observed the energies of these states were taken from the reaction results given in fig. 5. The 3 member at 431.2 keV is confirmed by the coincidence pair 431.2-444.8 keV. The branching ratios of the transitions de-populating this $ state are within the errors the same as obtained from the in-beam experiments. The assignments 5- [532] and 5’ [413] as main components of the levels at 1113.5 keV and 876.0 keV, respectively, are suggested by the excitation j2) and de-excitation
588
L. FUNKE et al.
modes of these levels. The 876.0 keV level de-populates to the 5’ [404] level and to the first four members of the 3’ 141l] band in a similar way as the 3; [413] state ‘*) in ’ 65Ho. The preferred branching to the 3 member of the 4’ band in 163H~ can be explained by a small admixture of the $‘[404] configuration (strongly populated from the state 5’ [413]) in the level I, K” = S, 3’. A detailed discussion of this coupling is presented in subsect. 4.3. From the comparison with the neighbouring Ho isotopes 3W18)the y-vibrational level built on the ground state con~~Iration is expected near 600 keV. The 614.3 keV transition found in the decay as well as in the reactions is probably de-exciting this vibrational state. The 253.9 keV transition might be the transition to the 3’[411] band head. Recent calculations 20) on the basis of the microscopic theory predict this vibrational state to be at 1015 keV. 4. Discussion 4.1. QUASIPARTICLE
EXCITATIONS
As a result of our experiments several levels with predominant quasiparticle structure were found in l(j3110 (see figs. 5 and 6) and 161Ho [refs. 2, “)I, A comparison of their excitation energies with those of the levels in the neighbouring isotopes 165H~ [ref. ’ “)I and ’ 5gHo [refs. “*‘“)] is given in fig. 7. On the right hand side of fig. 7 the experimental energies of the odd-proton system Z = 67 are shown. In order to distinguish particle and hole states they are plotted above or below the ground state, respectively. The considerable increase of the level density between the mass numbers A = 165 and 159 is noticeable. This effect can neither be explained by the quasipanicle-phonon interaction 20) nor by rotation-particle coupling. On the other hand different values of the energy gap A and of the deformation parameters s2 and eq might be responsible for this level compression. The theoretical energies calculated with the Nilsson model 23) including pairing corrections are given on the left-hand side of fig. 7. The chemical potential is assumed to be very near to the $- [523] orbital [ref. ’ 5)]. In order to show the influence of the parameters Q, .s2and A they have been changed in a direction as it is expected for decreasing mass number. As shown in the fig. 7c a larger gap parameter A gives a higher level density. However, the assumed change from 500 to 1000 keV is in disagreement with the gap values calculated 25) from the odd-even mass differences. These values are constant at about 900 keV for the treated odd-A holmium isotopes. The quadrupole deformation sZ is known 31) to decrease from 165H~ to 159H~ by about 0.02 and the hexadecapole deformation eq changes “) in the range of 0 (165H~) to -0.02 (‘5gHo). The figs. 7a and 7b show the influence of .sZand .s4on the energies of the orbitals _t- [541] and 3’ [404] to be large. Going from higher to smaller mass numbers the energy of the a- level is Iowered by the variation of &4and is raised by the variation of e2, but the 27 * level is lowered by changing all the parameters under discussion. This simple picture may explain the large decrease of the $‘[404] level
“=Ho
ROTATIONAL
589
BANDS
experiment
theory
Z-67
-I
712*
7/2+[LOLl
l/T
IF l/2'
1/2-
7/T[5231
7/2-15231
3/2* ~3,2*UllI
-c\5,2+[4,3 5/2+[L131
\
\
E, = 0.28 EL--o.02 E‘ = 0 A- 5OOkeV
-
5/2-
E, = 0.28 E, = 0.30 A=
@
-em_
S/2-15321
CL= 0 500 keV
@I
E, =0.28 EL= 0 A=lOOOkeV A= 5WkeV
(9
Fig. 7. Comparison of the experimental single-proton excitations in the Z = 67 system with model predictions. The quasi-particle energies displayed in (a), (b) and (c) were calculated using different values for the energy gap d as well as for the deformation parameters eZ and ~4.
with decreasing mass number and the relative constancy of the excitation energy of the +- [541] state in 163H~ and 161Ho, but the general tendency of the level compression is not completely understood. 4.2.
DESCRIPTION
OF
THE
ROTATIONAL
BANDS
bands built on the Nilsson states In 163H~ just as ‘) in 161Ho five rotational ;- [523], 3’ [404], 3’ [41 I], Ti+ [411] and +- [541] were found (see fig. 5). At first the Bohr-Mottelson formula 26) E(6 K) = E,(K)
+
Az(I+ 1) +EqZ(l+
1))2 + c(z(I+
1))3
+ (- 1)r+K[(z+K)!/(z-K)!](A~K+B2~z(z+
l)),
(1)
has been used to analyse the energies of these bands. The parameters A, B, A, and Bl or A, B, C and A,, were taken for fitting the energies of the bands with K = 4 or
L. FUNKE
590
et al.
TABLE 5 Rotational
parameters
and gyromagnetic
C
AK
&K
(l&j
(c”v,
(mev)
WV)
(eW
11.15
-0.3
-8.3
12.80 (15.63) (11.13) 9.89
-8.0 (-68) (4.3) -3.6
IP[m?,fl]
$- [523] $‘[404] 3’[411] t+]4111 +- ]5411
factors
of the bands
in 163H~ x2/f”)
0.11 x10-6 -1.0 x10-6 (4.0 X 10-q (-5.8) 26.00
(580)
(-6.5) -85
i(cwd/Qoi
9
levels b,
5
9(S to 9)
2 2400 1700 2
5G to $) 7(% to T)
$- [523] I”
Fitted
IO@ to V) 7(9 to Y) ‘)
-Y-
$ -
$-
.IZ2
Y-
z2
23Y-
0.111
0.116
0.110
0.122
0.130
0.133
(0.106)
8’
$+
?$ +
0.130
0.082
0.159
++[411] In
lb-SR)/QC, “) “) ‘) d,
9
4’
5 0.053
9’ 0.176
x2 per degree of freedom. Number and spin values of the levels used in the fit. Except the levels 5, 9, Aj and 9. The errors are typically of the order of 0.005 to 0.015.
K # 4, respectively. The results of the least-squares fits are summarized in table 5. (For comparison with the values of 16iHo see table 3 of ref. ‘)). The values x2 per degree of freedom given in column 7 show that the fit for the bands 3’ [41 l] and 3’ [41 l] is very bad. These bands can practically not be described by the above formula. An explicit Coriolis coupling calculation has to be carried out. The rotational bands s- [523], 3’ [411], 3’ [41 l] and 3’ [404] in 163H~ and also in 16iHo have been analysed in terms of the Nilsson model including quasiparticle corrections and Coriolis interaction “). The unperturbed bands are assumed to be describable by the formula E(Z) = E,(K)+AZ(Z+ The Coriolis M K,K+l
=
matrix elements
&
7
CjKCjK+l
l)+Z?(Z(Z+
between
J(j-K)(j+K+
l))‘+~,,A,(
-l)‘++(Z+f).
(2)
bands with K and K+ 1 read l)d(Z-K)(Z+K+
1)
where CjK are the coefficients of the Nilsson wave functions in the coupled basis. The strength factor RK,K+l allows one to vary the coupling strength between bands K and K+ 1. In all the coupling calculations the single-particle energies were evaluated,
le3Ho
ROTATIONAL
591
BANDS
if possible, from the experimental band head energies in a similar way as described in refs. ‘*““). F ur th er energy values and the wave functions of the single-particle con-
~~~~
~~~~
r-
,y2 1712 ,9i2 ,1/2’32
2~2
23/2
9/2 I
7l2+[LO11 _
13
r 13
I Ii2
13/2
1712
E/2
19/2 2”2
I ‘#2’!13Ll
--_._
--x_
‘5’tio
--*
12 Tii
--_
‘*-
¶!2
2712
2512
232
1112
1312
IV2
--__
--a
1712
1%
-;:--r.l 9'1
D .
Iv2
%-
SPIN
I
VALUE
(I’scale)
15/2
1712
-e
SPIN VALUE (I’scale)
lr$m;i;;:
,wT
0.05
0.05 i
I 0
13n
712
* 92
1lR
13/2
15/2
SPIN I;
:X2
f----iO 1912
7R
912
IliZ
IL 1312 1512 1712 19/Z 2112
SPIN I;
values are given by dots; Fig. 8. Coriolis coupling effects in 163H~ and 16iHo. The experimental values obtained from the Coriolis coupling calculations are connected by solid lines; dashed lines should only guide the eyes. The highest spin used in the fit is indicated by a vertical stroke. Furthermore the quantities of the fitted parameters were inserted in the figure.
592
L. FUNKE
et al.
figurations as well as the Coriolis matrix elements were obtained from the Nilsson model 23) using the parameters p = 0.625 (N = 4) p = 0.63 (N = S), K = 0.05, Ed = 0.3 and s.+ = 0. The gap parameter (corrected for blocking) has been taken from Soloviev ““) as being d.,,(Ho) = 700 keV. In fig. 8 the energies and intensities are analysed in order to show non-adiabatic effects. Using e.g. formula (2) the exhibited quantities [E(I)--E(I-1)]/21 (for K # 3 bands) and Q[E(lf2)+E(I-2)-2E(f)] (for K = 3 bands) should follow a smooth curve if they are plotted versus Z2. The fluctuations of the experimental values are assumed to be caused by the Coriolis interaction. The results of our Goriolis coupling calculations obtained by a fitting procedure and indicated in fig. 8 by solid lines reproduce the experimental values sufficiently well. The values of the rotational parameters A (indexed by the corresponding K quantum number) and B, the decoupling parameter a = Al/A and the strength factors RR,K+I of the Coriolis matrix elements which were handled in the least-squares fits as free parameters are inserted in fig. 8. The $- [523] ground state band of the Ho isotopes is known to be perturbed by Coriolis coupling with the other states arising from the h, subshell state, i.e. the $- [%O], $- [54i ], s- 15321,p- [514] and -$$- [505]. The interaction of all these states was included in our calculation. In order to get comparable results for 16rHo and “j3Ho only the levels up to spin -$l- were fitted. The experimental energy difference of the orbitals $- [532] and $- [523] has been taken to renormalize the energy scale of the Nilsson model [see ref. ‘)I. Thus the single-particle energies applied in this calculation are smaller in ’ 61Ho than in 163Ho. The rotational parameters A = &“/2$ and B assumed to be the same for all bands and the strength factors R,,% and R,,, were used in the fit as free parameters. Other strength factors are assumed to be R = 1. The results concerning the description of the $- [523] band in i61Ho agree with those obtained by Rensfelt et aE. ‘*) except for the somewhat different values of A and R R.K+ 1. The increasing perturbation of the $- [523] band with decreasing mass number is expressed by the differently strong fluctuations in the holmium isotopes [see fig. 8 and ref. 29)] and is caused by rising of the level density (shown in fig. 7) and of the rotational parameter A. Although the matrix element of Coriolis coupling between the bands -1”[41 I] and 3’ [411] is only about a tenth 18) of those reponsible for the coupling within the h+ shell a strong perturbation of both bands were observed in the holmium isotopes. This is caused by the small energy distance of the corresponding coupled states. The perturbation which is strongest expressed in the large energy displacements within the 3”’ band can sufficiently well be described by its coupling with only the +‘[4111 band (see fig. 8). For both bands the same B-value but different rotational parameters A were used in the fit. In the coupling matrix element the mean value of A were applied, It must be noted, that for both 163H~ and 16’Ho the experimental coupling matrix elements Mexp = R+,+MNilsson are 20-40 “/, larger than the Nilsson value. Further calculations including up to 6 additional states have shown the influence of
l’=Ho
ROTATIONAL
BANDS
593
these states on the level energies of the bands 3’ [41 I ] and 3’ [411] to be small. The transition probabilities, however, are sensitive to such weaker couplings as shown in subsect. 4.3. The $‘[404] band is shown in fig. 8 to behave differently in both Ho isotopes. Whereas the smooth curve of 16rHo is typical for an unperturbed band, the 163H~ curve represents small fluctuations. This perturbation is caused by a mixing with the levels of the &’ [411] band being very close in energy. The energies of the members of the 3’ band were fitted in a four-band Coriolis coupling calculation as described in subsect. 4.3. Although the f- [541] band is coupled with the s-[532] band as shown e.g. in refs. 7S8) t he o b served levels of this band can be well fitted by the Bohr-Mottelson formula (1). However, the high-lying level sequence (Z+f = even) which is most influenced by the Coriolis interaction was not found in the Ho isotopes. An analysis of the gyromagneti~ factors on the basis of the ratios of cascade (cc) to crossover (co) intensities Z,(cc)/Z,(co) has been performed using the adiabatic formula ’ (If l)(Z+K-
l)(Z-K-l)
2P(2Z-1)
_-I
1* (4)
The experimental values of (Se--g&/Q0 obtained for the 3- [523] band and the strongly perturbed 3’ [411] band in 163Ho are given in table 5. Whereas the values of the ground state band increase slightly with the spin, the values for the 3’ [41 I] band offer significant fluctuations as also shown in fig. 8. Then the ratios of cascade to crossover intensities of the 3’ [41 l] band were calculated using the mixed wave functions from the energy fit for determining the MI and E2 transition probabilities. The single-particle contributions in the E2 transitions were neglected. The quantities j(gK -gR)/QO] calculated with formula (4) using these theoretical cascade to crossover intensity ratios reproduce the experimental values fairly well, if the parameters Q, = 7b, g, = 0.4 and gIff = 0.5gF are used (fig. 8). The theoretical values increase for lower gR and/or larger gzff. Using the same parameters and a pure configuration a constant value of (gK -gR)/QO = 0. I6 for the 3’ [41 I] band is obtained. The interband transitions between the 3’ [411] and the if[41 l] bands can also be roughly reproduced by means of the mixed wave functions. 4.3. El TRANSITION
PROVABILITIES
As shown in figs. 5 and 6 several El interband transitions were observed in 163H~. Their reduced transition probabilities have been estimated “) by a comparison of the El intensities with the intraband E2 transition probabilities on the basis of the formula B(E2) = (5e2~16~)Q~(Z2~O~Z~)‘. Although within the 2’ [404] band of ’ 63Ho no E2 transitions could be found, from their intensity limits minimal values of the El transition probabilities of transitions connecting the 3’ [404] band with the i- [523]
L. FUNKE
594
et al.
TABLE 6
Comparison
of El transition probabilities
in 163H~ and 161Ho
163H~
lGIHo
Er WV)
B(E1) “) (e’ * b)
j$ (kev)
B(E1) “) (e* . b)
s,s-
439.9
J2!,Z + %,H$9 f; -+ Y, S3 ,z -+ %.S;,sH32Ifi +,B++ C,%-
588.0 622.5 658.9
(> 7 x10-y > 5x 10-7 2 5x10-6 89x10-6
252.7 412.2 452.6 489.2
z 7x10-6 3.3 x 10-e 4.4x10-6 5.9 x 10-e
431.2 552.1
2.5 x lo-’ 7x10-s
(353.2)
Ii, Kin + Ir, W
f, g -+
<2x10-9
“) These values have been evaluated from the branching ratios as described in the text.
ground state band were estimated. In table 6 some of these B(E1) values are compared with the values obtained “) for 161Ho. The El transitions between both $ bands are similarly fast, or even still faster, in 163H~ than in 161Ho. The experimental B(El) values were shown “) to be much larger than the Nilsson values. Nilsson retardation factors of about 0.02 to 0.03 had been estimated. The reason for this high transition probability is not yet clear. Most surprising in 163H~ are the strong K-forbidden (AK = 3) El transitions from the 3 (and q-) member of the +’ [41 l] band to the ground state band (corresponding transitions have not been found in ’ 61Ho). The occurrence of these transitions can be understood assuming a small admixture of the close-lying $‘[404] configuration in the wave functions of the members of the _t’ [41 l] band. Comparing the El transition probability of B(El,439.9 keV) > 7 x 10e6 e2 . b extrapolated from the other B(E1) values in 163H~ and 161Ho [see table 6 and ref. ‘)I with the value B(E1, 431.2 keV) = 2.5x 10v7 e2 . b an admixture of less than 3 % of the s’ [404] configuration in the Z_,t’ state was derived. A similar value is obtained from the intensity ratio of the transitions at 444.8 and 436.1 keV which populate both the 4’ levels from the $‘[413] state (see subsect. 3.2). In order to describe the observed mixing of states with AK = 3 a Coriolis coupling calculation of first order was performed [see also ref. ““)I. For the interesting spin values 3 and y the interaction matrix was diagonalized in the space of the Nilsson configurations +‘[411], +‘[411], $‘[413] and 4’ [404]. For the parameters A, B and a as well as R,,, the values obtained from the energy fit given in fig. 8 were used. The other coupling strength factors were assumed to be R,, 5 = R,, + = 1. As the coupling of the states under discussion is mainly caused by their small energy separation we examined their behaviour for approaching each other by varying the single-particle energy of the 3’ [404] orbital. The result concerning the mixing of the 3 states is given in fig. 9. The amplitude a;,$ of the admixed _5[404] configuration in the 3 member of the 3’ [41 l] band assumed to be responsible for the high El transition rate is plotted versus the energy separation of the mixed 3 states. The calculated value of the admixture (u~,~)’ at the experimental energy separation being approximately 1 ‘A is in gross
t-Ho
ROTATIONAL
BANDS
595
agreement with the experimental upper limit of 3 %. Our calculations yield a minimum of the energy separation of the mixed states (of about 1.5 keV) quite similar to the well-known case of a mixing of two states with d.K = 1. At this point the two Nilsson configurations are equally divided among both the mixed states, while the contributions of all the other configurations are much smaller. The value of the minimum separation depends mainly on the coupling strength.
exp. value
A E,2 &eV 1 Fig. 9. Mixing amplitude of the 5’ 14041 configuration in the wave function of the rotational level f, f+ [41 I] plotted as a function of the energy separation between both states. The curve resulted from a Coriolis coupling calculation including the bands 4’ [41 I], 2’ [411], g+ [413 J and $+ [404], if the single-particle energy of the $+ [404] state is varied.
5. conclusions Several non-adiabatic effects such as energy displacements and fluctuating gyromagnetic factors caused by the Coriolis force have been studied in 163H~ as well as in ’ 61Ho. Intense K-forbidden EI transitions between members of the band 3’ [41 l] and the $- 15231 ground state band in 163H~ are explained by an admixture of the $‘[404] con~guration in the members of the *‘[411] band. This case of Coriolis mixing of close-lying states differing in iK by several units 30) is investigated on the basis of first-order coupling. If levels with the same spin and parity but different K quantum number come very close in energy in every case a remarkable mixing can be expected. Furthermore, information concerning the single-particle model was obtained. The increasing level density in the holmium isotopes with decreasing mass number was tried to explain by a change of the energy gap and the deformation parameters. The high El transition probabilities of the interband transitions between the bands %‘[404] and f- [523] are in disagreement with the Nilsson values. This problem is still unsolved. We want to thank Dr. D. Netzband for careful reading of the manuscript and for several critical comments. We are very grateful to Mrs. J. Kerber, Mr. E. Will and Mr. K. Heidel for valuable help during the experiments. We are also indebted to the
596
L. FUNKE
et al.
staffs of the Rossendorf cyclotron and of the betatron at the Jena University. The support of this work by the Ministerium fiir Wissenschaft und Technik of the German Democratic Republic and by the Deutsche Akademie der Wissenschaften zu Berlin is gratefully acknowledged. References 1) G. Winter, L. Funke, K. H. Kaun, P. Kemnitz and H. Sodan, Phys. Lett. 33B (1970) 161; Nucl. Phys. Al76 (1971) 609 2) L. Funke, K. H. Kaun, P. Kemnitz, H. Sodan and G. Winter, Nucl. Phys. A170 (1971) 593 3) K. H. Kaun, L. Funke, P. Kemnitz, H. Sodan, G. Winter, E. Will, K. J. Gromov, S. M. Kamalchodjaev, W. G. Kalinnikov and H. Strusny, Nucl. Phys., to be published 4) L. Funke, K. H. Kaun, P. Kemnitz, H. Sodan and G. Winter, Proc. Conf. on nuclear spectroscopy and theory, Dubna, June, 1971; and annual report ZfK-223, 1971 5) G. Winter, L. Funke, K. Hohmuth, K. H. Kaun, P. Kemnitz and H. Sodan, Nucl. Phys. A151 (1970) 337 6) L. Funke, K. H. Kaun, P. Kemnitz, H. Sodan, G. Winter, R. Arlt, K. J. Gromov, S. M. Kamalchodjaev, A. F. Novgorodov, H. Strusny, D. de Frenne and E. Jacobs, Nucl. Phys. Al75 (1971) 101 7) P. Kemnitz, L. Funke, K. Hohmuth, K. H. Kaun, H. Sodan and G. Winter, Nucl. Phys. Al64 (1971) 513 8) P. Kemnitz, L. Funke, K. H. Kaun, H. Sodan and G. Winter, Proc. Conf. on nuclear spectroscopy and theory, Dubna, June 1971, p. 147; Nucl. Phys., to be published 9) P. Kemnitz, L. Funke, K. H. Kaun, H. Sodan and G. Winter, Proc. Conf. on nuclear spectroscopy and theory, Dubna, June, 1971, p. 153 10) C. L. Hammer and M. G. Stewart, Phys. Rev. 106 (1957) 1001 11) L. Funke, H. Graber, K. H. Kaun, H. Sodan and J. Frana, Nucl. Phys. 84 (1966) 471 12) L. Funke, H. Graber, K. H. Kaun and H. Sodan, ZfK-PhA 23, Rossendorf, 1966 13) R. Babadjanov, W. Butzev, K. J. Gromov, Sch. Schelev, W. Kalinnikov, J. Mareev, F. Michtasimov, U. Nasarov, Conf. on nuclear structure, Dubna, 1966 14) C. R. Gossett, L. A. Beach, L. R. Medsker and P. P. Singh, Bull. Am. Phys. Sot. 16 (1971) 539 15) 0. W. B. Schult, M. E. Bunker, D. W. Hafemeister, E. B. Shera, E. T. Jurney, J. W. Starner, A. Backlin, B. Fogelberg, U. Gruber, B. P. K. Maier, H. R. Koch, W. N. Shelton, M. Minor and R. K. Sheline, Phys. Rev. 154 (1967) 1146 16) T. Yamazaki, Nucl. Data A3 (1967) 1 17) S. Allam and H. J. Keller, Proc. Conf. on nuclear spectroscopy and theory, Dubna, June, 1971, p. 192 18) M. E. Bunker and C. W. Reich, Rev. Mod. Phys. 43 (1971) 348 19) L. Funke, W. Andrejtscheff, H. Graber, U. Hagemann, K. H. Kaun, P. Kemnitz, W. Meiling, H. Sodan, F. Stary and G. Winter, Nucl. Phys. A118 (1968) 97 20) V. G. Soloviev and S. I. Fedotov, JINR E4-6055, Dubna, 1971 21) A. A. Abdurazakov, Sch. Schelev, W. Kalinnikov, U. Nasarov and J. Urbanez, lzv. Akad. Nauk SSSR (ser. fiz.) 32 (1968) 781 22) J. S. Geiger, R. L. Graham and M. W. Johns, Bull. Am. Phys. Sot. 14 (1969) 1225 23) B. E. Chi, Nucl. Phys. 83 (1966) 97 24) V. G. Soloviev, Teorija sloschnich jader, (Izd. Nauka, Moscow, 1971) 25) W. Ogle, S. Wahlborn, R. Piepenbring and S. Fredrikson, Rev. Mod. Phys. 43 (1971) 424 26) 0. Nathan and S. G. Nilsson, in Alpha-, beta- and gamma-ray spectroscopy, ed. K. Siegbahn (North-Holland, Amsterdam, 1965) 27) A. K. Kerman, Mat. Fys. Medd. Dan. Vid. Selsk. 30 (1955) no. 15 28) K. G. Rensfelt, A. Johnson and S. A. Hjorth, Nucl. Phys. Al56 (1970) 529 29) R. M. Diamond, Proc. Int. Conf. on the properties of nuclei far from the region of beta-stability, Leysin, August, 1970 30) P. Kemnitz, L. Funke, K. H. Kaun, H. Sodan and G. Winter, Phys. Lett. 39B (1972) 179 31) K. E. G. Lobner, M. Vetter and V. Honig, Nucl. Data A7 (1970) 495
(1912) 576-596;
@
North-Holland
Publishing
Not to be reproduced by photoprint ar microfilm without written permission
ROTATIONAL L. FUNKE,
Co., Amsterdam from the publisher
BANDS AND FAST El TRANSITIONS IN ‘63H~
K. H. KAUN,
Zentralinstitutfiir
P. KEMNITZ, Kernforschung, Received
H. SODAN
and
RossendorfiDresden,
11 April
G. WINTER DDR
1972
Abstract: The level scheme of the deformed odd-proton nucleus le3Ho has been investigated by inbeam and decay spectroscopic methods. Single y-ray spectra, conversion electron spectra, y-y coincidences and angular distributions of the y-rays were measured in the reaction rL3Dy(d 2ny) at a deuteron energy of about 13.5 MeV. Single y-ray spectra were also taken in the 16’Dy(p, ny) reaction with 6.7 MeV protons. Additional information on the 163H~ level scheme was obtained by re-investigating the y-radiation in the electron capture decay of 163Er. The proposed level scheme of re3Ho contains in addition to the ground state band $- [523] the rotational bands built on the intrinsic states 3’ [404], 3’ [411], )+ [41 l] and &- [541] (band heads at 439.94, 360.36, 297.88 and 471.25 keV, respectively). Further levels at 1113.5, 876.0 and 614.3 keV are interpreted as being mainly the quasiparticle excitations &- [532], 8’ [413] and possibly the ground state y-vibration, respectively. A comparison of the quasiparticle excitations in the Ho isotopes is performed on the basis of the Nilsson model including pairing corrections. Discontinuities in the rotational bands are described by Coriolis coupling effects. Several fast El interband transitions were observed in le3Ho. Some of them connect levels of the 4’ [411] band with the ground state band t-15231. The appearance of these K-forbidden transitions is explained by a weak mixing between states of the bands 4’ [411] and 4’ [404] caused by Coriolis interaction. NUCLEAR E
REACTIONS 163Dy(d, 2ny), Ed = 13.5 MeV; measured Er, Zr, I,,, EY, Zr. 163H~ deduced oCEr. or). 7-y coin., rb3Dy(p, ny), Ep = 6.7 MeV; measured levels, .I, n, cc, B(E1). Enriched target; Ge(Li) detectors. RADIOACTlVITY ‘63Er [from 164Er(Y, n)]; measured Eu, I?, y-y coin., 163H~ deduced levels, J, n. Enriched target: Ge(Li) detectors.
1. Introduction In the framework of a systematic study of the deformed odd-proton nuclei in the rare-earth region the nuclei 1ss*157Tb [ref. ‘)I, 161,163H~ [refs. “-“)I, r6’Tm [refs. 5, “)I, 171*173Lu [refs. ‘,“)I, and i “3 179Ta [ref. ‘)I were investigated by means of in-beam spectroscopic methods and in some cases also by decay measurements. In this paper our results on the 163H~ level scheme are given. Since 1957 an isomeric level lo) in 163H~ near 300 keV is known, which has been interpreted as the $‘[411] Nilsson state. In 1966 the levels of l‘j3Ho were studied [refs. 11,12)] in our laboratory in the electron capture (EC) decay of 163Er. AS a result of this investigation the quasiparticle excitations 3’ [4O4], 3’ [413] and -2- [532] were found at energies of 440, 876 and 1110 keV, respectively. The multipolarities of the two strongest transitions at 436 and 440 keV were determined by Babadjanov et al. 13) to be Ml (or E2) and El, respectively. 576
l’=Ho
ROTATIONAL
577
BANDS
In order to search for further quasiparticle states such as the orbitals sf [41 l] and ?-^ [541] expected ‘) at low energies and to study the rotational structure we investigated the y-radiation and conversion electrons in the reactions 163Dy(d, 2n) and 163Dy(p, n) as well as the y-radiation in the decay of 163Er. Very recently 14) we learned of an investigation of the 163Ho levels in the reaction 164Dy(p, 2n), but no detailed information was available. Preliminary results of our in-beam studies were presented previously 4S30). 2. Experimental procedures and results 2.1. IN-BEAM
EXPERIMENTS
The in-beam experiments were performed at the Rossendorf cyclotron U-120 with deuterons of 13.5 MeV and protons of 6.7 MeV. For the investigation of the y-radiation a 30 mgjcm2 thick dysprosium oxide target enriched to 93 % 163Dy has been used. Conversion electron measurements were carried out with an enriched 163Dy metallic target of 2 mg/cm2 thickness. Further details of the experimental arrangements are described in earlier publications 5S‘,I ‘).
I
b?
O~-.-~ LOO
600
800 CHANNEL
looolzco-----7ls---~~o
IL00
NUMBER
Fig. 1. In-beam y-ray spectrum recorded with a 0.4 cm3 Ge(Li) spectrometer during the bombardment of 163Dy with 13.5 MeV deuterons. The spectrum {a) has been taken without absorber, the spectra (b) and (c) with absorbers of 0.15 mm Cd+0.5 mm Cu. Most of the lines assigned to the reaction le3Dy(d, 2n)‘63Ho are marked by their energy value. Crosses indicate background lines.
578
L. FUNKE
et al.
TABLE 1 Gamma-rays
Ey (kev)
assigned
Ir Cdl3)
to re3Ho from the reactions
1, (P) Ir (d)
1 52.74 57.80 “) 59.25 62.48 80.16 84.45 87.71 97.03 100.04 112.4 122.14 123.52 131.44 135.72 136.17 142.62 144.41 154.40 158.27 159.38 “) 160.24 “) 163.61 165.14 168.0 173.38 175.7 181.59 183.5 187.76 192.74 195.53 197.51 204.87 220.85 222.27 223.54 229.57 232.86 239.6 254. I 263.0 “) 266.62 267.20 280.35 282.48 294.37 297.88
2
3
2ny) and lh3Dy(p,
1.oo 0.95 0.79 0.62 0.63 0.36 0.24 0.63 0.30 0.47 0.50 1.40 0.14 < 0.15 0.22 0.44 < 0.2 0.85 0.07 1.15 0.44 0.04 1.26 0.58 ” 0.1 < 0.05 0.28 0.27 0.49 < 0.1 0.40 1.oo 0.04 0.17 0.38 1.30 < 0.06 0.10
ny)
Assignment Ii, Kin + If, K,=
I tot
4
5
6
cz 10
z3 1.8 1.7 2.4 3.7 3.4 3.1 3.2 62.0 I 0.2 57.5 6.0 2.1 3.0 2.4 1.0 41.4 1.1 7.9 1.6 1.7 3.3 25.3 x2 1.9 0.7 14.7 S 0.5 12.6 8.0 2.4 4.0 6.4 20.3 8.5 6.2 2.8 2.5 0.6 1.0 11.0 13.0 3.8 3.1 7.4 8.9 1OOb)
Deduced spin value
‘e3Dy(d,
(20) 26 22 18 15.5 12.5 236 150 13.5 4.8 6.61 5.3) 1.7 84 1.2 8.7 2.91
0.03(l) 0.25(10) -0.06(7) 0.09(4) 0.17(6) 0.05(l) -0.25(15) -0.15(4)
I 3.6 43.5 ” 3 2.1 1.1 15.6 5 0.8 19.0 8.5 5.0 9.0 23.8 10.0 7.2 3.6 3.2 0.7
0.06(5)
0.02(4) 0.14(3) 0.14(6) 0.28(7) 0.04(9) _-0.24(17)
-0.05(2) 14.21 4.2) 3.2 8.0 9.5 131
0.09(14) 0.18(7) 0.08(3) 0.00 b)
7
‘=Ho
ROTATlONAL TABLE
E,(keV)
I,(dl3)
1, (P) $, Cd)
552.07 558.7 “) 568.5 “) 585.7 “) 588.0 590.4 611.6”) 614.6 622.5 652.5 “) 658.9 688.3 “)
80
. (
0.54 x 0.8 .: 0.1
7.6 3.0 2.0 4.0 3.2 3.0 5.7 4.0 4.7 3.7
Deduced spin value
1
4 i Gw
I 0.62 < 0.2 1.75 1.18 0.72 0.55
Xl
I ,Ot
Assignment
A2 Ii, 6
5 16.0 7.7 5.9 1.8
4” + h, KC’ 7
0.17(2) 0.13(5) 0.11(5) -0.06(5)
7.0 2.0 9.2 2.1 2.4
0.22(6)
high
< 0.1
4.0 4.0
5.8 2.5
0.27(5)
7 hYgh IOW low (8) (V)
O.lO(2) 0.18(15)
46.3 3.0 1.6 10.9 5.0 2.2 1.2 xl
0.08(4) O.ll(6) 0.24(24)
low 4.0 4.0
0.54
(‘$1
1.6 0.80
low low high
0.67 1.10
(3) low
4.0
1.25
low
5.7 4.0
1
-0.04(5) 0.03(5) 0.19(15) -0.30(15) O.OO(12) -0.06(10) O.Ol(5) -0.14(7)
3.7
=5
Column 1: The errors decimals certain.
0.07 0.10 0.19
15.0 7.3 5.6 1.6 6.9 2.0 8.9 2.1 2.4 2.9 5.6 2.4 2.2 46.0 2.9 1.6 10.8 5.0 2.2 1.2 Xl Z8
309.58 312.73 314.96 326.8 331.12 339.95 352.90 359.2 364.9 384.4 392.65 399.0 417.2 “) 431.16 434.45 436.1 439.94 452.00 465.9 469.0 478.0 514.5 “)
579
1 (continued)
4
3
2
1
BANDS
and smaller
than
of the energies are smaller than 0.1 keV 0.3 keV for the others. “) The assignment
for energies given with two to the nucleus 163H~ is not
Column 2: Gamma-ray intensities measured with deuterons of 13.5 MeV energy at an angle of 125” to the beam axis. The errors of intensity values are of the order of 5 to 30 y0 depending on the line strength. b, Normalization value. Column 3: Intensity ratio of the y-rays emitted in the reaction with 6.7 MeV protons and 13.5 MeV deuterons. “) Normalization. Column 4: Probable spin value deduced from the intensity ratio of column 3 (further comments see text). “) Normalization. Column 5: Total intensity values calculated with the y-ray intensities of column 2 and theoretical conversion coefficients. Column 6: Angular distribution coefficients according to the formula W(B) = l+AtPz(cos 0). The errors of the AZ coefficients are given in parentheses in units of the last decimal.
580
L. FUNKE
et al.
Single y-ray spectra were measured using germanium detectors of different volumes during the bombardment of the 163Dy target with 13.5 MeV deuterons or 6.1 MeV protons. As an example the spectrum with the highest resolution (0.5 keV for the 100.04 keV line) taken with a 0.4 cm3 Ge(Li) spectrometer in the deuteron reaction is plotted in fig. 1. The spectra taken with larger detectors have much better statistics especially at energies above 200 keV. Those lines ascribed to the reaction 163Dy(d, 2n) 163H~ are indicated by their energy values. Additional transitions assigned to either 162,163,164~~, 162,164H~ or 19F were marked by crosses. Most of these background transitions are caused by the reactions (d, d’) and (d, p) on 163Dy as well as by the (d, 2n) reaction on the neighbouring dysprosium isotopes. For the identification of these transitions targets enriched to more than 90 % 16’Dy or “j4Dy were also bombarded with deuterons or protons. In this way most of the observed y-ray transitions could be attributed to a certain nucleus. Several background transitions belong to the low-energy levels in the target nucleus ’ 63Dy excited by inelastic scattering of deuterons. The energies of these transitions have been measured very accurately by Schult et al. ’ “) in the (n, 7) reaction. Therefore these energies could be used as calibration standards. In table 1 a summary of the experimental data concerning the transitions assigned to 163H~ from the study of the reactions 163Dy(d, 2n) and ‘63Dy(p, n) is given. As the angular momentum transfer in the (d, 2n) reaction is higher than in the (p, n) reaction, high-spin states are excited much weaker in the (p, n) than in the (d, 2n) reaction. Thus from the y-ray intensity ratio of a transition in the (p, n) and (d, 2n) reaction given in column 3 of table 1 valuable conclusions to the spin of the state from which this transition arises can be drawn. However, this ratio depends also on the excitation mode of the initial state, quite similar to the cases discussed in refs. ‘, ‘). Nevertheless, the most probable spin values deduced from the intensity ratios Z,(p)/Z,(d) are g’iven in column 4 of table 1. These values (except for transitions de-exciting members of the $‘[404] band) were obtained using the spin dependence of the intensity ratios of the transitions within the well-established ground state band as normalization. Angular distribution measurements of the y-radiation have been performed to get additional information on the level scheme. For this purpose single y-ray spectra in the reaction with deuterons at angles of 18, 30, 45, 60, 75 and 90” to the beam axis were measured. As normalization, the intensity of the isomeric 297.9 keV transition has been used. Although in the (d, 2n) reaction the anisotropy is only a half of that in the (~1,2n) reaction [for comparison see table 1 of ref. “)I this information is valuable to check the proposed level scheme. The experimental A, values given in column 6 of table 1 support in a consistent way r6) the proposed level scheme. For the establishment of the level scheme extensive y-y coincidence experiments were performed in the reaction with deuterons. Two characteristic coincidence spectra are shown in fig. 2. The spectrum in coincidence with 100.0 keV offers mainly the transitions of the bands $- [523] and 3’ [404]. The second spectrum is typical for the
lc3Ho
-
“0 ; -
2 %
ROTATIONAL
BANDS
581
2’ 1~
Or
300 ENERGY
(k&j
Fig. 2. Two selected y-y coincidence spectra, taken with two germanium detectors of 14 and 27 cm3 volume. Transitions supposed to be in coincidence have their energy values given in keV. TABLE
Gamma-gamma
coincidences
observed
2
in the reaction
‘63Dy(d,
2n)163Ho
ET,l WV)
I+,, (keV) “)
100.0
122.1, 144.4, (158.3), 165.1, 187.8, 204.9, (220.8), 229.6, (239.6), 266.6, 309.6, (312.7), 331.1, 352.9, 392.6, (434.5), 452.0, 465.9, (478), (514), 552.1, 588.0, 590.4 100.0, 144.4, 165.1, 187.8, 204.9, 229.6, (239.6), 309.6, 352.9, 392.6, 434.5, 465.9,
122.1 123.5 132 136 144.4 158.3 181.6 192.7 197.5 220.8 223.5 282.5 431.2
“) Coincidences
(478), (622) (97.0), 158.3, 181.6, 197.5, 220.8, 282.5, 294.4, (223.5) (80.2), (84.5), 87.7, (97.0), (131), (136) 100.0, 122.1, 165.1, 187.8, 204.9, 222.2, 229.6, 154.4, 220.8, 282.5, 331.1, 354, 366, 431.2, 552 (123.5), 154.4, (181), 197.5, 282.5, 431.2 (112.4) 181.6, 282.5 123.5, 154.4, 158.3, 312.7, 326.8, 331.1, (399), (80), (131) 158.3, (181.6), 197.5, 220.8 97.0, (131), (136), 154.4, 158.3, 181.6, 197.5, 312.7, 315.0, 326.8, (359), (365), (384), 399.0, given
in parentheses
are weak
312.7
239.6,
352.9,
392.6, 434.5
431.2
220.8, (403)
or not very certain.
232.9,
(267),
282.5,
294.4,
582
et al.
L. FUNKE
de-excitation of the other bands. All coincidences The coincidence spectra were also quantitatively In order to get information on the multipolarity the conversion
electron
spectrum
observed are summarized in table 2. evaluated. of the intense 431.2 keV transition
has been measured ’
29i.9
,K392.6_?
in the deuteron
200
250
CHANNEL Fig. 3. Part of the in-beam special arrangement
using
’
1
I
150
reaction
50
300
31
NUMBER
conversion electron spectrum recorded with a silicon detector during the bombardment of r6aDy with 13.5 MeV deuterons.
in a
TABLE 3 Conversion
coefficients
(2,)
‘Y (rel.)
k (rel.)
266.6 291.9 309.6 312.7 315.0 392.6 431.2 439.9
13.0 100 “) 15.0 1.3 I 5.6 5.6 46.0 10.8
1.3 15.8 “)
and multipolarities
IL
c&c
‘*I.
(rel.)
(exp.) ‘)
(exp.)
10.8 “)
0.85 0.2 0.33 0.07
“) Normalization value. b, Errors are given in parentheses
of some transitions
0.10 (4) 0.158 “)
0.108 “)
0.030(15)
x 0.1
in units
0.035(15) 0.007(3) 0.007(4)
(0.002)
in 163H~ Multipolarity
(the%y )
0.07 0.155
(E2) (E3)
E2 E3
0.044
(E2)
W)
0.023 (E2) O.O063(El) 0.006 (El)
E2 El El
of the last decimal.
a Si(Li) detector of 50 mm2 x 2 mm in a special arrangement. A homogeneous magnetic field is applied to select the electrons from heavier charged particles and to reduce the y-ray background. At a distance of 20 cm between target and detector the transmission of the device was some percent for electrons of 200-400 keV. The complete electron spectrometer is described elsewhere “). A portion of the conversion electron spectrum is shown in fig. 3. Although the resolution is limited by the thick-
l’=Ho
ROTATIONAL
BANDS
583
ness of the target some essential information on transitions near 400 keV was obtained. The conversion electron intensities (related to the y-ray intensities by means of the well-known 297.9 keV E3 transition) and multipolarities of some transitions are given in table 3. The 431.2 keV transition was determined to have the multipolarity El. 2.2.
DECAY
EXPERIMENTS
The l’j3Er activity was produced by the (y, n) reaction on an erbium oxide target enriched to 65 % 164Er. A 100 mg target has been irradiated several times for 1 h at
VI i/
CHANNEL
5
NUMBER
z 5 I
CHANNEL NUMBER
Fig. 4. Gamma-ray spectra from the decay 163Er(EC)163Ho. (a) Single y-ray spectrum taken with a 18 cm’ germanium detector (absorber: 0.3 mm Cd). The lines assigned to the le3Er decay are marked by their energy values. (b) Selected parts of the y-y coincidence spectra taken with two germanium detectors of 18 and 22 cm3 volume.
the bremsstrahlung beam of the 30 MeV betatron of the Jena University. The irradiation technique is described elsewhere I’). Single y-ray spectra and y-y coincidence spectra were taken by means of germanium detectors of 18 and 22 cm3 volume. In order to find out the transitions decaying with the 163Er half-life three to four successive spectra were recorded. In every case an absorber between source and detector had to be used to reduce the very intense X-ray radiation caused by the strong allowed unhindered electron capture transition to the ’ 63Ho ground state. In fig. 4 the y-ray spectrum and a portion of the y-y coincidence measurements are shown. In addition to the transitions attributed to the 163Er decay the strongest transitions of the decay of * 61Er [ref. “)I and 167H~ [ref. ’ “)I as well as a few unidentified transitions having shorter or longer half-life were observed. The data concerning the transitions assigned to the 163Er decay are listed in table 4.
584
L FUNKE
et al.
TABLE 4 Gamma rays from the decay 163Er(EC)163Ho
Ey WV) 9
(80.5) 100.0 123.6 164.6 192.6 253.9 297.8 331.0 339.8 417.1 431.2 436.1 439.9 444.8 452.3 484.0 552.0 558.5 568.4 578.1 614.3 711.3 875.8 1013.6 1113.5 “) b, ‘) d,
(1) (2) (2) (2) (2) (1) (3) (2) (2) (2) (1) (1) (2) (2) (3) (3) (2) (2) (2) (1) (2) (2) (3) (3)
b, “)
b)
“) b, “)
I tot (per IO4 decays) a4 14.7 1.8 4.0 4.4 3.3 1008) 1.8 29 7.6 12.5 248 240 7.9 6.0 2.4 2.8 5.1 7.5 11.6
w 0.2 0.67 0.05
(8) (5) (5) (4) (5)
(1) (7) (9) (5) (5) (9) (6) (5) (7) (9) (8) (9)
29 (1) 10.7 (9)
b)
339.8,436.1
0.06 0.04 1.63 0.02 0.37 0.10 0.16 3.10 3.00 0.10 0.07 0.03 0.03 0.06 0.09 0.14 0.36 0.13 0.75 0.09 5.30 =gc)
(5)
60 (3) 7.5 (9) 426 (12)
Coincidence with
444.8 339.8,439.9 436.1 431.2
Normalization value. Not shown in the decay scheme. Taken from ref. II). Errors are given in brackets in units of the last decimal.
The very weak population of the excited states of 163H~ compared to that of the ground state is the reason why the coincidence experiments are of poor statistics. For instance the coincidence peaks 431.2-444.8 keV include only 5 to 10 events (see fig. 4b) but the coincidence relation is unambiguously certain because the background is very weak. 3. Construction of the level scheme 3.1. LEVELS
EXCITED
IN THE
REACTIONS
(d, 2n) AND
The level scheme of 163H~ obtained from fig. 5. The ground state band could very easily coincidence spectrum with 100.0 keV of fig. 2). but no clear coincidences have been observed state.
(p, n)
our in-beam experiments is shown in be followed up to spin y (see e.g. the They level was tentatively introduced because of the weak excitation of this
-Ho
ROTATIONAL
BANDS
585
586
L. FUNKE
et al.
From our former decay investigations ‘i) the position of the 5’ [404] single-particle level near 440 keV was known. The angular distribution of the 439.9 keV transition as well as its intensity ratio in the proton and deuteron induced reactions are similar to that of the 252.7 keV transition ‘) in i6iHo. Its assignment to the s’ state seems, therefore, to be certain. In addition the coincidence, excitation and angular distribution data and the comparison with the ’ 61Ho level scheme “) allow us to construct the band built on the $‘[404] state. The levels of this band de-populate by fast El interband transitions to the $- [523] ground state band. No intraband transitions were found, but in some cases the upper limit of their intensity values were estimated (see table 6). Additional to the strong transitions within the ground state band and weaker ones de-exciting the t’ [404] band several intense transitions were assigned to ’ 63Ho which could not readily be attributed to a certain band. The 297.0 keV transition de-excites the known lo) isomeric state _t’ [41 I]. A strong 431.16 keV transition with multipolarity El and the coincidence 100.0-331.1 keV suggests a 5’ level at 431.16 keV, but no band with K = 5 can be found on it. Otherwise several coincidences with the transitions at 33 1.1 and 43 1.2 keV were found as shown in fig. 2 and table 2. The 43 1.16 keV state can plausibly be explained as being the 3 member of the 4’ [411] band. An explanation of the intense K-forbidden transitions (AK = 3) from the 3 and 9 members of the f’ [41 l] band to the levels of the ground state band is given by a Coriolis coupling treatment in subsect. 4.3. The coincidence behaviour of the 123.52 keV transition is very similar to that of the 431.16 keV line. Therefore, this transition should also de-populate the 431.16 keV level. This assignment leads to a level at 307.64 keV being apparently the 3 member of the +‘[41 I] band. Support for a separation of only 9.8 keV between the 3 and 3 members is also obtained by transitions feeding these states from the lowest members of the bands +‘[411] and $- [541]. Using the coincidence data (table 2) and the information given in table 1 the states I+ 3 = even of the 4’ [411] band up to spin 9 and the states of the 4’ [41 l] band up to -‘+$ (tentatively -$?) were established quite similar “) to those in ’ 61Ho. The 552.07 keV transition de-populating the y member of the 3’ band is fixed by the coincidence with 100.0 keV but its intensity in the coincidence measurement is only a half of that in the single spectrum. This is consistent with the assumption of another transition at the same energy. The second 552.07 keV transition de-excites the 3 member of the 4’ [404] band. The levels I++ = odd of the 3;’ [411] band are supported to a certain extent by the coincidence measurement. Apparently, the 4 member de-excites also to the 3 member of the +’ [41 l] band. Since the intensity of this 3 state branches off to several transitions it is difficult to observe clear coincidences. The 84.45 keV transition were assigned between the 3 and 3 members of the +‘[411] band without contradictions to the experimental facts. The relative small separation of both these members compared to that in other nuclei 2, “) is explained by t h e C oriolis coupling with the members of the close-lying 3’ [41 l] band (see subsect. 4.2).
‘=Ho
ROTATIONAL
The rotational levels with the spin 8, Jg, J$ and y found on the basis of the coincidences data. Assuming of *61Ho [ref. ‘)I and ’ 67Tm [ref. “)I we looked for members of the +- [541] band and found transitions namely proper energy and intensity values, no strong ties in the (p, n) reaction. 3.2. DECAY
SCHEME
55-r
BANDS
of the &- [541] band were also this band to be similar to that the position of the $, 3 and 3 with the expected behaviour, coincidences and large intensi-
163Er(EC)163Ho
The decay scheme of 163Er to the ’ 63Ho levels is shown in fig. 6. The main features of this scheme have already been known from our former work “). Two levels ten‘gErsS(75 min) / 0.06
52
O.OL
70
_‘__
x-Vibr.
7/2+'lLOLl
7l2'
t:9:5
Y2* -
312'ILlll
3Q2.i 36O.L
3/2.
307.5 297.6
-m---
912-
7Kl5233
1.1 set
100-0 0
E,(keV)
99.8 I,&%)
:.a log ft
Fig. 6. Decay scheme of le3Er(EC) 163H~. The assignment of transitions marked by full dots is supported by the coincidence measurement. Energies are given in keV, total intensities per lo4 decays. The multipolarities of transitions are taken from ref. 13).
tatively introduced in ref. rl) were not confirmed. Additional information has been obtained on the population of members of the 4’ [411] band. As the transitions deexciting the 3 and 3 members of the 4’ band could not be observed the energies of these states were taken from the reaction results given in fig. 5. The 3 member at 431.2 keV is confirmed by the coincidence pair 431.2-444.8 keV. The branching ratios of the transitions de-populating this $ state are within the errors the same as obtained from the in-beam experiments. The assignments 5- [532] and 5’ [413] as main components of the levels at 1113.5 keV and 876.0 keV, respectively, are suggested by the excitation j2) and de-excitation
588
L. FUNKE et al.
modes of these levels. The 876.0 keV level de-populates to the 5’ [404] level and to the first four members of the 3’ 141l] band in a similar way as the 3; [413] state ‘*) in ’ 65Ho. The preferred branching to the 3 member of the 4’ band in 163H~ can be explained by a small admixture of the $‘[404] configuration (strongly populated from the state 5’ [413]) in the level I, K” = S, 3’. A detailed discussion of this coupling is presented in subsect. 4.3. From the comparison with the neighbouring Ho isotopes 3W18)the y-vibrational level built on the ground state con~~Iration is expected near 600 keV. The 614.3 keV transition found in the decay as well as in the reactions is probably de-exciting this vibrational state. The 253.9 keV transition might be the transition to the 3’[411] band head. Recent calculations 20) on the basis of the microscopic theory predict this vibrational state to be at 1015 keV. 4. Discussion 4.1. QUASIPARTICLE
EXCITATIONS
As a result of our experiments several levels with predominant quasiparticle structure were found in l(j3110 (see figs. 5 and 6) and 161Ho [refs. 2, “)I, A comparison of their excitation energies with those of the levels in the neighbouring isotopes 165H~ [ref. ’ “)I and ’ 5gHo [refs. “*‘“)] is given in fig. 7. On the right hand side of fig. 7 the experimental energies of the odd-proton system Z = 67 are shown. In order to distinguish particle and hole states they are plotted above or below the ground state, respectively. The considerable increase of the level density between the mass numbers A = 165 and 159 is noticeable. This effect can neither be explained by the quasipanicle-phonon interaction 20) nor by rotation-particle coupling. On the other hand different values of the energy gap A and of the deformation parameters s2 and eq might be responsible for this level compression. The theoretical energies calculated with the Nilsson model 23) including pairing corrections are given on the left-hand side of fig. 7. The chemical potential is assumed to be very near to the $- [523] orbital [ref. ’ 5)]. In order to show the influence of the parameters Q, .s2and A they have been changed in a direction as it is expected for decreasing mass number. As shown in the fig. 7c a larger gap parameter A gives a higher level density. However, the assumed change from 500 to 1000 keV is in disagreement with the gap values calculated 25) from the odd-even mass differences. These values are constant at about 900 keV for the treated odd-A holmium isotopes. The quadrupole deformation sZ is known 31) to decrease from 165H~ to 159H~ by about 0.02 and the hexadecapole deformation eq changes “) in the range of 0 (165H~) to -0.02 (‘5gHo). The figs. 7a and 7b show the influence of .sZand .s4on the energies of the orbitals _t- [541] and 3’ [404] to be large. Going from higher to smaller mass numbers the energy of the a- level is Iowered by the variation of &4and is raised by the variation of e2, but the 27 * level is lowered by changing all the parameters under discussion. This simple picture may explain the large decrease of the $‘[404] level
“=Ho
ROTATIONAL
589
BANDS
experiment
theory
Z-67
-I
712*
7/2+[LOLl
l/T
IF l/2'
1/2-
7/T[5231
7/2-15231
3/2* ~3,2*UllI
-c\5,2+[4,3 5/2+[L131
\
\
E, = 0.28 EL--o.02 E‘ = 0 A- 5OOkeV
-
5/2-
E, = 0.28 E, = 0.30 A=
@
-em_
S/2-15321
CL= 0 500 keV
@I
E, =0.28 EL= 0 A=lOOOkeV A= 5WkeV
(9
Fig. 7. Comparison of the experimental single-proton excitations in the Z = 67 system with model predictions. The quasi-particle energies displayed in (a), (b) and (c) were calculated using different values for the energy gap d as well as for the deformation parameters eZ and ~4.
with decreasing mass number and the relative constancy of the excitation energy of the +- [541] state in 163H~ and 161Ho, but the general tendency of the level compression is not completely understood. 4.2.
DESCRIPTION
OF
THE
ROTATIONAL
BANDS
bands built on the Nilsson states In 163H~ just as ‘) in 161Ho five rotational ;- [523], 3’ [404], 3’ [41 I], Ti+ [411] and +- [541] were found (see fig. 5). At first the Bohr-Mottelson formula 26) E(6 K) = E,(K)
+
Az(I+ 1) +EqZ(l+
1))2 + c(z(I+
1))3
+ (- 1)r+K[(z+K)!/(z-K)!](A~K+B2~z(z+
l)),
(1)
has been used to analyse the energies of these bands. The parameters A, B, A, and Bl or A, B, C and A,, were taken for fitting the energies of the bands with K = 4 or
L. FUNKE
590
et al.
TABLE 5 Rotational
parameters
and gyromagnetic
C
AK
&K
(l&j
(c”v,
(mev)
WV)
(eW
11.15
-0.3
-8.3
12.80 (15.63) (11.13) 9.89
-8.0 (-68) (4.3) -3.6
IP[m?,fl]
$- [523] $‘[404] 3’[411] t+]4111 +- ]5411
factors
of the bands
in 163H~ x2/f”)
0.11 x10-6 -1.0 x10-6 (4.0 X 10-q (-5.8) 26.00
(580)
(-6.5) -85
i(cwd/Qoi
9
levels b,
5
9(S to 9)
2 2400 1700 2
5G to $) 7(% to T)
$- [523] I”
Fitted
IO@ to V) 7(9 to Y) ‘)
-Y-
$ -
$-
.IZ2
Y-
z2
23Y-
0.111
0.116
0.110
0.122
0.130
0.133
(0.106)
8’
$+
?$ +
0.130
0.082
0.159
++[411] In
lb-SR)/QC, “) “) ‘) d,
9
4’
5 0.053
9’ 0.176
x2 per degree of freedom. Number and spin values of the levels used in the fit. Except the levels 5, 9, Aj and 9. The errors are typically of the order of 0.005 to 0.015.
K # 4, respectively. The results of the least-squares fits are summarized in table 5. (For comparison with the values of 16iHo see table 3 of ref. ‘)). The values x2 per degree of freedom given in column 7 show that the fit for the bands 3’ [41 l] and 3’ [41 l] is very bad. These bands can practically not be described by the above formula. An explicit Coriolis coupling calculation has to be carried out. The rotational bands s- [523], 3’ [411], 3’ [41 l] and 3’ [404] in 163H~ and also in 16iHo have been analysed in terms of the Nilsson model including quasiparticle corrections and Coriolis interaction “). The unperturbed bands are assumed to be describable by the formula E(Z) = E,(K)+AZ(Z+ The Coriolis M K,K+l
=
matrix elements
&
7
CjKCjK+l
l)+Z?(Z(Z+
between
J(j-K)(j+K+
l))‘+~,,A,(
-l)‘++(Z+f).
(2)
bands with K and K+ 1 read l)d(Z-K)(Z+K+
1)
where CjK are the coefficients of the Nilsson wave functions in the coupled basis. The strength factor RK,K+l allows one to vary the coupling strength between bands K and K+ 1. In all the coupling calculations the single-particle energies were evaluated,
le3Ho
ROTATIONAL
591
BANDS
if possible, from the experimental band head energies in a similar way as described in refs. ‘*““). F ur th er energy values and the wave functions of the single-particle con-
~~~~
~~~~
r-
,y2 1712 ,9i2 ,1/2’32
2~2
23/2
9/2 I
7l2+[LO11 _
13
r 13
I Ii2
13/2
1712
E/2
19/2 2”2
I ‘#2’!13Ll
--_._
--x_
‘5’tio
--*
12 Tii
--_
‘*-
¶!2
2712
2512
232
1112
1312
IV2
--__
--a
1712
1%
-;:--r.l 9'1
D .
Iv2
%-
SPIN
I
VALUE
(I’scale)
15/2
1712
-e
SPIN VALUE (I’scale)
lr$m;i;;:
,wT
0.05
0.05 i
I 0
13n
712
* 92
1lR
13/2
15/2
SPIN I;
:X2
f----iO 1912
7R
912
IliZ
IL 1312 1512 1712 19/Z 2112
SPIN I;
values are given by dots; Fig. 8. Coriolis coupling effects in 163H~ and 16iHo. The experimental values obtained from the Coriolis coupling calculations are connected by solid lines; dashed lines should only guide the eyes. The highest spin used in the fit is indicated by a vertical stroke. Furthermore the quantities of the fitted parameters were inserted in the figure.
592
L. FUNKE
et al.
figurations as well as the Coriolis matrix elements were obtained from the Nilsson model 23) using the parameters p = 0.625 (N = 4) p = 0.63 (N = S), K = 0.05, Ed = 0.3 and s.+ = 0. The gap parameter (corrected for blocking) has been taken from Soloviev ““) as being d.,,(Ho) = 700 keV. In fig. 8 the energies and intensities are analysed in order to show non-adiabatic effects. Using e.g. formula (2) the exhibited quantities [E(I)--E(I-1)]/21 (for K # 3 bands) and Q[E(lf2)+E(I-2)-2E(f)] (for K = 3 bands) should follow a smooth curve if they are plotted versus Z2. The fluctuations of the experimental values are assumed to be caused by the Coriolis interaction. The results of our Goriolis coupling calculations obtained by a fitting procedure and indicated in fig. 8 by solid lines reproduce the experimental values sufficiently well. The values of the rotational parameters A (indexed by the corresponding K quantum number) and B, the decoupling parameter a = Al/A and the strength factors RR,K+I of the Coriolis matrix elements which were handled in the least-squares fits as free parameters are inserted in fig. 8. The $- [523] ground state band of the Ho isotopes is known to be perturbed by Coriolis coupling with the other states arising from the h, subshell state, i.e. the $- [%O], $- [54i ], s- 15321,p- [514] and -$$- [505]. The interaction of all these states was included in our calculation. In order to get comparable results for 16rHo and “j3Ho only the levels up to spin -$l- were fitted. The experimental energy difference of the orbitals $- [532] and $- [523] has been taken to renormalize the energy scale of the Nilsson model [see ref. ‘)I. Thus the single-particle energies applied in this calculation are smaller in ’ 61Ho than in 163Ho. The rotational parameters A = &“/2$ and B assumed to be the same for all bands and the strength factors R,,% and R,,, were used in the fit as free parameters. Other strength factors are assumed to be R = 1. The results concerning the description of the $- [523] band in i61Ho agree with those obtained by Rensfelt et aE. ‘*) except for the somewhat different values of A and R R.K+ 1. The increasing perturbation of the $- [523] band with decreasing mass number is expressed by the differently strong fluctuations in the holmium isotopes [see fig. 8 and ref. 29)] and is caused by rising of the level density (shown in fig. 7) and of the rotational parameter A. Although the matrix element of Coriolis coupling between the bands -1”[41 I] and 3’ [411] is only about a tenth 18) of those reponsible for the coupling within the h+ shell a strong perturbation of both bands were observed in the holmium isotopes. This is caused by the small energy distance of the corresponding coupled states. The perturbation which is strongest expressed in the large energy displacements within the 3”’ band can sufficiently well be described by its coupling with only the +‘[4111 band (see fig. 8). For both bands the same B-value but different rotational parameters A were used in the fit. In the coupling matrix element the mean value of A were applied, It must be noted, that for both 163H~ and 16’Ho the experimental coupling matrix elements Mexp = R+,+MNilsson are 20-40 “/, larger than the Nilsson value. Further calculations including up to 6 additional states have shown the influence of
l’=Ho
ROTATIONAL
BANDS
593
these states on the level energies of the bands 3’ [41 I ] and 3’ [411] to be small. The transition probabilities, however, are sensitive to such weaker couplings as shown in subsect. 4.3. The $‘[404] band is shown in fig. 8 to behave differently in both Ho isotopes. Whereas the smooth curve of 16rHo is typical for an unperturbed band, the 163H~ curve represents small fluctuations. This perturbation is caused by a mixing with the levels of the &’ [411] band being very close in energy. The energies of the members of the 3’ band were fitted in a four-band Coriolis coupling calculation as described in subsect. 4.3. Although the f- [541] band is coupled with the s-[532] band as shown e.g. in refs. 7S8) t he o b served levels of this band can be well fitted by the Bohr-Mottelson formula (1). However, the high-lying level sequence (Z+f = even) which is most influenced by the Coriolis interaction was not found in the Ho isotopes. An analysis of the gyromagneti~ factors on the basis of the ratios of cascade (cc) to crossover (co) intensities Z,(cc)/Z,(co) has been performed using the adiabatic formula ’ (If l)(Z+K-
l)(Z-K-l)
2P(2Z-1)
_-I
1* (4)
The experimental values of (Se--g&/Q0 obtained for the 3- [523] band and the strongly perturbed 3’ [411] band in 163Ho are given in table 5. Whereas the values of the ground state band increase slightly with the spin, the values for the 3’ [41 I] band offer significant fluctuations as also shown in fig. 8. Then the ratios of cascade to crossover intensities of the 3’ [41 l] band were calculated using the mixed wave functions from the energy fit for determining the MI and E2 transition probabilities. The single-particle contributions in the E2 transitions were neglected. The quantities j(gK -gR)/QO] calculated with formula (4) using these theoretical cascade to crossover intensity ratios reproduce the experimental values fairly well, if the parameters Q, = 7b, g, = 0.4 and gIff = 0.5gF are used (fig. 8). The theoretical values increase for lower gR and/or larger gzff. Using the same parameters and a pure configuration a constant value of (gK -gR)/QO = 0. I6 for the 3’ [41 I] band is obtained. The interband transitions between the 3’ [411] and the if[41 l] bands can also be roughly reproduced by means of the mixed wave functions. 4.3. El TRANSITION
PROVABILITIES
As shown in figs. 5 and 6 several El interband transitions were observed in 163H~. Their reduced transition probabilities have been estimated “) by a comparison of the El intensities with the intraband E2 transition probabilities on the basis of the formula B(E2) = (5e2~16~)Q~(Z2~O~Z~)‘. Although within the 2’ [404] band of ’ 63Ho no E2 transitions could be found, from their intensity limits minimal values of the El transition probabilities of transitions connecting the 3’ [404] band with the i- [523]
L. FUNKE
594
et al.
TABLE 6
Comparison
of El transition probabilities
in 163H~ and 161Ho
163H~
lGIHo
Er WV)
B(E1) “) (e’ * b)
j$ (kev)
B(E1) “) (e* . b)
s,s-
439.9
J2!,Z + %,H$9 f; -+ Y, S3 ,z -+ %.S;,sH32Ifi +,B++ C,%-
588.0 622.5 658.9
(> 7 x10-y > 5x 10-7 2 5x10-6 89x10-6
252.7 412.2 452.6 489.2
z 7x10-6 3.3 x 10-e 4.4x10-6 5.9 x 10-e
431.2 552.1
2.5 x lo-’ 7x10-s
(353.2)
Ii, Kin + Ir, W
f, g -+
<2x10-9
“) These values have been evaluated from the branching ratios as described in the text.
ground state band were estimated. In table 6 some of these B(E1) values are compared with the values obtained “) for 161Ho. The El transitions between both $ bands are similarly fast, or even still faster, in 163H~ than in 161Ho. The experimental B(El) values were shown “) to be much larger than the Nilsson values. Nilsson retardation factors of about 0.02 to 0.03 had been estimated. The reason for this high transition probability is not yet clear. Most surprising in 163H~ are the strong K-forbidden (AK = 3) El transitions from the 3 (and q-) member of the +’ [41 l] band to the ground state band (corresponding transitions have not been found in ’ 61Ho). The occurrence of these transitions can be understood assuming a small admixture of the close-lying $‘[404] configuration in the wave functions of the members of the _t’ [41 l] band. Comparing the El transition probability of B(El,439.9 keV) > 7 x 10e6 e2 . b extrapolated from the other B(E1) values in 163H~ and 161Ho [see table 6 and ref. ‘)I with the value B(E1, 431.2 keV) = 2.5x 10v7 e2 . b an admixture of less than 3 % of the s’ [404] configuration in the Z_,t’ state was derived. A similar value is obtained from the intensity ratio of the transitions at 444.8 and 436.1 keV which populate both the 4’ levels from the $‘[413] state (see subsect. 3.2). In order to describe the observed mixing of states with AK = 3 a Coriolis coupling calculation of first order was performed [see also ref. ““)I. For the interesting spin values 3 and y the interaction matrix was diagonalized in the space of the Nilsson configurations +‘[411], +‘[411], $‘[413] and 4’ [404]. For the parameters A, B and a as well as R,,, the values obtained from the energy fit given in fig. 8 were used. The other coupling strength factors were assumed to be R,, 5 = R,, + = 1. As the coupling of the states under discussion is mainly caused by their small energy separation we examined their behaviour for approaching each other by varying the single-particle energy of the 3’ [404] orbital. The result concerning the mixing of the 3 states is given in fig. 9. The amplitude a;,$ of the admixed _5[404] configuration in the 3 member of the 3’ [41 l] band assumed to be responsible for the high El transition rate is plotted versus the energy separation of the mixed 3 states. The calculated value of the admixture (u~,~)’ at the experimental energy separation being approximately 1 ‘A is in gross
t-Ho
ROTATIONAL
BANDS
595
agreement with the experimental upper limit of 3 %. Our calculations yield a minimum of the energy separation of the mixed states (of about 1.5 keV) quite similar to the well-known case of a mixing of two states with d.K = 1. At this point the two Nilsson configurations are equally divided among both the mixed states, while the contributions of all the other configurations are much smaller. The value of the minimum separation depends mainly on the coupling strength.
exp. value
A E,2 &eV 1 Fig. 9. Mixing amplitude of the 5’ 14041 configuration in the wave function of the rotational level f, f+ [41 I] plotted as a function of the energy separation between both states. The curve resulted from a Coriolis coupling calculation including the bands 4’ [41 I], 2’ [411], g+ [413 J and $+ [404], if the single-particle energy of the $+ [404] state is varied.
5. conclusions Several non-adiabatic effects such as energy displacements and fluctuating gyromagnetic factors caused by the Coriolis force have been studied in 163H~ as well as in ’ 61Ho. Intense K-forbidden EI transitions between members of the band 3’ [41 l] and the $- 15231 ground state band in 163H~ are explained by an admixture of the $‘[404] con~guration in the members of the *‘[411] band. This case of Coriolis mixing of close-lying states differing in iK by several units 30) is investigated on the basis of first-order coupling. If levels with the same spin and parity but different K quantum number come very close in energy in every case a remarkable mixing can be expected. Furthermore, information concerning the single-particle model was obtained. The increasing level density in the holmium isotopes with decreasing mass number was tried to explain by a change of the energy gap and the deformation parameters. The high El transition probabilities of the interband transitions between the bands %‘[404] and f- [523] are in disagreement with the Nilsson values. This problem is still unsolved. We want to thank Dr. D. Netzband for careful reading of the manuscript and for several critical comments. We are very grateful to Mrs. J. Kerber, Mr. E. Will and Mr. K. Heidel for valuable help during the experiments. We are also indebted to the
596
L. FUNKE
et al.
staffs of the Rossendorf cyclotron and of the betatron at the Jena University. The support of this work by the Ministerium fiir Wissenschaft und Technik of the German Democratic Republic and by the Deutsche Akademie der Wissenschaften zu Berlin is gratefully acknowledged. References 1) G. Winter, L. Funke, K. H. Kaun, P. Kemnitz and H. Sodan, Phys. Lett. 33B (1970) 161; Nucl. Phys. Al76 (1971) 609 2) L. Funke, K. H. Kaun, P. Kemnitz, H. Sodan and G. Winter, Nucl. Phys. A170 (1971) 593 3) K. H. Kaun, L. Funke, P. Kemnitz, H. Sodan, G. Winter, E. Will, K. J. Gromov, S. M. Kamalchodjaev, W. G. Kalinnikov and H. Strusny, Nucl. Phys., to be published 4) L. Funke, K. H. Kaun, P. Kemnitz, H. Sodan and G. Winter, Proc. Conf. on nuclear spectroscopy and theory, Dubna, June, 1971; and annual report ZfK-223, 1971 5) G. Winter, L. Funke, K. Hohmuth, K. H. Kaun, P. Kemnitz and H. Sodan, Nucl. Phys. A151 (1970) 337 6) L. Funke, K. H. Kaun, P. Kemnitz, H. Sodan, G. Winter, R. Arlt, K. J. Gromov, S. M. Kamalchodjaev, A. F. Novgorodov, H. Strusny, D. de Frenne and E. Jacobs, Nucl. Phys. Al75 (1971) 101 7) P. Kemnitz, L. Funke, K. Hohmuth, K. H. Kaun, H. Sodan and G. Winter, Nucl. Phys. Al64 (1971) 513 8) P. Kemnitz, L. Funke, K. H. Kaun, H. Sodan and G. Winter, Proc. Conf. on nuclear spectroscopy and theory, Dubna, June 1971, p. 147; Nucl. Phys., to be published 9) P. Kemnitz, L. Funke, K. H. Kaun, H. Sodan and G. Winter, Proc. Conf. on nuclear spectroscopy and theory, Dubna, June, 1971, p. 153 10) C. L. Hammer and M. G. Stewart, Phys. Rev. 106 (1957) 1001 11) L. Funke, H. Graber, K. H. Kaun, H. Sodan and J. Frana, Nucl. Phys. 84 (1966) 471 12) L. Funke, H. Graber, K. H. Kaun and H. Sodan, ZfK-PhA 23, Rossendorf, 1966 13) R. Babadjanov, W. Butzev, K. J. Gromov, Sch. Schelev, W. Kalinnikov, J. Mareev, F. Michtasimov, U. Nasarov, Conf. on nuclear structure, Dubna, 1966 14) C. R. Gossett, L. A. Beach, L. R. Medsker and P. P. Singh, Bull. Am. Phys. Sot. 16 (1971) 539 15) 0. W. B. Schult, M. E. Bunker, D. W. Hafemeister, E. B. Shera, E. T. Jurney, J. W. Starner, A. Backlin, B. Fogelberg, U. Gruber, B. P. K. Maier, H. R. Koch, W. N. Shelton, M. Minor and R. K. Sheline, Phys. Rev. 154 (1967) 1146 16) T. Yamazaki, Nucl. Data A3 (1967) 1 17) S. Allam and H. J. Keller, Proc. Conf. on nuclear spectroscopy and theory, Dubna, June, 1971, p. 192 18) M. E. Bunker and C. W. Reich, Rev. Mod. Phys. 43 (1971) 348 19) L. Funke, W. Andrejtscheff, H. Graber, U. Hagemann, K. H. Kaun, P. Kemnitz, W. Meiling, H. Sodan, F. Stary and G. Winter, Nucl. Phys. A118 (1968) 97 20) V. G. Soloviev and S. I. Fedotov, JINR E4-6055, Dubna, 1971 21) A. A. Abdurazakov, Sch. Schelev, W. Kalinnikov, U. Nasarov and J. Urbanez, lzv. Akad. Nauk SSSR (ser. fiz.) 32 (1968) 781 22) J. S. Geiger, R. L. Graham and M. W. Johns, Bull. Am. Phys. Sot. 14 (1969) 1225 23) B. E. Chi, Nucl. Phys. 83 (1966) 97 24) V. G. Soloviev, Teorija sloschnich jader, (Izd. Nauka, Moscow, 1971) 25) W. Ogle, S. Wahlborn, R. Piepenbring and S. Fredrikson, Rev. Mod. Phys. 43 (1971) 424 26) 0. Nathan and S. G. Nilsson, in Alpha-, beta- and gamma-ray spectroscopy, ed. K. Siegbahn (North-Holland, Amsterdam, 1965) 27) A. K. Kerman, Mat. Fys. Medd. Dan. Vid. Selsk. 30 (1955) no. 15 28) K. G. Rensfelt, A. Johnson and S. A. Hjorth, Nucl. Phys. Al56 (1970) 529 29) R. M. Diamond, Proc. Int. Conf. on the properties of nuclei far from the region of beta-stability, Leysin, August, 1970 30) P. Kemnitz, L. Funke, K. H. Kaun, H. Sodan and G. Winter, Phys. Lett. 39B (1972) 179 31) K. E. G. Lobner, M. Vetter and V. Honig, Nucl. Data A7 (1970) 495