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Collective vibrational states in even erbium nuclei
1.E.4:
[
2.L._._]
Nuclear Physics A107 (1968) 3 8 5 ~ 0 1 ; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
COLLECTIVE VIBRATIONAL STATES IN EVEN E R B I U M NUCLEI P. O. T J O M t and B. E L B E K
The Niels Bohr Institute, University of Copenhagen, Denmark Received 2 October 1967 Abstract: The cross sections for inelastic scattering of 12 MeV deuterons f r o m all the even Er isotopes have been measured at 90 ° and 125 ° by means of a magnetic spectrograph. The 2 +' and 4 +' states in the g a m m a vibrational bands were observed in all nuclei, but only in a few cases the K : 0 fl-vibrations were observed. Several octupole vibrational states were identified in each nucleus below an excitation energy of approximately 2.3 MeV. The reduced transition probabilities B(E2) and B(E3) were determined from the observed inelastic cross sections.
E
NUCLEAR R E A C T I O N S 16~,1e~,16616s l~OEr(d ' d') Ea = 12.1 MeV; measured ~r(Ea,,O). 16~,le4,166,x6s,lV°Er deduced levels J, B(E2), B(E3). Enriched targets.
1. Introduction In some earlier investigations 1- 3), the inelastic scattering of 12 MeV deuterons was used for the identification of collective vibrational states in the Sm and Gd nuclei. The interpretations were based mainly on the absolute cross sections and on the ratio R between the 90 ° and the 125 ° cross sections. The B(E2) and B(E3) values were evaluated from the inelastic cross sections which were assumed to be proportional to the transition probabilities between the ground states and the excited states. In this work the even Er isotopes have been studied by the same methods.
2. Experimental methods Targets of all the stable even Er isotopes were bombarded by 12.1 MeV deuterons obtained from the Niels Bohr Institute tandem accelerator. The reaction products were analysed in a magnetic spectrograph at the angles 60 °, 90 ° and 125 °. Simultaneously with the (d, d') spectra, the (d, p) and (d, t) spectra from the same targets were recorded. These results will be reported separately 4). All the targets were prepared at the University of Aarhus isotope separator and had an isotopic purity of > 99 %. They contained small amounts of light impurities, mostly Na, Si, C1 and K or Ca, which in some cases did obscure small peaks in the spectra. The absolute inelastic cross sections were obtained in the same manner as described t On leave from the University o f Oslo, Norway. 385
386
P. O. TJ~iM AND B. ELBEK
earlier 1- 3). The values used for the sum of the elastic and inelastic 2 + cross section were 410 mb/sr at 60 °, 64 mb/sr at 90 ° and 15 mb/sr at 125°. Spectra for the five Er targets are shown in figs. 1-5. The level energies, which are the averages of the measurements at 90 ° and 125 °, and the cross sections are listed in EXCITATION ENERGY 2.5 '
I
'
'
'
=
[
(HEY)
1.5
2.0 ,
,
,,
I.,
*
1.0 ~-,,
0.5
I ' ' '
'
~
'
I
4+
162Er (d,d') Ed= 12.087 HeY e = 125*
350
0
I ' '
0+ m
300
250 E E 200 b.I 0,. (/) 150
3si ~- 100
o
i2-+)¢ ,+
11-)
cs_,
50
I
2
6+
(s-)
0
_
65
7O
75 DISTANCE ALONG
PLATE
80 (cm)
85
Fig. 1. Spectrum o f deuterons scattered f r o m 16~Er.
tables 1-5. These tables also contain the previously known energies and assignments and the level interpretation based on this work. 3. R e s u l t s and d i s c u s s i o n
The results presented here are part of a general survey of the collective states in the deformed nuclei. Much of the information obtained cannot be analysed in detail without supplementary measurements and the emphasis is therefore on the strong excitations of multipole type E2 or E3. In all nuclei, the data obtained thus far have revealed a strong quadrupole ex-
387
Er COLLECTIVE VIBRATIONAL STATES
citation to the gamma vibrational band, which is characterized by a strong excitation of the 2 +' and 4 +' states t. The cross section for the 2 +' state within the experimental errors is proportional to the B(E2) value between this state and the ground state in cases where this quantity is known. The cross section for the 4 +' state does not seem EXCITATION 2.5
2.0
IIII 350
I
ENERGY
1.5 ~
'
'
'
I
(HEY)
1.0 '
'
'
'
I
0.5 '
'
'
'
I
'
~+
I
~64Er(d,d') E d =12.089 HeY El =125"
30+
300
250 3-
E E 200 Si
W ca 150 (J
(3-'/'+)i
hi.-
4'+
100
50
0
60
65
70 75 DISTANCE ALONG PLATE (cm)
80
Fig. 2. Spectrum of deuterons scattered from 164Er.
to be related to that for the 2 +' state, which strongly suggests that the 4 +' state is excited partly by a direct E4 excitation from the ground state. Such excitations have earlier been discussed in connection with the inelastic scattering cross sections for the 4 + states in the ground state rotational band 14). The data on the K = 0 quadrupole excitations, which are often called beta vibrations, are more incomplete. Strong excitations of this type are generally found in the most neutron-deficient nuclei for a given element. The 0 +'', 2 +'' and 4 +'' states t In a n a l o g y to the earlier papers, we indicate the K~ = 2 + v i b r a t i o n by a single p r i m e a n d t he K~ -----0 ÷ excitations by a double prime.
388
1,. O . T J I ~ M A N D
B . ELBEK
seem to be populated with roughly equal intensity. Judged on the basis of the inelastic scattering cross sections, the K = 0 + bands are much less collective than the K = 2 + bands, and in several nuclei it has not been possible to locate this vibrational mode at all. EXCITATION ENERGY (HEY) 2.0 1.5 1.0
2.5 I
I
I
I
I
I
I
[
I
[
I
I
I
I
l
I
t ~-
0.5 I
0 I
I
I
I
166Er (d,d')
350
E~ = 12,084 O
i
FleV
= 125 °
250 ~-
2+
E E
/.+
200 -3-
c5 ILl [2. £/3 Y (D
150 ,+
<
,+
c~ I--
100
3-
6+
0
,
50
55 DISTANCE
60 ALONG PLATE
65
(cm)
Fig. 3. Spectrum o f deuterons scattered from lenEr.
Each of the erbium nuclei studied here possesses two or more levels for which a collective 3 - assignment is indicated. In the samarium 1,2) and gadolinium 3) nuclei studied earlier, a number of K s = 0 - octupole bands were observed. The 1 - and 5 states of the bands were populated there with an intensity approximately one order o f magnitude less than that of the 3- state. The lack of possible 1 - states of observable intensity for the lowest octupole bands in the erbium nuclei is taken as evidence for a K-quantum number different from 0 or 1. The ratio R of the 90 ° intensity to the 125 ° intensity has been of considerable assistance for the assignment of the multipolarity of excitation. For the well-established
Er
389
COLLECTIVE VIBRATIONAL STATES
octupole excitations in the erbium nuclei, this ratio is roughly 1.25, which is somewhat less than found for the samarium and gadolinium nuclei. A systematic decrease in R with increasing atomic weight is evident from the data available at the present time, but there are additional fluctuations in the R-values, the nature of which is not EXCITATION 2.5 '
350
ENERGY
2.0
I
'
'
'
'
l
(MeV)
1.5 '
'
'
'
I
1.0 [
'
'
'
I
0
0.5 '
'
'
'
I
,
I
r
I
i~+
16aEr (d. d" )
0+
Ed = 12.098 HeM 8
= 125°
I i
300
i i
250 E E m
I!
200
c~
3-
!
3-
LLI Q. O3
150
!
Si
(..)
<~ Q~
(3-
~-+)
6+
100
2+
fl
50
5O
55 DISTANCE
60 ALONG PLATE
65
70
(crn)
Fig. 4. Spectrum of deuterons scattered from 16aEr.
understood. The assignments of multipolarity, especially for the weaker transitions, must therefore be considered as tentative. However, for a survey work of the type presented here, the ease of the method probably outweighs its drawbacks. 3.1. T H E N U C L E U S Z6~Er
The only states known 5) in 162Er are the states in the ground state rotational band up to the 10 + state. In the present work, the ground state band is populated up to the 6 + state. The 2 +' and 4 +' states of the gamma vibrational band are found at 897 keV and 1124 keV, respectively. The assignments are readily made on the basis of the R-values
390
P. O. T J ~ M A N D B.
ELBEK
and the absolute cross sections. The intensity of the 4 +' group will be discussed in sect. 5. In the (d, d') spectra obtained for 162Er, there is evidence for a low-lying K = 0 band. The relatively strongly excited level at 1166 keV has an angular dependence in EXCITATION ENERGY (HEY) 2.0 1.5 1.0
2.5 i
350
I
I
''n''''*
I
'
t
'
l
I
'
0.5 l
l
I
l
0 '
'
'
'
l~0Er (d,d') E a = 12.11/, H e V 8 = 125 °
300
250 E E 200 (%1 n.," W fit. (,n ~C (j. < n," I.--
150 4+
loo Si 3-
50
•
3-
,~5-1 v
,
50
Fig.
]
2,+
I'+)
"÷
6+
(1
55 60 DISTANCE ALONG PLATE (cm) 5.
65
Spectrum of deuterons scattered from 17°Er.
agreement with a 2 + assignment. A corresponding 0 +'' state is expected approximately at the energy of 8 + rotational state (1090 keV). It should be noted that the group observed at 1081 keV is considerably stronger than expected for an 8 + rotational state. It is therefore likely that this group, at least in part, corresponds to a 0 +'' state. The 4 +'' state can then be responsible for the small deformity (1369 keY) on the high-energy side of the 3- group at 1351 keV. The first 3 - state is observed at 1351 keV with R = 1.16, which corresponds to the average for other E3 excitations in the Er and Yb isotopes. The large cross section shows that this 3 - state is strongly collective and, as the
Er COLLECTIVE VIBRATIONAL STATES
391
g r o u n d state b a n d i n d i c a t e s a w e l l - d e f o r m e d s h a p e f o r X62Er, o n e w o u l d e x p e c t to o b s e r v e a r o t a t i o n a l b a n d a s s o c i a t e d w i t h t h e o c t u p o l e e x c i t a t i o n . N o 1 - state o f s u c h a b a n d is o b s e r v e d b e l o w t h e 3 - state a n d K " = 0 - o r 1 - t h e r e f o r e seems to b e r u l e d out. O n t h e basis o f t h e e n e r g y s y s t e m a t i c s f o r o c t u p o l e b a n d s a n d t h e l i m i t e d TABLE 1
Levels populated in le~Er Energy (keV) 0 101 327 663 897 1081 1124 1166
1351 1369 1423 1464 1594 1616 1725 1740 1910 1955 1996 2033 2116 2288 2306 2332 2399 2444 2520 2553 2567 2618
Energy previous (keV) 0 101 327 662
(da/d.Q)aoo (dtr/d.Q)l~so
Ratio 90°/125 ° R
~b/sr)
Q~b/sr)
58800 5270 115 8 162 ~2 12 31 163
12300 2700 96 9 80 5 20 16 140 ~2 7 11 15 26 ~ 11 2 9 15
4.78 1.95 1.20 0.91 2.02 ~-,0.51 0.57 1.90 1.16
3 17 5 6 7 4 3 4 5 5
1.37 0.98
7 4 11 29 12 ~3 5 13 9 6 4 17 6
1 2 3
Assignment previous
present
0+ 2+ 4+ 6+
1.06 0.32 0.77 1.10 ~ 1.08 1.87 0.53 0.90
2 +t
(0 +'') 4 +'
(2 +'' ) 3(4 +'' ) (5-) (1-) 3-) (5-)
(3-, 4 +)
(3-, 4 +)
0.97
0.36 0.42 0.55
experimental material available on R-values and cross sections for 5-
states, w e
assign t h e level at 1464 k e V as the 5 - r o t a t i o n a l state in t h e o c t u p o l e b a n d . T h e n e x t 3 - state is o b s e r v e d at 1616 k e V w i t h an i n t e n s i t y o f a p p r o x i m a t e l y 20 o f t h a t o f t h e first 3 - state. It is t e m p t i n g t o assign t h e levels at 1594 k e V a n d 1725 k e V as t h e 1 - a n d 5 - states, respectively, o f t h e r o t a t i o n a l b a n d . T h e e n e r g i e s a n d Rv a l u e s a r e c o m p a t i b l e w i t h s u c h a n a s s i g n m e n t , b u t t h e a b s o l u t e cross s e c t i o n s a r e c o n s i d e r a b l y l a r g e r t h a n o b s e r v e d f o r the K = 0 a n d K = 1 o c t u p o l e b a n d s in t h e S m a n d G d isotopes.
392
v.o.
T J e M AND B. ELBEK
The relatively strong levels at 1955 keV and 2288 keV have R-values consistent with 3-
or 4 + assignments. TABLE 2 Levels p o p u l a t e d in 16~Er
Energy (keV) 0 91 299 614 858 1057 1313 1387 1433 1469 1482 1568 1631 1798 1952 1968 2000 2036 2067 2288 2337
Energy previous (keV) 0 91.3 299.2 613.8 858 1056 1308
1466
(da/dO)ooo (~ub/sr) 58200 5740 106 10 163 24
114 4 20 50 ~2 ~2 7 14 13 4 7 15 9
Ratio 90°/125 ° R
(do/dJ2)xzso (~ub/sr) 12070 2930 102 11 68 37 3 7 94 6 10 ~39 3 4 9 13 15
4.84 1.96 1.04 0.96 2.40 0.65
1.22 0.71 2.00 1.27 ~0.67 ~0.50 0.75 1.06 0.86
19 7
~0.78 1.35
Assignment previous
present
0+
2+ 4+ 6+ 2 +'
2 +/
4 +'
4 +'
2+ 34+ (2 + ) 3(5-) (5-) (3-, 4 +) (3-, 4 +)
(3-, 4 +) (3-)
TABLE 3 Levels p o p u l a t e d in leeEr
Energy (keV) 0 81 265 544 786 956 1512 1662 1698 1719 1759 1901 1973 2238 2463
Energy previous (keV) 0 80.6 264.9 545 787 957 1516 1662 1716
(dtr/d-Q)90o (#b/sr) 57600 6400 83 10 134 41 85 4 5 40 8 8 13 25
(d~r/dO)12so (pb/sr) 12130 2870 86 15 45 48 74 7 6 30 10 9 8 20 7
Ratio 90°/125 ° R 4.74 2.23 0.97 0.68 2.90 0.85 1.15 0.65 0.79 1.33 0.80 0.89 1.56 1.25
Assignment previous
present
0+
2+ 4+ 6+ 2 +'
2 +r
4 +'
4 +t
31-
3-
3-
3-
Er COLLECTIVE VIBRATIONAL STATES
393
3.2. THE NUCLEUS le4Er
T h e levels o f the 164Er nucleus have been investigated with the 165Ho(p, 2n)164Er r e a c t i o n 6,7) by which the g r o u n d state b a n d was p o p u l a t e d u p to the 10 + state. In this work, the r o t a t i o n a l levels u p to the 6 + state are observed. T h e u p p e r limit for the 125 ° cross section o f the 8 + state is 2 pb/sr. The K ~ = 2 + b a n d has been observed before and the levels at 858 keV a n d 1057 keV c o r r e s p o n d to the previously k n o w n 2 +' a n d 4 +' states. TABLE 4 Levels populated in leSEr Energy (keV) 0 80 264 550 821 926 994 1189 1215 1261 1357 1428 1445 ~1538 1630 1733 1843 1910 2170 2228 2257 2274
Energy previous (keV) 0 79.8 264.1 548.7 821.2 928.3 994.7 1187 1354
(dtr/d~)a0o (~b/sr) 57800 6220 86 19 133 1 51 5 4 ~3 ~8 46 5
1541.6
1906
40 12 3 23 6 3 35 5
(dtr/df2)125o (pb/sr)
Ratio 90°/125° R
11860 3140 80 18 46 2 53 6 2 3 5 37 3 ~2
4.88 1.98 1.07 1.04 2.89 ~0.63 0.96 0.96 2.33 ~0.86 ~1.55 1.25 1.57
12 3 22 8 3 31 7
1.00 1.00 1.06 0.75 1.00 1.11 0.67
Assignment previous
present
0+
2+ 4+ 6+ 2 +'
2t+
8+
8+
4 +'
4 +'
33(3-) (3-, 4 +) (3-, 4+) 3+
A K = 0 b a n d with levels at 1308 keY (2+), 1466 keV (4 +) a n d 1703 keV (6 +) has been proposed earlier o n the basis of conversion electron spectra following the 165Ho(p, 2n) reaction 6). The energy of the 0 ÷ state calculated from the energies of the other states is ~ 1238 keV. A t this energy, the 125 ° (d, d ' ) spectrum has a relatively low background. It is therefore possible to give a n upper limit of 2 / a b / s r for the 125 ° cross section for p o p u l a t i o n of this state. C o r r e s p o n d i n g to the 2 + state proposed, there is a peak at 1313 keV in the 125 ° spectrum, b u t u n f o r t u n a t e l y a Si impurity g r o u p obscures this region of the 90 ° spectrum. It is therefore impossible to check the 2 + assignments, b u t the level at 1469 keV has a n intensity a n d a n g u l a r dependence in agreement with the 4 + assignment. It is thus seen that the (d, d') spectra
394
P . o . TJDM A N D B. ELBEK
do not give any strong support to the K = 0 band proposed from the (p, 2n) data. In fact, the failure to observe the 0 + state could indicate that the band in question does not have K ~ = 0 +, but perhaps K ~ = 2 +. TABLE 5
Levels p o p u l a t e d in ~7°Er Energy (keV) 0 79 261 541 880 931 959 1102 1122 1304 1335 1370 1399 1477 1539 1575 1709 1931 2019 2068 2112 2154 2190 2398 2606 2657 2719
Energy previous (keV)
(da/dO)9oo Q~b/sr)
(da/d~Q)lzso Ozb/sr)
0 79 261 542
57000 7000 77 11
930
91 6 19 7 ~16 ~25
11750 3250 101 22 ~3 45 2 ~25 15 12 29 9 10 2 3 42 3 26 4
3 49 ~2 33 6 9 3 17 16
7 10
10 7 4
Ratio 90°/125 °
R
Assignment
previous
4.85 2.15 0.76 0.51
0+
2.03 2.51 ~0.78 0.47 ~1.36 "~0.86
2 +'
present
2+ 4+ 6+ (0 +tt) 2 +'
(2+') 4 +'
(4 +" ) 3-
(4+)
1.60 1.15 ~0.67 1.23
(1-) 3(5-) 3-
1.72
The relatively strongly populated level 1482 keV seems to be a 2 + state, but it is not clear how this level is related to the other quadrupole excitations in this nucleus. The lowest 3 - state is found at 1433 keV. Unfortunately, the Si impurity group in the 90 ° spectrum obscures here a possible 1- state at 1387 keV which is observed at 125 °. The level at 1631 keV can be the 5- state of the rotational band. The estimated R-value and intensity are similar to those of other 5- states. The strongly excited level at 1568 keV is also given in a 3 - assignment. There is no clear evidence for a 1 state, but the 5 - member of the band could be at 1798 keV where there is a group with the expected cross section and angular dependence. The levels at 1968, 2000 and 2288 keV have R-values which indicate 3- or 4 + states, but we have no possibility of making definite assignments. The weakly populated level at 2337 keV is probably a 3 - level.
Er COLLECTIVE VIBRATIONAL STATES
395
3.3. THE NUCLEUS le~Er
The level scheme of 166Er has been extensively investigated by various techniques [refs. s - l o ) ] . In this work, the ground state band is observed up to the 6 + state. The 2 +', 3 +', 4 +' and 5 +' states of the gamma-vibrational band are known lO). We observe the 2 +' and 4 +' states at an energy of 786 keV and 956 keV, respectively. The 3 +' level at 860 keV is not populated in the (d, d') reaction for which the upper limit of the 125 ° cross section is 2 #b/sr. A 0 + state at 1460 keV has been observed in the decay 1i) of 166Ho, but the level is not observed in the decay i 0) of 166Tm which, however, might populate a corresponding 2 + state of a K ~ = 0 + band at 1530 keV. These levels are not observed in the present work and are therefore hardly connected with a collective fl-vibration. The strongly excited level at 1512 keV is the 3- state in a K ~ = 2 - band 10). The possible 2 - state at 1460 keV, as expected, is not populated in the (d, d') reaction. On the basis of the energies in the rotational band, the unobserved 5 - state is expected around 1680 keV. There is no peak at this energy in the spectrum. Possible 5states of the octupole band are found at 1662 keV and 1698 keV, but it is then necessary to accept considerable deviations from the rotational energy formula. The (d, d') data suggest a 3 - assignment for the level at 1719 keV, which has a cross section and an R-value of the same magnitude as the 3- states in the other Er nuclei. An associated 1- state could correspond to one of the levels at 1662 keV or 1698 keV discussed above, whereas the level at 1901 keV could be the 5 - state. A third possible 3-state observed is at an energy 2238 keV, but no rotational states of the band can be identified. A 3 - state at 1920 keV, which could have K ~ = 3 - , is observed in the decay 10) of 166Tin. In the (d, d') reaction, this state is not populated and it is therefore hardly the collective K ~ = 3 - state expected on the basis of the simplest theories. We can give an upper limit of 3/~b/sr for the 125 ° cross section, which corresponds to a B(E3) ____0.2 s.p.u. 3.4. THE NUCLEUS leSEr
The excited states of 16SEr have been studied from the decays li) of 16STm and 168Ho and by different reactions. The latest investigation is performed by means of the 167Er(n, y)16SEr reaction 12). The level scheme proposed includes the ground state rotational band, the K ~ = 2 + gamma-vibrational band and, in addition, several negative-parity states which are collected into two rotational bands with K ~ = 3 and K ~ = 4 +, respectively. In the present work, the rotational band is observed up to the 8 + state. The 2 +' and 4 +' states are found at 821 keV and 994 keV, respectively, in agreement with the earlier observations. Several unassigned weakly populated levels are observed in the region from 1189 keV to 1428 keV, but there is no positive evidence for ascribing any of these to a K ~ = 0 + band. The level at 1428 keV with R = 1.25 is a 3 - octupole vibrational level. N o groups
396
P.O.
T , / ~ M A N D B. E L B E K
corresponding to possible 1 - and 5- states are observed with certainty. The 5 - level can be obscured by the strong peak at 1630 keV which is not observed in the 90 ° spectrum because of a plate joint. The 1630 keV level has been suggested as 3 - on the basis of intensity only. Between 1630 keV and 2700 keV there is a number of rather strongly populated levels. This is in contrast to the 166Er case where the corresponding energy region contains only a few levels. The levels at 1773 keV and 1910 keV have R-values somewhat lower than the average for E3 excitations. These levels are possibly populated by direct E4 transitions from the ground state. For the 2257 keV state, 3- is the most probable assignment. In 168Er, a K s = 3 - band is known up to the spin 7 - level 12). The band head is at an energy of 1541 keV to which the weakly populated level at 1538 keV can COlrespond. The small cross section for this state indicates that this state is much less collective than the other 3 - states observed. 3.5. THE NUCLEUS tT°Er The ground state band is known up to the 6 + state, and a 2 +' state at 930 keV has been seen in Coulomb excitation 9). N o other excited states have been reported. In the (d, d') spectrum, the ground state band is observed up to the 6 + level. The level at 931 keV corresponds to the 2 +' state reported before 9). The levels at 1102 keV and 1122 keV have R-values equal to 0.8 and 0.47, respectively. One of these must be the 4 +' state. The 1102 keV level is pleferred for this assignment because the R and the cross section are in line with those for the 4 +' states in the other Er nuclei. No 3 ÷' state is observed. The groups at 880, 959 and 1102 keV could be the 0 ÷'', 2 +'' and 4 +" states of a lowlyingK ~ = 0 + band. Suchbands t3)have been identified in t6syb, 17°yb and t72yb. The level at 1304 keV is the first excited 3 - state in this nucleus. It is considerably weaker than the lowest 3 - states in the other Er nuclei. The next 3 - state is observed at 1575 keV, and the 1539 keV and 1709 keV levels are probably the 1 - and 5 - states of the associated rotational band. Finally, at 1931 keV, there is a relatively strongly populated level which also seems to be populated by an E3 excitation. The level at 1335 keV has R = 0.86, which indicates an E4 excitation. This state is perhaps analogous to the 4 + state observed at 1172 keV in 172yb by means of the (d, p), (d, t) and (d, d') reactions 13). The Nilsson states ½-[521] and ~-[521] are the ground states in 171yb and 173yb, respectively. The level at 1172 keV in 172yb is the 4 + member of a K ~ = 3 + band which mainly has the two-quasiparticle configuration ½- [521 ] + { - [512 ]. In the (d, d') reaction, this 4 ÷ state is strongly populated. In 17 OEr' the situation is similar, because the Nilsson states ½- [521 ] and ~ - [512 ] are also the ground states 4,8) of 169Er and 171Er, respectively. We therefore expect to see a 4 ÷ state in 17°Er with a similar configuration as in ~72yb. The state at 1335 keV in 17°Er has a cross section and an angular dependence which correspond well to those of the 1172 keV level in 172yb.
Er COLLECTIVE VIBRATIONAL STATES
397
4. Determination of reduced transition probabilities I n a n e a r l i e r p a p e r z), it was c o n c l u d e d that, w i t h i n t h e e x p e r i m e n t a l e r r o r , t h e i n e l a s t i c cross s e c t i o n s f o r E2 a n d E3 e x c i t a t i o n s in s a m a r i u m w e r e p r o p o r t i o n a l to t h e r e d u c e d t r a n s i t i o n p r o b a b i l i t i e s b e t w e e n t h e g r o u n d state a n d the 2 + o r 3 - state in q u e s t i o n . T h e p r e s e n t m a t e r i a l allows a s i m i l a r c o m p a r i s o n f o r t h e E r nuclei, b u t unfortunately
the n u m b e r
of accurately known
t r a n s i t i o n p r o b a b i l i t i e s are h e r e
rather limited. TABLE 6
Comparison of the 90 ° cross sections and B(E2) values for the first 2 + levels Isotope
(d~/d~Q)90 o (,ub/sr)
leZEr le4Er le6Er 168Er 17°Er
5270 5740 6400 6220 7000
B(E2) a)
dtr/d,Q B(E2)
4.89 5.20 5.78 5.80 5.53 Av.
1080 1100 1105 1080 1260 1125
The B(E2) values are in units ofe 2 X 10-48 cm 4. n) Ref. 15). TABLE 7 Reduced transition probabilities for gamma vibrations Isotope
X62Er 16~Er 168Er 16SEr 17°Er
Energy (keV)
(d~r/dO)90o Q = - 1 (#b/sO
897 858 786 821 931
160 160 131 131 90
B(E2) a)
0.18 0.21 0.17 0.10
da/dO B(E2)
923 643 788 930
B(E2)d, a'
B(E2) (s.p.u.)
0.185 0.185 0.152 0.152 0.105
7.1 7.1 5.8 5.8 4.0
The B(E2) values are in units of e~× 10-48 cm 4. The B(E2)d, d, have been derived from the (d, d') cross sections on the assumption that (da/dO)/B(E2) = 860. 1 B(E2)s.p.u./e 2 = 0.026 × l0 -4s cm 4. a) Ref. 9). A c o m p a r i s o n o f t h e 90 ° c r o s s section a n d t h e w e l l - k n o w n B ( E 2 ) v a l u e s f o r t h e first 2 + r o t a t i o n a l level is g i v e n in t a b l e 6. T h e cross section p e r B ( E 2 ) u n i t is a p p r o x i m a t e l y c o n s t a n t w i t h a n a v e r a g e v a l u e 1125 /~b/sr c o m p a r e d to t h e a v e r a g e v a l u e 1 0 7 3 / z b / s r f o r t h e G d nuclei. T h e s a m e c o m p a r i s o n is m a d e f o r t h e 2 +' states o f t h e g a m m a v i b r a t i o n , a n d the d a t a are c o l l e c t e d in t a b l e 7. T h e B ( E 2 ) v a l u e s are t a k e n f r o m ref. 9). T h e 90 ° c r o s s section, r e d u c e d to Q = - 1 M e V b y m e a n s o f fig. 8 in ref. 3), p e r B ( E 2 ) u n i t is 821 pb/sr. T h i s n u m b e r is l o w c o m p a r e d w i t h the v a l u e s o b t a i n e d f o r G d a n d S m n u c l e i
398
r. O. TJI~MANDB. ELBEK
[refs. 2, a)]. The C o u l o m b excitation data 9) were obtained u n d e r experimentally difficult conditions, a n d the systematical trends in the B(E2) values for g a m m a vibrations m a k e some of the e r b i u m results look suspiciously high. Better B(E2) values can perhaps be o b t a i n e d from the ratio (da/dog)/B(E2) = 860 (/tb/sr)e 2 x 10 -48 cm 4 which was o b t a i n e d by i n t e r p o l a t i o n from the inelastic cross section for the even isotopes of Sm, G d a n d T h a n d U. As a further check, the excitation probability (i.e. the ratio between inelastic a n d elastic scattering) was measured for the 2 +' state in 166Er by m e a n s of 16 MeV alpha particles. A t 90 °, this probability was f o u n d to be 1.08 x 10- 3. The b o m b a r d i n g energy is rather close to the height of the C o u l o m b TABLE 8 Reduced transition probabilities for 3- states Isotope
Level (keV)
"~Er
1351 1616
(dtr/cLQ)g0* Q= 0 ~b/sr)
B(E3)d,d'
B(E3) 4) (s.p.u.)
173 32
0.133 0.025
12 2.1
122 55 (17) (12)
0.094 0.042 (0.013) (0.09)
8.1 3.6 (1.1) (0.8)
l"Er
1433 1568 (1968) b) (2337)
l"Er
1512 1719 2238
92 46 33
0.071 0.035 0.025
6.1 3.0 2.2
aeSEr
1428 (1630) (1910) 2257
49 (45) (28) 47
0.038 (0.035) (0.022) 0.036
3.3 (3.0) (1.9) 3.1
170Er
1304 1575 1931
17 54 40
0.013 0.042 0.031
1.1 3.6 2.7
The B(E3) values are in units of e=x 10-72 cm6. The B(E3) values have been derived from the (d, d') cross sections on the assumption that (dtr/d.Q)/B(E3) = 1300 ~b/sr)/e~ × 10-72 cm6. a) B(E3)s.p.u./e2 = 1.16 × 10-7~ cm6. b) Parentheses indicate that the assignment is doubtful. barrier, b u t it seems that C o u l o m b excitation is still the d o m i n a n t reaction 2). If we assume pure C o u l o m b excitation, the observed probability corresponds to B(E2) = 0.15e2 x 10 -48 cm 4, which is in good agreement with the value determined from the (d, d') data in table 7. I n table 8 are listed the energies, the 90 ° cross sections reduced to Q = - 1 MeV, a n d the B(E3)d,d, values. The B(E3) values have been calculated from (d, d ' ) cross sections with the assumptions that (dtr/d~o)/B(E3) = 1300 (pb/sr)e2x 10 -72 cm 6. This value has been f o u n d by i n t e r p o l a t i o n in the same way as explained for the E2 excitations.
Er COLLECTIVE
VIBRATIONAL
399
STATES
It should be stressed that the fundamental data obtained here are the inelastic scattering cross sections and that the B(E2) values are based on a proportionality and a normalization, both of which have not been verified experimentally to very good accuracy. Additional measurements of B(E2) values by Coulomb excitation and extensive D W B A calculations are needed to improve the B(E2) values obtained from the inelastic deuteron scattering data.
5. Conclusions The data for the ground-state rotational bands supplement those obtained earlier 14). The population of the 2 + state is roughly proportional (cf. table 6) to the B(E2) for this state. The 4 + states have considerably lower cross sections than ob-
-f
- - T
. . . .
F ........
[
[
E r , 4 + GR. BAND
!
150
100
4 :=t Z
o lOO
I
[
I
I
166
168
.J
_
Er, 4 ' + y - BAND
0 162
164 NASS
170
NUNBER
Fig. 6. Cross sections for the 4 + state in the ground-state band and the 4 +' state in the g a m m a band.
served in the Gd nuclei, and at the same time, the R-values are reduced. These observations can be considered as additional evidence for a direct E4 component 1~) in the excitation of the rotational 4 + states in the beginning of the rare-earth region. In the Er isotopes, this component is then considerably weaker and the excitation of the 4 + state is probably mainly of multiple E2 nature, which could explain the lowering of the R-values. The cross sections for the 6 + rotational states are somewhat less
400
P. O. T J f l M A N D B. E L B E K
than those in the G d isotopes, but show a similar regular increase with neutron number. The mechanism o f the 6 ÷ excitations is not clear. The cross sections for the 2 +' states o f the g a m m a vibrations decrease with increasing neutron n u m b e r and thus reflect a reduction in the B(E2) value also evident from the earlier C o u l o m b excitation data 9). All the 4 ÷' states are strongly excited with a m a x i m u m in 166Er (fig. 6). The variation in the 4 ÷' cross section is not connected to the variation in the 2 ÷' cross sections, which rules out a simple multiple m o d e of excitation. It is more likely that the excitation is partly by a direct E4 transition from the g r o u n d state. In this connection it is noteworthy that the cross section for the 4 +' state in the g r o u n d state has a m i n i m u m where the 4 +' cross section has a m a x i m u m (fig. 6). T
2.0
T - - - - - I
t,
a:
--
I
--
~ - - - -
Er, RATIO 9o°/125.
• o
o
o •
1.0
I
Er
o •
__1
_]
t
__[___
FIRST 3SECOND 3 -
0.20
z O.lO m
I tt
t • 162
L
I __ I _ ~ . . . . . 166 168 170 MASS NUMBER
16/.
Fig. 7. Cross sections and R-values for the first and second excited 3- states. The R-values for the strongest states assigned as 3 - (cf. fig. 7) are remarkably constant, which, together with the systematic trends in the excitation energies and the B(E3) values, lends support to the correctness o f the assignments. As fig. 7 shows, the absolute transition probabilities for the lowest 3 - state are rapidly decreasing with increasing mass number, whereas the transition probabilities for the next 3 state are fairly constant. The present data give only little information about the Kq u a n t u m numbers o f the 3 - states observed. As mentioned in the discussion, no possible 1 - states have been observed in the lowest octupole bands, which is a strong
Er C O L L E C T I V E V I B R A T I O N A L
STATES
401
a r g u m e n t against K = 0 or 1. Indeed, in 166Er it is k n o w n 10) that the lowest octupole state observed here belongs to a K ~ = 2 - band. I n 166Er, this state appears to be very similar to the lowest octupole state in the other e r b i u m nuclei, which indicates a general K = 2 - assignment for the lowest 3 - state. The K - q u a n t u m n u m b e r s for the other 3 - states m u s t r e m a i n u n k n o w n until additional i n f o r m a t i o n is obtained. It should be m e n t i o n e d , however, that in 166Er a n d 168Er K = 3 - b a n d s are already k n o w n , b u t these are n o t collective according to the present data. The authors are pleased to t h a n k Mrs. A n n a Grete Jorgensen for efficient a n d accurate scanning of the n u m e r o u s photographic plates. One of us (P.O.T.) wants to t h a n k " N o r g e s Teknisk-Naturvitenskapelige Forskningsrgtd" for economic support.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15)
B. Zeidman, B. Elbek, B. Herskind and M. C. Olesen, Nuclear Physics 86 (1966) 471 E. Veje, B. Elbek, B. Herskind and M.C. Olesen, to be published R. Bloch, B. Elbek and P. O. Tjom, Nuclear Physics A91 (1967) 576 P. O. Tjom and B. Elbek, to be published H. Morinaga, Nuclear Physics 75 (1966) 385 R. Graetzer, G. B. Hagemann, K. A. Hagemann and B. Elbek, Nuclear Physics 76 (1966) l P. G. Hansen, O. B. Nielsen and R. K. Sheline, Nuclear Physics 12 (1959) 389 Nuclear Data Sheets, National Academy of Sciences, Washington, D.C. Y. Yoshizawa, B. Elbek, B. Herskind and M. C. Olesen, Nuclear Physics 73 (1965) 273 J. Zylicz, M. H. Jorgensen, O. B. Nielsen and O. Skilbreid, Nuclear Physics 81 (1966) 88 I. Marklund, B. van Nooijen and Z. Grabowski, Nuclear Physics 15 (1960) 533 H. Koch, Z. Phys. 192 (1966) 142 D. G. Burke and B. Elbek, Mat. Fys. Medd. Dan. Vid. Selsk. 36, No. 6 (1967) B. Elbek, M. Kregar and P. Vedelsby, Nuclear Physics 86 (1966) 385 P. H. Stelson and L. Grodzins, Nucl. Data 1 0965) 21
[
2.L._._]
Nuclear Physics A107 (1968) 3 8 5 ~ 0 1 ; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
COLLECTIVE VIBRATIONAL STATES IN EVEN E R B I U M NUCLEI P. O. T J O M t and B. E L B E K
The Niels Bohr Institute, University of Copenhagen, Denmark Received 2 October 1967 Abstract: The cross sections for inelastic scattering of 12 MeV deuterons f r o m all the even Er isotopes have been measured at 90 ° and 125 ° by means of a magnetic spectrograph. The 2 +' and 4 +' states in the g a m m a vibrational bands were observed in all nuclei, but only in a few cases the K : 0 fl-vibrations were observed. Several octupole vibrational states were identified in each nucleus below an excitation energy of approximately 2.3 MeV. The reduced transition probabilities B(E2) and B(E3) were determined from the observed inelastic cross sections.
E
NUCLEAR R E A C T I O N S 16~,1e~,16616s l~OEr(d ' d') Ea = 12.1 MeV; measured ~r(Ea,,O). 16~,le4,166,x6s,lV°Er deduced levels J, B(E2), B(E3). Enriched targets.
1. Introduction In some earlier investigations 1- 3), the inelastic scattering of 12 MeV deuterons was used for the identification of collective vibrational states in the Sm and Gd nuclei. The interpretations were based mainly on the absolute cross sections and on the ratio R between the 90 ° and the 125 ° cross sections. The B(E2) and B(E3) values were evaluated from the inelastic cross sections which were assumed to be proportional to the transition probabilities between the ground states and the excited states. In this work the even Er isotopes have been studied by the same methods.
2. Experimental methods Targets of all the stable even Er isotopes were bombarded by 12.1 MeV deuterons obtained from the Niels Bohr Institute tandem accelerator. The reaction products were analysed in a magnetic spectrograph at the angles 60 °, 90 ° and 125 °. Simultaneously with the (d, d') spectra, the (d, p) and (d, t) spectra from the same targets were recorded. These results will be reported separately 4). All the targets were prepared at the University of Aarhus isotope separator and had an isotopic purity of > 99 %. They contained small amounts of light impurities, mostly Na, Si, C1 and K or Ca, which in some cases did obscure small peaks in the spectra. The absolute inelastic cross sections were obtained in the same manner as described t On leave from the University o f Oslo, Norway. 385
386
P. O. TJ~iM AND B. ELBEK
earlier 1- 3). The values used for the sum of the elastic and inelastic 2 + cross section were 410 mb/sr at 60 °, 64 mb/sr at 90 ° and 15 mb/sr at 125°. Spectra for the five Er targets are shown in figs. 1-5. The level energies, which are the averages of the measurements at 90 ° and 125 °, and the cross sections are listed in EXCITATION ENERGY 2.5 '
I
'
'
'
=
[
(HEY)
1.5
2.0 ,
,
,,
I.,
*
1.0 ~-,,
0.5
I ' ' '
'
~
'
I
4+
162Er (d,d') Ed= 12.087 HeY e = 125*
350
0
I ' '
0+ m
300
250 E E 200 b.I 0,. (/) 150
3si ~- 100
o
i2-+)¢ ,+
11-)
cs_,
50
I
2
6+
(s-)
0
_
65
7O
75 DISTANCE ALONG
PLATE
80 (cm)
85
Fig. 1. Spectrum o f deuterons scattered f r o m 16~Er.
tables 1-5. These tables also contain the previously known energies and assignments and the level interpretation based on this work. 3. R e s u l t s and d i s c u s s i o n
The results presented here are part of a general survey of the collective states in the deformed nuclei. Much of the information obtained cannot be analysed in detail without supplementary measurements and the emphasis is therefore on the strong excitations of multipole type E2 or E3. In all nuclei, the data obtained thus far have revealed a strong quadrupole ex-
387
Er COLLECTIVE VIBRATIONAL STATES
citation to the gamma vibrational band, which is characterized by a strong excitation of the 2 +' and 4 +' states t. The cross section for the 2 +' state within the experimental errors is proportional to the B(E2) value between this state and the ground state in cases where this quantity is known. The cross section for the 4 +' state does not seem EXCITATION 2.5
2.0
IIII 350
I
ENERGY
1.5 ~
'
'
'
I
(HEY)
1.0 '
'
'
'
I
0.5 '
'
'
'
I
'
~+
I
~64Er(d,d') E d =12.089 HeY El =125"
30+
300
250 3-
E E 200 Si
W ca 150 (J
(3-'/'+)i
hi.-
4'+
100
50
0
60
65
70 75 DISTANCE ALONG PLATE (cm)
80
Fig. 2. Spectrum of deuterons scattered from 164Er.
to be related to that for the 2 +' state, which strongly suggests that the 4 +' state is excited partly by a direct E4 excitation from the ground state. Such excitations have earlier been discussed in connection with the inelastic scattering cross sections for the 4 + states in the ground state rotational band 14). The data on the K = 0 quadrupole excitations, which are often called beta vibrations, are more incomplete. Strong excitations of this type are generally found in the most neutron-deficient nuclei for a given element. The 0 +'', 2 +'' and 4 +'' states t In a n a l o g y to the earlier papers, we indicate the K~ = 2 + v i b r a t i o n by a single p r i m e a n d t he K~ -----0 ÷ excitations by a double prime.
388
1,. O . T J I ~ M A N D
B . ELBEK
seem to be populated with roughly equal intensity. Judged on the basis of the inelastic scattering cross sections, the K = 0 + bands are much less collective than the K = 2 + bands, and in several nuclei it has not been possible to locate this vibrational mode at all. EXCITATION ENERGY (HEY) 2.0 1.5 1.0
2.5 I
I
I
I
I
I
I
[
I
[
I
I
I
I
l
I
t ~-
0.5 I
0 I
I
I
I
166Er (d,d')
350
E~ = 12,084 O
i
FleV
= 125 °
250 ~-
2+
E E
/.+
200 -3-
c5 ILl [2. £/3 Y (D
150 ,+
<
,+
c~ I--
100
3-
6+
0
,
50
55 DISTANCE
60 ALONG PLATE
65
(cm)
Fig. 3. Spectrum o f deuterons scattered from lenEr.
Each of the erbium nuclei studied here possesses two or more levels for which a collective 3 - assignment is indicated. In the samarium 1,2) and gadolinium 3) nuclei studied earlier, a number of K s = 0 - octupole bands were observed. The 1 - and 5 states of the bands were populated there with an intensity approximately one order o f magnitude less than that of the 3- state. The lack of possible 1 - states of observable intensity for the lowest octupole bands in the erbium nuclei is taken as evidence for a K-quantum number different from 0 or 1. The ratio R of the 90 ° intensity to the 125 ° intensity has been of considerable assistance for the assignment of the multipolarity of excitation. For the well-established
Er
389
COLLECTIVE VIBRATIONAL STATES
octupole excitations in the erbium nuclei, this ratio is roughly 1.25, which is somewhat less than found for the samarium and gadolinium nuclei. A systematic decrease in R with increasing atomic weight is evident from the data available at the present time, but there are additional fluctuations in the R-values, the nature of which is not EXCITATION 2.5 '
350
ENERGY
2.0
I
'
'
'
'
l
(MeV)
1.5 '
'
'
'
I
1.0 [
'
'
'
I
0
0.5 '
'
'
'
I
,
I
r
I
i~+
16aEr (d. d" )
0+
Ed = 12.098 HeM 8
= 125°
I i
300
i i
250 E E m
I!
200
c~
3-
!
3-
LLI Q. O3
150
!
Si
(..)
<~ Q~
(3-
~-+)
6+
100
2+
fl
50
5O
55 DISTANCE
60 ALONG PLATE
65
70
(crn)
Fig. 4. Spectrum of deuterons scattered from 16aEr.
understood. The assignments of multipolarity, especially for the weaker transitions, must therefore be considered as tentative. However, for a survey work of the type presented here, the ease of the method probably outweighs its drawbacks. 3.1. T H E N U C L E U S Z6~Er
The only states known 5) in 162Er are the states in the ground state rotational band up to the 10 + state. In the present work, the ground state band is populated up to the 6 + state. The 2 +' and 4 +' states of the gamma vibrational band are found at 897 keV and 1124 keV, respectively. The assignments are readily made on the basis of the R-values
390
P. O. T J ~ M A N D B.
ELBEK
and the absolute cross sections. The intensity of the 4 +' group will be discussed in sect. 5. In the (d, d') spectra obtained for 162Er, there is evidence for a low-lying K = 0 band. The relatively strongly excited level at 1166 keV has an angular dependence in EXCITATION ENERGY (HEY) 2.0 1.5 1.0
2.5 i
350
I
I
''n''''*
I
'
t
'
l
I
'
0.5 l
l
I
l
0 '
'
'
'
l~0Er (d,d') E a = 12.11/, H e V 8 = 125 °
300
250 E E 200 (%1 n.," W fit. (,n ~C (j. < n," I.--
150 4+
loo Si 3-
50
•
3-
,~5-1 v
,
50
Fig.
]
2,+
I'+)
"÷
6+
(1
55 60 DISTANCE ALONG PLATE (cm) 5.
65
Spectrum of deuterons scattered from 17°Er.
agreement with a 2 + assignment. A corresponding 0 +'' state is expected approximately at the energy of 8 + rotational state (1090 keV). It should be noted that the group observed at 1081 keV is considerably stronger than expected for an 8 + rotational state. It is therefore likely that this group, at least in part, corresponds to a 0 +'' state. The 4 +'' state can then be responsible for the small deformity (1369 keY) on the high-energy side of the 3- group at 1351 keV. The first 3 - state is observed at 1351 keV with R = 1.16, which corresponds to the average for other E3 excitations in the Er and Yb isotopes. The large cross section shows that this 3 - state is strongly collective and, as the
Er COLLECTIVE VIBRATIONAL STATES
391
g r o u n d state b a n d i n d i c a t e s a w e l l - d e f o r m e d s h a p e f o r X62Er, o n e w o u l d e x p e c t to o b s e r v e a r o t a t i o n a l b a n d a s s o c i a t e d w i t h t h e o c t u p o l e e x c i t a t i o n . N o 1 - state o f s u c h a b a n d is o b s e r v e d b e l o w t h e 3 - state a n d K " = 0 - o r 1 - t h e r e f o r e seems to b e r u l e d out. O n t h e basis o f t h e e n e r g y s y s t e m a t i c s f o r o c t u p o l e b a n d s a n d t h e l i m i t e d TABLE 1
Levels populated in le~Er Energy (keV) 0 101 327 663 897 1081 1124 1166
1351 1369 1423 1464 1594 1616 1725 1740 1910 1955 1996 2033 2116 2288 2306 2332 2399 2444 2520 2553 2567 2618
Energy previous (keV) 0 101 327 662
(da/d.Q)aoo (dtr/d.Q)l~so
Ratio 90°/125 ° R
~b/sr)
Q~b/sr)
58800 5270 115 8 162 ~2 12 31 163
12300 2700 96 9 80 5 20 16 140 ~2 7 11 15 26 ~ 11 2 9 15
4.78 1.95 1.20 0.91 2.02 ~-,0.51 0.57 1.90 1.16
3 17 5 6 7 4 3 4 5 5
1.37 0.98
7 4 11 29 12 ~3 5 13 9 6 4 17 6
1 2 3
Assignment previous
present
0+ 2+ 4+ 6+
1.06 0.32 0.77 1.10 ~ 1.08 1.87 0.53 0.90
2 +t
(0 +'') 4 +'
(2 +'' ) 3(4 +'' ) (5-) (1-) 3-) (5-)
(3-, 4 +)
(3-, 4 +)
0.97
0.36 0.42 0.55
experimental material available on R-values and cross sections for 5-
states, w e
assign t h e level at 1464 k e V as the 5 - r o t a t i o n a l state in t h e o c t u p o l e b a n d . T h e n e x t 3 - state is o b s e r v e d at 1616 k e V w i t h an i n t e n s i t y o f a p p r o x i m a t e l y 20 o f t h a t o f t h e first 3 - state. It is t e m p t i n g t o assign t h e levels at 1594 k e V a n d 1725 k e V as t h e 1 - a n d 5 - states, respectively, o f t h e r o t a t i o n a l b a n d . T h e e n e r g i e s a n d Rv a l u e s a r e c o m p a t i b l e w i t h s u c h a n a s s i g n m e n t , b u t t h e a b s o l u t e cross s e c t i o n s a r e c o n s i d e r a b l y l a r g e r t h a n o b s e r v e d f o r the K = 0 a n d K = 1 o c t u p o l e b a n d s in t h e S m a n d G d isotopes.
392
v.o.
T J e M AND B. ELBEK
The relatively strong levels at 1955 keV and 2288 keV have R-values consistent with 3-
or 4 + assignments. TABLE 2 Levels p o p u l a t e d in 16~Er
Energy (keV) 0 91 299 614 858 1057 1313 1387 1433 1469 1482 1568 1631 1798 1952 1968 2000 2036 2067 2288 2337
Energy previous (keV) 0 91.3 299.2 613.8 858 1056 1308
1466
(da/dO)ooo (~ub/sr) 58200 5740 106 10 163 24
114 4 20 50 ~2 ~2 7 14 13 4 7 15 9
Ratio 90°/125 ° R
(do/dJ2)xzso (~ub/sr) 12070 2930 102 11 68 37 3 7 94 6 10 ~39 3 4 9 13 15
4.84 1.96 1.04 0.96 2.40 0.65
1.22 0.71 2.00 1.27 ~0.67 ~0.50 0.75 1.06 0.86
19 7
~0.78 1.35
Assignment previous
present
0+
2+ 4+ 6+ 2 +'
2 +/
4 +'
4 +'
2+ 34+ (2 + ) 3(5-) (5-) (3-, 4 +) (3-, 4 +)
(3-, 4 +) (3-)
TABLE 3 Levels p o p u l a t e d in leeEr
Energy (keV) 0 81 265 544 786 956 1512 1662 1698 1719 1759 1901 1973 2238 2463
Energy previous (keV) 0 80.6 264.9 545 787 957 1516 1662 1716
(dtr/d-Q)90o (#b/sr) 57600 6400 83 10 134 41 85 4 5 40 8 8 13 25
(d~r/dO)12so (pb/sr) 12130 2870 86 15 45 48 74 7 6 30 10 9 8 20 7
Ratio 90°/125 ° R 4.74 2.23 0.97 0.68 2.90 0.85 1.15 0.65 0.79 1.33 0.80 0.89 1.56 1.25
Assignment previous
present
0+
2+ 4+ 6+ 2 +'
2 +r
4 +'
4 +t
31-
3-
3-
3-
Er COLLECTIVE VIBRATIONAL STATES
393
3.2. THE NUCLEUS le4Er
T h e levels o f the 164Er nucleus have been investigated with the 165Ho(p, 2n)164Er r e a c t i o n 6,7) by which the g r o u n d state b a n d was p o p u l a t e d u p to the 10 + state. In this work, the r o t a t i o n a l levels u p to the 6 + state are observed. T h e u p p e r limit for the 125 ° cross section o f the 8 + state is 2 pb/sr. The K ~ = 2 + b a n d has been observed before and the levels at 858 keV a n d 1057 keV c o r r e s p o n d to the previously k n o w n 2 +' a n d 4 +' states. TABLE 4 Levels populated in leSEr Energy (keV) 0 80 264 550 821 926 994 1189 1215 1261 1357 1428 1445 ~1538 1630 1733 1843 1910 2170 2228 2257 2274
Energy previous (keV) 0 79.8 264.1 548.7 821.2 928.3 994.7 1187 1354
(dtr/d~)a0o (~b/sr) 57800 6220 86 19 133 1 51 5 4 ~3 ~8 46 5
1541.6
1906
40 12 3 23 6 3 35 5
(dtr/df2)125o (pb/sr)
Ratio 90°/125° R
11860 3140 80 18 46 2 53 6 2 3 5 37 3 ~2
4.88 1.98 1.07 1.04 2.89 ~0.63 0.96 0.96 2.33 ~0.86 ~1.55 1.25 1.57
12 3 22 8 3 31 7
1.00 1.00 1.06 0.75 1.00 1.11 0.67
Assignment previous
present
0+
2+ 4+ 6+ 2 +'
2t+
8+
8+
4 +'
4 +'
33(3-) (3-, 4 +) (3-, 4+) 3+
A K = 0 b a n d with levels at 1308 keY (2+), 1466 keV (4 +) a n d 1703 keV (6 +) has been proposed earlier o n the basis of conversion electron spectra following the 165Ho(p, 2n) reaction 6). The energy of the 0 ÷ state calculated from the energies of the other states is ~ 1238 keV. A t this energy, the 125 ° (d, d ' ) spectrum has a relatively low background. It is therefore possible to give a n upper limit of 2 / a b / s r for the 125 ° cross section for p o p u l a t i o n of this state. C o r r e s p o n d i n g to the 2 + state proposed, there is a peak at 1313 keV in the 125 ° spectrum, b u t u n f o r t u n a t e l y a Si impurity g r o u p obscures this region of the 90 ° spectrum. It is therefore impossible to check the 2 + assignments, b u t the level at 1469 keV has a n intensity a n d a n g u l a r dependence in agreement with the 4 + assignment. It is thus seen that the (d, d') spectra
394
P . o . TJDM A N D B. ELBEK
do not give any strong support to the K = 0 band proposed from the (p, 2n) data. In fact, the failure to observe the 0 + state could indicate that the band in question does not have K ~ = 0 +, but perhaps K ~ = 2 +. TABLE 5
Levels p o p u l a t e d in ~7°Er Energy (keV) 0 79 261 541 880 931 959 1102 1122 1304 1335 1370 1399 1477 1539 1575 1709 1931 2019 2068 2112 2154 2190 2398 2606 2657 2719
Energy previous (keV)
(da/dO)9oo Q~b/sr)
(da/d~Q)lzso Ozb/sr)
0 79 261 542
57000 7000 77 11
930
91 6 19 7 ~16 ~25
11750 3250 101 22 ~3 45 2 ~25 15 12 29 9 10 2 3 42 3 26 4
3 49 ~2 33 6 9 3 17 16
7 10
10 7 4
Ratio 90°/125 °
R
Assignment
previous
4.85 2.15 0.76 0.51
0+
2.03 2.51 ~0.78 0.47 ~1.36 "~0.86
2 +'
present
2+ 4+ 6+ (0 +tt) 2 +'
(2+') 4 +'
(4 +" ) 3-
(4+)
1.60 1.15 ~0.67 1.23
(1-) 3(5-) 3-
1.72
The relatively strongly populated level 1482 keV seems to be a 2 + state, but it is not clear how this level is related to the other quadrupole excitations in this nucleus. The lowest 3 - state is found at 1433 keV. Unfortunately, the Si impurity group in the 90 ° spectrum obscures here a possible 1- state at 1387 keV which is observed at 125 °. The level at 1631 keV can be the 5- state of the rotational band. The estimated R-value and intensity are similar to those of other 5- states. The strongly excited level at 1568 keV is also given in a 3 - assignment. There is no clear evidence for a 1 state, but the 5 - member of the band could be at 1798 keV where there is a group with the expected cross section and angular dependence. The levels at 1968, 2000 and 2288 keV have R-values which indicate 3- or 4 + states, but we have no possibility of making definite assignments. The weakly populated level at 2337 keV is probably a 3 - level.
Er COLLECTIVE VIBRATIONAL STATES
395
3.3. THE NUCLEUS le~Er
The level scheme of 166Er has been extensively investigated by various techniques [refs. s - l o ) ] . In this work, the ground state band is observed up to the 6 + state. The 2 +', 3 +', 4 +' and 5 +' states of the gamma-vibrational band are known lO). We observe the 2 +' and 4 +' states at an energy of 786 keV and 956 keV, respectively. The 3 +' level at 860 keV is not populated in the (d, d') reaction for which the upper limit of the 125 ° cross section is 2 #b/sr. A 0 + state at 1460 keV has been observed in the decay 1i) of 166Ho, but the level is not observed in the decay i 0) of 166Tm which, however, might populate a corresponding 2 + state of a K ~ = 0 + band at 1530 keV. These levels are not observed in the present work and are therefore hardly connected with a collective fl-vibration. The strongly excited level at 1512 keV is the 3- state in a K ~ = 2 - band 10). The possible 2 - state at 1460 keV, as expected, is not populated in the (d, d') reaction. On the basis of the energies in the rotational band, the unobserved 5 - state is expected around 1680 keV. There is no peak at this energy in the spectrum. Possible 5states of the octupole band are found at 1662 keV and 1698 keV, but it is then necessary to accept considerable deviations from the rotational energy formula. The (d, d') data suggest a 3 - assignment for the level at 1719 keV, which has a cross section and an R-value of the same magnitude as the 3- states in the other Er nuclei. An associated 1- state could correspond to one of the levels at 1662 keV or 1698 keV discussed above, whereas the level at 1901 keV could be the 5 - state. A third possible 3-state observed is at an energy 2238 keV, but no rotational states of the band can be identified. A 3 - state at 1920 keV, which could have K ~ = 3 - , is observed in the decay 10) of 166Tin. In the (d, d') reaction, this state is not populated and it is therefore hardly the collective K ~ = 3 - state expected on the basis of the simplest theories. We can give an upper limit of 3/~b/sr for the 125 ° cross section, which corresponds to a B(E3) ____0.2 s.p.u. 3.4. THE NUCLEUS leSEr
The excited states of 16SEr have been studied from the decays li) of 16STm and 168Ho and by different reactions. The latest investigation is performed by means of the 167Er(n, y)16SEr reaction 12). The level scheme proposed includes the ground state rotational band, the K ~ = 2 + gamma-vibrational band and, in addition, several negative-parity states which are collected into two rotational bands with K ~ = 3 and K ~ = 4 +, respectively. In the present work, the rotational band is observed up to the 8 + state. The 2 +' and 4 +' states are found at 821 keV and 994 keV, respectively, in agreement with the earlier observations. Several unassigned weakly populated levels are observed in the region from 1189 keV to 1428 keV, but there is no positive evidence for ascribing any of these to a K ~ = 0 + band. The level at 1428 keV with R = 1.25 is a 3 - octupole vibrational level. N o groups
396
P.O.
T , / ~ M A N D B. E L B E K
corresponding to possible 1 - and 5- states are observed with certainty. The 5 - level can be obscured by the strong peak at 1630 keV which is not observed in the 90 ° spectrum because of a plate joint. The 1630 keV level has been suggested as 3 - on the basis of intensity only. Between 1630 keV and 2700 keV there is a number of rather strongly populated levels. This is in contrast to the 166Er case where the corresponding energy region contains only a few levels. The levels at 1773 keV and 1910 keV have R-values somewhat lower than the average for E3 excitations. These levels are possibly populated by direct E4 transitions from the ground state. For the 2257 keV state, 3- is the most probable assignment. In 168Er, a K s = 3 - band is known up to the spin 7 - level 12). The band head is at an energy of 1541 keV to which the weakly populated level at 1538 keV can COlrespond. The small cross section for this state indicates that this state is much less collective than the other 3 - states observed. 3.5. THE NUCLEUS tT°Er The ground state band is known up to the 6 + state, and a 2 +' state at 930 keV has been seen in Coulomb excitation 9). N o other excited states have been reported. In the (d, d') spectrum, the ground state band is observed up to the 6 + level. The level at 931 keV corresponds to the 2 +' state reported before 9). The levels at 1102 keV and 1122 keV have R-values equal to 0.8 and 0.47, respectively. One of these must be the 4 +' state. The 1102 keV level is pleferred for this assignment because the R and the cross section are in line with those for the 4 +' states in the other Er nuclei. No 3 ÷' state is observed. The groups at 880, 959 and 1102 keV could be the 0 ÷'', 2 +'' and 4 +" states of a lowlyingK ~ = 0 + band. Suchbands t3)have been identified in t6syb, 17°yb and t72yb. The level at 1304 keV is the first excited 3 - state in this nucleus. It is considerably weaker than the lowest 3 - states in the other Er nuclei. The next 3 - state is observed at 1575 keV, and the 1539 keV and 1709 keV levels are probably the 1 - and 5 - states of the associated rotational band. Finally, at 1931 keV, there is a relatively strongly populated level which also seems to be populated by an E3 excitation. The level at 1335 keV has R = 0.86, which indicates an E4 excitation. This state is perhaps analogous to the 4 + state observed at 1172 keV in 172yb by means of the (d, p), (d, t) and (d, d') reactions 13). The Nilsson states ½-[521] and ~-[521] are the ground states in 171yb and 173yb, respectively. The level at 1172 keV in 172yb is the 4 + member of a K ~ = 3 + band which mainly has the two-quasiparticle configuration ½- [521 ] + { - [512 ]. In the (d, d') reaction, this 4 ÷ state is strongly populated. In 17 OEr' the situation is similar, because the Nilsson states ½- [521 ] and ~ - [512 ] are also the ground states 4,8) of 169Er and 171Er, respectively. We therefore expect to see a 4 ÷ state in 17°Er with a similar configuration as in ~72yb. The state at 1335 keV in 17°Er has a cross section and an angular dependence which correspond well to those of the 1172 keV level in 172yb.
Er COLLECTIVE VIBRATIONAL STATES
397
4. Determination of reduced transition probabilities I n a n e a r l i e r p a p e r z), it was c o n c l u d e d that, w i t h i n t h e e x p e r i m e n t a l e r r o r , t h e i n e l a s t i c cross s e c t i o n s f o r E2 a n d E3 e x c i t a t i o n s in s a m a r i u m w e r e p r o p o r t i o n a l to t h e r e d u c e d t r a n s i t i o n p r o b a b i l i t i e s b e t w e e n t h e g r o u n d state a n d the 2 + o r 3 - state in q u e s t i o n . T h e p r e s e n t m a t e r i a l allows a s i m i l a r c o m p a r i s o n f o r t h e E r nuclei, b u t unfortunately
the n u m b e r
of accurately known
t r a n s i t i o n p r o b a b i l i t i e s are h e r e
rather limited. TABLE 6
Comparison of the 90 ° cross sections and B(E2) values for the first 2 + levels Isotope
(d~/d~Q)90 o (,ub/sr)
leZEr le4Er le6Er 168Er 17°Er
5270 5740 6400 6220 7000
B(E2) a)
dtr/d,Q B(E2)
4.89 5.20 5.78 5.80 5.53 Av.
1080 1100 1105 1080 1260 1125
The B(E2) values are in units ofe 2 X 10-48 cm 4. n) Ref. 15). TABLE 7 Reduced transition probabilities for gamma vibrations Isotope
X62Er 16~Er 168Er 16SEr 17°Er
Energy (keV)
(d~r/dO)90o Q = - 1 (#b/sO
897 858 786 821 931
160 160 131 131 90
B(E2) a)
0.18 0.21 0.17 0.10
da/dO B(E2)
923 643 788 930
B(E2)d, a'
B(E2) (s.p.u.)
0.185 0.185 0.152 0.152 0.105
7.1 7.1 5.8 5.8 4.0
The B(E2) values are in units of e~× 10-48 cm 4. The B(E2)d, d, have been derived from the (d, d') cross sections on the assumption that (da/dO)/B(E2) = 860. 1 B(E2)s.p.u./e 2 = 0.026 × l0 -4s cm 4. a) Ref. 9). A c o m p a r i s o n o f t h e 90 ° c r o s s section a n d t h e w e l l - k n o w n B ( E 2 ) v a l u e s f o r t h e first 2 + r o t a t i o n a l level is g i v e n in t a b l e 6. T h e cross section p e r B ( E 2 ) u n i t is a p p r o x i m a t e l y c o n s t a n t w i t h a n a v e r a g e v a l u e 1125 /~b/sr c o m p a r e d to t h e a v e r a g e v a l u e 1 0 7 3 / z b / s r f o r t h e G d nuclei. T h e s a m e c o m p a r i s o n is m a d e f o r t h e 2 +' states o f t h e g a m m a v i b r a t i o n , a n d the d a t a are c o l l e c t e d in t a b l e 7. T h e B ( E 2 ) v a l u e s are t a k e n f r o m ref. 9). T h e 90 ° c r o s s section, r e d u c e d to Q = - 1 M e V b y m e a n s o f fig. 8 in ref. 3), p e r B ( E 2 ) u n i t is 821 pb/sr. T h i s n u m b e r is l o w c o m p a r e d w i t h the v a l u e s o b t a i n e d f o r G d a n d S m n u c l e i
398
r. O. TJI~MANDB. ELBEK
[refs. 2, a)]. The C o u l o m b excitation data 9) were obtained u n d e r experimentally difficult conditions, a n d the systematical trends in the B(E2) values for g a m m a vibrations m a k e some of the e r b i u m results look suspiciously high. Better B(E2) values can perhaps be o b t a i n e d from the ratio (da/dog)/B(E2) = 860 (/tb/sr)e 2 x 10 -48 cm 4 which was o b t a i n e d by i n t e r p o l a t i o n from the inelastic cross section for the even isotopes of Sm, G d a n d T h a n d U. As a further check, the excitation probability (i.e. the ratio between inelastic a n d elastic scattering) was measured for the 2 +' state in 166Er by m e a n s of 16 MeV alpha particles. A t 90 °, this probability was f o u n d to be 1.08 x 10- 3. The b o m b a r d i n g energy is rather close to the height of the C o u l o m b TABLE 8 Reduced transition probabilities for 3- states Isotope
Level (keV)
"~Er
1351 1616
(dtr/cLQ)g0* Q= 0 ~b/sr)
B(E3)d,d'
B(E3) 4) (s.p.u.)
173 32
0.133 0.025
12 2.1
122 55 (17) (12)
0.094 0.042 (0.013) (0.09)
8.1 3.6 (1.1) (0.8)
l"Er
1433 1568 (1968) b) (2337)
l"Er
1512 1719 2238
92 46 33
0.071 0.035 0.025
6.1 3.0 2.2
aeSEr
1428 (1630) (1910) 2257
49 (45) (28) 47
0.038 (0.035) (0.022) 0.036
3.3 (3.0) (1.9) 3.1
170Er
1304 1575 1931
17 54 40
0.013 0.042 0.031
1.1 3.6 2.7
The B(E3) values are in units of e=x 10-72 cm6. The B(E3) values have been derived from the (d, d') cross sections on the assumption that (dtr/d.Q)/B(E3) = 1300 ~b/sr)/e~ × 10-72 cm6. a) B(E3)s.p.u./e2 = 1.16 × 10-7~ cm6. b) Parentheses indicate that the assignment is doubtful. barrier, b u t it seems that C o u l o m b excitation is still the d o m i n a n t reaction 2). If we assume pure C o u l o m b excitation, the observed probability corresponds to B(E2) = 0.15e2 x 10 -48 cm 4, which is in good agreement with the value determined from the (d, d') data in table 7. I n table 8 are listed the energies, the 90 ° cross sections reduced to Q = - 1 MeV, a n d the B(E3)d,d, values. The B(E3) values have been calculated from (d, d ' ) cross sections with the assumptions that (dtr/d~o)/B(E3) = 1300 (pb/sr)e2x 10 -72 cm 6. This value has been f o u n d by i n t e r p o l a t i o n in the same way as explained for the E2 excitations.
Er COLLECTIVE
VIBRATIONAL
399
STATES
It should be stressed that the fundamental data obtained here are the inelastic scattering cross sections and that the B(E2) values are based on a proportionality and a normalization, both of which have not been verified experimentally to very good accuracy. Additional measurements of B(E2) values by Coulomb excitation and extensive D W B A calculations are needed to improve the B(E2) values obtained from the inelastic deuteron scattering data.
5. Conclusions The data for the ground-state rotational bands supplement those obtained earlier 14). The population of the 2 + state is roughly proportional (cf. table 6) to the B(E2) for this state. The 4 + states have considerably lower cross sections than ob-
-f
- - T
. . . .
F ........
[
[
E r , 4 + GR. BAND
!
150
100
4 :=t Z
o lOO
I
[
I
I
166
168
.J
_
Er, 4 ' + y - BAND
0 162
164 NASS
170
NUNBER
Fig. 6. Cross sections for the 4 + state in the ground-state band and the 4 +' state in the g a m m a band.
served in the Gd nuclei, and at the same time, the R-values are reduced. These observations can be considered as additional evidence for a direct E4 component 1~) in the excitation of the rotational 4 + states in the beginning of the rare-earth region. In the Er isotopes, this component is then considerably weaker and the excitation of the 4 + state is probably mainly of multiple E2 nature, which could explain the lowering of the R-values. The cross sections for the 6 + rotational states are somewhat less
400
P. O. T J f l M A N D B. E L B E K
than those in the G d isotopes, but show a similar regular increase with neutron number. The mechanism o f the 6 ÷ excitations is not clear. The cross sections for the 2 +' states o f the g a m m a vibrations decrease with increasing neutron n u m b e r and thus reflect a reduction in the B(E2) value also evident from the earlier C o u l o m b excitation data 9). All the 4 ÷' states are strongly excited with a m a x i m u m in 166Er (fig. 6). The variation in the 4 ÷' cross section is not connected to the variation in the 2 ÷' cross sections, which rules out a simple multiple m o d e of excitation. It is more likely that the excitation is partly by a direct E4 transition from the g r o u n d state. In this connection it is noteworthy that the cross section for the 4 +' state in the g r o u n d state has a m i n i m u m where the 4 +' cross section has a m a x i m u m (fig. 6). T
2.0
T - - - - - I
t,
a:
--
I
--
~ - - - -
Er, RATIO 9o°/125.
• o
o
o •
1.0
I
Er
o •
__1
_]
t
__[___
FIRST 3SECOND 3 -
0.20
z O.lO m
I tt
t • 162
L
I __ I _ ~ . . . . . 166 168 170 MASS NUMBER
16/.
Fig. 7. Cross sections and R-values for the first and second excited 3- states. The R-values for the strongest states assigned as 3 - (cf. fig. 7) are remarkably constant, which, together with the systematic trends in the excitation energies and the B(E3) values, lends support to the correctness o f the assignments. As fig. 7 shows, the absolute transition probabilities for the lowest 3 - state are rapidly decreasing with increasing mass number, whereas the transition probabilities for the next 3 state are fairly constant. The present data give only little information about the Kq u a n t u m numbers o f the 3 - states observed. As mentioned in the discussion, no possible 1 - states have been observed in the lowest octupole bands, which is a strong
Er C O L L E C T I V E V I B R A T I O N A L
STATES
401
a r g u m e n t against K = 0 or 1. Indeed, in 166Er it is k n o w n 10) that the lowest octupole state observed here belongs to a K ~ = 2 - band. I n 166Er, this state appears to be very similar to the lowest octupole state in the other e r b i u m nuclei, which indicates a general K = 2 - assignment for the lowest 3 - state. The K - q u a n t u m n u m b e r s for the other 3 - states m u s t r e m a i n u n k n o w n until additional i n f o r m a t i o n is obtained. It should be m e n t i o n e d , however, that in 166Er a n d 168Er K = 3 - b a n d s are already k n o w n , b u t these are n o t collective according to the present data. The authors are pleased to t h a n k Mrs. A n n a Grete Jorgensen for efficient a n d accurate scanning of the n u m e r o u s photographic plates. One of us (P.O.T.) wants to t h a n k " N o r g e s Teknisk-Naturvitenskapelige Forskningsrgtd" for economic support.
References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15)
B. Zeidman, B. Elbek, B. Herskind and M. C. Olesen, Nuclear Physics 86 (1966) 471 E. Veje, B. Elbek, B. Herskind and M.C. Olesen, to be published R. Bloch, B. Elbek and P. O. Tjom, Nuclear Physics A91 (1967) 576 P. O. Tjom and B. Elbek, to be published H. Morinaga, Nuclear Physics 75 (1966) 385 R. Graetzer, G. B. Hagemann, K. A. Hagemann and B. Elbek, Nuclear Physics 76 (1966) l P. G. Hansen, O. B. Nielsen and R. K. Sheline, Nuclear Physics 12 (1959) 389 Nuclear Data Sheets, National Academy of Sciences, Washington, D.C. Y. Yoshizawa, B. Elbek, B. Herskind and M. C. Olesen, Nuclear Physics 73 (1965) 273 J. Zylicz, M. H. Jorgensen, O. B. Nielsen and O. Skilbreid, Nuclear Physics 81 (1966) 88 I. Marklund, B. van Nooijen and Z. Grabowski, Nuclear Physics 15 (1960) 533 H. Koch, Z. Phys. 192 (1966) 142 D. G. Burke and B. Elbek, Mat. Fys. Medd. Dan. Vid. Selsk. 36, No. 6 (1967) B. Elbek, M. Kregar and P. Vedelsby, Nuclear Physics 86 (1966) 385 P. H. Stelson and L. Grodzins, Nucl. Data 1 0965) 21