A nuclear structure study of 165Ho using the (t, α), (α, t) and (3He, d) reactions

Nuclear Physics A246 (1975) 43 -- 60; (~) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilmwithout written permission from the publisher

A N U C L E A R S T R U C T U R E S T U D Y O F 16Silo U S I N G T H E (t, ~), (~, t) A N D (aHe, d) R E A C T I O N S L. K. WAGNER Florida State University, Tallahassee, FL 32306

D. G. BURKE and H. C. CHEUNG McMaster University, Hamilton, Ontario, Canada

P. KLEINHEINZ and R. K. SHELINE Florida State University, Tallahassee, FL 32306

Received 25 February 1975 Abstract: The level structure of a65Ho has been studied by means of the 166Er(t, ~¢)16SHo, 164Dy(a,t)16SHo, and ~64Dy(3He, d)~65Ho reactions using magnetic spectrographs and photographic emulsions. The results were interpreted on the basis of the Nilsson model with pairing and Coriolis mixing effects included. Experimental nuclear structure factors were obtained and compared with calculated results. Previously identified bands based on the ½[523], ~r[411], ½1411], ~[404], and ~[413] Nilsson orbitals were observed. The previously suggested ½[541] band was confirmed and levels up to spin ~ were assigned. The ~ member of the 51514] band was also identified. States assigned earlier as the spin ~ and [ members of the ~[532] band were reassigned to the ~[402] orbital. New evidence is presented which indicates that the previously assigned ~[413] band is actually the (Koh-2) 7-vibration based on the ~[411] state, with a large admixture ( ~ 50 %) of the ~[413] single-particle configuration.

E I

NUCLEAR REACTIONS 164Dy(oc,t), E = 27 MeV; measured t~(Et); 164Dy(aHe, d), E : 24 MeV; measured a(Ea); 166Er(t, ct), E = 15 MeV; measured a(Ea). 16SHe deduced levels, J, z~, L Enriched targets.

1. Introduction The o d d - p r o t o n nucleus 165Ho has been extensively investigated in n u m e r o u s r a d i o a c t i v e d e c a y studies 1 - 5). These earlier w o r k s p r o v i d e d firm assignments o f five N i l s s o n configurations, i.e., the ~[523], 2~[411 ], ½1411 ], ~[404] a n d the 51413] orbitals. These results have been s u m m a r i z e d in ref. 6). F u r t h e r m o r e , in a c o n c u r r e n t s t u d y o f the fl-decay o f the 1.26 rain 165Dy i s o m e r 7), a ½- state at 680 k e V was identified a n d suggested to b e the ½1541] b a n d head. C o u l o m b excitation experiments have p r o v i d e d m o r e i n f o r m a t i o n o n o t h e r levels o f this nucleus. T h e g r o u n d state b a n d h a s been established u p to the 2 a m e m b e r a n d the two ),-vibrational b a n d s a s s o c i a t e d with the g r o u n d state configuration were identified 8-11). T h e p r e s e n t p a p e r presents the results o f a study o f the (3He, d ) a n d (~, t) reactions p o p u l a t i n g the p r o t o n 43

44

L.K. WAGNER et

aL

particle states, and of the (t, a) reaction leading to the proton hole states in 16 Silo" Until recently, no single-nucleon transfer work concerned with the nuclear structure of 165Ho had been reported. During the final stages of preparation of the present work a paper by Lewis et aL tz) appeared which describes (3He, d) and (0q t) measurements made with 46.5 MeV 3He and 45.5 MeV 4He beams. Although these results overlap the stripping reaction data of the present work to a considerable degree, it still seemed worthwhile to publish the results taken at the lower energies. Firstly, the resolution is slightly better in the present results [~ 12 keV FWHM for the stripping reactions compared to ~ 15 keV in ref. 12)] and the spectra have considerably fewer background counts. More importantly, there are significant differences in the excitation energies, the relative spectroscopic strengths and the interpretations of certain levels. These differences are discussed in subsect. 4.11 of this paper. In the ground state of 165I-tO the odd proton occupies the ~:[523] orbital. This configuration originates from the h~ intruder shell model state, and the ground band members are expected to strongly Coriolis couple with those of other Nilsson states originating from the h~ shell. The single-proton transfer data provide evidence for this mixing in the form of large cross sections to the _it ground band member. The present study has also located a second Nilsson member of the h~ group, the -~z jmember of the ~[514] band, and provides a tentative assignment for the location of the ~ and ~ - -~[532] states. The data also provide conclusive evidence for a number of earlier tentative assignments. Among these are the ½[541] band, which is observed up to the spin-~ rotational member. The states previously assigned as the ~ and -~ members of the ~-[532] band have been definitely shown to belong to the I[402] configuration. A few states in the (t, a) reactions appear anomalously strong or anomalously weak. Attempts to explain their character through Coriolis mixing effects are discussed. 2. Experimental details and results

The (3He, d) and (a, t) experiments were performed with beams of 24 MeV 3He and 27 MeV 4He from the McMaster University FN tandem Van de Graaff accelerator. The 164Dy target was prepared from dysprosium oxide, enriched to 98.43 % 164Dy' obtained from the Holifield National Laboratory. The oxide was reduced to dysprosium metal by heating with lanthanum filings in vacuum, and the metal was vacuum evaporated onto 50/~g/cm z carbon foils. The target thickness was ~ 30 /zg/cm 2. The reaction products were analyzed with an Enge split-pole magnetic spectrograph and detected with photographic emulsions. The (t, ~) experiments were performed using a beam of 15 MeV tritons from the Los Alamos Scientific Laboratory FN tandem Van de Graaff accelerator. The 166Er target was fabricated, with an enrichment better than 99 %, on a 50/~g/cm 2 carbon backing using the isotope separator at Florida State University. The a-particles were analyzed in an Elbek

~~Ho

45

spectrograph and detected with photographic emulsions. The peak widths ( F W H M ) were ~ 12 keV for the (3He, d) and (~, t) reactions and ~ 19 keV for the (t, ~) reaction. Absolute cross sections for the stripping reactions were determined by comparing intensities of peaks with the elastic scattering intensity measured by a lithium drifted silicon detector at 0 = 30 ° in the spectrograph target chamber. The differential cross sections for elastic scattering at 0 = 30 ° were assumed to be 101.5 ~ and 111.7 ~o of the Rutherford values for 24 MeV 3He and 27 MeV 4He, respectively, as predicted by the distorted wave Born approximation (DWBA) calculations described below. Spectra were recorded at 0 = 25 ° and 60 ° for the (3He, d) reaction, at 0 = 45 ° and 60 ° for the (~, t) reaction, and at 0 = 30 °, 45 °, and 60 ° for the (t, c~) reaction. Only relative cross sections, however, were obtained in the (t, 00 reactions *. Typical spectra %{~[52~]e*} r~2 II ~z[A°4] ~ 7sz ~z

3,,z [4.]

7/2[~2~]

3t~d5/2

I'IlZt11/['541]2 ~/,,'

o

~,z{~,z[,loz].2.} '~Dy (Ot..t) ~ H o I/z E~ - 27 M~V I Ot

5/2 [40z] % 7/z

14~o

~

%

9/21514]I (

I00

o~ ~o

.

j 0

500

I000 Excitation

1500

~

2000

2500

Energy (keV)

Fig, I, Tritort s p e c t r u m f r o m the ~64Dy(~, t)~65Ho reaction at 0 ~ 45 °. T h e d a s h e d lines indicate

the positions of states which were known from previous works but which are weak or not resolved in this spectrum. The assignments in parentheses are tentative. are shown in figs. 1-3. The measured excitation energies, cross sections from the (3He, d) and (0q t) reactions, and relative cross sections from the (t, 0~) reactions for states populated in these experiments are presented in table 1. The probable error for the excitation energies is believed to be within 1 keV for states up to ,,~ 1 MeV excitation and 2-3 keV at higher energies. The absolute cross sections have uncertainties of ~ 20 ~ for strongly populated states. This is due mainly to uncertainties in the normalization procedure and relative intensities for well resolved peaks should have errors of only ~ ___10 ~. t Recent m e a s u r e m e n t s with the Q 3 D s p e c t r o m e t e r at Los A l a m o s have yielded a value o f 210 /zb/sr for the cross section to the 419.6 keV state at 0 = 30 ° with Et = 15 MeV.

46

L . K . W A G N E R et al. t64Dy (3He,d)l~eHo '~2{~2[,o2],2* } I/2 %

I £ E

I,

%{,~[,.]z+

% [~,,1

1000

(%) "~

N % '/~

d

E3H~24 MeV

0 d =60*

~0o

E

I

.....

m

500

1 IO00

•

1500

Excilalion

Energy

2000

2500

(keV)

Fig. 2. Deuteron spectrum from the ~64Dy(SHe, d)t6SHo reaction at 0 = 60 °. See caption to fig. 1.

'~zt,.] 3~ 5~z r/z 3~zs~21r/=

KeeEf(t.~ ) 16~Ho

,2) r~z %

%[,~1

(~z)

(%)

0,,t'30"

._o.

~n IOOO

i

==

%

%

ioo

0

J * °°i 1500

I000

500

Exeffotion

2000

2500

Energy (keY)

Fig. 3, Alpha spectrum from the 166Er(t, ~)165H0 reaction at 0 = 30% See caption to fig, 1.

3. Method of analysis The cross section for a stripping reaction on a doubly even target leading to a final state of spinj in a rotational band of a deformed nucleus, with Coriolis mixing effects included, is given by exp

i

\d~2/DWBA

where N is a normalization factor for the D W B A single-particle cross sections. The Cjz are expansion coefficients which describe the orbital in terms of spherical shell model states. The Al are the Coriolis mixing amplitudes of states with total angular momentum j, and the Ui are the emptiness factors. For pickup reactions, the cross

t6SHo

47

TABLE 1 Energies and cross sections for levels in ~6SHo Energy (keV) previous value ~) 0 94.7 210.1 345.0 ¢) 361.7 419.6 429.4 449.3 491.2 499.2 ~) 539.1 590.0 638 a) 680.1 ")

from

(~, t) 0 94 210 346 362 420 432 450

from (ZHe, d)

from (t, ~)

0 93 210

,~3 95 210 345 360 419

421 430 451

497

498 540 560 592

539

539

590

639 680

639 682

590 604 640

701 715 792 802 821 956 995 •057 1081 1129 1142

702 716 791 800

688.6 715.5 790.8 ~) 820.3 995.3 1055.9 1079.9 1140.5 1186.3

448

958 995 1058

~ 688 712 803 820 991 1058 1081

1128 1144

Cross section ~b/sr) (~, t) (ZHe, d) 0=45 ° 0=60 ° 3.7 5.8 121 0.8 3.0 69 76 3.0 22 ~ 1.2 7.0 1.1 ,,~ 3.6 48 82 ~ 8.2 69 ~4.2 18.8 2.7 88 3.6 1.8 1.8

2.1 ~ 1.0 21.2

~ 31.9 ~ 11.8 35.7

3.5 ~ 0.8 14.2 / ! 22.3 } 22.3 ~ 17.4 ~ 17.4 8.1 3.2 89

1194

1287

1244 1288

1337 1391 1470 1484 1534

1339 1390 1471 1486 1534

1288 1318

1486

4.4

3.0 1.2

3.4 4.0

1594 1616

1652 1675

1653

3.6 2.6 2.6 1.I 2.0

8.4 3.3 1.0 2.4 1.7

½ ½1411]

34.1

{[523] ~ ½1411]

56.6 ~ ½1411] 49.8 ~ H411] 26.6 ½ ~{~[523], 2 +} 16.8{~ ½ ½15411

4~ ([ [5231, 2 + }

138 48.3 < 20 24.1 112 460

~- ½1541] { ~[404] ½1541] _~ ½1541] ~ ½[404] ½1541] ~ ~[413] r) ~] ]][402] ~ ~[413] r) ~][402] ~ .~[4131

35.9 30.3

184

~[514]? ~ ~[53217

27.3 19.5 38 3.5

15.7 24.4

1.7 2.2

7.7 ~1

1649 1676

~ ½1411]

22.0

1552 1588 1594 1615

386

43.5 7.0

IK[Nn,A] ~ ½15231 ] {[523] ~ ~[523] 4~ ~[523] ,'.'.'] ~[4111 ~ ~[411 ]

m 2.4 m 1.4

1236

Assignment

13.6 48.8 968 < 10.0 112 1000

} 15.2

1188 1192

Relative cross sections ~) (t, ~) 0=30 °

H514] ½[4001 r) 26.9 400

4~t ~-[532]?

L, K. WAGNER et al.

48

TABLE 1 (continued) Energy (keV) previous valueb)

from (~,t)

from (3He,d)

1760

1760

1844

1844

from (t,~) 1719 1759 1776 1836

Cross section Relative cross (#b/sr) sections ~) (c~,t) (3He,d) (t, ~) 0:45 ° 0:60 ° 0=30 °

9.0

15.2

1.1

15.4

4.2

4.4

1912 1939

1939

40.1 86.1 ~) 82.8~) 35.5 ~)

111 37.5

2016

6.1 2025

2086 2106 2121

I K[Nn~A]

81.5

1943 1986 2053 2085 ~ 2111 ~ 2121

Assignment

58.9 4.5 4.2 2.6

3.0 32.2 11.6 14.5

") All cross sections for the (t, ~) reaction are normalized to the 419 keV peak at 30° as 1000 units. b) From ref. 6) unless indicated otherwise. c) From Nuclear Data Sheets. ~) From ref. 9). ~) From ref. 7). r) This state is believed to be a y-vibrational state and is populated in this work due to the admixture of the single-particle component indicated here. See text. ~) This region of the spectrum at 0 = 30° was obscured by a deuteron group from the 12C(t, d)13C reaction. From the data at the other angles it is seen that the transition strengths given here for the 1759+1776 keV states are too small by a factor of ~ 2 and that for the 1836 keV state is too small by a factor of ~ 8.

sections are o b t a i n e d by replacing the Ui with the fullness factors Vi. The nuclear structure factors, [~iC~I),A~U~] 2, are then given by (da]df2)cxp/2N(da/df2)owB A. The nuclear structure factors for all r o t a t i o n a l b a n d m e m b e r s observed are listed in table 2, where they are c o m p a r e d with theoretical values which are discussed in sect. 5. I n order to extract the experimental values, D W B A calculations were performed with the c o m p u t e r p r o g r a m D W U C K 13). The optical model parameters in these calculations were the same as those used by L u a n d A l f o r d 14) except that the lower cutoff for the radial i n t e g r a t i o n was scaled d o w n f r o m 9.6 fm to 9.43 fm. The n o r m a l i z a t i o n factor for the (3He, d) D W B A calculations was assumed to have the value N = 4.42 [ref. 13)]. The c o r r e s p o n d i n g factor for the (~, t) process is n o t as well k n o w n , a n d in the present work it has been assigned a value of 54, in order that the spectroscopic factors from the two stripping reactions have similar values for the w e l l - k n o w n -~- ~ [523 ], ½ ½[411 ] a n d ~ ½[411 ] states. This compares with values r a n g i n g f r o m 46 to 118 which have been used in recent studies. It was

•~[411]

½[523]

~[413]

~[4041

~[541]

~[5141

~,[532]

0.0 117.1 260.1 362.6 420.1 500.6 604.1 428.6 449.6 538.6 587.5 747.7 672.7 792.0 709.1 987.4 838.1 1275.5 719.2 829.0 995.3 1075.2 1177.9 1054.5 1136.5 1241.9 1451.9 1541.4 1656.5 1797,2 1405.6 1581.3

0.0 94.2 210.3 362.2 417.4 494.0 594.3 428.6 450.0 539.5 589.6 749.8 682.2 791.5 698.5 955,8 802.9 1212.1 715.5 820.5 995.6 1079.3 1186.6 1056.0 1140.5 1249.4 1428.7 1486,0 1572.3 1676.0 1424.4 1593.9

Calculated energy unpert, pert.

a) Total structure factor of two unresolved states.

-~

,~ ~[402] r

½

~

.~

.~

~

~:] ½ ½1411 ] .]

.~ ~t

I K[Nn~A]

State

TABLE 2

0.012 0.008 0,750 0.006 0.213 0.031 0.014 0.101 0.519 0.178 0.135 0.013 0.032 0.042 0.193 0.048 0.627 0.021 0.951 0.011 0.003 0.074 0.002 0.915 0.041 0,018 0.000 0.002 0.000 0.040 0.007 0.974

unpert, 0.013 0.009 1.027 0.001 0.291 0.024 0.019 0.101 0,525 0,142 0.158 0.010 0,032 0.047 0.235 0.068 0.891 0.034 0,997 0.011 0.006 0.026 0.002 0,871 0.027 0.015 0.000 0.003 0.000 0.198 0.005 0.723

mixed

0.82

1.12 ~ 0.07

0.042

1.30

O.104 ~ 0,118 ~ 0.38 0.10 ~ 1.41

0.80

1.22 ,,~ 0.032

1.67 ~ 0.04 0,034 ~ 0.08

0,046 0.080 0.39 0.13 1.22

,,~ 0.03 ~ 0,73 0.21 ~ 0.13

~, 0.110 0.61 0.23 0,21

~-, 0.49

0.023 0.092 1.40 0.025 ~ 0.52 ~ 0.017

(u, t)

0.037 ~ 0.087 1.49

(~He, d)

Nuclear structure factors for stripping calculated exp.

Experimental and calculated nuclear structure factors

0.011 0.007 0.651 0.022 0.739 0.109 0,049 0.017 0.086 0.029 0.022 0.002 0.003 0.004 0.018 0.004 0.058 0.002 0.093 0.001 0.032 0.910 0.024 0.052 0.002 0.001 0.001 0.046 0.010 0.922 0.000 0.037

0.015 0.009 0,971 0.016 0,767 0.121 0.047 0.017 0.092 0.009 0.042 0.001 0.003 0.004 0.020 0.005 0,072 0.007 0.151 0.004 0.042 0.819 0.025 0.034 0,003 0.000 0.001 O.103 0.013 1.636 0.000 0.124

calculated unpert, mixed

0.426

0.054

0.137 0.011 a) 0.012 0.411 0.048 0.077 0.004

0.029

0.290 0.030 0.055

0.013 0.027 0,693 0.066 0.767 0,071 a) 0.072

exp. (t, ~)

Nuclear structure factors for pickup

ta

m

4~

O

50

L . K . W A G N E R et al.

found in the present work that these normalizations resulted in structure factors which appeared to be ~ 30--40 70 larger than predicted by the Nilsson model, with pairing and Coriolis mixing effects included. This appears to be a general trend, as a number of recent studies 12,1 s-17) with (3He, d) reactions on deformed rare earth nuclei have reported spectroscopic factors ~ 30 % larger than expected. With this factor in mind, it is seen that the experimentally determined distributions of spectroscopic strength amongst the rotational band members are in good agreement with the calculated ones for the previously assigned Nilsson orbitals. For the (t, ~) reaction, where absolute cross sections were not obtained, only the relative values of the nuclear structure factors could be determined. These were then normalized so that the value for the strongly populated ~ ~[411] state was the same as the calculated value. The Coriolis calculations indicate that this state is relatively pure and that its nuclear structure factor is not strongly dependent on the parameters of the mixing calculations. The nuclear structure factors obtained in this way from the (t, u) spectra at different angles were in very good agreement with each other, and the values in table 2 are the averages of those obtained from the three angles. Two sets of calculated nuclear structure factors are presented in table 2. The first set labelled "unperturbed" are the values of and V 2C jr2 obtained from Nilsson calculations with 6 = 0.26, x = 0.0637, # = 0.600, and A = 700 keV. The Fermi levels in the ~66Er and 164Dy targets were assumed to be 250 keV above and 550 keV below the energy of the ~[523] single-particle state, respectively. The rotational constant was taken to be 11.0 keV. The set labelled "mixed" was obtained by performing Coriolis mixing calculations. Also listed are the unperturbed and perturbed

U2C~

,B,,l~"~ Rt C)

d,

£=lt=O

I0

% bcl -oh=

1.0

I

y ~ 0 5 6 ~

~

y

-

1

9

3

9

0.1

I

0

i

~

t

,

I

L

¢

~

,

I

~

i

~

i

I

p

,

I000 Excitotion Energy {keV)

,

,

I

,

2000

,

,

,

I

,

,

Fig. 4. Ratios of the (3He, d) cross sections at 0 = 60 ° to the (0~,t) cross sections at 0 = 45 °. The points indicate experimental data and the solid lines are the results o f D W B A calculations normalized as described in the text.

16Silo

51

energies. A discussion of the calculations and comparison of the results with experiment are presented later. Useful information can also be obtained from the ratio of the (aHe, d) and (~, t) cross sections for each state, as this ratio depends on the/-value of the transferred particle. These cross section ratios are shown in fig. 4 for some states populated in the present work. The solid curves shown in this figure are calculated ratios from the D W B A cross sections. It is seen that except for weakly populated states, the cross section ratios for previously assigned levels fall on or near the line representing the known/-values. The 1 = 1 data points are not near the I = 1 line but these states are populated very weakly in the (~, t) reaction and the discrepancy is probably due to inadequacies in the D W B A calculations for these cases, where the cross sections are very weak due to momentum mismatch. For this reason, it is felt that the nuclear structure factors extracted from the (aHe, d) results are more reliable for low/-values

20t6

4~..l 9 ~ 6 ~ • 1943 1844,-,A I:~1836E'-,k-- 1776 17E0"--I~'-'17i9-'IL'--1676 --&l If/21 --1616JI/2 I/2 [K;2]

--1594""'~11/2

~534 ~ L --1470-'~9/~

(5/2 [5~z] ?

9/21514]

- - - r]90 ..A --

K~38--A

~1236.r" - - r l 3 2 "-'lu c~

L

lle8--

9/2 - - 1 1 4 3 -.-A 7/2

_ _ H29._a. L108I.-~7/2

LI058

W

5/2

L99~---ASI 2

5/2 [K.+23

--957

- A 5/2

[4o2]

--'~ 7/2

"L-801 912 L~-821-'--~ 912 " - ~ 791 ~ : : t 3/2 70I

--560~A

~k-604--(9/2}

A-" 639 "--A 7/2 ~/2[K;~-3 ~__59~__.~.7/2

A- (497)-- 7/2 L 4 9 8

5/2 L715-.---& 7/2

"~-ee,-" ,/2 7/Z [404] 1/21541]

-JL 15/2 3/2 - - 4 3 1 ---~ 112

&--450

au-. 4 2 0 - - & 5/2 L361~312

tL--345--al'13/2

1/21411]

3/2 [411] L--2IO-JH/2

A - - 94 - - J

9/2

l.-- 0..--A 7/2

7'/2[523]

Fig. 5. Energy levels of 16Silo observed in the present experiments. Levels shown with triangles on the left side were observed in the pickup reaction and those with triangles on the right side were observed in the stripping reactions. Open triangles indicate that the peak was partly obscured by other nearby peaks. Assignments shown in parentheses are tentative.

52

L . K . WAGNER et aL

such as l = 0 or 1. On the other hand, the strengths of transitions with high/-values are obtained more reliably from the (0~,t) data, since these have rather low intensities in the (3He, d) spectra. Detailed comments on the level structure and interpretation of each band are reported in the following section, and discussion of the Coriolis coupling investigations is found in sect. 5. 4. Nilsson level structure of ~6SHo

The level structure of 165H0 is interpreted in terms of the Nilsson model. The rotational bands are discussed in order of increasing band head energies. Previously firm spin, parity and Nilsson assignments are not further discussed in this paper except when additional interpretation is possible. The resultant level scheme is presented in fig. 5. 4.1. THE ~[523] BAND

The ground state band has been established up to the spin-~3- member through multiple Coulomb excitation lO). The -~ and -~- members have previously been assigned energies of 94.7 and 210.1 keV, respectively 6). The three lowest members of the band are populated in all these experiments. The strong mixing of the ~ - state with higher lying members stemming from the h~ shell model state is evident from the data shown in table 2. The theoretical nuclear structure factors listed for this band cannot be calculated as accurately as in other cases since the U and V for this band are uncertain due to a lack of precise knowledge about the Fermi levels in 166Er and 164Dy. Also the energies of the higher lying ~[532], ~t[541], ½[550] and -~-[505] bands are unknown and the mixing from these bands is expected to be significant due to the large j_ matrix elements between appropriate Nilsson orbitals [these matrix elements are listed in ref. 6)]. The well established _~3_and 15_ members at 345.0 and 499.6 keV are populated weakly in the (~, t) reaction. As might be expected for two-step processes is), the cross section for the -J~-member is larger than that for the ~3 state. The (t, ~) spectrum shows the 345 keV state weakly populated but the 500 keV level is not well resolved from nearby states. Such second order processes are often observed in single-nucleon transfer experiments in the rare earth region and demonstrate that it is not safe to rely on spectroscopic factors for weakly populated states. 4.2. THE ?z[411] BAND

On the basis of decay scheme studies, the ~, ~ and ~ rotational members of the ½1411] band have been assigned at energies of 361.7, 419.6 and 491.2 keV, respectively 6). This sequence clearly indicates an alternation in apparent moments of inertia between successive band members .This is most reasonably explained on the basis of Coriolis coupling with the ½1411] band which is immediately above in energy.

16Silo

53

When the somewhat anomalous energy spacings of the ½1411] band members are admixed into the 31411] band by Coriolis coupling, it is quite reasonable to expect the previously unobserved ~2 member of the ~[411] band to be at about 604 keV. In the (t, c~) data the experimental nuclear structure factor for the 604 keV state agrees reasonably well with the calculated value for the ~ state and this tentative assignment is listed in table 1. According to Coriolis mixing calculations the ~z member is a relatively pure state and has therefore been chosen as the standard to which all nuclear structure factors obtained from the (t, ~) reaction have been normalized. 4.3. THE ~[411] BAND

The ½, ~, ~- and ~ members of the ½1411] band have previously been assigned energies of 429.4, 449.3, 539.1 and 590.0 keV, respectively, in decay scheme studies 6). In the stripping reactions these four members are observed with intensities in agreement with calculations. In the pickup reaction the strengths of all observed members in this band are larger than predicted. This effect is most obvious for the spin-~ member which is observed to have about three times the predicted strength. The difference may be due to uncertainty in the value of the Fermi energy in 166Er used in the calculations, since it has a major effect on the V2 for this band. 4.4. THE {~[523], 2 +} ;)-VIBRATIONAL BANDS

The nucleus 1 6 5 H o was the first odd nucleus in which a y-vibrational band was observed s, 9). The $, ~, and ~ members of the ~{~[523], 2 + } y-band were found to have excitation energies of 515.4, 566.7 and 638 keV [refs. 9-11)] respectively, in Coulomb excitation experiments. In the present single-nucleon transfer reactions, the rotational member of the ~{~[523], 2 +) y-band is weakly observed at 639 keV. A weakly populated state at ~ 688 keV observed in the (t, ~) reaction may be the 3~-{~[523], 2 + } band head. However the observed strength could also be due to the spin-½ member of the ½1541] band which lies about 7 keV lower in energy. The identity of the observed state is uncertain. 4.5. THE ½1541] BAND

The existence of the spin ½ and ~- members of this band, with a band head energy of ~ 680 keV, was first suggested by Bunker et aL 7). The present (aHe, d) and (~, t) results permit a definite assignment for the band up to a spin of ~2. The ~: and ~2members at ~ 791 keV and ~ 802 keV are not fully resolved from each other but the doublet in the (3He, d) spectrum is definitely wider than a normal peak. Also the centroid energy is shifted relative to that observed in the (~, t) reaction, in which most of the observed intensity is due to the ~ state. The observed level spacing and ordering in this band fits very well with systematic trends observed for the ½1541] orbital in the rare earth region 19). The pickup reaction weakly populates the ~2 member of this band at ~ 803 keV. Slight differences between the present results and those in ref. 12) for the z2 and 29-members are discussed in subsect. 4.11.

54

L.K. WAGNER et aL

4.6. THE ½[404] BAND The ~ and ~ members of the ½[404] band have previously been assigned energies of 715.5 and 820.3 keV in decay scheme studies 6). The ~ member is observed strongly in the stripping reactions as expected since its C~ is nearly unity. The spin-~ member is expected to be weakly populated in the stripping reactions and is observed as a weak shoulder on the 802 keV peak in the (~, t) reaction. In the (t, ~) reactions, the z state is definitely observed at all angles but is not resolved from the ~ ½[541] state at 701 keV. However, the ~ ~[404] level is expected to be seen more strongly due to its Coriolis mixing with the ~ ~[413] hole state. There is also weak evidence for the observation of the ~ state in two of the three angles. 4.7. THE PREVIOUSLY ASSIGNED ~[413] BAND Decay scheme studies have previously assigned the [, ~ and ~ members of the ~[413] band at energies of 995.3, 1079.9 and 1186.3 keV respectively 6). The ~ and members are observed only weakly in the stripping reactions, as expected, since this orbital is below the Fermi surface. The (t, ct) experiment populated all three members. The spin-~ member is expected to be observed most strongly since this orbital originates from a g] shell state, and this is indeed the case. However, the absolute strength to the spin-~ member is only about half as large as expected, suggesting this state is not a pure single-particle state. The Coriolis mixing calculations do not explain this reduction in the structure factor. However, calculations of the type performed by Soloviev e t al. 2o) predict a significant mixing between the ~[413] band and the (Ko+2) y-vibrational band built on the ½½1411] state. It is therefore likely that the K = ~ band based on the 995.3 keV level has a very complex structure containing large amplitudes of the ~[413] state and of the (Ko+2) y-vibration based on the ½1411] state. It is populated in the (t, a) reaction because of its large admixture (~ 50 ~ ) of the ~[413] single-particle state. A similar complex interpretation was also suggested by Mauron e t al. 2) in order to explain several anomalies concerning this band. In particular, the E2 y-decays from the 995.3 keV level to the ½1411] band are faster than those to the ~[411] band. Also the 995.3 and 1079.3 keV levels decay by strong transitions to y-vibrational states based on the ground state. All these considerations tend to confirm the suggestion that the K = ~ band beginning at 995.3 keV is largely a mixture of the (Ko+2) ~-band and the ~[413] state. For simplicity it is shown in figs. 1, 2, 3 and 5 as the y-vibrational band. Small admixtures of other three-particle components may also be present, as discussed by Mauron e t al. 2), in order to explain the observed logft values to this band. 4.8. THE ~[402] BAND Evidence for a K = ~ band with spin ~ and ~ members at 1055.9 and 1140.5 keV, respectively, has been presented by previous experiments 3, 21). It was assigned as the ~[532] band on the basis of logft values 2). The ~[532] band is a hole configuration and would be expected to have a large cross section to the spin-~- member in the

~SHo

55

pickup reaction. In the present work the (t, ~) spectra show no evidence for the population of an 1@member. The (3He, d) and (0c, t) reactions show a strong population to the previously assigned ~ member and the cross section ratio is consistent with l = 2. Such characteristics could be due only to the ~[402] orbital, which is above the Fermi surface, and for which the ~ member has a C~ of nearly unity. 4.9. THE ][514] ORBITAL A level at 1594 keV is populated by a fairly strong transition for which the (3He, d) to (~, t) cross section ratio indicates l = 5. This is most likely the 1@~[514] state, which has been observed in nearby odd-proton nuclei. The absolute strength and trend in excitation energy are consistent with this assignment. The ~[514] and ~[402] orbitals have similar slopes on a Nilsson diagram and intersect at a deformation of fi ~ 0.28. In the odd lutetium isotopes 22) the ~-~[514] state is within 400 keV of the ~[402] band head. In the thulium isotopes 17) the 9 - ~[514] state is found from 367 keV to 654 keV above the ~ ~[402] state, and in 16aHo this energy difference is 730keV [ref. 23)]. The 1594keY level in 165Ho is 540keV above the ~[402] band head, which fits in nicely with these systematics. No other peak is observed in the (~, t) spectrum below 2 MeV excitation energy with the strength appropriate for the ~ - ~[514] state. The predicted nuclear structure factor for the ~ band head of this orbital is very small. A state at 1470 keV is observed very weakly and this could perhaps be the member, since the energy separation from the ½~ state yields a reasonable rotational parameter of h 2 / 2 j ---- 11.3 keV. The observation of this band was not reported in ref. 12) and further comments on its assignments are found in subsect. 4.11. 4.10. HIGHER LYING STATES It is obvious in looking at the (t, a) data that there are two strongly populated hole states at 1486 and 1676 keV. Possible assignments for these states are the ~ and 1@ members of the ~[532] band. The (aHe, d) and (a, t) cross section ratios are consistent with this interpretation, although these ratios may not be reliable for the weak transitions to these hole states. Calculations indicate the ~ and ~ members of this band would have small spectroscopic factors and the observation of these states is not expected. Although the experimental strength for the ~ - state is less than the calculated value, the influence of higher bands on this orbital must be kept in mind. Since the energies of these bands are unknown, the calculated nuclear structme factor is uncertain. The assignment of this band must be considered highly tentative in view of the lack of definitive information. Another possibility is that the 1676 keV state may be an I ~ = 5 + state containing the remainder of the ~ ~[413] singleparticle strength which was missing from the band based on the 995.3 keV level. The only other possible Nilsson state with high spin is the ~ ~ [404] orbital but the Nilsson systematics suggest that it should lie above 2 MeV. In recent studies of 161,163H0 and 16 7,169, t 71Tm levels, (3He, d) angular distri-

56

L.K. WAGNER et aL

butions indicated I = 0 transitions with appreciable spectroscopic strength to states which were approximately 600-650 keV above the {[402] band head in each case [refs. 17,19)]. This energy difference is equal to the typical 7-vibrational energies in this region. Also, the only single-particle state with significant l = 0 strength in this region is the ½[400] orbital, which is expected to mix strongly into the ( K o - 2 ) y-vibration based on the { [402] state 24). Thus it is logical to assume that the observed I ~ = ½-+ levels are these vibrational states. Although angular distribution measurements have not been made in the present work, the (c~, t) and (3He, d) cross section ratios indicate that the levels at 1616 keV and 1844 keV have very low /-values, probably I = 0 or I = 1. The first of these is 560 keV above the ~[402] band head, and is likely the ( K o - 2 ) y-vibration, in analogy with the neighboring nuclides. A level in this region observed to have an I = 0 angular distribution 12) is very likely the 1616 keV state discussed here (see subsect. 4.11). A number o f higher states are observed but because of incomplete experimental evidence, no further Nilsson assignments have proven possible. 4.11. COMPARISON WITH OTHER STRIPPING REACTION STUDIES The interpretation of the present results had been established and the manuscript was in its final stages of preparation when a paper reporting (3He, d) and (~, t) measurements with higher beam energies appeared in print 22). In general, the results of the two works agree with each other, although some differences exist. Since many of these discrepancies are interrelated and some involve states which have not been given Nilsson assignments, a comparison between the two works is provided in this subsection. As expected, the higher beam energies of ref. 12) resulted in a larger amount of diffraction structure in the angular distributions, so that these measurements are more useful in determining l-values for clearly resolved peaks. It was indeed encouraging to see that the angular distribution measurements for strongly populated levels (such as the ~ ½1411], ½ ½1541] and ~ ~[402] states) led to the same interpretations as those which had been established on the basis of the present results. However, the increased beam energies make it more difficult to obtain spectra with good resolution and low background. Also, as Lewis et al. 12) pointed out, the increased diffraction structure makes the ratio of (aHe, d) and (~, t) cross sections less reliable as an indicator of/-value. In general the spectroscopic strengths extracted for pure single-particle configurations in the two works agree well with each other. In fact, it was found in both works that the nuclear structure factors were ~ 30 ~ larger than expected for well-known states when the standard value of N = 4.42 was used for the (3He, d) DWBA, calculations. The state lowest in excitation energy for which a discrepancy exists is the 234 keV level reported by Lewis e t al. There was no evidence for a level at this excitation energy in any of the (3He, d), (c~, t), or (t, c~) spectra of the present work [or in some

16Silo

57

preliminary unpublished (,, t) experiments by the present authors using 25 MeV 4He beams]. Although Lewis et al. describe this as the most puzzling of their unidentified levels, it is noted that their spectra show other "anomalous" peaks (i.e., ones which appear strongly in their spectra but which were very weak or not observed in the present study). These occur at 471 keV, 736 keV, 820 keV and 1076 keV. A possibl~ clue concerning their origin is suggested by the observation that each of these peaks is found as a "shoulder" on the high excitation-energy side of one of the largest peaks in the spectrum. The excitation energy quoted for each of these "anomalous" peaks is 15-25 keV higher than that of the large peak nearby. This suggests that the unexplained peaks may be due to some systematic experimental difficulty, such as target granularity or imperfect charged particle focussing. Although Lewis et al. state that they have observed similar results with different 264Dy targets and feel that the " a n o m a l o u s " peaks correspond to actual states, it seems more plausible that these peaks are actually shoulders belonging to the larger peaks near them. It is noted that the angular distributions shown for the " a n o m a l o u s " 234 keV and 820 keV peaks indicate the same/-values as those for the larger neighboring 210 keV and 798 keV peaks, respectively. Unfortunately angular distributions were not presented for the unexplained 471 keV and 736 keV peaks, so it is not possible to tell whether they exhibit the same behaviour as the larger neighboring 449 keV and 716 keV peaks. Whereas the 1076 keV peak is found on the high excitation-energy side of the strongly populated ~ ~[402] level at 1056 keV, the cross sections for these two peaks are similar in magnitude. This seems to indicate that the 1076 keV peak is due to an actual population in the reactions of ref. 22) in addition to possibly including a shoulder o f the 1056 keV peak. This is consistent with the fact that the angular distributions shown for the 1076 keV and 1056 keV peaks are not similar. Although such a strong population is not understood, it is known that the I ~ = -~+ level at 1079.9 keV has a very complex structure. It may be possible that the single-particleplus-phonon component of this state is populated through second order processes in the reaction mechanism at the higher beam energies. Due partly to the presence of the " a n o m a l o u s " peaks described above, there are some differences in the interpretation o f the ~ ½1541] and ~ ½1541] states in the two works. As discussed in subsect. 4.5, the present results show a closely spaced doublet of levels with energies of g 791 keV and ~ 802 keV, exhibiting low and high/-values respectively. These were assigned as the ~ and ~ members of the ½[541 ] band. In the work 'of Lewis et al. this doublet was assumed to be a single peak and its angular distribution was found to resemble that expected for an l = 1 transition. However such an angular distribution would also be expected for an unresolved doublet of the type found in the present work, since the I -- 5 component would have a considerably smaller cross section than the l = 1 component at the beam energies used in ref. 22). [This can be seen since the ~ ½1541 ] state would have a maximum cross section at an angle o f ~ 15 ° and it would be less than the ~ 100 pb/sr shown for the ~-~[523] state in fig. 8 of ref. 22). This is ~ ¼ as large as the cross section shown at the same

58

L.K. WAGNER et aL

angle for the 798 keV level in fig. 11 of the same work.] Thus the 1 = 1 component of the doublet would dominate the angular distribution and it would be difficult to detect the presence of the l = 5 state, even though it has a larger nuclear structure factor. The "anomalous" 820 keV peak also exhibited an l = 1 angular distribution and Lewis et al. did not decide which of the 798 or 820 keV peaks should be assigned as the z2½1541] state. In the present work no large peak was found near 820 keV, and the very weak population at that energy could be attributed to the ~ ~[404] state which was previously known at 820.3 keV. Another significant difference between the present results and those of ref. 12) involves the excitation energies for levels above 1200 keV. In particular, the levels they report at 1561 keV, 1586 keV and 1620 keV appear to correspond to those at 1594 keV, 1616 keV and ~ 1653 keV, respectively, in the present work. These discrepancies of ,~, 32 keV are much larger than the estimated probable errors of ___3 keV in the present work and _ 10 keV in ref. 12). Although no good explanation for this difference is available, it is worthwhile to comment that many similar (3He, d) and (~, t) experiments have been performed with the spectrograph at the McMaster University laboratory and the agreement of excitation energies with those from ),-ray results has led to the estimated probable error of ___2-3 keV for strong, clearlyresolved peaks at excitation energies o f 1-2 MeV. The values obtained from the (3He, d) and (~, t) experiments reported in this work are in very good agreement with each other, even though they were obtained on different days using different portions of the spectrograph focal plane. In the present work each spectrum was recorded on a single photographic plate so that no plate joints occurred in the spectra shown in figs. 1 and 2. The final difference to be discussed concerns the interpretation of the 1594 keV level [reported at 1561 keV in ref. 12)]. Lewis e t al. prefer an l = 6 assignment rather than l = 5 for this level, on the basis of their measured angular distribution. As discussed in subsect. 4.9, this level was assigned as the ~-~[514] state in the present work on the basis of (i) the ratio of (3He, d) and (~, t) cross sections which indicates I = 5, and (ii) the energy systematics for the 2~[514] orbital in this mass region. Whereas in favourable cases the angular distribution measurements can result in unique assignments of/-values, it is not clear that the angular distribution shown for the 1561 keV level in fig. 11 of ref. x2) can distinguish between l = 5 and l = 6. Although the experimental angular distribution was found to deviate from the DWBA curve shown for I = 5, it is seen to be very similar to the experimental angular distributions shown for other I = 5 states in figs. 7 and 8 of the same work. These known l = 5 transitions also have angular distributions which deviate from the DWBA curves in the same manner. In view of this uncertainty it seems that there is no reason for choosing an I = 6 assignment for this state rather than art 1 = 5. Thus when systematics are considered the ~-~[514] interpretation is preferred.

X6SHo

59

5. Coriolis coupling investigations An investigation of the Coriolis coupling effects upon the even parity bands observed in these experiments was performed to determine whether or not this could explain the anomalous cross sections observed in a few of these bands. These calculations were performed using the computer program COFITE 25), which calculates the Coriolis coupling among rotational bands in an odd-A nucleus and does a Z2 fit of calculated excitation energies to experimentally determined energies. The initial calculations investigated the mixing effects of higher lying even parity bands on the experimentally known lower lying bands. Since experimental energies for these higher lying bands are not available, their energies were estimated from the Nilsson model. These calculations were then compared to ones performed with only the five known bands included. The comparison revealed that mixing from higher lying bands had less thart a 10 ~ effect on the nuclear structure factors of the known states for the stlipping reaction and less than a 20 % effect for the pickup reaction. These effects are small since the j_ matrix elements between the unknown states and the known states are small, and reasonable changes in the estimated energies do not change the mixing significantly. The Coriolis mixing provided little improvement in understanding the discrepancies of the ~ ½1411] and ~ ~[413] states. As stated in subsect. 4.1, the mixing among the odd parity states from higher lying bands is expected to be significant but is uncertain since the energies of some of the higher states are unknown.

6. Conclusion The present studies have confirmed the interpretations for many previously assigned levels and permitted the assignments of additional rotational members for several bands. The ~ and ~ states at 1055.9 and 1140.5 keV, respectively, have been reassigned as members of the ~[402] band, and the ~ - member of the 2~[514] band has been identified. A highly tentative assignment of the -~ and ~1_ members of the ~[532] band is suggested, but the evidence is not conclusive. In the (t, a) data, the previously assigned ~ ~[413] state is observed with about half the expected strength, adding to earlier evidence that this state actually contains large components of the :~[413 ] state and the (K 0 + 2) ~-vibrational band built on the ½[411 ] state. The authors are indebted to O. Hansen, E. Flynn, S. Orbesen, R. Casten and T. Mulligan at Los Alamos for their assistance in making the (t, ~) exposures. Thanks are also due B. Leonard at Florida State University for the preparation of the 166Er target. Also gratefully acknowledged is the assistance of B. Nielsen in performing the Coriolis coupling calculations and the cooperation of B. Nielsen and M. E. Bunker in communicating unpublished results. Financial support for the work done at McMaster University was provided by the National Research Council of Canada in the form

60

L.K. WAGNER et al.

o f o p er at i n g grants to the M c M a s t e r U n i v e r s i t y t a n d e m accelerator l a b o r a t o r y an d to D. G. Burke, an d also in the f o r m o f a p o s t d o c t o r a l fellowship to H. C. Cheung. T h e w o r k d o n e at the Los A l a m o s Scientific L a b o r a t o r y and F l o r i d a State U n i v e r s i t y was s u p p o r t e d by the U S A t o m i c Energy C o m m i s s i o n .

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25)

R. Hardell, S. Malmskog and L. Persson, Ark. Fys. 25 (1963) 333 G. Mauron, J. Kern and O. Huber, Nucl. Phys. A181 (1972) 489 L. Persson, R. Hardell and S. Nilsson, Ark. Fys. 23 (1962) 1 L. Persson, Ark. Fys. 24 (1963) 89 H. Yamamoto, K. Kawade, K. Yoshikawa, J. Phys. Soc. Japan 34 (1973) 1676 M. E. Bunker and C. W. Reich, Rev. Mod. Phys. 43 (1971) 348 M. E. Bunker, private communication (1973); J. W. Starner, B. S. Nielsen and M. E. Bunker, Bull. Am. Phys. Soc. 19 (1974) 645 F. P. Cranston, Jr., M. E. Bunker and J. W. Starner, Bull. Am. Phys. Soc. 5 (1960) 255 R. M. Diamond, B. Elbek and F. S. Stephens, Nucl. Phys. 43 (1963) 560 J. S. Greenberg, D. A. Bromley, E. Bishop and G. Seaman, Proc. Symp. on direct interactions and nuclear reaction measurements, Padua, 1962, ed. E. Clemental and C. Villi (Gordon and Breach, New York, 1962) p. 941 D. A. Ward and B. Ader, Atomic Energy of Canada Limited report AECL-3668 (1970) p. 23 D. A. Lewis, A. S. Broad and W. S. Gray, Phys. Rev. C10 (1974) 2286 P. D. Kunz, Computer program DWUCK (1967), University of Colorado, unpublished M. Lu and W. P. Alford, Phys. Rev. C3 (1971) 1243 J. C. Tippett and D. G. Burke, Can. J. Phys. 50 (1972) 3152 D. G. Burke and J. C. Waddington, Nucl. Phys. A193 (1972) 271 H. C. Cheung, G. Lovhoiden and D. G. Burke, Can. J. Phys. 52 (1974) 2108 D. G. Burke and J. C. Waddington, Can. J. Phys. 50 (1972) 700 J. D. Panar and D. G. Burke, to be published V. G. Soloviev and P. Vogel, Nucl. Phys. A92 (1967) 449 J. Kern, G. Mauron and B. Michaud, Helv. Phys. Acta 41 (1968) 1280 R. A. O'Neil, D. G. Burke and W. P. Alford, Nucl. Phys. A167 (1971) 481 J. C. Tippett, Ph.D. Dissertation, McMaster University, Hamilton (1972) E. R. Marshalek and J. O. Rasmussen, Nucl. Phys. 43 (1963) 438 P. Morgan, B. S. Nielsen and C. Sondergaard, private communication (1974)