Absolute E1, ΔK = 1 transition probabilities between multi-quasiparticle high-spin states in 176Hf and 178Hf

Nuclear Physics A376 (1982) 45162 © North-Holland Publishing Company

ABSOLUTE El, dK = 1 TRANSITION PROBABILITIES BETWEEN MULTI-QUASIPARTICLE HIGH~PIN STATFS IN "6Hf AND "aHf L. K. KOSTOV T, H. ROTTER, C. HEISER, H. PRADE and F. STARY Zentralinstitutfrir Kern/ôrschuny Rossendor/; 8051 Dresden, DDR and W. ANDREJTSCHEFF r

Department of Physics, Rufgers Uniuersilr f', Nex" Brunsx" ick, Nex" Jersey 08903, USA . Received 4 August 1981 (Revised 11 September 1981) Abstract : Applying thegeneralized centroid shift method in (a, 2n) reactions, the half-lives of the 3080 keV I S* state in "6Hf and of the 1637 keV 5 - state in " B Hf have been measured as T Z = 0.20_* $;ôé ns and T~ = 0.40f0.10 ns, respectively. B(E 1) values of K-allowed E1 transitions n ~* [624] ~ ~- [514] are derived, and together with other data on similar transitions in odd-A nuclei, compared with predictions of the Nilsson plus pairing model. In "6Hf, the 15 + and 14 - states at 3080 and 2866 keV, respectively, appear as quite pure deformed 4QP configurations . In the 2QP state at 1637 keV in "°Hf, possible strong mixing of vibrational components is discussed coupled via 2QP K-admixtures arising from the partial alignment of the i, a ;a neutron.

E

NUCLEAR REACTIONS "°~ "6Yb(a, xn), E = 27 MeV ; measured Er , 1,, ay(t). "e . "6 . "', t,eHf levels deduced T, ;z, B(Â). Enriched targets. Germanium detectors. Nilsson plus pairing calculations .

1 . Introduction Nuclear spectroscopic investigations of the nuclides t' 6Hf and t' 8Hf [refs. t' 2)] revealed several rotational bands at higher excitation energies (> 1 Mew, some of them built on isomers. The results were interpreted in terms of prolate multi-quasiparticle Nilsson configurations. Calculations of level energies within a cranked HFB approach s) for t '6Hf provided further support for this interpretation. As these findings are of interest for the yrast spectroscopy of deformed nuclei, it appears important to extend the investigations considering in more detail absolute transition i Permanent address: Bulgarian Academy of Sciences, Institute of Nuclear Research and Nuclear Energy, 1113 Sofia, Bulgaria . rr Supported in part by the US National Science Foundation . 451

452

L. K. Kostovet al. /

i~e"

1~eNf

probabilities. From such studies, conclusions on configuration admixtures (i.e. on structural components of the wave functions involved) can be expected. One of the basic questions associated with the strw~ture ofhigh-spin states concerns their alignment, i .e. is the (noncollective) angular momentum of the quasiparticle(s) outside the core oriented along the axis of symmetry (deformation alignment) or along the axis of rotation (rotation alignment) or somewhere between (decoupling, partial alignment). Considering quasiparticle (QP) motion in a rotating frame, a procedure was proposed °) to obtain the degree of alignment in an experimental rotational band . In the case of deformation alignment, the spin projection K on the symmetry axis is a good quantum number. The wave functions are then presented by the Nilsson configurations of the quasiparticles involved, K-mixing can be neglected as a first approximation. In the cases of decoupling or rotation alignment, however, the spin projection K is no more a good quantum number and Kmixing (rather complicated if multi-quasiparticle states are involved) has to be taken into account. Thus, calculation of transition rates is quite simple if deformation alignment is assumed : the corresponding transition matrix elements are predicted by the Nilsson plus pairing model . Of course, the limitations of this model due to residual interactions should be considered, but they are mostly known from studies of transition rates between low-lying 1QP states [see e.g. ref. °)] . The multi~uasiparticle configurations in l'6. 1 'SHf are considered as deformation aligned. One of the strongest experimental arguments for this assumption is provided by the isomeric character l' s) of several Kforbidden transitions. However, model calculations of these Kforbidden transition rates were not performed so far because of the complexity of mixing calculations . The simple Nilsson plus pairing model can give predictions only for K-allowed transition strengths which are, on the other hand, difficult to determine experimentally due to the short lifetimes of the levels involved . The only Kallowed transition with a measured') strength between high-lying multi-quasiparticle configurations in these nuclei was the 22 - -" 20 - 97 .1 keV E2 transition in "6Hf. It has been shown 6), however, that such E2, dK = 2 transitions are strongly influenced by the quasiparticle-phonon interaction and the simple Nilsson plus pairing model fails to describe them properly. Nevertheless, we fmd that the E2 strength of the 97.1 keV transition [B(E2) = 3.2 x 10_ s e2 ~ b2] does not contradict the general trend of the systematics e) in deformed nuclei . In the present work, lifetime measurements of high-spin states in i'e. "BHf are described. Applying the generalized oentroid shift method, lifetimes below 0.5 ns were measured with germanium detectors in a delayed-coincidence experiment . From the experimental data, absolute transition strengths of Kallowed El transitions are derived and compared with predictions of the Nilsson plus pairing model as well as with similar results for low-lying 1QP and 2QP states in odd-A and odd-odd deformed nuclei, respectively .

L . K . Kostou et al. / ~, b . ~ieHÏ

453

2. Experimental techniques and analyzing procedure Using the 27 MeV a-particle beam of the Rossendorf cyclotron U-120, excited states in the yrast region of l '6Hf and l'BHf were populated following the'~4Yb(a, 2n) and "6Yb(a, 2n) reactions, respectively . The oxidic l '4Yb target (thickness about 20 mg/cm2) enriched to 97.5 % was deposited on a polyester foil of about 0.5 mg/emZ thickness. The enriched "6Yb target consisted of a 6 mg/cmZ self-supporting metallic foil . The timing measurements were performed by means of the y-r.f. method') . The start signals for the time-to-amplitude converter (TAC) were supplied by a planar Ge(Li) detector, while r.f. signals derived from the cyclotron oscillator were used to stop the TAC. The experiments on l' 6Hf were performed using a 10 ccn' planar Ge(Li) detector with an energy resolution of 2.4 keV FWHM at Ey ~ 200 keV. For investigating l'BHf where the 123 .1 keV transition of interest has to be separated reliably from a 121 keV transition, a 1 stns high-purity Ge detector (Ortec) with 0.6 keV resolution at EY x 120 keV was utilized . In the experiments on " 6Hf, the time resolution was 2to = 7.5 ns at Ey x 200 keV. In the case of "gHf, 2ia = 7 .5 ns at E,, x 130 keV was obtained . Both, delayed y-ray spectra and time distributions for selected y-ray energies (E,, x 80-1200 keV) were recorded for "6Hf. In "BHf, only time distributions in the region 80-460 keV were measured . The time distributions were taken in coincidence with up to 64 selected energy windows in the Ge spectrum and were stored in 64 x 128 channels. The time distributions were analyzed applying an advanced version a) of the centroid shift method (generalized centroid shift method). For each transition of interest three time distributions were measured with the energy selection windows set on the full energy peak and on the background above and below this peak . The background time distribution at the peak position was obtained by interpolating between the two measured background time distributions. Subtracting this interpolated background time spectrum from the time spectrum measured at the full energy peak position, the net time distribution of the full energy peak was obtained. Its centroid position depends on the transition energy and on the lifetime . Delayed y-ray transitions can be easily identified by the deviation of their centroid positions from the "zero-time line" obtained from prompt transitions. Ofcourse, it is important to define the "zero-time line" as exactly as possible, especially if half-lives down to 0.1 ns are to be determined. Compton background time distributions turn out to be delayed with about 0.2 ns for y-ray energies above 100 keV [ref. e)]. Intraband transitions between higher members of a rotational band are expected to appear prompt.

L. K. Koston et al. / "e . "sHf

454

3. Experimental results 3.1 . THE NUCLEUS "sHf

The centroid positions of time distributions measured for some y-ray transitions in t ' 8 Hf and "'Hf are displayed versus the transition energy E~ in fig. 1 .

~~6

Yb(a, 2n)»eHf

CEiJTROID POSITIONS OF TIME DISTRIBUTIONS o WITH INTERPOLATED BAp(GROUND SUBTRACTED " OF INTERPOLATED 84CKGROUNO

~n Z

Q 2 70 U 68

c

~66 W6~ Z Q 62

113.0 L-1.Ons 128.4

15

v

0

100

125

GAMMA-RAY ENERGY[keVl

150

Fig. l . Centroid positions of time distributions for some y-ray transitions in "8 Hf plotted versus the transition energy . The solid curve represents the zero-time line . The radius of thecircles corresponds to the statistical error of the centroid position . In the lower part, the y-ray energy spectrum observed with a l cm~ high-purity Ge detector is shown.

The time centroid of the 123 .1 keV transition in "BHf shows unambiguously a shift with respect to the zero-time line. The latter was defined in the energy region between 100 keV and 155 keV by M1 intraband transitions in t"Hf simultaneously produced by the ' ~6 Yb(a, 3n) reaction . From the centroid shift a half-life T}(1636.9 keV) = 0.40 f 0.10 ns

L. K. Kostou et nl. /

"eHf

"6 .

45 5

can be derived for the JK" = 55 - level de-excited by the 123.1 keV El transition (fig . 3). The error takes into account statistical and systematic uncertainties of the centroid position and of the zero-time line position . From the centroid shift of the time distribution obtained for the 113.0 keV transition in t "Hf, a half-life of T.~ = 0.70 ~ 0.15 ns was determined for the ~- level at 113 .0 keV . This result agrees within the errors with the already known 9) value T~ = 0.50 f 0.09 ns. 3 .2 . THE NUCLEUS "6Hf

In this case, the plot of centroid positions of time distributions versus the transition

»4Yb(a,2n)»6Hf

CENTROID POSITIONS OF TIME DISTRIBUTIONS c WITH INTERPOLATED 84CKGROl1~ID SUBTRACTED " OF INTERPOLATED BACKGROt1ND

r " Q17ns

0 2076 t-227ns

Z00

l

250

GAMMA-RAY ENERGY [keVl

300

Fig . 2. Centroid positions of time distributions for some y-ray transitions in " 6 Hf plotted versus the transition energy . In the lower part, the y-ray energy spxtrum observed with a 10 cm' planar Ge(Li) detector is shown . The hatched areas mark the positions of the energy windows selected . (See also caption to fig . 1 .)

L . K. Kostou et aJ. / "e . "aHj

456

01

°

energy (fig . 2) reveals a centroid shift of i(EY = 214 keV) = . 7±ô:ôs ns for the y-ray peak at 214 keV. However, this peak is a doublet and, therefore, the centroid position measured is due to contributions from two different time distributions. One component arises from the 9 -" 8 214.2 keV M1 intraband transition within the lowest K" = 6 band in t' Hf. The second component') is due to the 214.4 keV E1 transition between the 4QP states with J` = 15 and 14 in t' Hf (fig . 3). It appears that a level with spin J = 15 in a nucleus as heavy as t' Hf has

t°) +

+ 6

+

+

-

6-

-

274.0 MI/E2 I6+ 3266.4 K~ !6+ p7404,9514 ~4 .7

M0

249.7 UNI/E2) 14-

2866A K~14-

8- 11474 K~8 - 40s

24~4 I K*,415~ 401~.s

1781 .5 n151o,9624 1636.9 K 'S

K~rr, g+ 5 1 78r~s 6+ 1553~t 123 .1 EI 8- 1479 K~r_ 4+ K =8 n1510,7514 1330.3 EI

7~

1

6

6

j

4+ 306 .6 + ~93 .2 0

p7404,9514 n 5512, 7514

~~Hf loa

6

7iHf Ios

8

Fig . 3 . Partial level schemes of " Hf and " Hf according to refs . ' " ~) and this work . The framed halflives were measured in the present investigations.

indeed the chance to be populated appreciably in the (a, 2n) reaction at Ea = 27 MeV ifit is an yrast level. On the other hand, the 214.4 keV transition from the 15 level was not observed °) in the (a, 2n) reaction at EQ ~ 24 MeV but only in the (a, 4n) reaction . Other possible contributions to the 214 keV y-ray peak, e.g. from the 213 .8 keV transition tt) in ' Hf produced in the 'a Yb(a, 3n) and/or t' Yb(a, 2n) reactions or from the 213.4 keV transition s) in t' e Hf produced in the (a, 2n) reaction on the " Yb admixture of the target, were excluded because of missing of some other characteristic transitions in these nuclei . The half-life of the 15 state can be extracted from the centroid shift observed for the 214 keV peak if the intensity ratio of the 214.2 keV and the 214.4 keV transitions is determined . In ref. t°), the branching ratio I~214.2)/Ir(408 .3) = 1 .0/1 .2 for transitions from the 9 level is given. The experimental peak at 408 keV is, however, also a doublet t The interfering transition of 408.7 keV is an intraband transition from a higher lying 10 level. In our experiment, the ratio [Ir(214.4)+1~(214 .2)~/

+

t

6

ts

t

+

°).

+

-

3

L. K. Kostov et al. / "e . i'eHf

45 7

= 1 .1 was measured . On the other hand, in ref. 1°) the intensity ratio ly(408.3)/lY(408 .7) = 2.4 is observed at Ea = 22.5 MeV. At Ea = 27 MeV this value decreases as the population of the 10- level is expected to increase more strongly than that of the 9+ level . From all the above-mentioned considerations, we estimate the intensity ratio [1,,(214.4)+1.(214.2)]/L,(214.4) = 1 .7±0.4 in our experiment . The lifetime i associated with the 214.4 keV transition can be derived in the following way [lY(408 .3)+lY(408.7)]

I (214.2)+Iy (214 .4) t(214 s(214.4) = r .4+214 .2) = 0.29± °o ; ;e ns. lY(214.4) Thus, for the K` = 15+ level at 3080.4 keV the half-life Tt(3080.4 keV) = 0.20±ô :ôé ns results. This value can not be influenced by a possible half-life of the higher-lying K~ = 16 + level at 3266 .4 keV because it was not excited in our experiments with 27 MeV a-particles. The asymmetric right flank of the 184.8 keV 18F peak (fig . 2) is due to the 185:8 keV and 185 .9 keV transitions ") in "SHf, and not to the 186.0 keV transition 16 + -~ 15 + in "6Hf. From the centroid shift of the time distribution measured for the 207.4 keV transition in " SHf, a half-life Tt = 1 .56±0.15 ns was determined for the J~ _ ~+ level at 207 .4 keV, in good agreement with the value Tt = 1 .55 ns [ref. 9 )] . 4. Discus~on The 214.4 keV El transition in l'6Hfconnects two 4QP states with only one of the quasiparticles changing its configuration from the i,ILï = ~ orbital ~+ [624] to ~- [514]. The same configuration chânge occurs in the case of the 123.1 keV transition in l'SHf which connects two 2QP states. Thus, both transitions are Kallowed and their strength B(El) can be compared with predictions of the Nilsson plus pairing model via the hindrance factors FN = B(El)N/9(El) e=p. The parameters ofthe model used here are the same as in ref. 9). The of%ct of pairing correlations reduces electric transition moments by the correction factor P,~ = U,Uf- V,Vf, with U and Vbeing the occupation amplitudes : FN = FNP~. When the initial (i) and the final (f) quasiparticle states lie symmetrically with respect to the Fermilevel, the factor P,t becomes very small and thenthe accuracy of its calculation might be questioned . In the case of odd-A deformed nuclei, a BCS procedure including the blocking of%ct generally provides realistic occupation amplitudes [cf. e.g. refs.'" 8' 9)] . Massuran et al. is) derived occupation amplitudes for some Nilsson orbitals in several even-even nuclei, among them 1~6,1'BHf. For

458 ô p

~O

i

Nv

~O

rr+

~o

N

+ °~`~ o+v

r ~

~

Y~1 O

~ ~O

~D -

N O

f+'1

ri

r

N O

N

°z

~ _ ~L~

p  .~

^wV ~

~d

Ô ,.,

ô x

ô_ a

M

_

N

â

û rlrv I

u

pq

ô

x

~ N

O

V

ô

4. x

rw

0

r

~ N

W~

pp

ok+

+ -

. 0

i O

_C

. 0

0

~ N M

a

"_

~D

ôr+

N ~p

a

°~

v~ v1

Ö v1 _ C

M

N

~

O~

M vi

r M

r

? N M

~?

v,

o t~j

-

N

O N O

êd

O

~_ h r

In r Ö h C

rr+

Nn

+ v ~

r ~O O

Ô

v N ~

O 00

o0

-

-

vi O~

O 00

~

N

~ N

r

N ~

~ N

h

"-. N

t~+1

N

O -_

O+ O

N O

r N ~

a~ 'O

v N O

O

O

N Ô

O

Ô

O

~D N O

'C

W

ô

V a

x

N

u ..

N+ O" ~ -~ ~N~

âé

~~ I T n~ ~ ~?

N O

âc

M

O

~O

~

oo

N

N

N

N

'~

e ~ns~

v z

>

v '3 w'S

N

a °

2

2

ô

w

N

w

M

m i O q x

1

~

°

H

Ç

'~N

vi b ~ ~ u~p w

~O

ev i o

b

X

x

r

d

w

~.

w C .. 7 ~ .

mu

C -~ eO,Ç ~ O p ~ Nnz ~z ,C "C > u O y â~ . ~ "~ E ô '- v+ N U ~ N LL ~Ll ~ > YO .G .. ~ C u _ u ~. L .~ ôE4;~oF^ô "C b

~ cE "Ç a .~ cNd ,~ C C ~°+ û " o ~o ._ 3

~~,-0 .'~, .C ~ ' N ~. d g, â â ."= c x ~~oe ~ :: ;; II ~..O y ,~,ai ' ~ C Ç w w ua L Ô C -. ,C3 Yd$,O " ~ Y "v ~ N 3 ~ ~ _a çN ~~a " : ~ ûs

^âr yC~ y c`ivr .C ~ Ci C U ,G ô N a o

a_ ~ c E "pâ,~~ C

d~ ,~, °~ °~ L a

. cd , O "r ~ u _ ° ~ c a~ .Q~y ~ >~'C "° N ~~3 É~= C

op

p,

O

'-

N

M

C 3 â f1

"c v

m

P _

E w

N "ti .O ' N ~z=~G~~~ .oô=~'~~ ~ ;, o c oo

~,oô v E o^v ~ .C ô ~ a û ~ Û C Ô. ~, C ~~'c,,°~'~~ .c

w

vi

3

y " Ow0 . a~ C .: Ç`I",

~' a .°

w ~

7 ~O ".cu..w C ~. wrv ~ ~ ~ ~ C .~ "~~~ ~ " _ Y " O U :Ô q ~ ~. y

V1

oh C w C

O N

~ ^ N

â

ô 3

M

Ô

N

L

d ß

y ~ Ç û ~ a O' cd ad n ' F C_ ~ F ~ C ed d ~... ~ .C r "F ~ O ea ti âi Ç C ~ >, "00 N a  . "o v ç " ô .> :~~ a ~â C' Q y +'Ç ~ ~ Ç N ~~ ~ .a~ 83 . . ~ x~. ?' v ~ ~ â~~.~=

~-- a~ ~ w z .~

"~ ~ r~

L. K. Koston et al.

/'~b.

"BHj

459

these nuclei, we use their results. Their procedure appears quite careful ; it should be mentioned, however, that they neglected blocking effects and used interpolations of single-particle energies near the Fermi surface. In the analysis of E1 transitions between 2QP states in odd-odd nuclei'3), the consideration of the transition moment GGexP proved to be rather instructive GGexp- {B(E1)~LC(E1 ;A,Z)KhI

K,Kt - IC~I~rKrip~rl 2]} # .

The values GGexP of E1, dK = 1 transitions in odd-odd nuclei were shown' 3) to be systematically larger than those in neighbouring odd-A isotopes . The effect has been interpreted as arising from higher-order vibrational admixtures coupled via RPC and p-n interaction mixings. The moment GGexP was introduced in an effort to find a sensitive measure of experimental single-particle transition strengths which is independent of spin and mass-number, and is suitable for comparison of transitions between 1QP states in odd-A nuclei and multi-QP states in even-A nuclei . It contains, however, the pairing factor P,t and thus the possible uncertainties in its calculation. In table 1, the new data on the ~+ [624] .-. ~- [514] E1 transitions in l'6 .1'eHf are compared with earlier results for low-lying 1QP states in odd-A nuclei. So far, no corresponding data on transitions between high-lying (3-4 MeV) multi-QP states were available. Because of the higher level density and the different competing modes of excitation at these energies, larger transition moments are generally expected. Indeed, the experimental transition probabilities B(E1) in i'e. "g Hf turn out to be. considerably larger (by one or more orders of magnitude) than those in the odd-A nuclei . Besides, their values 2.1 x 10 -6 eZ ~ b and 1 .8 x 10 -6 e 2 ~ b are approximately equal. The pairing factor in "6Hf is nearly the same as those in the odd-A nuclei considered (P~ x 0.2). With this factor, the experimental transition rate is in reasonable agreement with the prediction of the Nilsson plus pairing model : FN = 0.4. This is a strong indication that the simple description of the " 6 Hf states involved as 4QP deformation-aligned Nilsson configurations works here reasonably . Nevertheless, the transition moment of the 214.4 keV transition GGexP = 0.068 is several times higher than those in the odd-A nuclei . In the spirit of the discussion in ref. i s), this higher value of the transition moment traces here some small admixtures in the wave functions, probably of vibrational type. The conclusions concerning the E1 transition in l' B Hf are less unambiguous. With the amplitudes U and V from ref. i2), a very small pairing correction factor Pc = 0.0023 follows, inevitably with large uncertainty. At this point it would be desirable to study the sensitivity of the theoretical factor P;t to variations of some nuclear parameters, e.g. deformations e2 and e4 within reasonable limits . It should be mentioned that the hexadecapole deformation e4 varies rapidly in this mass region ' e) and this affects thesingle-particle level scheme . It is not clear whether these variations

460

L. K. Koston et al. / ~'a . "e Hj

are accounted for by the use ' z) of empirical single-particle energies. Such studies are, however, beyond the scope of this paper and for l'6" l'gHf we consider here only the PZ values resulting from ref. ' i) (in table 1 only the Nilsson hindrance factors FN are calculated for different quadrupole deformations). With regard to the above-mentioned uncertainties, we would like to discuss two cases : (i) the "true" pairing correction factor in "gHf is as large as that in "6Hf (P~ z 0.2) and (ü) the calculated factor Frf = 0.0023 is realistic. We discuss here case (i) mainly as a precaution . Some basis for such a discussion is provided by the fact that the two B(E1) values in "6. l ' g Hf are approximately equal and that the BCS procedure 12) needs further refinements before drawing absolutely reliable conclusions on the small but crucial values ofthepairing correction factor . In case (i), the conclusions from the measured E1 transition rate between the 2QP states in l ' g Hf would be similar to those for "6 Hf. Appreciable, but not very strong, vibrational admixtures in the transition matrix elements (GG~ xn 0.066) have to be assumed. The situation changes drastically in case (ü). With FN = 0.004, the Nilsson plus pairing model does not provide a reasonable description of the transition rate. The transition moment GGexP = 0.66 is much larger than all the corresponding quantities in table 1 . Such value can be explained only by strong vibrational admixtures . The 5 level at 1636.9 keV in "gHf is also de-excited by a 1330.3 keV four-fold Kforbidden E1 transition to the 4+ member of the ground-state rotational band . The corresponding value B(E1) = 3 x 10-9e2 ~ b appears too large 9) for this degree of Kforbiddenness. This fact provides support for the case (ü), i.e. for strong vibrational admixtures in the 5 - state at 1636.9 keV. Nothing is known about the possible location of Kx = 4 - , 5 - vibrational excitations whichmight directly couple to the 1637 keV state under consideration (assuming couplings with dK = 0, 1). In ref. ia), K" = 0- , 1 - , 2 -, and 3 - octupole states are calculated and compared to some experimental data . It is important to mention that strong K-mixing is found ia) for these states, i .e. all the above-mentioned Kvalues between 0 and 3 might contribute to the wave function of a certain octupole vibrational level. In l 'g Hf, a 5 - state results from the calculations at about 1 .6 MeV as a rotational member of an octupole band with predominantly K = 2. The energy spacing to the experimental 1637 keV 5 - 2QP state suggests a possible strong 2QPvibrational mixing . The presence of many 2QP combinations with different K-values arising from vibrational excitations in the wave function of the 1637 keV state could explain qualitatively the experimental E1 transition probabilities in consideration. For example, in 1saGd, values of B(E1) x 10()Q~000x 10- gee ~ b are found for 5 - -~ 4+ transitions from Kx = 0- and 1 - vibrational bands's) . However, in order to realize such mixing, 2QP components with K < 5 should be present in the wave function of the Kx = 5 - 2QP state . In the analysis of several 2QP negative-parity bands of "o " l'2Yb including one i~.~neutron, Walker et Q1. 16) arrive at the conclusion that these bands can be con-

L . K. Kostou et al . / ~ ~s . ~'BHj

461

sidered as "semi-aligned" : the i~ neutron is decoupled from the core, while the angular momentum of the other particle is oriented along the axis of deformation. With the formalism of ref. a) we analyzed the alignment of these bands in l'o, i~z~ and compared the results with those for the K` = 5 - band in t'eHf involving the ~ + [624] i~. orbital. For all these bands we found at low rotational frequencies about the same aligned angular momentum of i x Zit. If we assume that the i ~ neutron in the 5 - state ( t'eHf) is at least partially aligned, the presence of i~ < ~ admixtures in the wave function becomes understandable . The resulting Kmixings in this state can then couple to 5- vibrational excitations with lower Kvalues . The idea that in a 2QP state the i ~ neutron is often dewupled from the core (while the other particle is not) is supported also by other examples . In several even-even nuclei, 8 - -" 8+ El transitions with dK = 8 (7 K-forbidden) are observed . If the t~aH~, K` = 8 - states in these cases involve an i~ neutron (ireYb, tsoW, tez~ s~ -to the transition rates B(El) ~ 10 -10-16 ez " b are considerably higher 9) than 10-tsez " b (teo, tszH~, In the those where no i~. neutron is involved, B(El) K" = 15- 4QP yrast state in l 'sHf, discussed above, the i~, neutron appears oriented along the deformation axis ; no strong admixtures are needed for the explanation of the El transition matrix element (~ = 0.4). A plausible explanations for the different degrees of alignment of the i,~ neutron in these hafnium isotopes might be associated with the increasing ta) hexadecapole deformation from l'sHf to t 'BHf. Thereby, the level spacings in the i,~ shell become somewhat smaller and the Coriolis effects stronger . 5. Summary and conclusions With the generalized centroid shift method, subnanosecond lifetimes of a 4QP 15+ state in t'6Hf and of a 2QP 5 - state in "BHf have been measured in the (a, 2n) reaction . From the experimental results, absolute transition strengths of K-allowed E1 transitions between multi-QP states are derived. In both cases, the transition is realized by changing the configuration of a quasineutron : ~+ [624] -~ -~-[514] . Together with data on similar transitions between 1QP states in odd-A nuclei the new experimental results are compared with predictions of the Nilsson plus pairing model. An important result of the present work is the conclusion that the 15- (3080.4 keV) and 14 + (2866.0 keV) states in "sHf appear as quite pure deformed 4QP configurations with some small vibrational admixtures . In the case of the 2QP state at 1637 keV in l 'SHf, some ambiguity is introduced by the uncertainty in the calculation of a very small pairing correction factor . If the occupation amplitudes U and V from ref. tz) are correct, strong vibrational admixtures have to be assumed in order to explain the experimental transition strength . Such admixtures could be introduced via 2QP K-mixings, e.g. in the wave function t We are indebted to the referee for this suggestion .

462

of the initial 2QP 5 - state. In this case, the i,~ neutron (~ + [624]) appears as decoupled from the core. Indication for decoupled i,~ neutrons in 2QP states are observed also in other even-even deformed nuclei from the analysis of side bands te) as well as from the transition strengths of highly Kforbidden E1 transitions. We are indebted to Professors K. H. Kaun, Zh. Zhelev, and G. M. Temmer for their interest in this work. The support in computational problems of Dr. G. Winter and discussions with Dr. S. Frauendorf are greatly appreciated. References 1) T. L . Khoo, F . M . Bernthai, R . A . Warner, G . F. Bertsch and G . Hamilton, Phys . Rev . Lett . 35 (1975) 1256 ; T. L . Khoo, F . M . Bernthai, R . G . H . Robertson and R . A . Warner, Phys . Rev . Lett. 37 (1976) 823 2) T. L . Khoo and G . L¢vh~iden, Phys . Lett. 67B (1977) 271 3) A . Faessler and M . Ploszajczak, Phys . Rev . 16 (1977) 2032 4) R . Bengtsson and S . Frauendorf, Nucl . Phys. A327 (1979) 139 5) W . Andrejtscheft; Sov. J. Part. Nucl . 7 (1976) 415 6) W . Andrejtscheff and P. Manfrass, Phys . Lett . SSB (1975) 159 7) W . Andrejtscheff, F . Dubbers, P . Manfrass and K . D . Schilling, Nucl. Phys . A190 (1972) 489 8) K . D . Schilling, L . Kâubler, F . Stary and W. Andrejtscheff, Nucl . Phys. A265 (1976) 58 9) W . Andrejtscheff, K. D . Schilling and P. Manfrass, Atomic Data and Nucl . Data Tables 16 (1975) 515 10) T . L . Khoo,1 . C. Waddington and M . W . Johns, Can. J . Phys . 51 (1973) 2307 11) G . D . Dracoulis and P . M . Walker, Nucl . Phys . A342 (1980) 335 12) H . Massmann, J . O. Rasmussen, T . E. Ward, P . E . Haustein and F . M . Bernthai, Phys . Rev . C9 (1974)2312 13) W . Andrejtscheff and K . D . Schilling, Z . Phys . A289 (1978) I07 14) K . Neergard and P. Vogel, Nucl . Phys. A145 (1970) 33 I S) R . C. Greenwood, C . W . Reich, H . A . Baader, H . R . Koch, D. Breitig, O. W. B . Schult, B . Gogelbert, A . Bäcklin, W . Mampe, T . v. Egidy and . K . Schreckenbach, Nucl . Phys. A304 (1978) 327 16) P. M . Walker, S. R. Faber, W . H . Bentley, R . M . Ronningen and R . B . Firestone, Nucl . Phys . A343 (1980)45 ; P. M . Walker, W . H . Bentley, S. R . Faber, R . M . Ronningen, R . B . Firestone, F . M . Bernthai, J . Borggreen, J . Pedersen and G . Sielten, Nucl. Phys. A36d (1981) 61 17) A. R . Agnihotry, K . P . Gopinathan and H . C. Jain, Phys. Rev. C9 (1974) 336 18) V . G . Soloviev, Theory of complex nuclei, ch . 7 (Pergamon, New York, 1976) p. 264