Isomerism in 176Hf and some neighbouring even nuclei

Nuclear Physics A96 (1967) 561--587; (~) North-Holland Publishing Co., Amsterdam

I 1.E.4: 3.A

Not to be reproduced by photo!~rint or microfihn withoat written permission from the publisher

ISOMERISM

I N 176Hf A N D S O M E

NEIGHBOURING

EVEN NUCLEI

J. B O R G G R E E N , N. J. S. HANSEN, J. PEDERSEN, L. W E S T G A A R D t , J. ZYLICZ+t and S. BJ~)RNHOLM

The Niels Bohr Institute, University of Copenhagen, Denmark Received 24 January 1967 Abstract: Isomeric states in some doubly even nuclei are investigated with the use of a pulsed beam technique. In *76Hfa level at 1562 has a half-life of 10.3/zs and a level at 1335 keV has a half-life of 13.0/zs. In lr~Yb an isomeric state at 1520 keV with a half-life of 820 Its is studied. In ~7(;Yb, an isomeric level with a half-life of 12 s is lying at 104l keV, and in as°W an isomeric level with a half-life of 5.2 ms and an energy of 1530 keV above the ground state is studied. All the isomers are ascribed to two-quasiparticle states which decay to a lower lying rotational band by Kforbidden 7-transitions. The level at 1562 keV in ~7~Hf is ascribed to the coupling of the two proton orbitals ~+[404] and ~- [514] to a spin and parity 8 -. The other isomer in 17~Hf, at 1335 keV, and the one in mYb, are ascribed to the coupling of the neutron orbitals ?~ [512] and }-[514] to give K ~t = 6% The two isomeric states in a76Yb and ~s~W are due to the coupling of the neutron orbitals ½-[514] and ~-[624] to a spin and parity 8 . The branching ratios of the decays of the isomeric states are analysed and compared to theoretical predictions. The energies of the two-quasiparticle states are compared to calculations of the energy gap based on the Nilsson model. Comparisons are also made with pairing energies calculated on the basis of empirical neutron and proton separation energies.

E

N U C L E A R REACTIONS 176Lu(p, nT), lSITa(p, 2n7), E = 10, 12 MeV; measured PT" delay, l~aYb(d, PT), 17~yb( d, d'),), E = 12 MeV; measured d7-delay, a~GHf, ~74'176yh, ~8°W levels deduced T~. Enriched 'TC'Lu, 173,176yb targets, Ge(Li) detector. RADIOACTIVITY l:6mHf, 174m,176myb, 18°roW; measured E;,, I v, lee, 77-, Vce-cOin, ~,cedelay, l:6Hf, lVa,l:6yb, Js°W deduced levels, T@, J , m

1. Introduction T r a n s i t i o n s b e t w e e n levels o f d i f f e r e n t r o t a t i o n a l b a n d s i n n o n - s p h e r i c a l n u c l e i m a y b e h i g h l y r e t a r d e d c o m p a r e d t o t h e s i n g l e - p a r t i c l e e s t i m a t e s o f t h e t r a n s i t i o n r a t e s 1, .~). i f t h e d i f f e r e n c e in K - q u a n t u m

number

]AK°I is l a r g e r t h a n t h e m u l t i p o l e o r d e r L,

it is i m p o s s i b l e t o c o n s t r u c t a v e c t o r t r i a n g l e f r o m t h e s p i n s I~ a n d If o f t h e i n i t i a l a n d f i n a l n u c l e a r s t a t e s w i t h p r o j e c t i o n s K ° a n d K~° a n d t h e a n g u l a r m o m e n t u m outcoming

L of the

p h o t o n . T r a n s i t i o n s m a y be c o n s i d e r e d t o o c c u r b y v i r t u e o f s m a l l K-

admixtures to the main components of the wave functions. We denote the unperturbed p r o j e c t i o n s b y K °, A K °, etc. T h e d e g r e e o f K - f o r b i d d e n n e s s is g i v e n b y t h e v a l u e t Present address: The Swedish Research Councils' Laboratory, Studsvik, Nykbping, Sweden. tt On leave from The Institute of Nuclear Research, Swierk near Warsaw, Poland. 561

562

J. BORGGREEN et al.

v = ] A K ° I - L . The amount of retardation per unit of v depends on the purity of the states involved as well as on the specific transition rates associated with the admixtures. One may write the retardation factor, Fw, i.e., the ratio of the measured half-life to that predicted according to the Weisskopf single-particle estimate 1), t~(exp)/t,(s.p.e.), in the form

Fw = (fw) v,

(1)

where fw is the degree of forbiddenness per unit of v. if several K-forbidden 7-rays of the same multipolarity issue from an isomeric level, the relative intensities follow the rules of Bohr and Mottelson a) provided, generally, that only leading order non-vanishing terms from the admixed K-impurities contribute to the transition probabilities. The Bohr-Mottelson expression represents a generalization of the Alaga rule 4) valid in first order for K-allowed transitions. In the case LAK°[ > L (or v > 0), it simply predicts relative intensities equal to those obtained by the use of the Alaga rule with Ki = K °-T-v and Kr = K °. A minus sign applies if K ° > Ke° and a plus sign if K ° < Kf°. In other words, the effect of all the possible K-admixtures which give rise to transitions of the type L = I K i - K f l is equivalent to a hypothetical case in which the initial state contains an admixture Ki = K ° -T-v whereas the final states are regarded as pure. The two rules can be regarded as expressions for the leading order contributions to a more general expansion of the transition rates in powers of the angular momenta. Higher order effects have been anticipated a) and are frequently observed with Kallowed transitions; see, e.g., ref. 5). An especially simple formulation of the correction terms, taking into account admixtures of the type K i = Ki°+ ( v + 1) or, more correctly, transitions of the type L = I g j - g e [ + l , has been proposed by Michailov and Michailova6). For our purpose ]AK°J > L, Ki° > Ke° # ½ their formula reads B ( L; I i --~ If) = 2

× (/i + Ki°)!(/i - K i ° + v)[ M 2 ( I + 3 ) 2 , ( I i - / ( ° ) ! ( I , +K~ ° - ~)!

(2)

where ,~ = [It(If+ I ) - I ~ ( I ~ + l)]al.

(3)

Here, M and al are constants. The Bohr-Mottelson rule corresponds to al = 0, the Alaga rule to v = 0 and al = 0. In even nuclei of mass numbers around 180, a number of high-spin levels are found to be K-isomers, and several more may be expected. These levels are interpreted as two-quasiparticle configurations. Isomerism is particularly likely if the lowest twoquasiparticle configuration - the (K, K + 1) state in the slightly awkward notation of

563

ISOMERISM I N E V E N N U C L E I

G a l l a g h e r and Soloviev 7) _ has a high spin projection, (K > 5). The energy o f such a state m a y in first a p p r o x i m a t i o n be assumed to equal twice the pairing energy. Thus, E ( i s o m e r ) = x / A Z + ( ~ l - - d . ) z + \ / A 2 + ( ~ 2 - - , , ~ ) 2 ~.~ 2A,

(4)

where A is the p a i r i n g energy, el and e2 are the single-particle eigenvalues for the K and K + 1 Nilsson states, respectively, and 2 is the chemical potential. The value o f A can be d e t e r m i n e d i n d e p e n d e n t l y f r o m odd-even mass differences. Alternatively, energies o f t w o - q u a s i p a r t i c l e levels can be calculated on the basis o f the Nilsson scheme t a k i n g into account p a i r i n g effects. Early theoretical predictions 7) o f the spin, parities, configurations and energies o f the levels in question are given in table 1. TABLE 1 Two-quasiparticle levels which may occur as K-isomers in the A ~ 180 region. Two-neutron states (configuration and energies) Nuclei

17°Er, 172Yb 74Yb, lV6Hf

N

,~ [51211 {-[5141j 6+ (keV)

,~- [5141t 9+[6241j8(keV)

102 2000 104 1600 2300 ~rGYb, 178Hf, Is°W, lS2Os, a84Pt 106 2000 1500 18°Hf, ls~W 108 2000 Two-proton states (configuration and energies) Even isotopes of Z ~ ~[404]t ~+ [402]/ _[514]/ 8 ~-[5141J7~ (keV) (keV) Yb 70 2400 Hf 72 1000 1800 W 74 2000 1300

~-[512]] ~ ~[624]/ 7(keV) -2700 1700 2300 5+ [4021t 6+ 7,+[4041/ (keV) 2300 1900 1400

Energies calculated (ref. 7)) on the basis of the pairing model with the included effect of blocking and neglected spin-spin interaction. The present w o r k is d e v o t e d to K-isomers in ~76 Hf, 174, 176yb a n d ~8o W, p r o d u c e d in nuclear reactions and studied by spectroscopic techniques. The results are c o m p a r e d with d a t a for o t h e r isomers in this region o f the chart o f nucleides a n d it is f o u n d that (i). Two different n e u t r o n configurations with K ~ = 6 + a n d 8 - , respectively, a n d one p r o t o n configuration with K ~ = 8 - occur repeatedly. (ii). The r e d u c e d r e t a r d a t i o n factor fw, eq. (1), varies from 3000 to 30 for the E2 transitions a n d f r o m 50 to 230 for the E1 transitions considered. (iii). The b r a n c h i n g ratios for the E2 transitions deviate f r o m the predictions o f the generalised A l a g a rule. Consistency with e x p e r i m e n t a l results is obtained, however, using r e a s o n a b l e mixing p a r a m e t e r s a 1 a c c o r d i n g to eqs. (2) a n d (3). (iv). The excitation energies o f a p a r t i c u l a r two-quasiparticle configuration vary as much as 300 keV when going f r o m one nucleide to a n o t h e r with the same particle

564

J. BORGGREENet al.

number. In general, a prediction of the excitation energy on the basis of eq. (4) is accurate only within +200 keV.

2. Survey of K-isomers The existing literature sources on K-isomers of 176Hf, 174,176yb and ~S°W are briefly reviewed in this section. Studying the 176Hf(7, n) reaction, Brandi et al. 8) observed a 10.5 /is 1320 keV isomer in 176Hf for which they suggested a K = I = 5 assignment. Two-quasiparticle levels of K = 5 are, however, theoretically predicted to lie significantly higher in 176Hf (table 1, ref. 7)). Two other states seem to be more probable as 176Hf Kisomers: the two-proton {3- [514], ~ + [404]}8- analogue of the 8- levels 7) known in 17SHf and 18°Hf and the two-neutron {~ [514], -~[512]}6 + level predicted for the N = 104 isotopes at an energy of 1.6 MeV (table 1). In order to clear up the nature of the 1320 keV level and at the same time to search for other possible isomers, it was decided to produce )76mHf in the 176Lu(p, n) reaction and to study the delayed 7-transitions with half-lives longer than 51~s. The two-neutron 6 + configuration, expected to lie low in the N = 104 isotones, was ascribed to the 850 ps 1520 keV isomer of 174Yb observed by Kantele 9) in the beta decay of 174Tm (see also ref. 11)). The same level was found by Funke el al. 12) to be populated in the electron-capture decay of 174Lu. These authors, however, proposed the two-neutron {~--[512], °+[624]}7- configuration, in the present work, the above 174myb isomer was produced by the 173yb(d, p) reaction with 12 MeV deuterons. It was re-investigated with the aim to establish definitely its configuration. Observing delayed 7-rays after inelastic scattering of 14 MeV neutrons on 176yb, Kantele l o) found 7-lines of 391,293 and 190 keV decaying with a half-life of 11.7 s. He interpreted these lines as the rotational 8 + --+ 6 +, 6 + -+ 4 + and 4 + -+ 2 + transitions which might be associated with the decay of the two-neutron {~- [514], ~-+ [624]} 8- isomeric state. This configuration can also be ascribed to the 8- levels at 1148 keV in ~7SHf (see discussion in subsect. 8.1), an isotone of 176Yb (N = 106). The ~v6myb activity was produced in the present work by (d, d') or (d, pn) reactions with 12 MeV deuterons. The expected E1 isomeric transition as well as the E2, 2 + --+ 0 + rotational transition were found. After the completion of this experiment, Vergnes et al. ~a) reported similar results. They produced the isomer by the (n, n') reaction, however. The above {~- [514], ~+ [624]}8- two-neutron configuration might possibly also be ascribed to the 5.2 ms isomer of ~S°w (N = 106), refs. 1s-iv). According to Remaev et al. ~7), this isomer has an energy of 1.46 MeV and decays (i) to the 1.09 MeV 8 + rotational level of the ground state and (ii) to a 1.31 MeV 6 + level of unknown configuration. Also this 5.2 ms ~s°mw activity was reinvestigated. In the present investigation special attention was paid to the determination of the multipolarities of the isomeric transitions through measurements of relative "e-ray-

ISOMERISM IN E V E N N U C L E I

565

and K- a n d / o r L-conversion line intensities. A special effort was devoted to the determination of possible weak ?,-branches, issuing from the isomer levels in ~74Yb and 176Hf"

3. Experimental technique The measurements were performed at the tandem Van de Graaff laboratory of the Niels Bohr Institute. The spectrometric equipment was placed on line with the ion beam in such a way that the bombarded targets could serve, in situ, as sources of the radiations to be investigated. Bombardments were cut off periodically and the intervals between beam pulses were used to study the delayed transitions. The duration of these intervals was adjustable to the half-lives of the isomers under investigation within the limits 1 /xs < t~ < 100 s. The measuring periods were usually divided into two equal parts, hereafter called "early" and "late", and two corresponding spectra were accumulated simultaneously. It was possible, therefore, to observe the decay of different parts of the spectrum. The intervals between beam pulses were sometimes chosen longer than the measuring periods in order to decrease the background effect from longlived activities induced in the target. The procedure is almost the same as previously described in greater detail in ref. 18). The available experimental facilities made it possible to do the following types of measurement: (i) singles ?,-ray spectra, (ii) spectra of internal conversion electrons, (iii) ~-7 and e-7 coincidences and (iv) determinations of half-lives of the isomeric states. Singles ?'-ray spectra were measured mostly with a lithium-drifted germanium detector of 3 cm 2 x 0.4 cm, while ?,-?' coincidences were studied by means of the scintillation technique. Internal conversion spectra were measured in a magnetic six-gap fl-ray spectrometer. This instrument was also used for the investigation of e-;~ coincidences; the ?,-rays were here recorded with a 3.8 cm x 3.8 cm NaI scintillation counter placed close to the target. With the use of a time-to-amplitude converter, decay curves of selected ?,-peaks or internal-conversion lines were measured. The targets were sufficiently thin, a few mg/cm 2, to allow measurements of internal conversion lines with a momentum resolution of 1-2 %. They were prepared by the methods described in ref. 19) in the form of selfsupporting, isotopically enriched, metallic foils. The isotopic compositions of the targets were as follows:

176Lu target: 30 % 175Lu, 70 % 176Lu; ~73yb target: 0.3 % 17~yb, 1.41% ~72yb, 95.0 % 173yb, 2.89 % 174yb, 0.34 % 176yb; 176yb target: 0.16% 171yb, 0.29% 172yb, 0.29% 1v3yb ' 1.45% 174yb, 97.77% 176yb. The isomers of 176Hf were most extensively studied. These experiments, being typical, are described in some detail in the following section. The measurements concerning the other isomers are reported more briefly in sects. 5-7.

s. BORGGREENeta[.

566

4. The 13.0 and 10.3 #s isomers of X76Hf 4.1. SINGLE SPECTRA OF INTERNAL CONVERSION ELECTRONS AND 7-RAYS The 176Hf activity was produced by the ~:6Lu(p, n) reaction with 10 MeV protons, using targets enriched to 70% in 176Lu. A 1.5 mg/cm a target was used for the investigation of the low-energy internal conversion spectrum, while conversion lines of higher energies and the 7-ray spectra were measured with a target of 3.5 mg/cm a. With a T .

~

Lu~'+IO MeV P

~

20/50/50

2B 53 ~.s

ps

li 2000

Hf ~

L)

li

o~ w

<,!!

03 i-z 0 o

1000

i

i

/i i

I

i /

L

f i

!

// .~_.J 1100

1200

1300

B9

1/.00

fl50O

',GAUSS × cm,

Fig. 1. Part o f the i n t e r n a l - c o n v e r s i o n s p e c t r u m o f I~HnHf m e a s u r e d in " e a r l y " a n d "late" t i m e intervals.

10.5 Fs half-life of lV6mHfin mind 8), the irradiation period and the measuring periods were chosen to be 20 and 2 x 25/~s, respectively. A part of the internal conversion spectrum, measured during the "early" and "late" time intervals, is shown in fig. 1. All but two lines decay with a half-life shorter than 25/~s. The two lines decaying with a longer half-life are interpreted as L- and Mconversion lines of the 128 keV isomeric transition in tTSHf. This 49/~s isomer s) is produced here by the l VSLu(p ' n)tV smHf reaction. The spectrum of y-lines is presented in fig. 2. It shows the difference of the spectra obtained with the Ge(Li) detector in "early" and "late" time intervals. The 7-transitions of 88, 202, 307, 737 and 1045 keV

0

5x103

104

[

100

/ I

[~

X

88.~v

Kx~

50

/

KX •

(3C

O o

Z

O3

EL

400

......

128.,~

0

500

w 1000

J_

150

500

?00

~,~,,~ ~

250

I

800 900 ENERGY (keY)

ENERGY (keV)

200

i

/[

2o2,,v

600

62V°

737 keV

300

I

307 key

1000

350

I

1100

]135O/o

1Q45 keV

20/50/60 us

1200

I

400

SPECTRUM

Lu 176 + 10 t'4eV p

DIFFERENCE

Fig. 2. Gamma-ray spectrum o£ 176mHf. The 7-intensitics, given under the peaks, are corrected For the photopeak efficiency and normalized to the 202 keY peak, 1~,(202) ~ 79 %.

0

0

O3 I,-Z

rY Ld Q_

(J :3.,

15xI04

LO

1500

-4

1000

790~80

790_480

440i45

202

307

737

1045

6

98±

1031

1.9±

10

II

0.3

6.4::I= 0.7

54±

165

5 9 3 £ 1 2 0 a)

1K

5.45_0.8(--1) 5 ±2 1.2+0.2(0) 4.5±0.6

- -

--

- -

-2.0:k0.3 6.8il.0(--2) 3.2i0.4 5.9±0.9(3) 4.5:k0.6 3.5i0.5(--3)

- -

2.9±0.6(0) a)

~K K/L (exp)

7.3(2) 6.4 3.7(--2) 6.6

- -

-6.5 -6.7 2.5(3) 6.8 1.3(--3)

- -

7 . 1 ( - 2 ) a)

El

2.6(1) 1.5 1.2(--1) 2.1

0

3.5(0) a) 0.3 1.65(-- 1) ~) 1.8 5.3(--2) e) 3.0 6.5(--3) 5.3 3.2(--3) 5.8 2.8(--1)

E2

c~K

3.6(1) 0.6

1.2(2) a)

E3

K / L (theoretical)

7.2(1) 6.5 3.5(-1) 6.5

6.8 1.5(2) 6.8 6.3(-3)

6.8

7 . 7 ( - 1 ) ~)

MI

L-conversion data. Used as a standard to determine the ¢% value of the 88 keV transition and ~K value o f the 307 kcV transition. Used as a standard to determine the c~K values o f the 737 a n d 1045 keV transitions. Line observed only in the coincidence measurements, see table 4.

75{: 8

227

a) 7,) e) a)

192_'--20

173

54,1)

205=_20

Iv

88

(keV)

E

TABLE 2 T h e ?,-ray a n d internal conversion data for the isomers of *:~Hf

1.55(0) 4.2

1.4(I 1)~)

M2

M2

MI + E 2

El a)

E2

E2

E2

E2

E2

Multipole order

Z e~

8

569

ISOMERISM IN EVEN NUCLEI

are believed to be identical with those observed by Brandi et al. 8). The transitions of 173 and 227 keV, observed in the conversion spectrum as well, have not been reported previously. A summary of the 7-ray and internal conversion data is given in table 2. Here, experimentally determined K-conversion coefficients and K/L ratios are compared with the relevant theoretical values. In the calculation of the experimental K-conversion coefficients, the theoretical ~K values of 202 and 307 keV transitions have been i i

104 20/120 ~s

"G o

Ld O~ ED Z D 0 n-" (D

103

K202 tv=13

0±0

5ps

~x

"'k

U

z

~o

K 227 t,,2 =I0 3 + 0 59s

~n

~o io 2o #o ,*o- ;o us

10 2

Z

BACKGROUND

K

227

Z o c)

Ig BACKGROUND K 202

10 ~F

• I

0

l

L

I

I

f

50

I

I

_

\ L

r

100 TINE (.us)

I

I

r

r

I

-:

i

150

Fig. 3. Decay curves measured for the K-conversion lines o f the 227 and 202 keV transitions. The irradiation period was 20 #s; for the data in the insert: 5 #s.

used as standards; in the decay scheme these transitions are placed between levels of the ground-state rotational band and are therefore considered to be pure E2 transitions. The two high-energy 7-transitions are also found to be E2 transitions, while the newly observed transitions of 173 and 227 keV have multipolarities M1 + E 2 and M2, respectively. 4.2. D E T E R M I N A T I O N

OF H A L F - L I V E S

Measurements of the decay of the K-conversion lines of the 227 and 202 keV transitions individually revealed a small but definite difference. The K-227 line decays with the half-line of 10.3_+0.5/is, while the half-life determined for the other line is

570

J. BORGGREEN e t

al.

13.0+0.5 gs. The latter figure is to be compared to the value 10.5 ps reported by Brandi et al. s). The first decay measurements were carried out with 20/~s irradiation periods and 120 ps intervals for studying the decay of the activity. Decay curves are shown in fig. 3. The curve corresponding to the 227 keV transition is a straight line in the logarithmic plot while the initial part of the other plot deviates from linearity. This becomes even more clear when the measurements are repeated with an irradiation time of 5 gs, see the insert in fig. 3. The plot for the 202 keV transition has the characteristic shape of the time curve corresponding to an activity which undergoes simultaneous growth and decay. This suggests that the 13.0 ps isomer, represented by the 202 keV transition, is produced partly directly and partly through the decay of some other isomeric state of a comparable half-life. One might guess that the 227 keV transition has to do with such a new isomer of l W H f with a half-life of 10.3 ps. TABLE 3 Intensities o f 7-rays coincident with the K-conversion line of the 202 keV transition in 17~'Hf ;e-lines in coinc, spectr.

Intensities of 7-lines (~o 202 keV transitions)

(keV) measured 56 (K X-rays) 88 307 737 1045

140 b) 14--2 59~8 54-8 29~4

adapted a) 140 13 62 65 35

a) Intensities adapted for the decay scheme (fig. 4) on the basis o f the direct m e a s u r e m e n t s , table 2. b) Intensities from the coincident experiment are normalized to those adapted in the decay scheme for K X-rays.

4.3. E L E C T R O N - G A M M A

COINCIDENCE STUDIES AND DECAY SCHEME

In order to construct the decay scheme of the 13.0 ps isomer, a y-ray spectrum coincident with the K-202 line was measured with a resolving time of ~ 80 ns. The experiment clearly established coincidence between this line and K X-rays as well as with the y-lines of 88, 307, 737 and 1045 keV. All these transitions fit energetically into the scheme of levels shown in fig. 4. In addition, the intensity balance for each level based on data of table 2 supports the proposed placing of the transitions. Adding to the y-ray intensities conversion line intensities, one finds that (i) the 307 and 737 keV transitions have the same intensity and (ii) the combined intensity of the 737 and 1045 keV lines equals the intensity of the 202 and 88 keV transitions separately. The relative intensities of y-lines observed in the coincidence spectrum a~ree very well with those adapted for the decay scheme on the basis of direct measurements, see table 3.

571

ISOMERISM I N E V E N N U C L E I

A special delayed coincidence experiment was performed with the aim to find out whether there is a relation between the 10.3 and 13.0 #s isomers. The first o f these isomers was represented by the K-227 electron line and the second by the 737 keV scintillation peak. With an effective resolving time o f the coincidence circuit being equal to 60/is, r a n d o m coincidences played a considerable role. The total number o f delayed coincidences observed was 1433. In a control experiment where the scintillation counter was m o v e d away f r o m the target and a radioactive source was used instead to produce the same average counting rate in the 737_+ 50 keV channels, the equivalent n u m b e r o f (random) coincidences was 590, which corresponds closely to the resolving time 60 #s. The existence of true delayed coincidences was thus definitely established; the 10.3 #s isomeric activity has to be ascribed to the t76Hf nucleus. The coincidence experiment also established the sequence of the transitions: the 227 keV transition is followed by the 737 keV transition. TABLE4 Results of the e-7 coincidence experiment with the K-227 and K-173 lines K-conversion line

K-227 K-173

7-lines observed in the coincidence experiment K X-rays (56 keV) K X-rays (56 keV) and 54 keV (El)

7-ray intensities (% K-conversion transitions) calculated a)

measured

95 95

110 ± 15

!~ 166 71 b)l

180±20

a) Assuming the decay scheme as shown in fig. 4.

~') For the M1 or E2 multipole order of the 54 keV transition one calculates the intensity of 165o or 2 ~;;, correspondingly.

In the ?,-ray spectrum measured in fast coincidence with the K-227 line only one line occurred. The energy of this line corresponds to the energy o f Hf K X-rays. Within experimental errors its intensity is equal to the intensity of K X-rays emitted concurrently with the emission of the K-conversion electrons (fluorescence yield 94 °o). see table 4. Efficiency calibration was here based on the results of coincidence experiments with the K-202 line. It is concluded that the 227 keV transition connects the two 176Hf isomeric levels directly. Consequently, the 10.3 #s isomer has an excitation energy o f 1562 keV. In the y-ray spectrum coincident with the K-173 line, again only one line was observed and its energy is close to the energy of H f K X-rays. The intensity, however, is twice as high as expected from K-conversion alone (table 4.) This may be consistently explained by assuming the 1562 keV level to be deexcited by a cascade consisting o f the 173 keV transition and a previously unobserved transition of 54 keV parallel to the 227 keV transition. The 54 keV transition must be E l , because internal conversion

572

J. BORGGREEN et al.

would otherwise dominate over 7-emission and the excess of -~ 54 keV intensity observed in the coincidence spectrum could not be accounted for. The 54 keV line was not seen in the singles 7-ray spectrum (fig. 2) because its energy is almost the same as that of the K X-rays. On the "tail" of the L-88 line in the conversion spectrum E

(keY)

K l ~

1562

8

8-

1508

6

7+ - -

1Q.3 ~ 0 . 5 IJS .rE1, (26)

227

13.0 + 0.5~Js l

173

M2

M1 + E2

(23)

(26)

i 1335

6

6+

597

0

6+

2go

o

4+

88

0

2+

0

0

0+

i

737 E2

(65) 1045 E2 (35) !

307

E2 i65)

_ _ _ 4

. . . . .

i 202 E2 ,1100)

i 88 E2

(10¢0) H f 176

F i g . 4. D e c a y s c h e m e o f the 1335 a n d 1562 k e V i s o m e r s o f 176Hf.

two peaks appeared, which could be interpreted as L and M conversion lines of the 54 keV transition. This interpretation is ambiguous, however, because Auger-electron lines are expected at the same part of the spectrum. The intensity determination was not accurate enough to be a criterion in this case. The above experiment does not

573

ISOMERISM IN EVEN NUCLEI

tell us which o f the two cascading transitions is the first one. One m a y r e a s o n a b l y assume, however, t h a t the M1 + E2 t r a n s i t i o n o f 173 keV is the lower one, deexciting a r o t a t i o n a l state at 1508 keV built on the 1335 k e V isomeric level, as shown in fig. 4. 4.4. INTERPRETATION The E2 m u l t i p o l a r i t y o f the 737 a n d 1045 keV transitions, leading respectively to the 6 + a n d 4 + levels o f the g r o u n d - s t a t e r o t a t i o n a l band, indicate a spin o f 4, 5 or 6 a n d positive p a r i t y for the 1335 keV isomer. In view o f the lack o f E2 t r a n s i t i o n to the 2 + r o t a t i o n a l state, the 4 + assignment seems i m p r o b a b l e . C o n s i d e r i n g the 5 + a n d 6 + possibilities one w o u l d choose the 6 + assignment resulting f r o m the coupling o f the 5 - [512] a n d ~ - [514] n e u t r o n orbitals, since 5 + t w o - q u a s i p a r t i c l e levels in tV6Hf are calculated 7) to lie essentially higher. TABLE 5

Analysis of the rotational parameter A (Erot -- A 1 (I+ 1)) Head of the rotational band

ground state 1335 keV level

I = K~ 0 / 6 I = K -- ~ 5 t4

A (keV)

14.7--A 14.7 o/ (/o)

14.7 12.4 14.4 17.3

0 16 2 --18

The 1508 keV is assumed to be the first rotational state built on the 1335 keV level. The energy spacing between the isomeric level at 1335 keV a n d what m o s t p r o b a b l y is its first r o t a t i o n a l state at 1508 keV is further i n c o m p a t i b l e with a K = 5 assignment, whereas it agrees with the K = 6 assignment: A c c o r d i n g to the general predictions zo) based on c o n s i d e r a t i o n s o f the p a i r i n g effect, the m o m e n t o f inertia o f a t w o - q u a s i p a r t i c l e level is expected to be larger t h a n t h a t o f the g r o u n d state. F o l l o w ing the simple p r o c e d u r e p r o p o s e d by Peker ~ 1), one m a y quantitatively estimate the relative increase in the m o m e n t o f inertia o f any t w o - q u a s i p a r t i c l e state by a d d i n g the relative c o n t r i b u t i o n s o f each u n p a i r e d particle, such as these c o n t r i b u t i o n s are k n o w n 2o) f r o m o d d - m a s s nuclei. A p p l y i n g the p r o c e d u r e to the isomeric level u n d e r discussion, the m o m e n t o f inertia is p r e d i c t e d to be 15-30 ~ larger t h a n for the g r o u n d state. The p r e d i c t e d value o f A is then 10.6-12.4 keV, in agreement with the value calculated for K = 6 (table 5). I f the spin were 5, the e x p e r i m e n t a l value o f A w o u l d be 14.4 keV, or j u s t 2 ~ smaller t h a n for the g r o u n d - s t a t e band. Such a smaller effect o f the b r e a k i n g o f a p a i r is very unlikely. W i t h spin a n d p a r i t y 6 + for the 1335 keV level, the 1562 keV isomer can be assigned K = = 8 - a n d i n t e r p r e t e d s t r a i g h t f o r w a r d as the theoretically p r e d i c t e d t w o - p r o t o n excitation with the c o n f i g u r a t i o n {9-[514], ~ + [ 4 0 4 ] } 8 - . The ratio o f the cross

574

J. BORGGREEN et al.

sections ¢r(6)/a(8) for producing the two isomers in the (p, n) process is equal to one within the experimental uncertainty for proton energies between 8.6 and 10 MeV. This agrees with what would be expected when the target spin is 7. The absolute and relative transition probabilities of the 7-rays from the 1335 and 1562 keV levels as well as those deexciting other isomeric states, described in the following, are discussed together in the concluding section.

5. The 820 /~s isomer in 174yb The 174myb isomer k n o w n from studies of the 174Tm and 174Lu decays 9, I I , 12) was produced in the present work by the (d, p) reaction, bombarding 173yb targets with 12 MeV deuterons. The measurements aimed first of all at the determination of the K-conversion coefficient for the strongest, 994 keV, transition between the isomeric level and the 6 + rotational state in order to establish the multipole order of the transiTABLE 6 The 7-ray and internal conversion data for m Y b

E..

(keV) 76 176 273 365 a) 629 b) 994 1265

17 e) (relative)

1000 < 25 870-k 160 35±10

IK o) (relative)

K/L

220 68 < i

1.6-:0.2 e) 3.3~0.5 e)

/total

C/o decay)

3.3

(100) 100 96 <2 < 3 96 4

a) Unobserved here rotational 8+ -+ 6+ transition; energy calculated.

b) Unobserved transition between the isomeric level and the 8+ rotational state; the limit of the intensity is in agreement with Kantele et al. lo). e) From 7-~' coincidence experiment with 176 keV line. ~) Normalized to the ;e-intensities using the E2 K-conversion coefficients (6.8 × 10 2) for the 273 keV transition. e) Theoretical E2 values are 1.6 and 2.9, correspondingly.

tion and consequently the parity of the isomeric level. Knowledge of the parity would make it possible to distinguish between the {½- [514], 6 - [512]}6 + and the {3 + [624], 4 - [ 5 1 2 ] } 7 - assignments, proposed in ref. 9) and ref. 12), respectively. A search for two other 7-transitions of smaller intensity, leading to the 4 + and 8 + levels of the ground-state rotational band, was also undertaken. The half-life of the isomer was measured to be 8 2 0 + 50 Fs, in g o o d agreement with the value 850_+ 80/~s reported by Kantele 9). The results of other measurements are collected in table 6, in which the relative intensities o f internal-conversion lines and 7-rays are given. The latter were determined from the y-ray spectrum coincident with

575

ISOMERISM IN EVEN NUCLEI

the 176 keV rotational 7-transition. A 7-7 coincidence spectrometer with two 3.8 cm x 3.8 cm N a l crystals was used in this experiment. The high-energy part of the coincident 7-ray spectrum is shown in fig. 5. Above the 994 keV line there is a small peak corresponding to a 1265 keVtransition. The intensity is 4 ~ per decay of the isomer. This figure is somewhat smaller than given by Kantele 9) ( ~ 7 ~ ) but higher than the 1 °/ /o 250

DIFFERENCE SPECTRUM Yb "°~ ( d , p ) Y b '~ ,12 5 MeV d CO NCIDENCES

WITH 1'75 ;~eV -i/- RA¢

~i31!5 ms 200 994 keV

r,_) :::1.,

150 ~-

CY LIJ ID.. 0'3

100

Z Z) O

-

"'I'--'N.

50

j

1265 keV

o

i

800

1000

~

1200

ENERGY

c

2o~%

1400

(keV)

Fig. 5. High-energy part o f the v-ray spectrum coincident with the 176 keV, 4 + -+ 2 + rotational transition in 174Yb.

upper limit reported in ref. 1 2 ) . Recently, the 1.27 MeV peak observed in the 174Tm decay has been resolved into two components of about equal intensity, which agrees well with the present results l o). A possible cascade of a 629 keV 7-transition from the isomer to the 8 + rotational state followed by a 365 keV 8 + ~ 6 + E2 transition was not observed and only a limit of the intensity could be given ( < 3 %). A comparison of experimental and theoretical K-conversion coefficients (table 7) shows that the 994 keV transition is of E2 multipolarity. The parity of the 1520 keV level is therefore positive. The level may thus very well correspond to the 6 + con-

576

J. BORGGREEN et al.

figuration proposed by Kantele 9) and be the analogue of the 1335 keV level observed in 176Hf. Recent results of stripping experiments 22) tend to confirm the {~- [514], 3- [512]} 6+ assignment. The decay scheme of lv*myb is shown in fig. 6. TABLE 7 M u l t i p o l a r i t y of the 994 keV t r a n s i t i o n in 17~tyb

~K (theoretical) El 1.3(--3)

E2 3.1(3)

Experimental

E3 6.6(--3)

M1

M2

6.2(3)

1.5(2)

~K a) 3.0-:-0.5(3)

multipole order E2

a) The theoretical E2 K-conversion coefficient of the 273 keV t ra ns i t i on used as a s t a n d a r d ; e qua l total intensities of the 273 and 994 keV transitions are ass ume d to deduce the ratio o f y-intensities.

keV 1520

KI ~ 820+50JJs

65 +

994 :2

(961

i 1265 (4)

525

t 273 (9G) I

252 76 0

1L_+6 y 76

(1~) t:i; 0oo) ' y b 174

06+

0~+ 02 + 00 +

Fig. 6. Decay scheme of 17~myb.

6. The 12 s isomer of 176yb A target of t76yb 1.4 mg/cm a was irradiated with 12 MeV deuterons to produce the 11.7 s a76myb activity 13). The spectrum of delayed 7-transitions, measured with a scintillation counter, contained three lines with energies 383, 294 and 188 keV, a composite peak at about 100 keV, and Yb K X-rays. The first three lines decayed with

577

ISOMERISM IN E V E N N U C L E I

700

i

!

L)

DIFFERENCE SPECTRUM Y b "6 +12 MeV d ~ Y b '~6~

600 L ! Ji i 500 k I i

CO{NCIDENCES WiTH 383 keV ,,(*RAY

i

Kx{5~,evl

EL.

300 0 L)

200

10/L! s

94 key

I

400 p

i

j

1

l g 8 key

o

I

o

294 key

72*/,

1017 j

2o*/.

I 0

L

I

lOO

200 300 ENERGY (keY)

400

Fig. 7. Gamma-ray spectrum coincident with the 383 keV transition in 176yb. The y-intensities, given under the peaks, are corrected for photopeak efficiency and normalized to the 294 keV peak, Ir (294) --92%.

keY

K f IT" 12_+1s 94IE 1

1041 947

8808 +

f 383 E2 i

564

-----

~ .....

L

06 +

294 E2

2?0

! 188 E2

04 +

82 0

82IE 2

02 + 00 +

y~76

Fig. 8. Decay scheme of 176rnyb.

578

J. BORGGREEN et al.

a 12 s half-life and could therefore be identified with the three transitions reported by Kantele 13) (sect. 2). Possible low energy-lines of 176myb were masked by the 104 keV transition from the 6.5 s 177myb activity induced by the (d, p) reaction. For this reason, and because the spectrum showed a poor effect-to-background ratio, it was decided to study the decay properties of 176myb in a coincidence experiment. The 383 keV line was recorded with a 7.6 cm x 7.6 cm N a l detector, coupled to a single-channel analyser, while the ~'-ray spectrum coincident with this transition was measured with a 2.5 cm x 3.8 cm Nal detector (resolving time ~ 60 ns). The axis through one counter and the target was placed perpendicular to the other countertarget axis in order to avoid registration of background annihilation radiation from the target. The 104 keV line disappeared in the coincidence spectrum (fig. 7) and two new transitions of 82 and 94 keV could be clearly observed. Fig. 8 shows the proposed TABLE 8 T otal conversion coefficient of the 94 keV t r a n s i t i o n in l r 6 y b Theoretical

Experimental

El

E2

MI

M2

0.40

4.4

4.2

41

0.42 ± 0.09

decay scheme. The requirement that the intensity of the transitions feeding and deexciting the 8 + rotational state be equal leads to an E1 assignment for the 94 keV transition (table 8). The 1041 keV isomeric level may thus be interpreted as the theoretically expected two-neutron state with the configuration {7- [514], 9 + [6241}8-. A similar decay scheme of 176myb has been proposed by Vergnes et al. 14) who used the (n, n') process to produce the isomer. The only difference between their results and ours lies in the measured total conversion coefficient of the 94 keV transition. The value reported in ref. 14) is higher than the theoretical one for a pure E1 transition and the authors were therefore led to suggest either an M2 admixture or a nuclear-structure effect. Such assumptions may not be justified in view of the present result (table 8). 7. The 5.2 ms isomer o f

18°W

A bombardment of tantalum with 12 MeV protons produced the known 15-17) 5.2 ms activity of 18°roW through the 181Ta(p, 2n) reaction. The delayed radiation was studied in the beta-ray spectrometer and with a 3.8 cm x 3.8 cm Nal scintillation detector. The spectrum of internal-conversion electrons is shown in fig. 9. The periods of irradiation and measurement were chosen equal to 5 and 10 ms, respectively; the latter time interval was not divided into the "early" and "late" parts in this (very early) experiment. The conversion lines observed in the spectrum correspond to five different

o

200

400

600

80O

~~~~]

50

100

L 1Q~ ~

150

K

L

-

~

250

ELECTRON ENERGY (keY)

200

2 3 & ~e¥

-

Torget t h,c~me£s 0 8 mG /Cm 2 ~

300

r-

3~1~v L 't

350

400

2rl)W

'a:-~ ,

450

12 NeV p.

500

Fig. 9. Conversion line spectrum of ~somW. As indicated, the low-energy part was measured with targets of 0.8 mg/cm2; at higher energies a 1,7m g/cm 2 target was used.

O

g

1000

1500

ToTM (p,

580

J. BORGGREEN et al.

y-ray transitions. Four of them can be placed between levels of the tS°W ground-state rotational band; the fifth, at 390 keV, is interpreted as the isomeric transition leading to the 8 + rotational state. All five transitions can easily be identified with the corresponding7-1ines reported by Remaev et al. iv). These authors observed an additional transition of 0.15 MeV which they placed in the decay scheme between the isomeric level at 1.46 MeV (according to their energy determination) and a level at 1.31 MeV. This transition was not detected in the present work; consequently the decay scheme of 180mw shown in fig. 10 does not include any level at ~ 1310 keV. Our attempt to find a possible 841 keV transition from the isomeric state to the 6 + rotational level keY

K 111: 5.2+-.2ms ,

1530

8 8 -

39O El I

l

1140

---

~

--

08 +

a~

689

-

'

06 +

i

35~

I

338

. . . .

~

-

0

4+

234 l

104

. . . .

~

----

02 +

104

0

~

W1Bo

O0 +

F i g . 10. D e c a y s c h e m e o f is°roW.

led to a negative result. A lower limit on the intensity of the K-841 line is 0.02 % of the lS0mw decay rate. The internal conversion studies were supplemented by measurements of the y-ray spectrum. The results of both types of measurement are shown in table 9. Intensities of conversion- and y-lines are normalized with the help of the theoretical E2 K-conversion coefficient (0.11) of the 234 keV transition. The values of ~K~5t and ~K,51 agree with the theoretical predictions for E2 transitons. A similarly good agreement is found between the theoretical (E2) and the experimental K / L ratios of the 234, 351 and 451 keV transitions. The K/L ratio could not be determined for the 390 keV isomeric transition, because the L-390 and K-451 lines remained unresolved. The experimental value of ~390 is only compatible with an E1 assignment to the 390 keV transition.

ISOMERISM IN EVEN NUCLEI

581

A n 8-assignment to the 1530 keV isomer is therefore indicated, a l t h o u g h K ~ = 9 c a n n o t be excluded. The level m a y be i n t e r p r e t e d as the t w o - n e u t r o n state with the {~- [514], ~+ [624]}8- configuration, theoretically p r e d i c t e d as the lowest lying configuration for all the N = 106 nuclei. Recently, Burde, D i a m o n d and Stephens 23) p u b l i s h e d results similar to the present ones. In a d d i t i o n these authors p e r f o r m e d a n g u l a r c o r r e l a t i o n m e a s u r e m e n t s which showed u n a m b i g u o u s l y the K = 8 assignm e n t to be the correct one. TABLE 9 Experimental data for is°roW

E (keV)

~K K/L Theory

Experiment 1~,a)

IK a)

104

26±5

234

88--8

351

90--20

3.5::0.4

451

97_--15

1.8:L0.2 c)

390

81~25

1.O~0.1

10 --1

~K K/L

1.1 (--1) 2.1 ,-0.5 3.9~1.0(--2) 3.6~1.0 1.8"=0.3(2) 3.6--1.1 1.2~0.4(--2)

El 2.8(--1) 6.1 3.7(--2) 7.0 1.3(2) 6.7 7.5(--3) 6.8 1.0(-2) 6.7

E2 8.0(--1) 0.42 1.1(- 1) 2.0 3.7(2) 3.1 2.0(--2) 3.8 2.9(2) 3.4

Multiple order MI 3.6(0) 7.2 3.5(--1) 6.7 1.2(--1) 7.0 6.3(--2) 7.0 9.0(--2) 6.9

E2 E2 ~) E2 E2 E1

a) Intensities normalized with the use of the theoretical E2 K-conversion coefficient (0.11) of the 234 keV transition. ~) Assumed multipole order. e) Contribution of the L 390 line is subtracted, the estimate being based on the theoretical El K/L ratio and the experimental intensity of the K 390 line.

8. Discussion The results r e p o r t e d in the preceding sections together with other published results (e.g., ref. 23)) show t h a t the existence o f high-spin K i s o m e r s in the A ~ 180 region o f d e f o r m e d nuclei can be p r e d i c t e d theoretically. This fact m a y be considered to be a r e m a r k a b l e success o f the simple nuclear m o d e l based on the Nilsson scheme o f single-particle levels a n d p a i r i n g correlations. N o w the question arises, to w h a t extent there is a q u a n t i t a t i v e agreement between the predictions o f the m o d e l and the exp e r i m e n t a l data, The p r o b l e m m a y be studied, for instance, by analysing the degree o f r e t a r d a t i o n o f K - f o r b i d d e n 7-transitions. This gives us an idea o f the deviations f r o m the m o d e l o f a d i a b a t i c r o t a t i o n o f an axially s y m m e t r i c nucleus, according to which K is a g o o d q u a n t u m n u m b e r . The a d m i x t u r e o f different K values to the isomeric a n d r o t a t i o n a l levels can further be traced (see the i n t r o d u c t i o n ) t h r o u g h an analysis o f the b r a n c h i n g ratios o f K - f o r b i d d e n transitions. Finally, a c o m p a r i s o n o f

21. B O R G G R E E N e t al.

582

t h e e n e r g i e s o f t h e i s o m e r i c l e v e l s w i t h t h e e x p e c t a t i o n s is o n e o f t h e m o s t s t r a i g h t forward ways of checking the pairing element of the theory. These three aspects of K isomerism are discussed below. TA~I.E 10a Retardation factors of K-forbidden E1 transitions ( I ~ K ~ t = 8,8-) --+ ( I ~ K ~

Nucleus Configuration of the isomeric Ee state (keV) - - ~ -

ar6yb 17SHf a) ls°w

~+[624]n [514]n

ls2Os ls~Pt aS°Hf

= 8,0 +)

Experimental half-life (s)

t7 e)

94 89 390

12 4.8 5.2 x 10 -3

17 11 5.3 × 10 -3

553 610 58

= 7

Retardation factors d)

ref.

tl ~)1

7+[404]p ,~-[514]p

v -- z ] K - - 1

FW

this work

6.6 × 10 '3 3.6 x 1013 1.5 × 1012

0.8x10 3 ~0.8×10-3 l.OxlO a ~2 x l O -a

2a) this work 23) 2a)

~6 ~2

2.0 × 104

z~)

3.8 × 10 ~6

4.1 x 10~

×1011 x l O ~2

fw

95 87 55 ~48 ~57 234

a) The 1148 keV 8- isomeric level considered here has probably (ref. 24)) mixed the two-proton and two-neutron configurations; it is believed, however, that the isomeric transition is due to the neutron c o m p o n e n t (see text). b) The half-life of an isomeric level. e) The partial half-life in respect to an isomeric 7-transition. a) Weisskopf estimate of the half-life: t w = 6.73A-~ E, l ~ (MeV) 10 6 ns (ref. ~)). TABLE 10b Retardation factors of K-forbidden E2 transitions

Nucleus

Isomeric state

E~.

1K ~

(keV)

17~Hf

66 ~ a)

~4yb

66 + a)

17~yb

33 +b)

737 1045 994 1265 913 1095

Experimental half-life (its)

Retardation factors (~) ref. --

13 8.2 X 102 8 . 7 x l 0 -s

20 this work 37 8.5 X 102 this work 2 x 104 1 . 1 x l 0 ~ 36) 4.5 x 10 .o

4.6 × 105 4.8 × 10~ 8.6 x 107 7 x 109 l.Sx10 ~ 2.9 >~ l0 a

4 4 1

26 47 96 2.9 × 102 1.8×10 a 2.9 x 10~

a) The {5-[512]n, z [514]n}6 + states decaying to the 6 + and 4 + levels of the ground-state rotational band. b) The {.~-[512]n, ½ [512]n) 3 ~ state decaying to the 4 + and 2 + levels of the ground-state rotational band. e) F o r the definition of t i and tT, see caption to table 10a. a) Weisskopf estimate of the half-life: t w -= 9.37 x A ~ E~ -6 (MeV) ns.

ISOMERISM IN EVEN NUCLEI

583

8.1. RETARDATION FACTORS The experimental decay rates of the individual isomeric y-transitions are compared with the Weisskopf estimate 1). The retardation factors, Fw, calculated for the Kforbidden El and E2 transitions between the isomeric levels and levels of the groundstate rotational bands are given in tables 10a and 10b. These tables contain also the calculated degrees of K-forbiddenness per unit of v, denoted fw. Considering the E1 transitions characterized by v = K - 1 = 7 (table 10a), one finds a difference between the decay rates of the two-neutron levels (tV6yb etc.) and twoproton (18°Hf) levels with K ~ = 8 - . The/~w factor is equal 3.8 x 1016 for the proton state while it is smaller than 10X4for the neutron levels. Therefore, the 1148 keV 8level in 178Hf is listed here with the two-neutron levels. The 178mTa electron-capture data 24) indicate the 1148 keV state to be a mixture of the two-proton and two-neutron configurations. For the y-decay, however, only the latter component will be essential. * Table 10b gives data for the E2 transitions deexciting the 6 + two-neutron levels of 176Hfand 174yb, investigated by the present authors, as well as the 3 + level in 172yb, a two-neutron configuration which was studied by Herskind and Fossan 26). The v-values are different here, being 4 and 1, respectively. The retardation, fw, per v-unit should therefore be compared rather than the total retardation factors Fw. For the E2-decay of these isomeric levels one would expect admixtures of the y-vibrational states with K ~ = 2 + to play an important role. These admixtures will overcome the K-forbiddenness and they are usually connected to the ground state by large B(E2) values. The exceptionally high fw value in 172yb may perhaps be connected with the lack of a strongly collective y-vibrational state in this nucleus. The lowest K" = 2 + level in this nucleus is indeed expected, according to Soloviev's calculations 27), to a 99.6 ~ pure two-quasiparticle state; the B(E2) value may then be relatively small (see also r e f . 2 2 ) ) . The once K-forbidden E 1 transition with the energy 54 keV in 176Hf has a retardation factor fw = Fw ~ 107, while the K-allowed M2 transition in the same nucleus with the energy 227 keV has Fw = 33. 8.2. BRANCHING RATIOS In this section the branching ratios of the K-forbidden E2 transitions deexciting the 6 + levels of 176Hf and 174yb, and the 3 + level of 172yb (ref. 26)), are analysed on the basis of the Bohr-Mottelson 3) and the Michailov-Michailova 6) formulae discussed in the introduction, eqs. (2) and (3). The results are presented in table 11. The experimental reduced branching ratios disagree in all three cases with the leading order predictions of the Bohr-Mottelson formula. This means that it is not enough here to consider only those admixtures to the initial and final states which reduce the difference in K q u a n t u m numbers to 2. One has to include also the contribution of the A K = 1 transitions (and the contribution of the A K -- 0 transitions which See also the discussion in ref. 23).

584

J. B O R G G R E E N

et al.

TABLE 1 1 Branching ratios for the K-forbidden E2 transitions Nucleus

G a m m a Transition Gamma energy intensity (keV) llKt~ i ItKf~ ~ (relative)

Reduced branching ratios experiment

theory BM a)

lr~Hf

337 737 1045

80 ~ <0.15 66 + -> 60 + 1 40 + 0.56~0.08

a~aYb

629 994 1265

80 + 66 + ~ 60 + 40 +

0.03 1 ~,0.04

913 1095

33 ~ - > 4 0 + 20 +

0.24~0,03 1

~2ybe)

<0.8 l 0.097±0.04

M M b) parameter a~

M M b)

0.11 1 0.27

0.26(±0.02) 1 0.097(±0.014)

~i:~0.3 1 ~0.013

0.11 1 0.27

0.46 1 0.013

0.595±0,074 1

0.40 1

0,595(±0.074) 1

~ 0 . 0 1 8 ( . ! 0.002) /t ~ 0.035 /~ N,

~ 0.014(~_0.005)

a) ReL a). b) Ref. ~). e) Experimental data taken from reL 2~); pure E2 multipole orders of the 913 and 1095 keV transitions assumed. TABLE 12 Comparison of the energies of the isomeric levels with the theoretical expectations Nucleus Deformation Configuration

1K~

Two-quasiparticle energy exp. (keV)

176Hf ~TSHf lS°Hf

0.252] 0.232 t 0.229

[2v+ [404]p t i9_[514]pj -

88-

mYb 176Hf

0"2661 0.252J

I~ [512]nt /.~ [514]nJ

66--

l~6Yb 17~Hf ~s°w IS2Os

0.260-~ 0.232 / 0.22l} ~0.196)

aa4Pt

~0.183

a) 4) e) ~)

1562 (1148)1480 d) 1142 / ,

I~ -[5141n] (~+[624]nj

88-

1520 1335 1041 1148(1480) ~) 1530 1830 1836

Energy gap

calc. a) (keV)

calc. a) (keV)

calc. b) (keV)

from exp. masses e) (keV)

1300

1460

1810 1860 1870

1370ac70

1500

1450

1400 1440

1356~6 1440--30

1430

1470

1330 1440 1510 ~1700 ~-,1800

1178±12 1388±8

Based on ref. 2s). Based on ref. 29). Based on ref. a0). The two 8 levels of 1148 and 1480 keV are believed to be highly mixed (ref. 24)), see text.

in this particular

case cannot be distinguished

is t a k e n i n t o a c c o u n t t h r o u g h

the correction

from the AK = 1 contributions).

This

f a c t o r (1 + 5 ) 2 o f t h e M i c h a i l o v - M i c h a i -

l o v a f o r m u l a . W i t h t h e l a t t e r f o r m u l a it is p o s s i b l e t o fit t h e e x p e r i m e n t a l d a t a f o r 176Hf and t72yb with the at parameter equal to 0.018 and 0.014, respectively. The

ISOMERISM IN EVEN NUCLEI

585

value a 1 = 0.035 deduced from the intensity ratio of the 994 and 1256 keV transition in 174yb gives a somewhat too high prediction for the intensity of the 629 keV 7transition. I f we consider the E2 transition rate to be the result of an admixture of the 7vibrational state to the isomeric levels, as discussed in subsect. 8.1, then the al values are to be associated with admixtures of lower K-values to the 7-vibrational state. The effect of K-impurities in the 7-vibrations has been observed systematically 5) and analysed in terms of the mixing parameter z which is related 6) to at by z = 2all ( 1 - 4 a l ) . Typical z values are 0.04-0.06, corresponding to a t = 0.0243.03. It is seen that the at values determined presently in a more indirect way are compatible with the general systematics. 8.3. E N E R G I E S

OF THE ISOMERIC

LEVELS

In table 12 the experimentally determined energies of the isomeric levels are compared according to eq. (4) with theoretical pairing calculations due (i) to Bang and Michailov 28), (ii) to BOs and Szymafiski 29), and (iii) with empirical estimates of the energy gap (Whineray et aL 30)). Bang and Michailov have used projected wave functions and thus improved the early calculation of Gallagher and Soloviev 7) which overestimates the effect of blocking, cf. table 1. Their calculation is restricted to one nucleide for each configuration, and does therefore not predict how the energy of a particular two-quasiparticle state changes from one nucleide to the next. B6s and Szymafiski 29) have calculated the energy gap in even nuclei as a function of deformation. The table shows the predicted gaps corresponding to the experimentally determined deformations. These are taken from the compilation by Stelson and Grodzins 3t), except for 182Os and I84pt. In these two cases, the moment of inertia was calculated from the energy of the 2 + rotational level. F r o m a crude interpolation in a moment-of-inertia versus deformation plot 32) we subsequently get an estimate of the deformation parameter. The empirical values of the energy gap are based on the most recent results so) of mass determinations in this region of isotopes, where previously a number of inconsistencies have caused difficulties. The three estimates of the proton gap in tVSHf disagree rather seriously between themselves, making a comparison with the measurement ambiguous. The estimates for the neutron systems are more consistent: only the ~76yb case is unsatisfactory. The comparison in table 12 seems altogether to reveal two different tendencies. The first one is a more or less smooth, systematic effect, illustrated by the large increase in the experimental energy of the 8- state from l : 6 y b to ts4pt. The pairing calculation by B6s and Szymafiski 29) reproduces this rather well. It may therefore be understood as a result of tile decrease in deformation, which is brought about by the addition of protons and gives rise to an increase of the pairing energy for the neutron system. The second effect is of a more local character and is illustrated by the two 8- states

586

J. BORGGREEN et

al.

in lVSHf. A s s u m i n g s m o o t h trends, one m i g h t have predicted the t w o - p r o t o n state in this nucleus to lie at 1350 keV by i n t e r p o l a t io n between the energies in 176Hf and 18°Hf. Similarly, i n t e r p o l a t i o n places the t w o - n e u t r o n state at 1285 keV. Th e actual 8 - states lie 130 keV above and below these interpolated values, respectively. It is therefore as if the two states t h r o u g h some p r o t o n - n e u t r o n interaction were pushed apart f r o m an original spacing of a b o u t 65 keV to a final one of 332 keV. Such a large displacement implies considerable mixing of the two configurations. As already mentioned, the electron capture leading to the two 8 - states does indeed give evidence for an almost fifty-fifty mixing 24). The pure states are expected to be p o p u l a t e d with log f t values 4.7 and 6.9, respectively, whereas the measurements give log J°t = 4.9 for b o t h states 7,24). A l t h o u g h the independent quasiparticle a p p r o x i m a t i o n thus seems to provide a valuable first order estimate of the experimental energies, higher order effects are present and m ay cause deviations o f the order o f 100-200 keV. The authors wish to th a n k Professor Aage Bohr, Z. Szymariski and Jens Bang for stimulating discussions and M o g e n s Olesen and Per H o y - C h r i s t e n s e n for technical support. One o f the authors (J. Z.) is grateful for the hospitality o f the Niels Bohr Institute and for a F o r d F o u n d a t i o n grant.

References 1) A. H. Wapstra, G. J. Nijgh and R. van Lieshout, Nuclear Spectroscopy Tables (North-Holland Publ. Co., Amsterdam, 1959) 2) A. Bohr and B. R. Mottelson, Lectures on nuclear structure and energy spectra (The Niels Bohr Institute and NORDITA, Copenhagen 1962-64) to be published 3) A. Bohr and B. R. Mottelson, Atomn. En. 14 (1963) 41 4) G. Alaga, K. Alder, A. Bohr and B. R. Mottelson, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 9 (1955) 5) O. B. Nielsen, in Proc. Rutherford Jubilee Int. Conf., Manchester 1961, ed. by J. B. Birks (Heywood, London, 196l) p. 317 6) V. M. Michailov and M. A. Michailova, in Program of the 16th Conf. on Nucl. Spectroscopy and Nucl. Structure, Moscow, 1966 (Nauka, Moscow, 1966) p. 99 and Izv. Akad. Nauk USSR 30 (1966) 1337 7) C. G. Gallagher and V. G. Soloviev, Mat. Fys. Skr. Dan. Vid. Selsk. 2, no. 2 (1962) 8) K. Brandi, R. Engelmann, V. Hepp, E. Kluge, H. Krehbiel and U. Meyer-Berkhout, Nuclear Physics 59 (1964) 33 9) J. Kantele, Phys. Lett. 11 (1964) 59; J. Kantele, K. M. Broom and D. M. Chittenden II, Ann. Acad. Sci. Fenn. A VI (1964) 3 10) J. Kantele, E. Liukkonen and A. Sarmanto, to be published 11) C. J. Orth, Bull. Am. Phys. Soc. 9 (1964) 498 12) L. Funke, H. Graber, K. H. Kaun, H. Sodan and L. Werner, Nuclear Physics 61 (1965) 465 13) J. Kantele, Phys. Lett. 2 (1962) 293 14) M. Vergnes, G. Rotbard, G. Ronsin and J. Kalifa, Phys. Lett. 18 (1965) 325 15) D. Softky, Phys. Rev. 98 (1955) 736 16) A. M. Morozov, V. V. Remaev and P. A. Yampolsky, ZhETF (USSR) 39 (1960) 973 17) V. V. Remaev, Yu. S. Korda, A. P. Klyucherev, Izv. Akad. Nauk USSR 28 (1964) 1599 18) S. Bjornholm, J. Borggreen, H. J. Frahm and N. J. Sigurd Hansen, Nuclear Physics 73 (1965) 593

ISOMERISMIN EVENNUCLEI

587

19) L. Westgaard and S. Bjornholm, Nucl. Instr. 42 (1966) 77 20) O. Nathan and S. G. Nilsson, Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1965) 21) L. K. Peker, Izv. Akad. Nauk USSR, 28 (1964) 295 22) D. G. Burke and B. Elbek, Mat. Fys. Medd. Dan. Vid. Selsk., to be published 23) J. Burde, R. M. Diamond and F. S. Stephens, Nuclear Physics 85 (1966) 481 24) C. J. Gallagher and H. L. Nielsen, Phys. Rev. 126 (1962) 1520 25) Nuclear Data Sheets, Oak Ridge National Laboratory, Oak Ridge, Tennessee 26) B. Herskind and D. B. Fossan, Nuclear Physics 40 (1963) 489 27) V. G. Soloviev, Nuclear Physics 69 (1965) 1 28) J. M. Bang and 1. N. Michailov, Dubna Report R-1573 (1964) USSR 29) D. R. B6s and Z. Szymaflsky, private communication (1966) and Nuclear Physics 28 (1961) 42 30) S. Whineray, W. McLatchie, J. D. MacDougall and H. E. Duckworth, to be published 31) P. H. Stelson and L. Grodzins, Nuclear Data A1 (1965) 21 32) B. Elbek, Thesis (Munksgaard, Copenhagen, 1963)