Two-proton and proton-neutron states in the doubly closed shell 50132Sb81Sn82 region

I.E.I:3.A[

N , clear Physics A195 (1972) 177--191; ~ ) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

TWO-PROTON

AND PROTON-NEUTRON

IN T H E D O U B L Y C L O S E D S H E L L

STATES

laz~s0:~ns2 R E G I O N

A. KEREK, G. B. HOLM, S. BORG and L.-E. DE GEER Research Institute for Physics, Stockho#n 50, Sweden and Research Institute of National Defence, Stockhohn 80, Sweden

Received 17 April 1972 (Revised 21 June 1972) Abstract: Two states in 134Sb with half-lives of 0.85 =0.10 sec and 10.3-:-0.5 sec have been observed. The two states are ascribed the configurations (ngk, vfk) with spin assignments 0- and 7-, respectively. In the decay of the 10.3 sec (7-) state two excited 6 ÷ states in ~34Te at 1691.3 and 2397.6 keV are populated. The lower 6 + state decays by a stretched E2 cascade via a 4 + state at 1576.1 keV and a 2 + state at 1279.1 keV to the ground state. The observed states of ~z4Sb and 134Te are compared to theoretical predictions using a 6-force interaction. RADIOACTIVITY 13'*Sb (from 2asU fission) measured T½, E~,, ly, Ecc, 1c¢, E#--° yT-coin, ~7-delay; deduced Iogft, Q. ~34Te levels, J,~,cc,~,-multipolarity. Isotopically separated source, Ge(Li), Si(Li), anthracene detectors. Ge(Li)-Ge(Li) coin.

1. Introduction The spectroscopic i n f o r m a t i o n a b o u t the nucleides a r o u n d the "classical" d o u b l y closed shell nuclei is very rich (e.g. i n t h e regions a r o u n d 16,-,8u8,4O~2o~a20a n d 2°8pb126). This is in striking c o n t r a s t to the situation a r o u n d nuclei close to the d o u b l y magic 48 20Ca28, 56 28Nl28, 100t~ 50~n50 and 132,', 50:~n82 which all lie far from the line o f fl-stability. •

The main reason for this lack o f knowledge is, o f course, the experimental difficulty in reaching these regions. A very fruitful way to p o p u l a t e high-spin states in a classical d o u b l y magic region such as 2°apb, is to use particle transfer a n d / o r heavy-ion induced c o m p o u n d - r e a c t i o n studies. A trivial prerequisite for these investigations is the existence o f stable targets. The magic tin regions are both far from the line where stable isotopes occur. T h e limiting factor for reaching the neutron deficient ~00~ 50anso region t h r o u g h reaction experiments is the low binding energy o f the p r o t o n s . On the other hand, the p o p u l a tion o f levels in nuclei in the neutron-rich t s2~_50~,na2region by reaction studies is impossible because o f the a b o v e m e n t i o n e d target p r o b l e m . However, many o f the isotopes a r o u n d ta2Sn occur in the fission o f u r a n i u m . Because o f the c o m p l e x i t y o f the fission process, the isotope s e p a r a t o r on-line technique is necessary for the most short-lived isotopes and convenient for the others. The nuclei with two extra-core 177

178

A. KEREK

etal.

particles or a particle and a hole in the t 3 2 S n region which have been investigated in detail so far are 132Sn [ref. l)] and 134Te[ref. 2)]. (The experimental goals, methods and preliminary results in the region were reported at the Leysin conference 3).) The excited states of t 3,,~ 5:1e82 are expected to be due to the coupling of the two extracore protons. These move preferentially in the lg~. and the 2d,r orbitals. Another interesting aspect of the t3'*Te study is the comparison which can be made with the other N = 82 nuclei. The single-particle states which are most likely to be responsible for the ground state of t 3 4 S b a r e : for the 51st proton lg~ and for the 83rd neutron 2f~. Thus, the most probable configuration (ng~, vf~) is of such a type that one can expect a lowlying negative-parity isomeric state with the maximum spin: Jm~x= ~.+2~ = 7 not far from the ground state with the predicted spin Jm~, = r~ --~l = 0. The spin predictions are further discussed in subsect. 3.1. The situation is similar to the one which is known to exist in the lead region for 2~°Bi, where the (nh~_, 1'g~)9- isomer is observed 268 keV above the ground state. In violation of the socalled Nordheim's strong rule, the ground state of 210Bi has spin and parity 1 - The (nh~, vg~) o- state is found at an excitation of 46.5 keV. Consequently we must consider the possibility of seeing two half-lives in the fldecay of 13~Sb83. One of them, the 7- state, should populate the excited states of the two-proton nucleus ~34~ 52/e82 • The ground state and the lowest excited states of a two-particle nucleus such as 13'*Te or 210po are expected to be members of t h e (j2) multiplet with spins 0,2, . . . , ( 2 j - 1). In the case of 2 1 ° p o , j = "~ (arising from the h~ subshell) and in 134Tej = ~ (from gl). Delucchi et al. 4) have measured the cumulative fission yield of ~34Sb and reported a 11.1 +0.8 sec half-life. The 11.1 sec half-life was suggested to be associated with the S b ( 0 - ) ~ Te(0 ÷) fl-decay. However, our preliminary investigations 2)already showed a result which differs from this suggestion. Recently two different groups s. 6) reported delayed radiation from t 34Te in the subus region. Both experiments have used the spontaneous fission of 2"~2Cfand detected the fission fragments plus delayed y-rays in the 50 ns-10 ps interval. Three ~,-rays had a common half-life (0.2/Is). The same delayed y-rays were observed by Griiter et al. 7) using a gas-filled fission-product separator and time-of-flight techniques. In the present work an effort was made to identify the possible isomers of 134Sb and to establish and interpret the level scheme of t3'*Te within the framework of the two-particle picture.

2. Experimental procedure and results 2.1. ISOTOPIC I D E N T I F I C A T I O N A N D SINGLES SPECTRA

The samples were produced in the central beana of the on-line isotope separator OSIRIS 8). The OSIRIS ion source which is placed close to the core of the 1 MW R 2 - 0 reactor at Studsvik contains 150 mg of 235U. The reactor power during these

'3ZSn REGION, 2p AND pn STATES

179

experiments was kept between 50 and 100 kW. The A = 134 ion beam was collected on a tape which could be moved continuously or stepwise. The previously known members o f the A = 134 isobaric mass chain produced in thermal-neutron induced fission and which are observed at O S I R I S are: 13"tSb

10 s~ ,o-

42 rain

13"tTe __--+ #-

52.8 rnin ~. t3"tXe(stab)

13,tI

#-

134[

.2 rain

In order to reduce the activity caused by the daughter products o f '3"tTe the tape was moved continuously. The velocity was approximately 0.7 cm/sec ( - a detector cup diameter/half-life for t 345b). The ./-ray spectrum recorded in this way is displayed

l

/!,xi~!!~ 1152 2970

11~ -

6" .4"

I

•

4" +2" 7063

-,,0,+ 00 +_+

12791 2 t -0"

6"j6'

,x+ tl-, ,++u,:, ,~ , p,,,,+., ++'+'~ + +" '+',o+,,i ,+-y-, + 1 "I ~,, +++01,

,,

,

',

m~,~, ' +

"""++'++,,~',,,,,,Jl ~+" i:~+ ',+, +;,, LJ++i,+ ,,

,+

x+

'o'.-

,, ,,,...,., +

I

= =

lOOO CHANNEL NUMBER

,

+

i

' ..... ~.--

2000

Fig. I. Gamma-ray singles spectrum recorded at a tape velocity of 0.7 cm/sec and a background spectrum collected I rain after the beam was shut off with the tape stationary. in fig. 1, which also contains the background spectrum recorded 10 min after the beam was shut off. The ~,-rays were detected by means o f coaxial Ge(Li) detectors ( F W H M 2.3 keV at 1332 keV). A PDP-9 computer equipped with a NS-625 dual A D C was used for the analyses. In table I the energies and intensities o f the ,,,-rays observed in fig. 1 are tabulated. The intensities are normalized, for ?-rays in t3+Xe, to the 846.7 keV 2 + --* 0 + transition ~), and for ./-rays in '301, to the 766.7 keV (1 +) ~ (3 +) transition 10). The remaining "/-rays are normalized to the one at 1279.1 kcV occurring in 134Te with one exception, namely the 272.1 keV "/-ray. This "/-ray is known ~*) to be one of the transitions de-exciting the 3.2 min isomeric state in 13'tl. The other one at 316.3 keV is not observed here due to its low intensity.

A. K E R E K et al.

180

TABLE 1 Encrgies, intensities a n d isotopic a s s i g n m e n t s o f T - t r a n s i t i o n s observed in the prescnt s t u d y o f the isobaric chain .4 ~ 134

E~

17(Sb -~ Te)

(keV)

(%)

79.4.-:[0.1 101.3±0.2 115.2+0.1 135.4+0.2 139.0_±0.2 180.9-t-0.1 201.2±0.1 210.5±0.1 235.3i0.2 272.1 ±0.1 ~') 277.9___0.1 297.0±0.1 351.4:t:0.2 405.4±0.2 435.0±0.1 460.9±0.1 464.5 i: O. I 488.5 ± 0 . 2 514.0±0.2 540.7+0.2 565.9-1-0.1 595.2±0.2 621.6i0.2 627.6t0.2 677.2:t_:0.2 706.3::t:0.1 712.7-_0.2 730.5~0.2 742.4&0.1 766.9-_t-0.1 846.9~0.1 857.2-0.2 884.0::t:0.1 947.8_--_0.2 974.5±0.2 1040.5±0.3 1072.6::t:0.2 1102.7+_0.3 1136.4--0.2 1279.1 ±0.1 1456.3 _-kO.3 1470.0±0.4 1613.7~0.4 1741.1 :{-0.4 1806.5~0.3

l y ( T e -,- I) (o,~)

L/(! --> Xe) ( o,/o)

75 2.0 49 4.5 1.6 64 33 82 2.0 (36~ 73 97

0.5 7 66 31 15

2.0 3 7 70 11 10 2.0 8 57 18 1.0 54 100 100 6 66 4 6 2 15 1 10 100 2 0.8 6 3 7.5

") 3.2 rain isomeric transition in '34I; Unless stated otherwise, the uncertainties in the intensities :L~O ,o forl:, . : 5/0. o, arc - 5 ~ : , f o r l T ~ 2 0 ° / ' ; : ~ l O ', ; o f o r 2 0 % > l y ~ ' 5 ° , / o a n d ~ °"

~a2Sn REGION, 2p AND pn STATES

181

2.2. HALF-LIFE MEASUREMENTS The half-lives o f the four strong transitions (115.2, 297.0, 706.3, 1279.1 keV) were studied by using the PDP-9 in the multi-scaler mode with gates set at the respective peaks t2) (fig. 2). These four transitions, having a c o m m o n half-life o f 10.3 + 0 . 5 sec, are assigned to the decay of 13aSb. The half-life measured in the present work agrees well with that reported by Delucchi et al. 4 who give 11.1+__0.8 sec. Furthermore, three of the lo*

a)

°u

."

N,~

13)

297.0 keV

7063 keV

.& .,.

~ t

1°)

i

t

20

~o

i

so

eo

I ~_

":"

.. \

t

i

lOO

v~,..s...,,.,,v1279.1ked~ •

1279.1 keY

.

102

1

c)

o

! j

"~".',~-.~.....,...,~.

2o

\

,

t

i

A

i

i

i

i

40

~o

eo

loo

2o

40

_

L

i

eo

80

1

lOO

i

~2o

TIME(sec)

'

.

L•

L-i,,,, 0

.... I

, .... 2

,j

) sec

Fig. 2. Decay curves for (a) 297.0 keV, (b) 706.3 keV and (c) 1279.1 keV transitions showing a common half-life of 10.3 sec. Part (d) displays the 1279.1 keV gate on an enlarged time scale, indicating that the ground state transition does not contain any short-lived (0.85 sec) component. transitions have similar energies (115, 297 and 1279 keV) to those observed in refs. 5,6). F r o m level systematics (cf. fig. 10) we can, with great confidence, assign the 1279.1 keV y-ray to be the 2 + --* 0 + transition in 13aTe. The same conclusion was drawn by John et al. 5). If one o f the possible ,6-decaying states in 134Sb by analogy to the situation in z ~0Bi ' has the spin 1 -, the 1279.1 keV 2 + state would be populated via a first-forbidden transition. Therefore the decay curve of this transition was carefully investigated, using the above mentioned method but employing other time ranges. The result from one o f them, that with the shortest range, is shown in fig. 2d.

182

A. K E R E K

eta/.

We can interprete this result by saying that:

(i) the half-life of the supposed l - isomer in ~3~Sb is shorter than 0.1 sec (which is the approximate experimental limit) or, (ii) the observed half-life is close to 10 sec or, (iii) there is no isomeric state with spin 1 -. 2.3. C O N V E R S I O N

ELECTRON

MEASUREMENTS

In order to facilitate the multipolarity assignments, the internal-conversion electron spectrum was recorded simultaneously with the 7-spectrum. |n this way, after an TABLE 2 I n t e r n a l c o n v e r s i o n c o e m c i e n t s for t r a n s i t i o n s o b s e r v e d in the e l e c t r o n s p e c t r u m o f the p r e s e n t s t u d y Ettans

Shell

115.2

K L K K K K K K K K K K

180.9 201.2 210.5 272.1 277.9 297.0 435.0 706.3 766.9 846.9

Decay

~x 0.76 ::0.07 0.22 --0.04 0.18 ::0.025 0.115 ::.0.025 0.093 - 0 . 0 2 0 0.185:0.025 0.046 - - 0 . 0 0 9 0.031 - - 0 . 0 0 6 0.011:0.002 0.0031:!0.0006 0.0023..! 0.0005 0.001 -.:0.0004

Sb ---* Te Te-~-I Te-~-I T e -~. 1 ml--" I Te-~-[ Sb-~Te l-~-Xe Sb-~-Te Te ~ I i -~- Xe

10 --

1152

M ultipolarity

-

E2 MI MI MI E3 MI MI MI MI MI

or or or or or or or or or

MI+E2 E2 o r E2 o r M2 E2 o r E2 o r E2 o r E2 o r E2 o r E2

I ~

(]['K

2721 0.1

2779 2970

O.Ol

~35.0

.

.

.

.

.

.

.

.

7o&3

t,"I

1

OOOl - ~Xe

I 100

~

t

i , 1E11E2E3 500

1000keV

Fig. 3. E x p e r i m e n t a l v a l u e s of:~K c o m p a r e d to t h e o r e t i c a l p r e d i c t i o n s t3).

MI-;-E2 MI-~ E2 MI-i-E2 MI-hE2 MI-FE2 MI-:-E2 M I -.',-E2

132Sn REGION, 2p AND pn STATES

183

effciency calibration of the electron-7 detection system, using the 527 keV M4 transition in t aSXe ' the internal conversion coefficients for the strongest transitions could be d e t e r m i n e d (table 2). T h e e l e c t r o n s were d e t e c t e d by the use o f a c o o l e d , 2 m m

11,5.2

30o

297 keV GATE

20O

1279.1

100

7063~

f

m~ ~

60

2970

I---U350 0

706 keV GATE

115.2 I

30

1279.1 •-eqrF'liffv'q1"q'*r-~'i'1'r~r~r~r~qrrlqlr'lq~L r,-T~-rr,~..q

rrrr r,.1"qn~,F.,~..,~1 ~ o

r~wy'.,f~,,w1~'~rv~'w'wb--

]

1ooo lOO

297.0

115~

1279 keY GATE

: 1152.2970

, ~

.......

1 500

0

7063

0

1

z

10

15i00

,

A

CHANNEL NUMBER

I 2000

Fig. 4. Gamma-gamma coincidencc spectra with the given selection conditions.

60~'~°t r 116

706.3

297 keY DELAYED GATE 1279

I I

~t~0 ~0

127~ ke~/- DELAYED GATE

706.3 115

297

I

I

2

/

I

l

I

I

I

500 CHANNEL NUMBER

Fig. 5. Delayed 7-Y coincidence spectra recorded with ~ 100

)

100 ns

delayed gate signals.

184

A. KEREK

et al.

thick, S1MTEC Si(Li) surface-barrier detector, having a resolution of 4 keV at an electron energy of 482 keV. In fig. 3 the experimental c(K values are compared to the theoretical ones calculated by Hager and Seltzer 13). For the 115.2, 29?.0 and ?06.3 keV transitions in 134Te it is possible to exclude all transition multipolarities with the exception of M1 or E2. In the case of the 115.2 keY transition the (K/L) ratio of 3.44-0.5 suggests a pure E2 multipolarity. The theoretical ratios are 7.7 for Ml and 3.3 for E2. 2.4.

COINCIDENCE

MEASUREMENTS

Two large coaxial Ge(Li) detectors were used to detect the coincident y-rays. The coincidence (and background) windows were set at (and round) selected peaks and the gated spectra were collected and analysed by the PDP-9 computer. In fig. 4 the 706.3 keV and 1279. l keY gated coincidence spectra are shown. Since a time-to-pulse-

!

C

E, t

4

,

5

6

7

8

5

6

7

8

9 MeV

9

MeV

Fig. 6. Beta-spectra recorded with an anthracene crystal with (a) 13 sec and (b) 1.3 sec build-up times (see subsect. 2.5). height-converter system was used to register the coincidence events, it was also possible to perform a delayed coincidence measurement. The results are shown in fig. 5 and indicate that the 115.2, 297.0 and 1279.1 keV ,/-rays arrive later at the detectors than the 706,3 keV ?-rays. Consequently, the 706.3 keV transition terminates at the 1691 keY 162 ns isomeric state s. 6.7). 2.5. THE Q-VALUE DETERMINATION The Q-values associated with the t34Sb fl-decay are estimated to be considerably higher (Qp ~ 8.5 MeV) than the ones connected with the decay of 134Te (QB -- 1.4

la2Sn REGION, 2p AND pn STATES

185

MeV) and la4I ( Q / i - = 4.15 MeV). In order to determine the l o g f t values, the decay energy as well as the fl-branching and the half-life must be known. The maximum fl-energy for the 10.3 sec l agSb decay was determined by using the following technique. The fl-particles were detected with the help of an anthracene crystal placed I l cm from the collection position, and a 13 sec long build-up time was used. The samples were then transported (3 sec) to the measuring position with the help of the moving tape and the fl-spectrum recorded during 13 sec. This procedure was repeated more than 500 times (fig. 6a). [n fig. 6b the Fermi plot of the fl-spectrum

EXPERIMENT

CALCULATION

0.8SS O" 10.3S 7-

--~=~7 23976

3 sT-

64 .'// ~0, \

t

12791

6" ........

,-~'-U#/

..........

4"..///, r~

297o0oo)r ......

g~ dsn

\ O13- = 8.4 MeV

~ 'i

12791(100)

01. . . . . . . . .

o

o','

134-~

52/e82

Fig. 7. Decay schemes for the 10.3 sec and 0.35 sec states of 134Sb. The levels of i34Te are comparcd to calculated ones using a ?J-forceinteraction (see subsect. 3.2.). of 0.85 sec 134Sb (discussed below) is shown. In this case the collecting and measuring times were only 1.3 sec and the transport time 1 sec. From the Fermi analysis the E~-ma, for the 10.3 sec 134Sb could be determined to be 6.8_+0.3 MeV and for the 0.85 sec 8.4+_0.3 MeV. In fig. 6a a lower energy fl-component (E,,~, ~ 6 MeV), corresponding to a transition to the 2397.6 keV level, is also observable. 2.6. THE LEVEL ASSIGNMENTS OF '3"lTe The four 7-rays (706.3, 115.2, 297.0 and 1297.1 keV)observed in the 10.3 sec ~34Sb decay form a cascade (fig. 7). Since the intensities of the I I 5.2, 297.0 and 1279. l keV transitions are the same, their order could not be determined. However, from

186

A. K E R E K et aL

systematics for the even tellurium isotopes ,4) and for the N = 82 nuclei we can with certainty place the transitions as shown in fig. 7. The conversion electron measurement d e m a n d positive parity for all the levels observed in ' 3"~Te, but the spin assignments for the first three excited states (2 +, 4 + and 6 +) are deduced from the Z = 52 and N = 82 systematics. The multipolarity o f the 706.3 keV },-ray de-exciting the 2397.6 keV level is M l or E2 or a mixture o f both. The log J? value o f the/3-transition to the 1691.3 keV 6 + state 6.4, implies a first forbidden type (AI = 0 or 1, An = yes). This is also the case for t h e / 3 - branch to the 2397.6 keV state in 134Te ( l o g f t = 6.0). F r o m shell-model considerations it is not possible to have 7 +, 8 + spin states at these energies, so that spin 6 + is assigned to this level.

10s #

lOt' ~: o z

E

Z~ 0

t~ oJ (DO

c0103

!

F

T,~=lO.3*-O.5,ec

,,

/ f T1/2 = 0.85~0.10 sec

":"", :, ~¢'.-':"~:".",',:. e)

',

5

10 15 20 TIME (see)

25

Fig. 8. Decay curves For *'~'*Sb with fl- energies greater thai] (a) ~ 3 MeV (b) ~ 5 MeV (c) ~ 6 MeV, respectively. 2.7. T H E 0.85 scc 134'5b D E C A Y

As was mentioned in sect. 1, one o f the possible alternative spins for the ground state o f 134Sb is 1-. However, no positive evidence was found for the existence o f such a state in 1345b (sect. 2.2). On the other hand, ifthe spin and parity o f t h e ground state is 0 - (which actually is that theoretically predicted) one may expect a strong/3branch to the g r o u n d state o f 134Te. The m a x i m u m energy for t h e / # d e c a y 1 3 4 S b ( 0 - ) 134Te(0+) would then be ~ 8 MeV. By measuring the time spectrum of the fl-particles it was possibie to observe two different half-lives a m o n g the high-energy ones, namely 0.85 __+ 0.10 sec and 10.3 + 0.5 sec (fig. 8). By increasing the threshold energy, the 0.85 sec c o m p o n e n t became more and more intense in comparison to the 10.3 sec component, as expected for at 1 3 4 " 5 h ( 0 - ) -"* 134Te(0 + ) transition. O f course, the high energy o f the 0.85 scc beta decay does not directly prove the

132Sn REGION, 2p AND pn STATES

187

element assignment. However, other possibilities are very unlikely, since the Q-values are considerably smaller for Z > 52 in the A = 134 isobaric chain and for 13~Sns, the expected fission yield is an order of magnitude smaller than that for 134Sb.

3. C o n c l u s i o n s

3.1. THE TWO /3-DECAYING STATES OF ~34Sb As was previously mentioned the proton and the neutron outside the doubly magic 132Sn core are most probably in the gl and f; orbitals, respectively. Nordheim's strong rule (as well as the Brennan and Bernstein rule) predicts 0 - for the ground state of 1345b. Using short-range •-forces is. 16) the level spacing within the (ng~, v~) configuration can be calculated. The result of these calculations is shown in

t'x I~,\ t ,

-

-

-

-

3

",

-

\ \\ \

a

b

c

Fig. 9. The splitting of the different members (a) of the (~g~, ~,f; I configuration due to (b) ~-forces and (c) the possible influence of tensor forces. fig. 9. A comparison with other pn nuclei, for example 2~°Bi, shows that a more realistic description of the nucleus requires the inclusion of tensor forces tT). This tensor force mainly influences the 0- and l - states in such a way that the energy difference between these states tends to decrease. Next in order above the 0- and 1 levels we find (fig. 9) the state with the highest spin value possible in the configuration considered, namely 7-. The origins of the 0.85 sec ( 0 - ) and 10.3 ( 7 - ) sec states of 134Sb are most likely the ones discussed above and shown in fig. 9. The relative energy spacing of the two levels could not be determined experimentally because of the uncertainty involved in the Ea_ o,~ determination. The two /3-decaying states are unequally populated in the fission process. The measurements show that the 10.3 sec ( 7 - ) state is fed by about a factor of 5 more than the 0.85 sec ( 0 - ) one. This is in line with what can be expected. From fig. 9 it is evident that the majority of the fission fragments with spin > 3 will cascade to the 7- isomer. (Although this figure is only approximately correct, it gives a general outline of the

188

A. K E R E K

et al.

expected level spectrum.) As shown by e.g. Nix and Swiatecki aa) it is much more probable that the fission fragments have spin > 3 than 0, 1 or 2. The 10.3 sec state should consequently be favoured. 3.2. T H E L E V E L S O F ta'*'Te

The nucleus 134Te, with two protons more than ~3z,5oans2, should be one of the best cases for checking the nuclear shell model in this nuclear region. According to this model the orbitals available for the two protons are gl- and d.1.. The energy needed to lift one proton from the g~ to the d,z subshell is 963 keV t 9) in the nucleus 133Sb82. If both protons are in the lowest orbital (g,) the possible spins for the (g2) configuration are: 0 +, 2 +, 4 + and 6 +. A coupling between g~ and d~ can give spins: 1+, 2 ÷, 3 ÷, 4 +, 5 + and 6 +. The simplest way to calculate the energy splitting between the different members of the same configuration is to apply a short-range f-force. According to de-Shalit and Taimi t6) the energy distance between the degenerate and non-degenerate states of the (jr ,J2) two-particle multiplet, if the interaction is described by b-forces, is

AE(jl ,J2, .I) = (-2jt+I!(2Jz-+I!(jt½J2-½IJO)2VF°(6)

for

( - ) " + ' ~ - ~ = +1,

for

(_)t,+t2-, = - 1 .

2J+l

,JE(j, ,j2,d) = 0

Here Jl, Jz, It and / 2 a r e the quantum numbers of the particles, d is the spin of the two-particle system, IJl-j21 < J
e 2 •fm

4.

xs2Sn REGION, 2p AND pn STATES

189

By assuming that the admixture o f other configurations to the (g~)6 + and (g~)4 + states is low, we can calculate the B(E2, 6 + ~ 4 +)th value. The transition within the multiplet is given by de-Shalit and Talmi 16) as B(E2; (j2)j I ~ (j2)jf) _

1

2Ji + 1

((j2),

(j2)

j,ll2e,rfrZYzll(J2), ji>2,

MeV

43t77

3"~ 2 e e l

/J , 25511

3-

"', 2398

5"

"~ ]/'~/"

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190

A. KEREK et al.

where ecrf is the effective charge o f the proton. Using simple harmonic oscillators as wave functions and r 2 = 28.5 fm z, one gets B(E2; (g2)6÷ --+ (g~)4 ÷) = 28(eeff/e)2e 2 . fm 4. Consequently ecfr = 1.74e, which is in good agreement with the corresponding values observed in the lead region 20). Several theoretical 2t-.,3) and experimental 24) works have been devoted to the N = 82 isotones. In fig. I0 a comparison is made between the levels o f 134 Te and the excited states of the heavier N = 82 nuclei. Heyde et al. 22), using a surface-6 interaction, have calculated the purity o f the 6* and 4 + states for 52 < Z < 64 and N = 82. In the 134Te case the admixture to the (g]) is as low as 2.4 % for the 6 ~ and 1.8 % for the 4 + levels. This estimated high purity o f the 4 + and 6 + states supports the validity o f the effective-charge value given above. Shell-model calculations have also been performed by Wildenthal and Larson 23). F o r the heavier N = 82 nuclei large hindrance factors were deduced for the E2 transition from the 6 + to the 4 + states. In fig. 11, ,Fhind" (6 ~ --+ 4 +) is shown for the N = 82 isotopes when only the (g]) contiguration is used. The effective proton charge o f 1.74e was applied (i.e. Fhi,d" is normalised to 134Te). The variation of the hindrance factors reflect nicely the filling o f the g.} and d~ proton shells with increasing proton numbers. Kownacki et al. 24) could somewhat reduce the hindrance factors by taking the pairing correlation between the nucleons into account, but it seems that in order to explain the remaining differences, other admixtures to the 4 + and 6 + states have to be considered (for example (g_,, d.~)o+, (g~, d,})4, and (d~.)4- etc.). The authors are very grateful to P. M611er for the construction o f the Fermi analysis p r o g r a m at the P D P compt, ter and to him and P. Carl6 for assistance in the measurements and evaluations o f the data. We are also indebted to J. Blomqvist, C. J. Herrlander, H. Ryde and K. Ryde for reading the manuscript and offering helpful comments. The maintenance o f the isotope separator by L. Jacobsson and the assistance in its operation by him, O. Jonsson and G. Skarnemark is gratefully acknowledgcd. References

1) A. Kcrek, G. B. Holm, P. Carl6 and J. McDonald, Nucl. Phys. A195 (19721 159 2I S. Borg, P. Carl6, L.-E. de Gcer, G. Holm and A. Kcrek, Annual report 1970, Research Institute for Physics, Stockholm, Sweden, p. 26; A. Kerek, S. Borg, P. Carl6, L.-E. de Geer and G. Holm, Annual report 1971, Research Institute for Physics, Stockholm, Sweden, p. 114 3/ G. B. Holm, CERN 70-73, p. I001 ft. (1970) 4) A. A. Delucchi, A. E. Greendale and P. O. Strom, Phys. Roy. 173 (196g) 1159

132Sn REGION, 2p AND pn STATES 5) 6) 7) 8) 9) 10) I I) 12) 13~ 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24)

191

W. John, F. W. Guy and J. J. Wesolowski, Phys. Rev. C2 (1970) 1451 J. B. Wilhelmy, S. G. Thompson, R. C. Jared and E. Cheifetz, Phys. Rev. Left. 25 (1970) 1122 J. W. Gr/iter, K. Sistemich, P. Armbruster, J. Eidens and H. Lawin, Phys. Lett. 33B (1970) 474 S. Borg, I. Bergstr6m, G. B. Holm, B. Rydberg, L.-E. de Geer, G. Rudstam, B. Grapengiesser, E. Lund and L. Westgaard, Nucl. Instr. 91 (1971) 109 W. G. Winn and D. G. Sarantitcs, Phys. Rev. 184 (1969) 1188 V. Berg, K. Fransson and C. E. Bemis, Ark. Fys. 37 (1968) 203 H. N. Ertcn, G. D. Coryell and W. B. Waiters, Bull. Am. Phys. Soc. 14 (1969) 1255 H. Agvald and B. Rydberg, Annual report 1969, Research Institute for Physics, Stockholm, Swcden, p. 82 R. S. Hager and E. C. Seltzer, Nucl. Data 4 0968) l A. Kerck, Nucl. Phys. A176 (1971) 466 K. Sasaki, Nucl. Phys. 71 (1965) 95 A. de-Shalit and I. Talmi, Nuclear shell theory (Academic Press, New York, 1963) Y. E. Kim and J. O. Rasmussen, Nucl. Phys. 47 (1963) 184 J. R. Nix and W. J. Swiatccki, Nucl. Phys. 71 (1965) l G. B. Holm, S. Borg and B. Rydherg, CERN 70-30, p. 1006 (1970) G. Astner, 1. Bcrgstr/)m, J. BIomqvist, B. Fant and K. Wikstr6m, Nucl. Phys. A182 (1972) 219 M. Rho, Nucl. Phys. 65 (1965) 497 K. Heyde, M. Waroquier and G. van den Berghe, Phys. Lett. 35B (1971) 211 B. H. Wildenthal and D. Larson, Phys. t,ett. 37B (1971) 266 A, Filevich, J. Kownacki and H. Ryde, AI76 (1971) 155