The low-seniority shell-model structure of 212At

Nuclear Physics A376 (1982) 294 © North-Holland Publishing Company

ziZAt THE LOW-SE1vIORITY SHELL-MODEL STRUCTURE OF T. LÔNNROTH and V. RAHKONEN Department of Physics, University of Jyväskylä (JYFZ.), Nisulankatu 78, 407201yväskylä 72, Finland and B. FANT

Department of Physics, University of Helsinki, Siltavuorenpenger 20, 00170 Helsinki 17, Finland Received 14 September 1981 Abelrrd: Using the reaction z°9Bi(a; n), states in the nucleus zizAt were populated. The decay of excited states wasstudied usingwnventional in-beam y-ray and conversion-electron apectrosoopy . A great number of new levels were established and assigned spins and parities and the previously reported yrast cascade was confirmed. A new Ti~z=32t1ns isomer at 275.4 keV is reported and interpreted to be the S - state of the ~jô'lrvizv89~z configuration. The configurations were calculated as belonging to the neutron-proton seniority-2 multiplets where the available orbitals are bv~z, f~iz and üaiz for the protons and ß9z, üi~z and jis~z for the neutrons. Configuration mixing is shown to be essential in order to account for the experimental findings . On the basis of isomeric lifetimes the effective charges are discussed. E

NUCLEAR REACTIONS z°9Bi(a, n), E =18.0-20.8 MeV; measured yy coin, Xy coin, zizAt deduced level scheme, spins and parities ; Ti~z, Ir le-, W(B), excitation functions. configurations proposed and configuration mixing discussed, B(A) .

1. Introduction Nuclei in the vicinity of the doubly magic nucleus z°sPb, but with both neutron and proton particles, i.e. N> 126 and Z > 82, are little investigated with in-beam methods. This is due to the lack of suitable targets and/or corresponding neutronrich beam . Some investigations have been made using the transfer reaction Z°9Bi(d, p)Zr°Bi [refs. t .s )], the "spallation" reaction asaU(a°Ar, X) ZrZBi [ref. 3)] and the fusion-evaporation reaction 2°aPb('Li, X) 2'3At, Zt2Po, 2t°Pb [ref . a )] . Attempts have also been made with heavy ions, but then the fission channel largely spoils the in-beam investigations . The J~ = 1 - ground state of ZisAt and also an J~ = 9- isomeric state, which are both a-decaying, were identified almost two decades ago s) and thereafter studied in detail by many physicists ~). The strongest branches of these decays are shown in fig. 1 . The intensity of the 63 keV line in 2°8Bi will be of importance when discussing the level scheme of ztaAt in sect . 3. If one assumes seniority to be a good quantum number, a fact well substantiated by experience, states in ZrZAt should be described as arising from coupling the odd 29

T. Lönnroth et al. / z1zAt

30 212At

M.+rl

7.6071 7.669 I _ 7.826 I 9 7.B88 I

REFERENCE 5 6 8 20 I 17 15 80 I 81 63 80 I 67 68 20 I 30 31

Fig. 1 . The a-decay of the 1 - (g .s.) and 9 - states in z' z At. The level energies are adopted from ref. s) . The energy of 62 .94 f 0 .05 keV for the 4 + -~ 5 + transition in z°sBi is obtained in this work ; this value is in agreement with the previously reported value 62 .9 f 0.5 ke V, cf . ref . 9) . z

neutron in one of the orbitals of z°9Pb (i.e . gviz, illiz or jt5iz) to states in ' l At [ref . t° )] . The states in z1 'At can be of two types, namely seniority-1 states or single-proton states in z°9 Bi (i .e . h9iz, f7 ~z or i, 3 i z ) and seniority-3 states, for the low-lying states mostly of the configuration h9~z . The available seniority-2 multiplets in ztzAt thus obtained are given in table 1 . As is seen, appreciable mixing of the low-lying negative-parity configurations is expected, since the energy differences are rather small. In the energy range below 1500 keV tens of excited states are

thus expected . zl1 Po [ref. ")], Encouraged by the results of a recent study of the N =127 isotope ztzAt. same reaction, viz. (a, n), to produce excited states in The we have used the TAHLE 1 Proton-neutron configurations °), spin-parity ranges and wroth-order b) z1zAt excitation energies for seniority-2 states in Configuration l19/2g9/2 h9/zill/z l1 9/z113/2 f~/zB9/z f7/zill/z f7/zils/z i13/zg9/z 113/2111/2 i13/z]ls/z

J~

Ea (keV)

Number of states

0--9 1 -10 3 +-12+ 1 --8 2--9 4+-11 + 4+-11 + 1 +-12 + 1 --14 -

0 778 1422 674 1452 2096 1355 2133 2777

10 10 10 8 8 8 8 12 14

') The proton single-particle energies are from z"At. The proton-neutron interaction energies are typically amactive by 40-900 keV, depending on the orbitals involved .

T. Lönnroth et al.

/ 2~2

At

31

Q-value of the reaction is for the present case even less favourable than for the z "Po case, -15.279 and -14.960 MeV, respectively, and the Coulomb barrier is at about 19 MeV. This makes the total cross section of the reaction very low at the available a-energies, cf . ref. ") . A recent study of high-spin states in Z'ZAt using the reaction 2°8Pb('Li, 3n) revealed a high-spin cascade built on the J~ = 9- isomer'Z). As will be seen below, we observe the same high-spin cascade in the (~, n) reaction at EQ ^-20 MeV. In addition a great number of near-high-spin states built on the 9- state, and low-spin states built on the 1- ground state, are observed .

2. Experimental methods The in-beam experiments were performed at the MC-20 cyclotron of the Physics Department at the University of Jyväskylä (JYFL) . Alpha-particle beams in the energy range 18 .0-20.8 MeV were used at intensities of about 0.2-10 nA electric current. The Z°9Bi target thicknesses were 0.6, 4 and 10 mg/cma , the thick ones for the y-ray investigations and the thin target for the conversion electron measurements. 2.1 . SINGLES SPECTRA AND EXCTTATION FUNCTIONS Singles y-ray spectra were measured at a-particle energies of 18 .3, 19 .0, 19 .7 and 20 .8 MeV, respectively . Both large coaxial Ge(Li) and small intrinsic Ge X-ray detectors were used, since low-energy transitions were expected, in analogy with z' °Bi [refs.''2)] . Sample singles spectra are shown in fig. 2. The excitation functions clearly indicate that the strong 161 keV line feeds the ground state and not the 9isomer . This conclusion is further substantiated from the intensity balance with the 63 keV transition in z°BBi, cf . fig. 1 and sect. 3. The y-ray intensities are given in table 2. 2.2 . COINCIDENCE MEASUREMENTS Two independent coincidence measurements were performed, one with two large Ge(Li) detectors and the other with a large Ge(Li) and an intrinsic Ge X-ray detector . This was done in order to obtain the positions of the low-energy y-rays in the decay scheme . Examples of background-subtracted spectra are given in fig. 3. The sum gate of the 478 + 184 + 662 keV transitions clearly shows that the transitions in the high-spin cascade feeding the 10- and/or 11 + state are observed . The coincidence spectrum obtained by gating on the 161 keV transition reveals that this transition is fed by a great number of lines, most of which are parallel . From the small-big combination the results from the gating on the lines 45, 55 and

32

zi2At T. Lönnroth at al. /

TABLE 2 Properties of transitions assigned to z1zAt in the reaction z°9 Bi(a, n)?1zAt at E, = 20.6 MeV

E,.

I,.

45 .1 55 .1 69.9

15 .7 10 .2 3.7

105.1 160.4 183.8 196.9 °) 239.E 251.0 278 .1 290.7 300.0

Az/A o

2.9

0.10 (3)

100 7.9 <30 ~10.6 2.9 4 .6 9.0 --1

-0 .06 (1) -0 .11 (3) 0.11 (2) 0.18 (5) -0 .0 (6) -0 .25 (9) -0 .10 (1)

308.9

3.9

363.E 366 .E 377.2 397.E 419.8 435 .E 442.0 478.E 514.8 526.4 536.7 567.1 570.3 580.3 587.7 608.E 618 .8+620 .0 650.1 662.5 675 .0 679.E 685.4 715 .1 728.2 760.5 765 .7 942.1

14 .5 5.5 5.7 5.0 4.5 4.4 2 20 .7 19 7.0 4.4 15 .4 1 .9 10.6 14 .9 9.1 15 .5 2.6 16 .9 15 .3 11 .6 6.9 19.6 7.4 14.2 4.9 11 .0

A,/Ao

exp

theory

25 .3 (a,~ M1 14.0 (a~) Ml 42.1 (a,~ E2 fll (a~) Ml ^-0 1.60 (a~ Ml -0 .01 (2) --0.7 (a y~ 3.36 (a~) Ml 0.13 (5) --0.03 (aL) 0.016 (aJ El -0 .09 (3). >0 .11 (aL) `) 0.27 (aJ Ml, E2 -0 .04 (9) 0.4 (9) -0 .3 (2) 0.13 (6) 0.10 Ml 0.09 (2) 0.60 (15) 0.51 Ml

-0 .04 (4) 0.09 (11) -0 .04 (2) -0 .29 (15) -0 .1 (2) 0.4 (4)

0.04 (6) 0.2 (2) -0 .2 (3) 0.3 (2) 0.2 (3) -0 .2 (5)

0.13 (3) -0.18 (8) -0.02 (9) -0.25 (14) -0.01 (8)

0.20 (4)

---0.1 -0.00 (10) 0.07 (8) 0.07 (2) -0 .14 (9) 0.04 (1) -0 .35 (10) -0 .30 (10) -0.2 (1) 0.11 (4) -0 .08 (10) 0.21 (10) 0.4 (3) -0 .3 (2)

K-conversion coefficients

-0.23 (14) 0.4 (2) -0.05 (13)

E2 10.43 M1 0.35 (5) 0.35 Ml 0.26 (4) 0.34 Ml 0.43 (5) 0.25 Ml 0.24 (4) 0.22 Ml 0.26 (7) 0.19 Ml 0.20 (5) 0.17 Ml a0 .1 0.16 Ml normalization (Ml) ~0.12 0.11 Ml 0.14 (3) 0.11 Ml 0.017 (5) 0.0085 El 0.090 (15) 0.084 Ml 0.34 (15)

>0 >-0 .15 0.04 (15) 0.086 (15) 0.10 (13) 0.080 (10) 0.16 (3) 0.079 (10) 0.26 (15) "-0.06 -0 .05 (2) 0.17 (5) ~0 0.046 (10) >0 0.068 (15) -0.1 (3) 0.073 (10) -0.01 (6) 0.011 (4) 0.08 (15) 0.061 (15) 0.04 (15) 0.0086 (20) 0 .2 (5) 0.012 (5) -0 .3 (3) -0 .02

f 0,07

0.082 Ml 0.077 Ml 0.072 Ml 0.067 Ml 0.058 Ml 0.14 M2 0.056 Ml 0.055 Ml 0.053 Ml 0.012 E2 0.048 Ml 0.011 E2 0.011 E2 0.026 Ml

Multipolarity M1 ~ Ml ~ E2 ~ Ml ~ Ml El Ml or E2 El ~ Ml E2+Ml

Ml Ml+E2 Ml Ml Ml Ml Ml (+E2) Ml adopted Ml Ml Ml (+E2) Ml M1 Ml Ml and E2 Ml M2 Ml+E2 Ml+E2 Ml E2 Ml E2 E2 Ml (+E2)

The table also contains transitions assigned to z'zAt (from Z-binding energies), but not placed in the level scheme . ') Ref.ls) . b) Only the coefficient with the best agreement is given. As is seen, the deviations from the theoretical values are generally less than --20%, whereas the values for different multipolarities diner by a factor of 3 or more . ~ See the text for a discussion of the multipolarity. a) Mostly contamination from the E2 line in 19F. The largest intensity allowed by the decay is --16 . ~ The value aK ~ 0.1 is derived from delayed intensities, since the electron line is strongly contaminated.

e

ss r.v

 ~ou s~rr

~~

~ 1

,

~

OIU p

105IuV

TLO

p L . ._ ~o

-

_"1

_

0 1~

160 YIW

Lpa

`

~10(Lf

f000 50+.~ I

00

â1

0 1051

o

S1< kW

~x~ m Y!

00(6 _

0

V J

iW

~"

~ ,y

__

yL _~. . -

«~

~rtL

~n c

0

ril..~ ~ .

.._J

1B4"478"662"kW

m.:

nu

,oo

0

_

L

000

Sn

sv I 1000

. -Jma~. .~u . ~.a.L H00

IiWI~ M~~t

. . .r lOOD

Fig. 3 . Background-subtracted coincidence spectra. The spectra are both from the combination of two Ge(Li) detectors and from the combination of an X-ray and a Ge(Li) detector .

T. Lönnroth ct al. / zizAt

35

105 keV are displayed in fig. 3 . As is clearly shown, the 45 and 55 keV lines belong to different cascades as does the 105 keV transition . 2.3 . TIME MEASUREMENTS IN THE ns REGION

The measurements of half-lives in the nanosecond region were performed both with a big and a small detector, either between the natural pulses of the cyclotron (pulse repetition ^-45 ns) or using a fast pulsing device' 3 ) at a ratio of 1 :11, the time region thus being -x500 ns. The two high-spin isomers at 885 .4 (11 + ) and 1615 .7 (15 - ) keV reported in ref.' 2 ) were confirmed. In addition it was found that the very strong 161 keV transition had a relatively large delayed component, cf . fig. 4. The same half-life (32 ns) was later also observed in the time curves of the

0

20

40

60

80 CHAMEL NUNBEFt

100

Fig. 4. Time spectra for the 70, 45, 160 and 184 keV transitions . The ratio of prompt-to-delayed intensities unambiguously foes the ordering . The 184 keV curve shows the half-life of the 11 + ~ 10 El transition .

36

T. Lönnroth et al. / zizAt

0 N

a a

C O

N

Ô N ~a

â

N N_ C

ö

N C O d t. d

ac

0 .. G O C

UO vi eô tî. l3NNt/H~ 213d S11~10~

T. Lönnrotk et al. / sisAt

37

45 and 70 keV transitions, of which the former has a prompt component while the latter has none . We thus propose an isomeric level at 275 .4 keV with a half-life of 32 t 1 ns . The prompt-to-delayed intensity ratios unambiguously fix the ordering of the depopulating transitions and the 70 keV transition as the isomeric transition . The time curve of the 55 keV transition, on the other hand, shows only a prompt component (fig . 4) ; due to this fact the corresponding cascade does not contain any isomeric levels . 2.4 . ANGULAR DISTRIBUTIONS AND CONVERSION ELECTRONS For multipolarity determinations both angular distribution and conversion electron measurements were performed. Angular distributions were measured in five angles between 90° and 150° with respect to the beam direction. The asymmetries for the transitions feeding the ground state are relatively small, partly due to low-spin values, partly because the z spin units of the target are isotropically distributed and partly because the reaction was performed close to the Coulomb barrier which enhances low-J population . The normalized distribution coefficients are listed in table 2. The conversion electron spectra were measured using a Si(Li) detector combined ia), with a magnetic lens the system having a transmission of 7%, ~ resolution of ~2 .4 keV at 1 MeV electron energy and a peak-to-background ratio of about 15 :1 for the strongest peaks. A singles conversion electron spectrum is shown in fig. 5. The experimental conversion coefficients are given in table 2. As is seen, the combined data from the angular distribution coefficients and conversion coefficients unambiguously determine the multipoles of almost all transitions. Additionâl support for the choice between dipole and quadrupole transitions is extracted from K/L conversion ratios, as displayed in fig. 6. The assignment of multipoles to the low-energy transitions is discussed in the next section .

3. The experimental level scheme of ZisAt The experimental level scheme of Z'ZAt as deduced from the present study is given in fig. 7. We take the ground state (1 -) and the isomeric 9- level as established, cf . refs . s-a) . The previously reported ~s) yrast cascade built on the 9- level is mainly confirmed . We did not populate the topmost levels reported in ref. lZ ), but instead we populated lower-spin levels with higher intensity. This enables the unambiguous assignment of spin-parity values to all levels in the yrast cascade, cf . the left-side part of the level scheme . In the gates of the 377 .2 and 278 .1 transitions a weak line of 75 .0 keV is observed, the (15 -)-> 13 - transition . That we populate the (15 -) isomeric state at 1616 keV is evident since the 13 - -> 12 + and 12 + -> 11 + transitions are seen in

38

T. Lônnrotk et al. / 2'ZAt a~ a~ s.o

4.0

2 .0

00

250

500

E

Y

750

Fig. 6 . Conversion ratios (a x /a~) for some transitions in zizAt . Where the M2 ratio would be possible, it is excluded by the absolute conversion values and by the absence of measurable half-lives .

delayed spectra. The proposed energy of the isomeric transition is in agreement with a recent prediction 15 ), see sect. 4. A cascade with decreasing spin values, consisting of the transitions 105 .1, 514 .8, 620.0, 239.6 and 366.6 keV, respectively, is also populating the 9- level. This cascade cannot populate the ground state for reasons discussed below. The multipolarity of the 105 keV transition is deduced indirectly : Since it has no measurable half-life (T,n < 1 ns) it cannot be of E1 or E2 multipolarity, since they would have ti 17 half-lives of ^-50 ns or ^-100 ns, the Weisskopf value, respectively [cf. refs . ' ) for a discussion of the retardation of B(E1) values]. Thus it is a magnetic dipole . The spin must be decreasing, since a 9- -> 9- transition would infer a 1 : 2 competition with the 478 .6 keV transition depopulating the yrast 10- state, and no transition from the 10 - state to the state at 328 keV is observed . The 10 - possibility is strongly ruled out by the yrast behaviour of the 10 - at 702 keV. Similar arguments hold for the other members of the cascade, cf . figs . 3 and 7 . The weak cross-over transition of 620.0 keV further supports this argument . The strongest line by far in the y-ray spectrum is due to the 160.4 keV transition . zizAt and the 62 .9 keV In order to establish a balance between intensities in transition in z°BBi fed by the ~-decay, cf. fig. 1, the 160.4 keV transition must feed the ground state. A large number of y-rays are coincident with this transition, cf . fig. 3, especially the two low-energy transitions of 45 .1 and 69 .9 keV. The order of these three transitions is unambiguously determined from the prompt-to-delayed ratios (fig. 4), as discussed in subsect. 2.3 . The 45 .1 keV transition has a prompt component, and due to this fact it must be a magnetic dipole, like the 160.4 keV transition, cf . table 2. This fixes the T,iZ = 32 ns isomeric state at 275 .4 keV to have J~ = 5-. The topmost level at 1457 .3 keV has positive parity as determined by the 536.7 keV transition .

T. Lönnroth et al. / zizAt

39 N" E G 0

d

~mn ~1O t)1 Y"NN

N 0

C

~i~i~~I~I~i~ r v~1

n

.ô û

m

I

.p, n

~~d .~n$û

°,^ ~nn

in~iv ~i i

moo

.G

Ô an

.C

T p

Q r

_d

~ N G .~ w m 0 w F.

N ~ r

N

_,11111~

Ô

iV ~.

.Y

_~ E ~ E

W

O

O d P

OrvO~ ~ .O

FÇ

d

m

N

~

y F.

O

F.

C) L ar

W

w

fE

a^ E E

w

é

r

~ Y d o ~

E

E 0

'C ~C ô. ~ô 0 Û

w~

O

40

T. Lönnroth

et

al.

/ 2'2At

Finally, on the far right a second set of low-spin levels, completely disconnected from the previous one, is displayed. The intensity of the strongest transition of 55 .1 keV is about 25% of the intensity of the 160.4 keV transition, indicating very low spins for the levels. The 55 .1 keV transition must be of multipolarity M1 by the same arguments as for the 45 .1 and 105 .1 keV ones . We interpret it to be the 0 - -s 1 - transition, which is thus analogous to the corresponding 47 keV transition 2'oBi, in cf . ref.'). Except for the levels at 622.7 and 635 .4 keV all levels in this set can be assigned an unambiguous spin-parity value. 4. Uiscassion 4.1 . EXCITATION ENERGIES

The excitation energies of levels in z'zAt are calculated within the shell model as arising from the coupling of an odd neutron in the g9iz, illiz and jis~z orbitals z of z°9Pb to seniority-1 levels in "At, i.e . configurations of the form ~jô~h9,z, Trjô~f,iz and -rrjâ~il3iz : Nine different configurations, as mentioned in table 1, can thus be achieved . In order to be able to use known (either empirical or theoretical) two-nucleon matrix elements'9) standard angular momentum algebra z° ) was applied to the four-nucleon configurations . The results of the calculations are shown in fig. 8, where the experimentally determined levels are displayed on the left . Those states which are identified with experimental levels are drawn with heavy lines . The seniority-4 levels displayed in fig. 8 are from ref.' s). These levels are also discussed in ref.' z) . Generally the correspondence between the calculated and experimental levels is satisfactory. It should be noted, however, that the calculations have been made under the assumption of pure configurations . This is certainly not exact since e.g . z') : already in z'°Po the admixture in the two-proton configurations is not negligible The wave functions of the two lowest-lying states as obtained in "approximation z') 2" by Kuo and Herling are given below: ~Oi ) =0 .82~h9~z)-0.40~iis~z ) +0 .37~f ;~z)+0 .15~fs~z) +- ~ ~ , ~2i) =0 .98~h9iz ) -O .ll~ii 3iz )+O .lO~f;~ z)+~ ~ ~ . As expected, the 0+ state involves the largest admixtures . In the h9~ z seniority-1 state the fractional parentage of the ~0+) state is 27% and thus the mixing is not negligible. It cannot, however, be taken into account in a straightforward manner, since in z"At the Pauli blocking in the h9 ~ z orbital changes the relative amplitudes of the h9~z and f~~z orbitals . In addition the iisiz component contains an admixture z°sPb, of the f,~z orbital via the coupling to the octupole vibration in viz. ~ +,

zo9Bi) =

0.93~i13,z) + 0.37~f~ iz 3- ;

+) .

T. Lônnroth et al. EXPERIMENT

/ Z ~ Z At

41

CALCULATION SENIORITY - 2

SENIORITY- i

h 9ri~132 't12 h94f7ihY1 1g~___ ___ `___ ___ 4"____ 1r

h3

10`

,"____ s .-_-=

h~'1sr~t 1fr -__

1r-___

h~f~i~

"____

e-____

T-____ ____

çlfyt

e

1

hY~'tY~9R

___ -



f

a ^n',vr

h~1.~,~ 7_

-

5 r 4_

~;____

1l,~si!i" ~1

14=_ _ _

-

1

r-___

2_

F~qn

3 htYt'11l1 1s=__.

10 --- -

w z w z O_ I"-

H

U X W

r

r Fig. 8. Comparison of experimentally determined and theoretically calculated levels in 2'ZAt. Tile theoretical seniority-4 high-spin levels at right are from ref. is). Levels drawn with heavy lines are tentatively identified with the experimentally determined ones . Levels of the highest-lying multiplet, Trh9/zü3/z~J~siz, are not displayed because the multiplet has a center of gravity at about 2.9 MeV. 22) where the admixed amplitudes are from ref. . Taking into account the many possibilities of admixtures, the results are satisfactory . Below we discuss some conspicuous features . The features of the ground-state multiplet, mainly of the ~rrh9i2vg9i2 configuration, are well reproduced . Only the levels 4-, 6- and 7- have not been observed. For the observed levels the mean and the rms deviations between theory and calculation

T. Lônnroth et al. / zizAt

42

are -14 and 38 keV, respectively . The 8- levels of the configurations rrhy~2vg9n and Trhg~2f,~2vg9~2 come very close in excitation energy, so they are probably strongly mixed. The most prôbable reason why the 7 - level of the ground-state multiplet is not observed, is that it lies just above the 9- level; the calculated z' difference is X40 keV, while it is 162 keV in ° Bi . It thus decays via a strongly retarded and highly converted E2 transition to the 9 - level and is therefore not observed . For the higher-lying multiplets the agreement between theory and experiment is not as good as for the ground-state multiplet, the mean deviation is small but the rms deviation is about 150 keV. This deviation is partly due to difficulties in the identification of levels and partly due to close-lying levels where the admixtures might shift the level energies by tens of keV. 4.2 . TRANSITION PROBABILITIES

The two identified E2 transitions in 2 ' ZAt, namely 5 - ~ 3 - and 15 - -> 13 - , are of z' interest since two corresponding transitions in °Bi are known, namely 7 - -> SZs and 5 - ~ 3 - [ref . )] . All these take place in the ~rh9i2vg9~Z multiplets, where n = 3 for the 15 - ~ 13 - transition and n =1 for all the others . Effectively it is thus a question of transitions involving the h9î2 proton and the g9~2 neutron. A collection of half-lives and deduced effective charges are given in table 3, where those from ZizAt are from the present work . As is seen in table 3, the proton h9î2 effective charge is practically unaffected by the seniority. In contrast to this, the neutron g9î 2 effective charge has to change, about 40% when going from 2 ' ° Bi to 2 ' °Pb or Zt2At, even a factor of two for the seniority-2 and seniority-4 transition in to TABLE 3 Half-lives and effective charges for identified transitions in z°9 Bi, z " 9Pb, zl°Po, z ' °Pb, z ' °Bi, zl 'At and z ' z At Nucleus 2o9B1

z°9 Pb zioPo

z' ° Pb zioBi zii At nz At zizAt

E,. (keV)

Tl ~ z (ns)

897 465 84 80,100 90,162

0.012 0.161 110 155,30 38,58

70 75

33 37

Orbital

eR/e

Ref.

h9iz f~~z sl/z hy~z B9~z B9/z h9~z B9/z Bv~z

1 .50 f 0 .06 4.0 f 0 .3 0 .42 f 0 .01 1 .53 f 0 .06 1 .16f0 .10 `) 0 .82 t 0 .07 `) 1 .53 t 0 .08 n) 1 .83 t 0 .12 1 .9 f 0 .3

za ) 25)

zs ) zs ) z~ ) za ) ze ) present work present work

`) Weighted mean from two transitions. °) Weighted mean from the ~- i zz- , ~--~ ~- and ~--~ u- transitions . It should be noted that the --. z- transition must proceed as E2 since the M1 matrix element is identically zero within any j" configuration (except lily ; B(Ml)= J(J+1)(2J+1)~5,,,,,.

T. Lônnroth et al. / Z ' Z At

43

âccount for the experimental half-lives . It should be noted that here the neutron effective charge is not corrected explicitly for configuration mixing, and it should thus not be regarded as "bare" effective charge . The value of the effective charge in 2' °Pb can easily be accounted for since the g9î2 neutron couples to the jts~z orbital via the collective octupole in the 2°8 Pb zz) core the coupling being 5% in 2°9 Pb . This value should, however, be increased in 21°Pb because of increased Pauli blocking giving a larger g9~z effective charge . zt2At A similar effect may be found in . As is known, the j,siz orbital in z°9Pb lies z at an excitation energy of 1422 keV [ref.' 9)], is lowered to 1065 keV in "Po zi3Rn z9) [ref . ")], to 896 keV in and to 772 keV in 2'sRa, respectively . In the particle-vibration mode1 22) the interaction between a particle in orbital j and a A -pole vibration is expressed as e.g . SE~ =-

2 ((j~A)I~H,n~~j) Et - E~, - hwa

S(j,I),

where I is the intermediate angular momentum - in our case j, I = z s, j~ = z and If A = 3. one assumes that the coupling interaction Hnt is (at least approximately) constant, then the effect of lowering the jlsiZ orbital gives an increased propagator value and an increased coupling . This, on the other hand, means an increased mixing of j,sis x 3 in to the g 9 i Z orbital and finally a larger effective charge, as is observed . References 1) C. Ellegaard, P.D . Barnes, R. Eisenstein and T.R . Canada, Phys . Lett . 35B (1971) 145 2) T.R . Canada, R.A. Eisenstein, C. Ellegaard, P.D . Barnes and J. Miller, Nucl . Phys . A205 (1973) 145 3) P.A . Baisden, R.E . Leber, M. Nurmia, J.M . Nitschke, M. Michel and A. Ghiorso, Phys. Rev. Lett . 41 (1978) 738 4) T.P . Sjoreen, U. Garg and D.B . Fossan, Phys. Rev. C21 (1980) 1838 5) W.B . Jones, Phys . Rev. 130 (1963) 2042 6) P.L . Reeder, Phys . Rev. Cl (1970) 721 7) H. Gauvin, Y. LeBeyec, J. Livet and J.L . Reyss, Ann. de Phys . 9 (1975) 241 8) K. Fransson, M. of Ugglas, D. Carlé and T. Erikson, USIP Report 76-09, Stockhohn (1976) preprint 9) D. Prcetel, M. Dost, E. Grosse, H.J . Köner and P. von Brentano, Nucl. Phys . A161 (1971) 565 10) I. Bergitröm, B. Fant, C.J . Herrlander, P. Thieberger, K. Wikström and G. Astner, Phys . Lett . 32B (1970) 476 11 . B. Fant, T. Lönnroth and V. Rehkonen, Nucl . Phys. A355 (1981) 171 12) T.P . Sjoreen, U. Garg, D.B . Fosen, J.R . Beene, T.K . Alexander, E.D . Earle, O. Häuser and A.B . McDonald, Phys . Rev. C20 (1979) 960 13) M. Kangas and R. Komu, JYFL Annual Report, University of Jyviiskylä (1978) p 16 14) J. Kantele, M. Luontama, A. Passoja and R. Julin, Nucl . Instr. 130 (1975) 467 15) J. Blomgvist, private communication 16) F. Rösel, H.M. Fries, K. Alder and H.C . Pauli, Atomic Data and Nucl. Data Tables 21 (1978) 291 17) T. Lönnroth, B. Fant, K. Fransson, A. Källberg and L. Végh, Phys. Scripta 23 (1981) 774 18) L. Rydström and J. Blomgvist, AFI Annual Report, Research Institute for Physis, Stockholm (1981) 3.4 .2, p. 109

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