The quadrupole moments of the 5− states in 116Sn, 118Sn and 120Sn

1l.E.3:2.B[

N&ear

Physics

A228

Not to be reproduced

(1974)

by photoprint

15-28;

@

North-Holland Publishing Co., Atusterdaol

or microfilm without written permission from the publisher

THE QUADRUPOLE MOMENTS OF THE 5IN “‘Sn, “*Sn AND ‘*‘Sn K. KRIEN,

B. KLEMME,

R. FOLLE

Institut fiir Strahlerr- aad Kerphysik Received

27 March

and

STATES

E. BODENST’EDT

der UnicersitSit Born 1974

Abstract: The quadrupole interaction frequencies o ,_,= 3eQl V.J41(2I1)ti in the 5 - state of ‘I %n have been measured by time differential perturbed angular correlation technique in Sn, Sb and (95P/, Sn+5% Sb) environments. The o,, for “%n was determined in Sn environment only. With the help of the known electric field gradient ‘) of Sn in a Sn lattice the quadrupole moments have been deduced asQ(5-, li8Sn) = &0.10(4) b and Q(5-, “%n) = _CO.165(60) b. These values together with the known *) quadrupole moment of the analogous 5- state in “‘Sn are interpreted in terms of the pure single-particle model. The data exhibit the expected strong systematic variation of Qr with the number of particles in the h+ subshell which is being filled with 1, 3 and 5 neutrons in “%n, lL8Sn, and 12”Sn, respectively.

E

RADIOACTIVITY

llsmSb

and 1’6mSb, measured deduced 5- states. 0,.

1~:‘(!3,coo, t)“%n

and

l18Sn:

1. Introduction For a nuclear state of spin I which results from the coupling of 11particles in a shell model orbit with angular momentum j, the theory predicts “) for the matrix elements of a spherical tensor xify’ of even rank k the relationship

this equation v is the seniority of the Ij”vZ) configuration. Thus the matrix elements of the tensor cJ/“’ are largest for IZ = 1; they become smaller when the subshell is

In

filled with more particles, passing through zero for a half filled shell and finally reaching a maximum value of opposite sign for a single hole in the subshell. Since the quadrupole operator is an even rank tensor this prediction may be tested by measuring the quadrupole moments of analogous states in neighboring isotopes, which differ only in the number of nucleons in the same orbit. For a subshell of high angular momentumj one has a series of nuclei available for a systematic investigation. Furthermore, for a large j large pairing forces make seniority impurities small. In addition there is always one shell model orbit within a major shell which has parity opposite to all the others. The choice of such an orbit for the investigation reduces the possibilities of configuration mixing. 15

K. KRIEN

16

cf
The 5- states of the even Sn isotopes (see fig. I ) fulfill all these conditions as they are interpreted as /(h,)“sl) configurations with II = I, 3 and 5 for ‘16Sn, “*Sn, and “‘Sn, respectively. Another attractive feature of the Sn isotopes is the magic proton number Z = 50 which reduces even more the space for configuration mixings. The long lifetimes of these states and the large anisotropies of y-cascades via these levels ‘- -‘) allow the determination of the quadrupole interactions in crystalline environments by the time differential angular correlation method. A calibration of the effective field gradients can be performed by use of the known quadrupole moment of the 3’ state of ‘i9Sn [refs. ‘* “)I. The excited states of the Sn isotopes are populated by EC decay. This decay involves the production of high charge states of the daughter atoms which could lead to uncertainties in the effective electric field gradient. This kind of after-effect can be completely eliminated by the use of metallic environments. Tin itself is a suitable host lattice because of its noncubic symmetry. We report in this paper measurements of the quadrupole moments of the 5- states in “*Sn and lj6Sn. Since the quadrupole moment of the 5- state in “‘Sn has recently been measured by Wolf et ul. 2), we have three quadrupole moments in a series to test relation (1).

2. Investigation 1.1.

EXPERIMENTAL

of quadrupole interactions in “*Sn

PROCEDURES

In order to determine the quadrupole interaction in the 2.32 MeV 5- state in “‘Sn (T+ = 21.7 nsec) we used the time differential perturbed angular correlation method with a conventional two detector apparatus, consisting of two 3.9 x 5.2 cm’ NaI(T1) crystals coupled to XP 1021 photomultipliers and commercial electronics. The energy window in one y-spectrometer was set such that the y-rays of the 254 keV transition populating the 2.32 MeV 5- state were detected. In the other spectrometer all events above 300 keV were selected. This is possible because the two cascades (254 keV1092 keV) and (254 keV-unobserved 1092 keV transition-1230 keV) have similar angular correlation coefficients “). Since the A, coefficients of these correlations are quite small, we restricted our measurements to the two angles 90’ and 180”. The corresponding time spectra were stored in separate subgroups of a 1024 channel analyzer. The time resolution in this experiment was about FWHM = 2 nsec. The radioactivity il*“‘Sb was produced at the Bonn cyclotron for the different measurements by one of the two reactions In(cr, sn)“8mSb and 1’8Sn(d, 2n)‘lpmSb. The targets consisted of approximately 10 mgjcm2 thick metal foils. The Sn foils were enriched in mass number 118 to better than 95 :d. We used beam intensities of 2 ,LLAand irradiated for about 5 1~. In the first experiment we used parts of the irradiated ’ i*Sn foils directly as source for our angular correlation measurements. This means that the observed perturbation

QUADRUPOLE

MOMENTS

17

IN “6*“8~t20Sn iK-i20Sb IT_-58d : EC/

EC

!

369 Ih$s.,$ - 320& -269

Fig. I. Decay schemes of “%b,

i -L90

lljiS@C

B”

5 53 nset

20

“*Sb

and rzoSb.

of the angular correfation is probably due to the interaction of the quadrupole moment of the S state with the field gradient arising from the noncubic Sn environment. However, it has been observed ‘> that carrier-free In radioactivity embedded in a Cd lattice clustered together although In is soluble in Cd. This effect was indicated by the fact that a superposition of two different quadrupole interactions was observed, one of which was identical to the one measured for In in an In lattice. Bodenstedt et a/. ‘) showed that the number of radioactive In nuclei experiencing an In environment was greatly reduced when small amounts of carrier were added and when the investigation was performed at temperatures close to the melting point of Cd. The single interaction observed under these conditions was attributed to the field gradient of the Cd host. At Iower tenl~e~dtures again a s~~perposition of interactions was observed, These observations could be explained by assuming that again the Tn impurity began to cluster at the grain boundaries. fn our experiment the situation is similar, since the nuclear reaction also produces carrier-free Sb in the Sn environment. In order to prove that in our case the observed quadrupole rotation corresponds to the interaction of the quadrupolc moment of “*Sn with the fiefd gradient arising from a Sn rather than a Sb surrounding we performed the following additional experiments: The irradiated “‘Sn foils and about 5 % natural Sb carrier were transferred into 5 mm diameter glass tubes which were evacuated. The tubes were mounted at the source position of the angular correlation apparatus and electrically heated to a temperature above the melting point of Sn, where Sn and Sb aIfoy easily (= 500 ‘K). The samples contracted to shiny liquid balls. Then the samples were allowed to cool

K. KRIEN

18

et rtl.

down to the temperatures at which the angular correlation experiments were to be performed, i.e. approximately 500 “K, 400 K” and 293 “K. The temperatures were monitored by thermocouples. If an effect similar to that reported by Bodenstedt et ul. ‘) for the In-Cd alloy existed for the Sb-Sn alloy as well, it should have shown up through changes of the interaction strength. In order to find out whether one should anticipate an increase or a decrease in the magnitude of the interaction and how large an effect was to be expected, we also measured the quadrupole interaction for l18Sn in an Sb lattice. For this purpose the irradiated In foils were dissolved in a few drops of concentrated nitric acid. A few mg SbCl, were added as carrier. Then 2 cm3 7M HCl were added and the Sb extracted by 5 cm3 isopropyl ether. The ether was washed by 3M HCI and then carefully evaporated. The residue was taken up in 4 cm3 4M HCI and the metallic Sb was precipitated by adding a few Zn grains. The Sb was separated by means of a membrane filter. washed several times and molten in a ceramic crucible. Finally the metallic probe was crashed and the resulting powder used as source for the angular correlation experiment. 2.2. RESULTS From ratios

FOR

“‘.%I

the measured

time spectra

at 90- and

I80

we calculated

the asymmetry

N(180”, t)- N(90”. t) R(t) = 2 ~~~~ N( 1800, r>-+ N(90’, r) These ratios are plotted in fig. 2 for Sn in Sn, in fig. 3 for Sn in Sn with 5 % Sb carrier at 500 “K, and in fig. 4 for Sn in Sb. For negligibly small A, coefficients the asymmetry ratios reduce to approximately R(t) z $A 2 C2(t). 2 N(180’,1)-N(90”,t) N(180°,t)+N(900,t) 015

00

60.0

120 0

tlme(nsec)

Fig. 2. Quadrtcpole rotation in the 5- state of ’ ’ %n in a pure Sn environment curve is a least squares fit of the function ;A,G,(r) to the experimental

at 293 data.

K. The solid

QUADRUPOLE

MOMENTS

IN

’ 16*118- lzoSn

19

2 N1180°.tl-N190",1) Ni180:t)+N(90°.tI

. 0.10

0.05

0.00

-0.05

00

120 0

60 0

Fig. 3. Same as fig. 2 for a (957$11-1-5’~Sb)

time (nsecl environment

at 500’ K.

2 N(lEO't)-N(90",t; N(l804t)tN(90",!) 0.15

010

005

0.00 I

00

I

1200

600

tlme(nsec)

Fig. 4. Same as fig. 2 for a pure Sb environment

ct)

I=5 andq=O

0 Fig. 5. Half

period

of theoretical

at 293’ K.

perturbation symmetry

/

I

Tr12

Tr

function parameter

*

G,(t) for a polycrystalline 17 = 0.

sample

and a-

K. KRIEN et al

20

where G2(t) is the perturbation

function.

For a spin Z = 5, a polycrystailine

sample

and an axially symmetric field gradient (q = (I/TY\.- VJY)/Vr_ = 0) half a period of the theoretical perturbation function G,(t) is plotted in fig. 5. From figs. 2-4 it is obvious that due to the short lifetime of the 5- state and the small interaction frequency we = 3@,V,,/41(211)h we observe only a small fraction of the interaction pattern. On the other hand the decrease of the anisotropies with time is large enough to ensure that a fit of the theoretical function to the experimental data (solid lines in figs. 2-4) yields reliable results, if the assumptions are correct that the field gradient is axially symmetric and frequency distributions are negligibly small. Proof for the validity of these assumptions will be given in context with the ‘r6Sn data. The fitted parameters A2 (u~~corrected for solid angles) and w0 are summarized in table I.

TABLE

f ittcd parameters Measurement

’ ’ %n

0.082 (2) 0.089 (2) 0.082 (2) 0.077 (2)

“sSn “%n

in Snf~5~~ Sb (293 K) in Sn;-5”;, Sb (400’ K) J’8S~~in SW 57: Sb (500’ K 1

3. Investigation EXPERIMENTAL

with

A, (uncorrected)

“%n in Sb (293’ K) * ‘% in Sn (293- K)

3.1.

I

for rne~sur~nlel~ts

0.083 (2)

1.26 1.63 1.85 1.60 1.73

(IO) (11) (12) (13) (91

of the quadrupole interaction in “%n

PROCEDURES

The radioactivity “‘“‘Sb was produced at the Bonn cyclotron by bombarding about IO mg/ctn2 thick metallic ” ‘Sn (enriched to > 95 y;,) foils with 2 ,L~Abeams of 18 MeV deuterons for roughly one hour. Due to the short lifetitne (7’) = 1 h) of i”Yb and due to special features of its decay scheme, angular correlation experiments with this isotope are difficult ‘). We therefore restricted the experiment to the investigation of the quadrupole interaction of the 5- state in Sn environnlent using parts of the irradiated Sn foils directly as radioactive sources. In the decay of ‘rhm Sb practically all cascades proceeding via the 5- level of interest have suficiently large anisotropies ‘) and negligibly small 11, coefficients. The 5- Ievel is populated either by the 410 keV or the 545 keV transition. However a good selection by a NaI(TI) detector cannot be achieved because of the large Compton background of higher energy lines and the intense 51 I keV anihilation radiation. We employed therefore 40 cm’ Ge(Li) detectors of about 3 keV overall energyresolution at 6oCo energies for the detection of these lower energy transitions. Since the lifetime of the 5- state in ” 6Sn (T, r = 320 nsec) is rather long, one is

QUADRUPOLE

forced to use weak radioactive

MOMENTS

IN

‘16* ‘I ‘*

21

lzoSn

sources in order to keep the random

coincidence

rate

low. For this reason it is difficult to obtain the necessary statistical accuracy. Therefore we used 7.8 x 7.8 cm* NaI(T1) detectors for the high energy y-rays of the cascades. The energy windows were set to accept all events above 1050 keV. This is possible, since the cascades via the 5- state in “‘Sn involving the 1075 keV and 1294 keV lines with unobserved intermediate transitions have similar anisotropies (in particular the same sign) of the angular correlations. The 974 keV transition has to be excluded, since its angular correlation coefficient is of opposite sign. A more decisive improvement in the statistical accuracy was obtained in the following way. We use the fact that the angular correlations of the cascades involving the 410 keV and the 545 keV y-lines have anisotropies of opposite sign. This allows one to restrict the spin rotation measurements to the angle 0 = 180” by measuring simultaneously the 410 keV-1.29 MeV (1.075 MeV) and the 545 keV-1.29 MeV (1.075 MeV) cascades by two different window settings for the Ge(Li) detector. We obtain the perturbation function G,(t) by defining an asymmetry ratio

R'(t) = 2

N545(1800, t)-N410(1801,

t)

N545(1800, t)+ N4”(1800,

t)

Here N545(1800, t) and N4’o(1800, t) are the time spectra at 180‘ coincident the 545 keV and 410 keV y-transitions respectively. Inserting the expressions N545(180’, r) = Ai45e-i.r(l

with

+A:45G2(t)),

PJ4’o(1 803, t) = AZ” esi’( 1+ Az”G,(t)) into the above equation

one obtains

approximately

Comparing this ratio with the conventional asymmetry ratio R(r)one finds an additional constant term depending on the relative effective intensities of the two cascades. This is of little importance in determining the interaction frequency o. as long as a sufficiently large part of the rotation can be observed. The usual factor +A2 of the perturbation function G*(t) is replaced by twice the intensity weighted difference of the two angular correlation coefficients. Since in this case AZ” is of opposite sign and approximately equal in magnitude to Az4’ the effective anisotropy is increased compared to the conventional asymmetry ratio R(t). In addition, since both time spectra are measured simultaneously one obtains more data within a given time interval. Finally, since the detectors do not have to be moved to different positions, an extension to a multidetector angular correlation apparatus is rather easily done. We used a system with four detectors (two Ge(Li) and two NaI(T1)) and routed the

et 01.

K. KRIEN

22

corresponding four time spectra into subgroups of a 1024 channel analyzer. Employing extrapolated zero strobe discriminators for the Ge(Li) detectors and conventional electronics otherwise, the time resolution was FWHM = 15 nsec. 3.2.

RESULTS

FOR

“%I

The much of the result

experimental ratios R’(t) as defined above are plotted in fig. 6. Due to the longer lifetime of the 5- state in “‘Sn we can observe an appreciable fraction period of the interaction frequency oO. The solid curve in fig. 6 represents the of a fit of the theoretical perturbation function C’,(r) plus a constant to the data for delays larger than z 40 nsec. The data points around t = 0 were excluded from the fit since they are disturbed by prompt coincident background. The parameters derived from the fit are: amplitude 00

constant

=

0.119(15),

=:

2.62(10)

MHz,

= - 0.096(9).

-0.11 et 0

302

6OL

906

(nsec)

Fig. 6. Same its fig. Z for * ‘“Sn.

4. Derivation

of the electric quadrupole moment of the 5- states in “?Sn

and “‘Sn

Before conclusions are drawn from the fitted parameters a discussion of their reliability may be useful. First we note that in all measurements the observed anisotropies are consistent with the theoretical A, coetficients. Furthermore it is obvious from our l’%n investigation that the experimental data are well described by the simple theoretical perturbation function. This indicates that our assumptions (YJ = 0 and no damping) were correct. Since the source preparation for our experiments in ’ * %n in Sn and ’ 18Sn in Sn were identical, these assumptions must also be correct for For the same reason it follows that the quadrupole rotations the “*Sn investigation. in the excited 5 states in “%n and “*Sn are due to the same field gradient. Therefore the ratio of the quadrupole frequencies gives directly the ratio of the quadrupole

moments

QUADRUPOLE

MOMENTS

IN

oo(5-, “*Sn)

Q(5-,

“%)

0,(55,

Q(5-,

li6Sn)

*‘6~‘1s*‘z0Sn

23

: 116Sn)

= 0.62(6).

Since systematic errors should be small the quoted error in this ratio is essentially the statistical uncertainty. In order to derive the absolute quadrupole moments the field gradient must be known. Since Sb and Sn alloy easily it should be expected that the Sb activity produced by the nuclear reaction does occupy regular lattice sites in the Sn matrix. That the carrier-free Sb activity does not cluster in grain boundaries can be concluded from the observation that the samples with a Sb carrier give the same interaction frequency as the carrier-free sample within the limits of error. In case of clustering a change should have been observed since the measurement for “‘Sn in Sb gave a 30 % smaller frequency. Therefore we can use the quadrupole frequency measured for the 23 keV state of r”Sn in a Sn lattice, we = 28.5 (10) together

with the known

“) quadrupole

moment

[ref. I], of this state,

Q1 = 0.06(2) b, for the field gradient

calibration.

We derive the field gradient

Vz:,” = 6.3(21) x 1OL7 V/cm*, and obtain

the quadrupole

moments

of the 5- states in “%n

and “‘Sn

Q(5-3 ‘18Sn) = 0.10(4) b, Q(55, “?Sn) The errors quoted are almost entirely moment of the 23 keV state in “‘Sn. preliminary result

= 0.165(60) b. due to the uncertainty 6, in the quadrupole Our value of Q(5-, ‘i8Sn) agrees with the

Q(5-. ’ '%n) = 0.094(31) b, of a measurement by Gerdau et al. “) who performed a perturbed angular correlation experiment similar to ours but using a different lattice (K(C,H20,,Sb(OH2))&HzO). A calibration of the field gradient was derived from a Mossbauer experiment ‘) in the same lattice with the 23 keV state of 1’ 9Sn. In the introduction we discussed already the problems which are involved in the use of insulating environments for sources decaying by EC because of the production of high charge states of the daughter atom. Wolf et a/. ‘) concluded from the shape of their Mossbauer spectrum that predominantly a single charge state is produced in the EC decay of ‘19Sb in (K(C,H20,Sb(OH2))$H20). They assumed that for the decays of the even isotopes ‘r8Sb and ‘*‘Sb the same charge state is effective,

et 01.

K. KRIEN

24

although in the latter decays long lived intermediate states of Sn have to be passed before the yy cascade of interest starts. The agreement of our result for Q,(5-) for “*Sn with that of Gerdau er al. “) proves that this assumption is correct. Therefore also the measurement of Q,(Y) for “‘Sn by Wolf et al. ‘) performed in the same environment should be reliable. It is interesting to note that Sn in Sn experiences a larger electric field gradient than Sn in Sb, whereas measurements with 99Ru and “‘In [ref. “)I gave in Sn an electric field gradient smaller by a factor of 2-.3 than that observed in Sb. We assume that this may be caused by covalent contributions to the bond in these metals.

5. Discussion

of the electromagnetic

properties of the negative parity states in “‘Sn, “*Sn and 12’Sn

In tables 2 and 3, we summarize the electromagnetic properties now known for the negative parity states in “%Sn, “‘Sn and iZoSn. Since the Sn isotopes have a closed Z = 50 proton shell, only neutron configurations need to be considered. In the neighboring odd mass Sn isotopes, states with spins and parities ++, 3+, and J;‘-- are the ground states or low excited levels. These can be interpreted as the neutron shell model states ss, d,, and h, , respectively. The lower neutron orbits g+ and d, in the major shell with 50 5 N 5 82 are just completely filled for the isotope it4Sn. Within this limited configuration space the 7- states in the even Sn isotopes can only be produced by the coupling of a h, single-particle to a d, single-particle. For the 5- states, a coupling of the h K-to a s3 or a d, single-particle has to be considered. The magnetic moments of the 5- states may perhaps decide which of the two configurations

is dominant

and whether

a large mixing

exists. In ref. ‘) it has been

shown that the experimental g-factors are in agreement with the Schmidt values for the I(h+s+) 55) configuration and in discrepancy with the Schmidt values for I(h +d+) 5-) states. TABLE

g-factors

of negative

Isotope

Level

’ tbSn

5-

-0.0738

(6)

‘t=Sn

5-

-0.065

(5)

‘*eSn

75-

-0.0978 --0.061

(6) (5)

parity

gerp “)

states

2

in “6Sn.

Configuration

Schmidt values

/(h’ +;)5 1(h’jdt)5-. /(h3+s+)5-:

--0.058 -0.385 -0.058 -0.385 -0.219 -0.058 -0.385

i(h3+dt)5-

“) Mean b, Using

averages from refs. 4. 5*11*12). experimental g-factors, see text.

’ t8Sn and tZoSn

j(h3+d+)7l(h5 “s+)5-/ J(hS+dt)5-\

Single-particle estimate with effective g-factors b) -0.0975 -0.254 -0.0968 -0.266 --0.0970 -0.089 -0.266

(20) (30) (20) (30) (IO) 1 (20) (30)

QUADRUPOLE

MOMENTS

IN

“b~“8~‘20Sn

25

TABLE 3 Quadrupole Isotopes

moments Levels

~_~~..~ “?Sn

5-

’ ’ *Sn

and E(E2)

Qrfbl B(E2)

’ r6Sn

5-

” sSn “*Sn

“) “) ‘) “)

h-0.165

5-

57- - s-

5-

Exp. values

____ Q,[bl

7- -* 5-

lZoSn

rates for negative

Exp. quantity

[e*

“‘Sn

transition

/*0.094

1+0.10

(31) b) (4)

&0.021 (8) d, 0.14 ‘)

0.62

Qr(““SnJ Ql(“*Sn)

0.22

Subshell filling factor = (2j+ Ref. s). Recalculated from ref. r2). Ref. *).

in “%I,

(6)

rrsSn

Subshell filling factor “)

and rzoSn s.p. estimate qcrr. = 7 e

1.0

-0.235

~(hJys+)5-

0.6

-0.140

j(h3 y d+)7+l(h3+st)5-

I .o 1.0

75.6

;(h5 y s+)5 j(hs+dt)7-,(h5+s+)55,

0.2 1.0 1.0

-0.046 75.6

(60)

fm’]

QA”%) QrVL6Sn)

states

Configs.

2.2 ‘)

Qrfbl B(E2) [eZ. fm”]

parity

:(h3+s+)5-

/

0.6

0.6

0.33

0.33

ich*+st)5-, (2)

l(h5+s+)5-

N(h3+st)5-,~

I -2/r)/(2j-

1).

However. it is known that the Schmidt values are often only moderate estimates for the magnetic moments and that effective spin and orbital magnetic moments should be used [e.g. ref. ‘“)I. One way of taking these effective moments into account is the use of experimental magnetic moments of the single-particle levels in the neighboring odd Sn isotopes and to calculate the g-factors of the 5- states in even Sn isotopes

by means of the additivity

relation

(2) Using the known g-factors of the ((hY)2 IO’) configurations in “‘Sn and “‘Sn [(ref. ’ “)I and of the s+ ground states in ‘r ‘Sn, l1 ‘Sn and ‘19Sn [ref. “)I as well as the value extrapolated by Nagamiya r3) for the d, orbit we obtain the g-factors given in table 2. The good agreement in the g-factor of the 7- state in “‘Sn indicates the validity of the additivity rule. For the 5- states the calculated g-factors for the I&s,) 5-) configurations are about 50 % larger than the measured values, whereas the ](h\_dj)5Y) configuration gives even larger values (~4 times the measured data). We conclude that the ](h;d+) 5-) admixture must at least be very small. Possible explanations for the remaining discrepancy in terms of violation of the additivity rule or different effective g-factors in the odd and even mass isotopes are not satisfying. The discrepancy can not be removed by configuration mixing within

26

K. KRIEN

et t/l.

the same major shell 14) either. However, we noticed that quite a small admixture (~5 2,) of a coupling of the si state with the spin-orbit partner h4 reproduces the experimental data. The reason for especially large effects of small admixtures of a spin-orbit partner is the fact that in this case the amplitude of the admixed wave function enters linearly via a term of the Ml transition matrix element of the type
= ;;

y

Q<,,,(h ?).

In this equation the numerical factor results from the decomposition ‘(‘) of the coupled states into the uncoupled states. Only one term remains after the decomposition because a s+ state does not have a quadrupole moment. The factor &(12-2n) accounts for the extra neutrons in the h,; orbit. We take IZ = 1, 3 and 5 for “‘Sn, “*Sn and “‘Sn, respectively. It should be noted that the quadrupole moments, but not the B(E2) values, depend on this factor, since the single-particle transitions proceed from the singly occupied d+ orbit to the s+ orbit. In terms of this model the ratios of the quadrupole moments are given by the ratios of the subshell filling factors (table 3). The agreement of this prediction with the experimental ratios confirms the validity of relation (1). To calculate the single-particle quadrupole moments and E2 transition probabilities we used (h Ylr’lh I!) = 32 fm2 and (d+lr21st) = 36 fm2. The first value was estimated by assuming (hYlrZ/hl) = (N++)h/ mo and substituting tie = 41/A+ MeV and N = 5. The second value was interpolated using the above formula from the values for “0 and “‘Pb given in ref. ‘O). With these values and using for the effective charge of the neutron q,,,(n) = + r we obtain the theoretical quadrupole moments and transition probabilities in table 3. The single-particle estimates of the quadrupole moments seem to agree with the experimental values. However this agreement may be somewhat accidental, since we used rather arbitrarily an effective charge qerf(n) = _te. Ishihara et at. I “) deduce from measured B(E2; (vh ,; )’ IO+ + (vh y )’ 8’) values, effective charges of I .84 and 1.92 for the h+ neutron orbits in “‘Sn and I ‘*Sn, respectively. If these effective charges are indeed as large it might indicate that our experimentally derived quadrupole moments for the 5- states are too small in absolute value by about a factor of 2. The most probable reason for such a discrepancy could come from the calibration of the electric field gradient, which relies entirely on the correctness of the derivation of the quadrupole moment of the 23 keV state in ” 9Sn by Ruby ef al. “).

QUADRUPOLE

It might also indicate configurations

MOMENTS

IN

that the 5- states in the even Sn isotopes

as indicated

by g-factor

27

“6*‘rs*1zoSn

measurements.

do not have as pure

Our above

estimates

of the


und Forschung

References 1) J. C. Soares, K. Krien, A. G. Bibiloni. K. Freitag and R. Vianden, Phys. Lett. 45A (1973) 465 2) H. J. Wolf, P. Steiner, E. Gerdnu, W. K. Miller, U. Lewandowski and A. Roggenbuck, 2. Phys. 232 (1970) 256 3) A. de-Shalit and 1. Talmi, Nuclear shell theory (Academic Press, New York, 1963) p. 531 4) E. Bodenstedt, H. J. Kiirner, E. Gerdau. J. Radeloff. K. Auerbach. L. Mayer and A. Roggenbuck. Z. Phys. 168 (1962) 370 and references cited therein 5) Cooperation of the angular correlation groups of Bonn and Hamburg. Nuci. Phys. 89 (1966) 305 6) S. L. Ruby. G. M. Kalvius, G. B. Beard and R. E. Snyder, Phys. Rev. 159 (1967) 239 7) E. Bodenstedt, U. Ortabasi and W. H. Ellis, Phys. Rev. B6 (1972) 2909 8) E. Gerdnu. private communication, 1973 9) W. Haas and D. A. Shirley, J. Chem. Phys. 58 (1973) 3339 IO) M. Ishihnra, R. Broda and B. Herskind. Proc. Conf. on nuclear physics, Munich (1973) p. 256 11) M. Deutsch. A. Buym and L. Grodzins, Perturbed angular correlations. ed. E. Karlsson. E. Matthias and K. Siegbahn (North-Holland. Amsterdam, 1964) p. 186

28

K. KRIEN

et it/.

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