Effective nuclear moments in 207Pb

I1

l.E.3: l.E.4

Nuclear

Physics

86 (1966)

Not to be reproduced

EFFECTIVE H. J. KtjRNER,

395404;

by photoprint

NUCLEAR

K. AUERBACH,

II. Institut

@

North-Holland

MOMENTS

J. BRAUNSFURTH

fiir Experimentalphysik, Received

Publishing

Co., Amsterdam

or microfilm without written permission from the publisher

Universitiit

28 February

IN “‘Pb and

E. GERDAU

Hamburg

1966

angular Abstract: The magnetic moment of the 570 keV state in eo7Pb has been measured by perturbed correlations to be p = +0.6.5 *0.05 n.m. This value corresponds to an effective g-factory,, ell = state. The experimental result is discussed in terms (0.48&0.04)&, tree for the fs neutron-hole of the core polarization mechanism. The half-life of the f+ state was determined to be T+ = 129i3 psec. The effective charge of the ft-p; transition is calculated as 0.93 hO.03. An upper limit of 40 psec was derived for the half-life of the 894 keV pi level.

E

RADIOACTIVITY

207Bi; measured

n-delay,

yy(0,

t), yy(8,

H). Z07Pb level deduced

T+, ,u.

1. Introduction The level scheme of 2zlPb,2s is shown in fig. 1. The nuclear states populated in the decay of 207Bi are generally described I) as shell-model, single neutron-hole and f;. The lowest state which can be interpreted as arising states P+ , fI, P+, b_+ from the excitation of apt neutron to the next shell has an energy of 2.71 MeV(ref. “1).

1771 1447 1064 (8%) (0.16%)@7’/.) Cfl*EZ

E2

550 (316%) !100%) Ml P’i

E2

0

:-

Pb 207

Fig.

1. Decay

scheme 395

of 207Bi.

396

Furthermore The ground quite close to properties of experimental keV-570 keV parameter 6’

H. J. K6RNER

et Cd.

there is no evidence for levels due to proton excitation up to 2.4 MeV. state magnetic moment was measured 3, to +0.589 n.m., which is the Schmidt value +0.64 n.m. Information about the electromagnetic excited states and y-transitions can be obtained from the following data: Angular correlations have been measured 4, ‘) of the 1064 and 1771 keV-570 keV cascades, the latter one yielding the mixing = (7.2-J 1.6). 10m3 of the 1771 keV f*-f+ transition. The f+ and p+

levels have been populated by Coulomb excitation 6). The half-lives of the f+ and i, states are = lo-” set (refs. ’ - ’ ‘)) and 0.80f0.01 set (ref. I)), respectively. These data have been used to calculate effective charges for the p+-pt and p,-f, transitions and hindrance factors for the magnetic transitions I23 “). We present here a measurement of the magnetic moment of the f%.state and a redetermination of its half-life. An upper limit for the half-life of the p+ level is derived. These informations can be compared with model calculations to investigate the influence of configuration mixing and core polarization on the properties of lowlying states in 207Pb. 2. Experiments The source of 207Bi was obtained from the Radiochemical Centre, Amersham. Its purity has been checked over a period of three years by NaI(T1) scintillation counters and recently by a Li-drifted-Ge diode. No other y-lines than those reported in the literature ‘) could be detected. All experiments were performed with a liquid source of BiCl, in 3n HCl. ?. I. HALF-LIFE

MEASUREMENTS

The half-life results given in thus seemed to f,,-p+ transition

of the 570 keV state has been measured several times ‘- ’ I). The table 1 vary from T+ = 100 psec to 134 psec. A re-investigation be necessary for the determination of an effective charge of the and the magnetic moment of the 570 keV level. TABLE

Summary

of half-life

T; (psec) 90-30 1lOill IlOill loot I 134::9

measurements

I

on the 570 keV state in z”7Pb Ref.

Gerholm ‘) Gorodetrky et cl/. &) Lee and Wu “1 Sunyar I”) Rougny et nl. ” 1

The measurements were performed with two Radiotechnique XP 1020 phototubes with 38 mmx25 mm Naton 136 scintillators. The electronic equipment has been described elsewhere 14). The high voltage of the photomultipliers was adjusted to obtain minimum time resolution. The slow channels were set on the Compton edges of

EFFECTIVE

NUCLEAR

the 1064 keV and 570 keV transitions

with

391

MOMENTS

w 20% window

widths.

Prompt

time

spectra taken with a 6oCo source with identical settings showed a resolution of 325 psec (FWHM) with slopes of 41 psec. The half-life of the 570 keV state of “‘Pb can therefore be derived directly from the slope of the time spectrum. The calibration

10

10'

10;

10

180

19c

Fig. 2. Half-life

2co

2lC

determination

220

230

2-C

250

260

of the 570 keV level in %OrPb.

of the time-to-pulse-height converter was obtained by inserting different lengths of RG-58A/U 50 52 cables; their electrical length was carefully checked by radiofrequency standing wave techniques. The normal arrangement was a 180” geometry with the source placed between the detectors and the scintillators shielded by lead cones. From the energies of the various y-transitions one can estimate that scattering cannot influence the measurements with the single-channel settings used. This

398

H. 1. KijRNER et al.

assumption has been checked by independent runs in which the scintillators were completely shielded from each other by lead absorbers (90” geometry). Several runs were performed in which the source strength, geometry and calibration of the timeto-pulse-height converter was varied. The result of one measurement is shown in fig. 2. Least-squares fits were performed with and without consideration of the finite time resolution with identical results. The half-life of the 570 keV state was determined to T+ = 129+3

psec.

The error was derived from the variation of the different runs and the accuracy of the time calibration. This experimental value is in agreement with a recent result of Rougny et al. 11) but disagrees with those quoted by Gorodetzky et al. 8), Lee and Wu 9, and Sunyar lo). The reason for these discrepancies is not understood. Unfortunately the B(E2) values from Coulomb excitation 6, are not accurate enough to yield independent information about this half-life. Measurement of the half-life of the 894 keV pa level was attempted with the same equipment. Despite of the low intensity of the 1447 keV-894 keV cascade, this measurement is possible without perturbation by interfering transitions because the sum of the two y-lines corresponds to the energy of the highest level populated in the decay of “‘Bi. Only an upper limit of 40 psec could however be derived for this halflife. This value corresponds to the slope of a prompt curve obtained with a 6oCo source and to the slope of the 1447 keV-894 keV resolution curve. 2.2. DELAYED

ANGULAR

CORRELATION

OF THE 1064 keV-570 keV CASCADE

Perturbations by internal fields may disturb the Larmor precession and half-life measurements. The attenuation parameter & (ref. “)) of the 1064 keV-570 keV cascade can be derived from a delayed angular correlation experiment. The small A, term will be neglected in the following discussion. The time-dependent, angular correlation in the liquid source is given by W(O, t) = Ao(l)[l

+A,(W,(cos

@I,

with A,(t)

= A,(O)exp(-

it),

AZ(t) = A,(O)exp( - iz t). The experiment was performed with the same equipment as described in subsect. 2.1. The slow channels were opened to z 50% and three detectors were used simultaneously. Time spectra were recorded at 13= 90” and 180”. Fig. 3 shows the quantities A,(t) and AZ(t) as derived from one detector combination. A least-squares fit to the data yields 1, = 5.40_+0.10 d, = 0.24f

nsec-‘,

1.73. IO8 set-‘.

EFFECTIVE

Thus

NUCLEAR

399

MOMENTS

T+ = 128 f 3 psec and Gz = A/(,? + A,) = l.00f0.03.

Within

the limits

of

error no perturbation by internal fields is present; this result seems reasonable for such small lifetimes and spherical nuclei. After-effects due to the capture decay can be excluded because of the 0.8 set half-life of the 1634 keV state.

T1,2 .(1x23

1 p5ec

103

102

_

channel

number

I

-_

40

30 Fig. Lower

part:

A,(t)

2.3. MAGNETIC

3. Delayed

angular Upper = A,(O)exp(-&t).

MOMENT

OF THE

50

60

70

correlation of the 1064 keV-570 keV cascade. part: A,(t) = A,(O) exp(- J.r). The solid line corresponds to 1, = (0.24+1.73)

. 10” set-‘.

570 keV STATE

The Larmor precession measurements were performed in a three detector equipment described elsewhere 16). The 1064 keV-570 keV correlation was determined in an external magnetic field of + 55 200 G. The unperturbed correlation was measured in the same geometry. The experimental data are shown in fig. 4 in the form w(e, B = 0) and R(0, B) = 2 [W(0, + B)-W(B, -B)]/[W(B,+B)+W(B, -B)]. The result of a least-squares calculation is for B = 0 A, = +0.222+0.001,

A‘$ = -0.020+0.002,

400

andforB

H. J.

et at.

K6RNER

= +55200G A2 = +0.222+0.001,

A, = -0.021+0.002, * 10v3 rad.

oLz = (12.9kO.9)

The angular correlation coefficients have been corrected for the solid angle of the detectors 17) but not yet for a 5 % admixture of the 1771 keV-570 keV cascade. With the coefficients of ref. “) this correction yields A, = +0.232+0.007,

1

A, = -0.022+0.003.

R(O,B)

-,6'1.. 1 -I A'!..

\ 105

120

135

150

165

4 180 8

Fig. 4. Magnetic moment determination of the 570 keV state. Upper part: 1064 keV-570 keV angular correlation without magnetic field. Lower part: Relative variation R(0, B) of coincidence counting rate due to reversal of a magnetic field of 55 200 G. The solid line corresponds to a displacement qt = (12.910.9). IO-” rad.

EFFECTIVE

Assuming

NUCLEAR

401

MOMENTS

T+ = 129f 3 psec, we get g = +0.26+0.02,

p

=

+0.65+0.05

n.m.,

for the 570 keV f+ state in “‘Pb. A preliminary value for this g-factor reported at the Paris conference 18) should be replaced by this new number. During the preparation of this work an independent measurement was published by Gustafsson et al. 19) who obtained g = +0.34f0.05 assuming Tt = 110 + 10 psec. Within the limits of error the results agree, if the same half-life is assumed. 3. Discussion With these data we can calculate the effective charge of the fs-pt transition and discuss the effective g-factors which can be derived from the transition probabilities and the measured static magnetic moments. All radial matrix elements have been taken from the work of Blomqvist and Wahlborn 20). 3.1. EFFECTIVE CHARGE

OF THE fs-p+ TRANSITION

Assuming T+ = 129+3 psec, and LI = LX,+ 1.3 aL, we calculate

EY = 570 keV, aK = 0.019, aK/czL = 3.3 (ref. ‘)) z, = 191+ 5 psec and B(E2) (ref. 21)) 75k6 c5 P+) = ~ 4nEY5 r,, = (7.1 t0.3)

The single-particle

estimate

is given by 22)

4JE2, fs-pt) = i With (ft]r2]pt)

= -32.3

- 10e3[e2b2].

e~fr(f+lr21p+)2(3 4 2 Olf G2.

fm2, we get

B,,(E2,

f,-pt)

= 8.3 * 10m3 e$r[e2b2].

The effective charge of the ft--p+ transition eeff = [B,,,(E2)/B,,(E2)]3

is = 0.93 f0.03.

The Coulomb excitation data (j) yield approximately equal effective charges for the p+-f, and p;-p* transitions. There is, however, no possibility to calculate the p+ state lifetime and the corresponding Ml transition probability because the E2/M 1 mixing parameter of the 894 keV transition is not known. Using the measured B(E2, pt-pt) value, we calculate T*(894 keV) < lo-” sec. 3.2. DATA

ABOUT

The ground

MAGNETIC

state magnetic

PROPERTIES

moment

p(p+) = +0.589

n.m. fits well to the Schmidt

402

H. J. KtiRNER

value as is generally

the case with pt states. The effective g-factor 9s, eff

The

M4

transition

0.75kO.04 set-’ is given by ‘“)

=

o

probability

(assuming

19UL+lW+l) [(2L+ l)! !I2

With (iflr31ft)

= -227.3

=

of

0.93 g,,

free

is

*

the iY-fs

transition

is T,,,(M4,

c1k = 0.114, CL~/CL~ = 3.8). The single-particle

L-1lji)*(ji$LOl (&z)2L+1Ciflr fm3 and pL, = -1.91, T,,(M4,

Comparison

et d.

i,-f,)

=

estimate

jr*)' x p’, . lO*l set-‘.

we get

i, -+ 6) = 4.95 set-‘.

with the measured gs, ,,,(M4)

value T,,,(M4,

i4-f3)

yields

= (0.389 + 0.040)9,, free.

Calculations by Kisslinger and Sorensen 24), Gupta and Lawson ‘“) and de Miranda and Preston 26) h ave shown that the observed reduced M4 transition probability cannot be explained by configuration mixing caused by short-range residual interactions. In this case one has to assume contributions from other effects, for example core polarization. If we assume that the effective charge of the f$-f+ transition is identical with that of the ft-p+ transition we calculate, using (fJr*lf+) = +36.0 fm*, Tcalc(E2, f;- -+ f+) = 2.68 - 10”

set-i.

With 6* = (7.2+ 1.6) - 10d3 for the 1771 keV transition, T&Ml, Inserting as

(fglrolfs)

f; + 4)

1013 set-‘.

= 1.00 and ,u” = - 1.91, the single-particle T,,(Ml,

Comparison

= (3.72kO.93).

with the quantity

we get

estimate

is calculated

f% -+ f+) = 1.45. 1014 set-‘. T,,,,(M I, f+-f+) yields

s,,,,,(Ml)

= (0.5lfO.l1)9,,,,,,.

Our result for the f% state magnetic moment (+0.65 with the Schmidt value (cc,, = + 1.36 n.m.) to yield g,, ,,,(f:)

+0.05

n.m.) can be compared

= (0.48 fO.O4)g,, free.

This value cannot be explained by configuration mixing caused by short-range residual interactions. This conclusion can be drawn from the formalism developed by Freed and Kisslinger 27) with a choice of parameters according to the work of

EFFECTIVE

NUCLEAR

403

MOMENTS

Kisslinger and Sorensen 24), Furthermore we can compare our experimental result with calculations performed with the semi-phenomenological nuclear model of Amiet 28). The calculated 29) magnetic moment of the ft state in 207Pb is + 1.19 nm., which is too large compared to the experimental one. It has been suggested 30) that the reduction of effective g-factors in odd-mass nuclei should be explained by a long-range residual interaction between the outside particle (hole) and the particles of the core, the net effect of which is to align a number of core moments antiparallel to the moment of the outside particle. An interaction of this kind is provided by a spin-spin force which gives rise to a strong interaction in the singlet ‘S state between two alike nucleons and to a predominance of the triplet 3S interaction in the neutron-proton system. The magnetic moment operator with this choice of force is 31) I( = Psp+Ilpol? with &I01 = &Ls + sp( -

y24,

where the parameters 6g, and gp are constants for a given core and the operator { - Y2b} the tensor operator of rank 1 obtained by coupling Y2 to a. The experimental can be used to check this picture. information about effective g-factors in “‘Pb Combining the data for the pt- and f+ states we calculate 6g, = +3.14+0.25,

gp = +1.78*0.15.

With these parameters we calculate effective g-factors for the i, which can be compared with those derived for the M4 and Ml transitions these states. The result is: ss, -.&)

= (0.327*0.06%,

ss, err(M4) = (0.389 +0.040)9,, &,

s,,,ffW)

e,,

=

(0.302 + 0.06%,

=

(0.51+0.11)~~,,,,,,.

and f; states depopulating

free, free> free

9

Within the rather large errors, equal reduction is obtained for the static moments and the transition probabilities. It should be noted that the parameters 6g, and gp as calculated from the ground state moments of “‘Pb and 209Bi differ appreciably from those derived above. This cannot be explained with the moment operator quoted above because the p+ hole of the in 207Pb and the h, particle in “‘Bi should produce similar polarizations “‘Pb core. This fact has recently been investigated by Blomqvist et al. 32), who have performed more detailed calculations of the core polarization. They calculate ,u(f;) = +0.91 n.m. for 207Pb as compared to peXp = 0.65f0.05 n.m. The agreement of their calculated value with the experiment of Gustafsson et al. 19) is destroyed by the larger half-life adopted by us for the 570 keV level.

404 3.3. ANGULAR

H. J. CORRELATION

OF THE

K6RNER

et

cd.

1064 keV-570

keV CASCADE

The coefficients of a y(M4)+(E2)3 cascade are A, = +0.221 and A, = -0.018. Our experimental values are A, = +0.232+0.007 and A, = -0.022kO.003. If we take this small deviation serious we have to admit a small E5 admixture in the 1064 keV radiation.

The mixing parameter

would be 6’ GZ 10w3.

We thank Professor W. Jentschke for his interest in this work. We are also indebted to Dr. A. W. Sunyar and Dr. S. Wahlborn for communicating their unpublished results and to Dr. 0. Nathan for helpful comments on the manuscript. This investigation has been supported by the Bundesministerium fur Wissenschaftliche Forschung. References 1) Nuclear Data Sheets (Nuclear Research Council, Washington) 2) M. T. McEllistrem, H. J. Martin, D. W. Miller and M. B. Sampson, Phys. Rev. 111 (1958) 1636 3) I. Lindgren, in Perturbed angular correlation, ed. by E. Karlsson, E. Matthias and K. Siegbahn. (North-Holland Publ. Co., Amsterdam, 1964) 4) F. K. McGowan and E. C. Campbell, Phys. Rev. 92 (1953) 523 5) N. H. Lazar and E. D. Klema, Phys. Rev. 98 (1955) 710 6) P. H. Stelson and F. K. McGowan, Phys. Rev. 99 (1955) 122; 0. Nathan, Nuclear Physics 30 (1962) 332 7) T. R. Gerholm, Ark. Fys. 10 (1956) 523 8) S. Gorodetzky, R. Manquenouille, R. Richert and A. Knipper, J. Phys. Rad. 22 (1961) 699 9) Y. K. Lee and C. S. Wu, Phys. Rev. 132 (1963) 1200 10) A. W. Sunyar, private communication 11) R. Rougny, J. .I. Samueli and A. Sarazin, J. Phys. Rad. 25 (1964) 989 12) W. W. True and K. W. Ford, Phys. Rev. 109 (1958) 1675 13) G. Chilosi, R. A. Ricci, J. Touchard and A. H. Wapstra, Nuclear Physics 53 (1964) 235 14) J. Braunsfurth and H. J. Korner, Nucl. Instr. 34 (1965) 202 15) A. Abragam and R. V. Pound, Phys. Rev. 92 (1953) 943 16) E. Bodenstedt et al., Z. Phys. 163 (1961) 1 17) M. Y. L. Yates, in Perturbed angular correlations, ed. by E. Karlsson, E. Matthias and K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1964) 18) H. J. Korner et al., Contribution to the Int. Conf. of Nuclear Physics, Paris (1964) 19) S. Gustafsson, K. Johansson, E. Karlsson and A. G. Svensson, Phys. Lett. 10 (1964) 191 20) J. Blomqvist and S. Wahlborn, Ark. Fys. 16 (1960) 545 21) K. Alder et al., Revs. Mod. Phys. 28 (1956) 432 22) 0. Nathan and S. G. Nilsson, in Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1965) 23) S. Moszkowski, in Beta and gamma-ray spectroscopy, ed. by K. Siegbahn, (North-Holland Publ. Co., Amsterdam, 1955) 24) L. S. Kisslinger and R. A. Sorensen, Revs. Mod. Phys. 35 (1963) 853 25) K. K. Gupta and R. D. Lawson, Phys. Rev. 114 (1959) 326 26) A. F. de Miranda and M. A. Preston, Nuclear Physics 44 (1963) 529 27) N. Freed and L. S. Kisslinger, Nuclear Physics 25 (1961) 611 28) J. P. Amiet, Suppl. Nuovo Cim. 18 (1960) 89 29) J. Miiller, Diplomarbeit, Bonn (1963) Nuclear spectroscopy (Academic 30) B. R. Mottelson, Int. School of Physics “Enrico Fermi”; Press, New York, 1962) 31) E. Bodenstedt and J. D. Rogers, in Perturbed angular correlations, ed. by E. Karlsson, E. Matthias and K. Siegbahn (North-Holland Publ. Co., Amsterdam, 1964) 32) J. Blomqvist, N. Freed and H. 0. Zetterstrom, Phys. Lett. 18 (1965) 47