J. Phys. G : Nucl. Phys. 9 (1983) 1125-1 138. Printed in Great Britain

The nuclear magnetic moment of "Ir and the directional distribution of gamma rays in "Os

A L Allsop?, S Hornung?, D W Murray$§ and N J Stone? t University of Oxford, Ciarendon Laboratory, Parks Road, Oxford. U K $ California Institute of Technology, Pasadena, Ca 91 125, USA

Received 3 1 January 1983

Abstract. Angular distributions of gamma transitions between levels in I9OOs fed in the decay of I9'Ir aligned in a rhenium single crystal have been measured at temperatures down to 2 mK. Multipole mixing ratios in both gamma and electron-capture transitions are deduced and compared with various nuclear models. The angular distribution coefficients are applied to interpret very small anisotropies observed when I9'Ir is polarised in an iron host matrix, cooled to 2.5 mK. The deduced magnetic dipole moment of the 4 + ground state of I9'Ir is Ip(I9'Ir; G S ) ~ = 0.04( l)pN. Possible single-particle descriptions compatible with this result are suggested.

NUCLEAR MOMENTS: I9'Ir (from Re(a, n)): measured I,(@ from oriented nuclei in single crystal Re and polycrystalline Fe: deduced I9OOs S(E2/M1), Jp in electron capture, lpl(1901r ground state).

1. Introduction

Low-temperature nuclear orientation, where orientation is deduced from the spatial anisotropy of emitted radiations, has proved a useful technique for measuring nuclear magnetic dipole and electric quadrupole moments of radioactive nuclei and for determining nuclear level spins and gamma-ray multipole mixing ratios in the daughter nuclei. In the measurement of mixing ratios the method has special value, for it is sensitive to the relative phase of the contributing multipolarities as well as to small admixture amplitudes. In addition, nuclear orientation can provide details of the angular momentum characteristics of nuclear beta decay.

In this work we report on the nuclear properties of 1 9 0 0 s observed after the electron- capture decay of "'Ir aligned in a single crystal of rhenium, and also on the determination of the ground-state nuclear magnetic moment of "'Ir obtained from a study of 19'Ir polarised in a polycrystalline iron host.

The most widely used method of orienting nuclei at low temperatures is by means of the magnetic hyperfine interaction, - p a B , between the nuclear magnetic moment ( p ) and the magnetic field (B) experienced by impurity nuclei when dissolved in a ferromagnetic metal host. Appreciable orientation is achieved for magnetic interactions when the absolute temperature is reduced to T,<pB/Ik. (Here I is the nuclear spin and k is Boltzmann's constant.) However, in spite of the very large hyperfine field of 138 T at iridium nuclei in iron the I9'IrFe system showed minimal orientation even at the temperature of 2.5 mK

5 Present address: GEC Research Laboratories, Hirst Research Centre, Wembley, UK.

0 1983 The Institute of Physics 1125

1126 A L Allsop et a1

reached in the present experiment. This rendered it impracticable to determine the mixing ratios of individual transitions in I9'Os using a ferromagnetic host for the I9'Ir nuclei. However, the electric hyperfine interaction between the quadrupole moment of Ir and the electric field gradient at iridium nuclei in a crystalline rhenium lattice is comparatively large (Murray et al 1980) with considerable orientation being observed below 5 mK. Using this system a detailed study of the decay properties of I9'Ir to 19'Os is possible. The measured decay properties have been combined with the results of our experiment on "'IrFe to establish an upper limit for the magnetic moment of 19'Ir. The mixing ratios for transitions in 19'Os derived from this work and from gamma-gamma directional correlation experiments of other authors are compared with predictions of several nuclear models. We discuss also the implications of the small "'Ir magnetic dipole moment.

2. The '%Re experiment

2.1. Source preparation and cryogenics

A single hexagonal close-packed crystal of naturally abundant rhenium was irradiated with 40 MeV alpha particles at a current of 1 p A for 1200 s, producing 186-1901r activities. The short-lived 186-1881r activities were allowed to decay for several days before the experiment commenced, leaving predominantly I9'Ir (T1,2 = 12.1 d) and la91r (TI,, = 13.3 d) activities. The final source strength used was small in order to minimise radioactive heating in the sample.

The Re crystal and a 6oCoCo single-crystal thermometer were indium-soldered to the cold finger of a small PrNi, hyperfine-enhanced nuclear demagnetisation stage. The c axes of both crystals were collinear, and define the nuclear quantisation axis, 8=Oo. The stage was pre-cooled to 16 mK in an applied magnetic field of 2 T using a 3He-4He dilution refrigerator linked thermally to the stage by a tin wire heat switch. After turning the heat switch superconducting and demagnetising the PrNi, , the sample reached a temperature of about 2 mK. Throughout the experiments a small magnetic field was applied to the sample area to maintain the Re and the In solder in the normal, thermally conducting, state.

2.2. Gamma-ray detection

While the PrNi, stage warmed up from 2 to 20 mK, which typically took some seven hours, gamma rays were counted with a Ge(Li) detector placed at 0" with respect to the crystal c axes. Every 1000s an accumulated 4096-channel spectrum was written onto magnetic tape for analysis by computer. The demagnetisation cycle was repeated several times and after each cycle spectra were accumulated with the sample warmed to several hundred milliKelvin for normalisation purposes.

2.3. Data analysis

The gamma-ray intensities were derived by summing the channel counts in a peak and subtracting a linear background. After correction for the decaying source strength, the intensities were normalised to the isotropic 'warm' counts and analysed according to the relationship

w(e, T ) = I + B , ( H ~ , T ) U , A ~ e2 p2 (cos e ) + B, ( H ~ , T)U,A, Q, p4 (cos e). (1)

The nuclear magnetic moment of I9'Ir 1127

The coefficients B, describe the orientation of the 19'Ir nuclei, and depend on the nuclear electric hyperfine Hamiltonian HQ and the temperature T. The coefficients U, describe the angular momentum coupling through unobserved radiations between the oriented state and the state from which the observed gamma ray emanated, and the coefficients A , describe properties of the observed gamma ray itself. These coefficients are given in terms of angular momentum coupling factors and radiation multipole mixing ratios. The Pk are kth- order Legendre polynomials and account for the source-detector geometry in the experiment and the coefficients Q, correct for the finite solid angle subtended by the detector. These solid angle attenuation factors were computed for the Ge(Li) detector using the method described by Krane (1973).

3. Results

3.1. The coefjcients B,

The hyperfine Hamiltonian describing an axially symmetric quadrupole interaction is

where m is the projection of the nuclear spin onto the quantisation axis. At relatively high temperatures, where k T > H Q , the coefficient B4 is small and the m2 dependence of HQ gives B,, and hence the gamma-ray anisotropy, W(0, T ) - 1, a linear dependence on the reciprocal temperature. The quadrupole frequency, vQ, was derived from the anisotropies exhibited by the 5 18 and 295 keV gamma rays, both of which have well determined UkA, coefficients. The frequency, vQ = + 245.1 f 6.4 MHz, was interpreted elsewhere (Murray et a1 1980) and will not be discussed further here.

3.2. Electron-capture decays from 1901r arid y raj's in 1900s

The studies of Yates et a1 (1974) of the decays of I9OmRe and I9'Ir to 1 9 0 0 s and of the neutron-capture reaction IE9Os(d, P)'~'OS have established a comprehensive decay scheme for the lower-lying levels of 1900s, confirming much of the work of earlier authors (Scharff- Goldhaber et a1 1958, Yamazaki 1963, Harmatz and Handley 1964, Yamazaki et al 1969, Krane and Steffen 1971). Yates et a1 combined their y-ray intensities with the internal conversion electron intensity results of Harmatz and Handley to derive a, values and dominant multipolarities for many transitions. The most complete work using gamma-gamma directional correlations to measure multipole mixing ratios in I9O Os is that of Helppi et a1 (1974). An appropriately simplified decay scheme for I9'Ir is shown in figure 1. Our analysis was limited by the source strength to transitions carrying more than about 1.5% of the total gamma-ray intensity. Table 1 shows the measured U, A , values of 1 9 0 0 s y rays emitted after the decay of oriented I9'Ir, together with the observed multipolarities. Below we describe the decay properties in descending order of the energy of the initial level.

3.2.1. The 1682 keV level ( P K =5-3) . The conservation of angular momentum limits the total leptonic angular momentum, JBh, in beta or electron-capture decay to lZi -Ifl < Jp <Ii + I , , and so for the decay to this level Jp could be 1, 2, . . . , 9. In the so called 'normal approximation' for forbidden beta decays (cf Konopinski 1966), the matrix elements for Jp = O and Jp = 1 are of the same magnitude, whereas those for higher Jp

1128 A L Allsop et a1

756 T2

558 2+2 SL8 k*O

187 2'0

0 oto

Figure 1. Simplified scheme for the decay of I9'Ir to I9OOs.

values are successively suppressed by a large factor. The log f t of 6.9 for the decay is typical for a non-unique first-forbidden transition, and so we adopt pure J8 = 1. The disorientation coefficients for the y rays from the level are then U, =0.938(1) and U4 =0.794(4), where the small uncertainty is introduced by a very minor feed with unknown decay parameters. The 5 18 and 294 keV y rays are well known from conversion electron measurements to have E l and E2 multipolarity, respectively, and have, therefore, determined A , coefficients. As outlined above, these transitions were used to determine the hyperfine interaction, and become the reference transitions with which other y rays in I9O Os are compared. The 726 keV y ray has been measured by conversion electron techniques to have E l multipolarity. Our results are consistent with this assignment between levels of spin1-5 a n d I = 4 .

3.2.2. The 1.584 keV level (InK=#-3). The electron-capture feed to the level could have Jp -0 or Jp = 1 . Both the 1036 and 380 keV y rays observed from the level have been previously determined to have E l multipolarity, and the anisotropy of each favours a pure .Ip = 1 assignment. Within the experimental errors the modulus of the amplitude mixing

The nuclear magnetic moment of "'Ir 1129

Table 1. Measured U2A2 values and multipolarities for gamma rays in I9OOs emitted following the decay of oriented '%Re.

Initial level (keV)

Initial Final level level I "K I"K

Relative intensity'

1681.6 1681.6 1681.6 1583.8 1583.8 1386.9 1386.9 1203.8 1203.8 1163.1 1163.1 955.3 955.3 955.3 756.0 557.9 557.9 547.8 186.7

726.2 518.6 294.8

1036.1 380.0 431.6 223.6 656.0 447.8 605.1 407.2 407.2 768.6 397.4 569.3 558.0 371.2 361.1 186.7

5 -3 4'2 5 -3 4 '4 5 -3 3-3 4 - 3 4'0 4-3 5'2 3-3 4'2 3 -3 4'4 5'2 4'0 5'2 3'2 4'4 2'2 4'4 3'2 4'2 4'0 4'2 2 '0 4'2 2'2 3'2 2'0 2'2 0'0 2'2 2'0 4'0 2 '0 2'0 0'0

16.6

28.5 10.6 8.9

12.0 16.4 5.1

11.2

149

E } 20

9.7 28.7

125 132 100

230 57.1

Measured U2A 2

0.27(5) 0.2761(3)a

- 0.3 945( 4)a - 0.3 2( 7)

0.05(9) 0.1 O(8) 0.16(6) 0.72(23)

-0.48(7) -0.418(19)

Calculated Multipolarity L'2A 2

~~~ ~

0.27611) El E l 0.276 l(3) E2 - 0.3945(4) E l -0.360(17) E l 0. I3 l(6) El 0.1 1 O(5) E l 0.1 lO(5) MI + E 2 0.721(27) E2(+M3?) -0.339(12) E2 - 0.407(8)

0.255(39)b { 1;; } 0.238(37)

-0.386(32) E2 -0.357( 13) -0.344(20) E2 - 0.357( 13)

0.06 l(2) 0.06(3) M I + E 2 -0.387(20) E2 - 0.386( 33)

0.141(35) MI + E2 0.14 I ( 12) -0.33(3) E2 - 0.266(40) -0.075(6) E2 - 0.068(8)

~~

a Reference decays with well determined properties. Unresolved doublet. Yates et al(1974).

ratio is IA(Jp = l /Jp =O)l > 1. We note that the small positive anisotropy shown by the 380 keV y ray is consistent with the placement of Yates et al, but inconsistent with the earlier scheme of Yamazaki et al.

3.2.3. The 1387 keV level ( InK=3-3) . The electron-capture feed is assumed to be pure Jp = 1. Both the 224 and 432 keV y rays showed anisotropy consistent with their being E l transitions.

3.2.4. The 1204 keV level ( InK=5+2). The 656 keV y ray to the I" =4 ' level at 548 keV may have mixed E2/M1 multipolarity: we deduce d(656 keV)=-l.7?1::. The 447 keV y ray exhibited anisotropy somewhat larger than that expected for an E2 transition. The observed anisotropy could in principle be explained by a small M3 amplitude with 6(M3/E2)= +O.lSL:::;. Such a solution is not excluded by the aK measurements of Yates et al, but there seems no reasonable mechanism to account for the relative hindrance of the E2 amplitude in an intraband transition.

3.2.5. The 1163 keV level ( P K = 4+ 4). The well determined 5 18 keV y ray contributes about 54% of the feed to this level, with the electron-capture feed supplying a further 37%. The electron-capture decay is of the allowed type, and it is sufficient to consider only Jp = O and Jp = 1 contributions. The experimental values of the UkAk coefficients are compared with those predicted for Jp = O and 1 in table 2. The results favour a Jp = 0 assignment. Within the errors, the mixing is IA(Jp = l/Jp =O)l < 0.66. The 407 keV y ray to the 756 keV level was observed together with the 407 keV transition from the 955 to the 548 keV level. It was possible to define regions for which the mixing ratios of both

1130 A L Allsop et a1

Table 2. The experimental value of U z A 2 for the 605 keV 7 ray compared with predicted values for Jp = 0 and Jp = 1 electron capture to the 1 163 keV level in ' 9 0 0 s .

U 2 A 2 (predicted)

U 2 A 2 (experiment) Jp = O Jp= 1

- 0.4 18(5) -0.407(8) -0.382(7)

transitions gave acceptable fits t o the experimental data. No limit could be placed on the mixing ratio of the y ray from the 1163 keV level, but that from the 955 keV level was found to have 6(407 keV; 955-548 keV)=-6.5";::, where a predominantly M 1 solution was rejected on the basis of conversion electron measurements.

3.2.6. The 955 keV level (I"K = 4 + 2). The level is fed partially by direct electron capture from I9'Ir. The 397 and 768 keV y rays from the level have both been measured by conversion electron techniques to have E2 multipolarity. The spin sequence of each is from l= 4 to I = 2, and so both y rays will have the same UkAk coefficients. The averaged value is U 2 A 2 =-0.356(17), which favours a dominant J8 = 1 assignment to the electron- capture feed. At the limits of error we find /A(Jp = l / J p =O)l > 1.6.

3.2.7. The 756 keV level (InK=3+2). The anisotropy of the 569 keV y ray gives 6(569 keV) = -8. I 'i:: or +O.l3L;::. Conversion electron measurements indicate a predominant E2 multipolarity, and so we adopt the former solution.

1 - 0 4 1

Figure 2. Anisotropies observed as a function of reciprocal temperature for the 5 18. 371, 569. 187, 361 and 558 keV y rays.

The nuclear magnetic moment of 19'Ir 1131

3.2.8. The 558 keV level ( P K = 2 + 2). The 37 1 keV y ray has been measured previously as predominantly E2. Our results give 6(37 1 keV) = -1 3:; or -0.53 Tt:!;. Again, the former solution is adopted. The 558 keV y ray to the ground state must have E2 multipolarity. The experimental value of U2A2 =-0.387(20) is in excellent agreement with that of -0.385(30) computed from the decay scheme.

3.2.9. The 548 keV level (ZnK=4+ U). The 361 keV y ray feeds the first excited state ( I n = 2 + ), The anisotropy measured agrees well with that expected for an E2 transition.

3.2.10. The 187 keV level (I"K=2+ U). The decay to the ground state from the first excited state must have E2 multipolarity. The value of U2A2 =-0.075(6) measured for the 187 keV y ray is in good agreement with the value of -0.066(3) calculated from the decay properties derived in this experiment and given by other authors.

4. Analysis

4.1. The ' 9 0 0 s E2 andM1 amptitiides

The energy levels and E2 and M1 amplitudes in transitional nuclei are well known to deviate systematically from the predictions of the strong-coupling model in the adiabatic limit. Indeed, M 1 amplitudes are forbidden between pure collective states. Several models have been proposed to account for these phenomena by coupling together the intrinsic and rotational motions of the nucleus. This coupling results in a mixing of the low-lying rotational bands.

Two possible mixing modes between the ground-state (K = 0) and gamma-vibrational ( K = 2) bands are direct A K = 2 mixing and indirect mixing via a K = 1 band. To analyse these possibilities in 1900s we use a method due to Mikhailov (1966). The Hamiltonian is assumed to be the product of a power series of angular momentum operators with an operator that acts only on the intrinsic variables. By describing the wavefunction as a superposition of states with different K (the projection of the total angular momentum onto the intrinsic axis) it is possible to derive the spin dependence of the admixture amplitudes without specifying the physical form of the interband interaction.

We first examine the E2 intensities of transitions from the gamma-vibrational band (7) to the ground-state band (g). Including the first-order I-dependent terms in the intrinsic transition moment, the reduced E2 transition probability is

B(E2; Ii,-+If,)=2M~(Ii22-2/ZfO)2[l - a 2 f ( I i , I f ) I2

Table 3. The multipole mixing ratios in 1 9 0 0 s measured in this work.

Gamma-ray energy (keV) 6(E2/M 1)

(3)

t 1163 + 756 keV transition.

1132 A L Allsop et a1

wheref(Zi, If)=I,(Zi + l)-If(If + l), and the mixing parameter is

a2 = - M { / M 2 . (4)

In table 4 we show ratios of the B(E2) values for interband transitions together with the Alaga prediction for strong coupling. Also shown are the deduced values of the mixing parameter. Its mean value is u2 = +0.087(2). The constancy of a, for each ratio implies that the E2 intensities in ' 9 0 0 s are well accounted for by expression (3). However, this analysis makes no assumption about the type of mixing. The intrinsic matrix element Mi does arise from AK=2 mixing, but first-order Coriolis effects, which mix K = 1 components into the wavefunctions of the ground-state and gamma-vibrational bands, give a correction to equation (3) with the same spin dependence as the AK = 2 correction. This effectively renormalises a 2 . There is considerable uncertainty as to the significance of the AK = 1 contributions in general, although Gunther and Parsignault (1967) have estimated that they should be small.

To examine further the mixing modes we now analyse the MI intensities. For both types of mixing the M 1 matrix element between the gamma-vibrational and ground-state bands may be written as (Bohr and Mottelson 1975)

(Kf = 0, Zfllc g ( M 1)IK = 291, )

=(-1)zf-zq2(21f + l)Zf(Zf + l)]~'2(zflll~z,2)(Ml +M;f(J,zf)). (5 1 The intrinsic matrix elements M , and M ; do, however, depend on the nature of the mixing. Direct mixing gives M ; / M , = -4, whereas AK= 1 mixing gives Mf = O . It is assumed in this that the rotational g factors of both bands are equal.

From equation (3), the E2 matrix element is

(K,=O,Iflld(E2)(JKi =2,Zi)= [2(2Ii + 1)]"21M,(1,22-2(1~0)(1 -azf(J,If>).

Writing the ratio of matrix elements as A(E2IMl) we find

Table 4. Ratios of experimental reduced E2 transition probabilities compared with the Alaga strong-coupling prediction. The mixing parameter u2 is deduced from equation (3).

~~

Energy Measured Alaga Mixing Transition (keV) B(E2) ratio prediction parameter, a 2

558.0 2, + 0, 0.173(8) 0.7 0.084(2) 2, -+ 2, 371.2

569.3 3Y-12, 0.154(2 1) 2.5 3Y-14, 207.9

0.094( 3)

768.6 0.076( 17) 0.022( 10) 0.3395 4, + 2,

4, + 4, 407.2

The nuclear magnetic moment of '"Zr 1133

A(EZ/Ml) is given in terms of the multipole mixing ratio by

A = 6(E2/M1)/0.835EY (MeV).

Equation (6) is in a form suitable for graphical analysis. A plot of the right-hand side of (6) against f ( Z i , I f ) should yield a straight line of slope - $ ( M , / M 2 ) for direct A K = 2 mixing, or slope 0 for AK = 1 mixing. The results are shown in figure 3. It appears that the M I amplitudes are best explained by a dominant AK = 1 mixing, with M , / M 2 of about lOS(1.5) x pN e-' b- ' .

There is a seeming contradiction between the conclusions from the analyses of the E2 and M1 intensities. However, A K = 1 and A K = 2 admixtures may both be present, and will influence the observed transition matrix elements differently. Whereas the total M 1 matrix element has contributions of single-particle strength from both AK = 1 and AK = 2 mixing, the total E2 matrix element has a single-particle contribution from A K = 1 mixing but a collective enhanced contribution from AK = 2 mixing. Thus it is only the M1 matrix elements that can reveal the dominant mixing mode with certainty. This point highlights the value of comparing mixing ratios, rather than B(E2) values alone, with the predictions of nuclear models.

Mean experimental values of the downward B(E2) values for the 2, +2g and 2, -0, transitions are 0.284(19) e2 b2 and 0.047(3) e2 b2, respectively (Milner et a1 1971, Hoehn et a1 1977). From equation (3) we find values for the quadrupole intrinsic matrix elements of M , = + 0.705(24) e b and Mi = -0.060( 1 1) e b, where the signs are chosen by convention, (The mixing parameter from these values is a2 = +0.085( 16) which may be compared with the earlier value.) From the value of M , / M 2 we then find M , = 7.4(1.1) x p N .

A different phenomenological approach to the coupling between rotational and vibrational motions of the nucleus has been made by Faessler et a1 (1965) in the rotation-vibration model, in which they consider coupling between the lowest 13 bands.

I I I I I 1

I \ I i' 0031 \K=2

0 . 0 2 ~

I I I I

003- -

002 - -

2 001- *- a- 1

0-

-001-

I I I I

-10 -5 0 5 10 I I I I I

10 -10 -5 0 5 f ( I , , I f 1

Figure 3. Origin of the M1 amplitudes in transitions from the y-vibrational band to the ground-state band in i900s, according to equation (6). R ( A , Ii, 11) is the right-hand side of equation (6). The full circles refer to present results and open circles to those of Helppi et al (1974). The straight lines show the expected relationships for A K = 2 and A K = 1 mixing, with M , / M , -0.01 lpN e - ' b-I .

I;:

1134 A L Allsop et a1

Principal coupling occurs between the ground-state, gamma-vibrational and beta- vibrational (K = 0) bands. Using the admixture amplitudes and expressions for the E2 matrix elements of Faessler et a1 and the M1 matrix elements of Greiner (1966) we have calculated mixing ratios with the rotation-vibration interaction both 'on' and 'off'. The results are shown in table 5. The agreement with experiment is apparently quite good, although the inclusion of the interaction does not improve the 6 values to the extent that i t improves the B(E2) predictions for ' 9 0 0 s (cf Eisenberg and Greiner 1975). Our previous conclusion that whereas A K = 2 mixing was sufficient to describe E2 transitions, AK = 1 mixing was necessary to account for the M1 transitions may explain this, because the rotation-vibration model does not include significant AK = 1 -type mixing. The agreement of the predicted 6 values with those from experiment may be superficial and fortuitous for

Also shown in table 5 are values for 6 derived from the matrix elements calculated by Kumar (1969) using the pairing-plus-quadrupole model in which the matrix elements are derived on a microscopic level. The agreement with experiment is good, both in magnitude and phase.

1 9 0 0 ~ .

4.3. Electron-capture decays f rom '"Zr

In deformed nuclei the leading-order transition matrix elements vanish if IK, - Ki 1 > J p , and the transition is said to be n-times K forbidden where n = lKf -Ki 1 - J p . The ground state of 19'Ir has a configuration with IRK = 4 + 4, and so the electron-capture decay to the InK = 4- 3 level at 1584 keV is K allowed for Jp = 1, but once K forbidden for Jp = 0. Our measurement, which favours a Jp = 1, is in accord with this selection rule. Further, for final states within the same band, the electron-capture branching ratios are just ratios of Clebsch-Gordan coefficients:

ft(Zi Ki --t I f K f ) - (Ii Ki Jp AKIZ/Kf)2 f t(IiKi +I{Kf) - ( I iKi Jp AKlZfK,)' *

For the decays to the Z=5, 4 and 3 members for the Kn=3- band in 1900s this rule implies

ft(Zf = 5 ) : ft(Zf = 4): f t ( I f = 3)= 1 :O. 11:0.03.

Table 5 . A comparison between experimental values of the multipole mixing ratios in the y-vibrational and ground-state bands in I9OOs with those calculated using the rotation-vibration model and the pairing-plus-quadrupole model.

Initial Final SRV Energy level level (keV) I R K I nK Scxpt 'on' 'off' JppQC

- 656 5'2 4 '0 - 1 . 7 ( + 3 - 3.0 - 5.4 569 3'2 2 '0 - 8.1 ( L :::)a - 6.4 -8.1 -9.9 407 4'2 4'0 - 3,4( ' g:p - 5.8 - 3.2 -

371 2 + 2 2 + o - 13(';5)a - 7.4 -5.6 -1.6 208 3'2 4 '0 - 16(':0)~ - 3.6 -2.2 -4.6 198 3'2 2 + 2 - 9(':)b -11.8 -14.0 -7.1

a This work. yy correlations (Helppi et al 1974). Kumar (1969).

The nuclear magnetic moment of I9'Ir 1135

The measured f t values give ratios of 1:0.16:0.02, in good agreement with theory. (Neergard and Vogel (1969) have studied the low-lying octupole band in deformed nuclei and conclude that it is Coriolis mixed with a K = 2 band. However, decays to the K = 2 component from 19'Ir are K forbidden, and the branching ratios to the K = 3 component should still be given by the above relationship.)

The electron capture to the InK=4+ 4 level at 1163 keV is of the 'allowed' type and is K allowed for both Jp = 0 (Fermi) and Ja = 1 (Gamow-Teller) decays. However, the isospin selection rule is expected to strongly inhibit Fermi decays in heavy nuclei, where the Coulomb interaction admixes states of different isospin and dilutes the isotopic purity of any one particular state. That the decay to the 1163 keV level appears to favour a Fermi-type decay is remarkable, and most likely can only be explained by some abnormal hindrance of the Gamow-Teller transition due to nuclear structure effects. The log ft value of 7.9 for this transition is indeed quite large for an allowed decay.

The electron-capture feed to the InK = 4+ 2 level at 955 keV is of the allowed type. It is, however, once K forbidden for Jp = 1 and twice K forbidden if Jp = 0, and thus we expect a dominant Jp = 1 transition. This is in accord with our results.

5. The IwIrFe experiment

5 .1 . Experimental details

The 19'Ir activity was produced by bombarding naturally abundant Re powder with 22 MeV alpha particles. The resulting '87-'901r activities from (a, n) and (a, 2n) on '*'Re and 18'Re were chemically separated from the rhenium and deposited onto an iron foil. The foil was heated at I150 OC for 12 h in a hydrogen atmosphere to diffuse the Ir activity into the iron, and finally etched to remove any surface activity.

The sample foil was In-soldered, together with a 6oCoCo single-crystal thermometer, to the PrNi, demagnetisation stage. The cryogenic and data collection procedures were essentially the same as those described in 95 2.2 and 2.3. In this experiment, however, a magnetic field of 0.8 T was applied to the sample foil to produce magnetic saturation. The direction of the field defined the quantisation axis and was collinear with the c axis of the cobalt crystal.

5.2. Data analysis

The anisotropies observed for "'IrFe were minimal even at 2.5 mK, so that the orientation parameter B, is negligible compared with B,. The normalised gamma intensities were accordingly analysed using the modified statement of equation (1):

(7) The correction factor f is the fraction of Ir nuclei in full-field lattice sites; the remaining 1 - f is assumed to be unoriented. This simple empirical model for the solubility of impurity nuclei in Fe has been used with success for Ir nuclei by Allsop et a1 (1 982). For the present sample f was determined to be 0.72(1) from the saturation behaviour of the anisotropy of the 2214 keV gamma ray in the decay of the '"Ir present in the sample. The orientation of 18*IrFe has been discussed by Berkes et a1 (1980) and Hornung (1 979).

The observed anisotropies, W(0)- 1, of the gamma transitions at 186, 361, 371, 518, 558 and 605 keV were normalised by dividing first by the appropriate U,A, coefficients

W(0, T ) = 1 + fB,(H, T)U2A2Q,P,(cos e).

1136 A L Allsop et a1

measured in our experiment on '"IrRe and second by appropriate Q2 coefficients. The resulting values offB,(H, T ) are independent of the observed gamma transition, and were averaged at each temperature point. These averages are plotted against reciprocal temperature in figure 4.

6. Results

6.1. The 'goIrFe hyperfine interaction

The magnetic hyperfine interaction Hamiltonian is

H M = -,uBm/I.

To this we have added a term with the form of equation (2) to account for the electric quadrupole interaction at the iridium sites arising in second order from the spin-orbit interaction in iridium in iron (Aiga and Itoh 1971, Johnston and Stone 1972, Johnston et a1 1972, Hagn et a1 1980). The total Hamiltonian is H = H M + HQ, and we used vq =-15.7 MHz. A least-squares fit to the data shown in figure 4 yields a magnetic interaction of

lpB( = 2.7(7) x J.

6.2. The lgOIr ground-state magnetic moment

The effective magnetic field B acting at the iridium nuclei is the vector sum of the hyperfine and applied magnetic fields. Hyperfine fields in iron have been measured for several iridium isotopes, but are not immediately applicable because 19'Ir is likely to exhibit a substantial hyperfine anomaly. Hyperfine anomalies may be large for heavy nuclei in which a small resultant moment arises from cancellations between larger contributions with different spatial distributions.

However, the largest anomalies measured for nuclei in the A - 190 region are about lo%, and so lie well within the uncertainty of +25% in our present measurement of the

o.ior I I

- 0.05 1 Figure 4. Values of fBz(H, T ) for '"IrFe plotted as a function of reciprocal temperature. The data were least-squares fitted for the hyperfine interaction.

The nuclear magnetic moment of Ig0Zr 1137

hyperfine interaction. We therefore neglect the anomaly, and use an averaged hyperfine field of 138.5(9) T appropriate to the Z=i state at 73 keV in 1931r (Hagn et a1 1980). This state is believed to exhibit only a small anomaly. After correcting for the applied field we deduce

1~(1901r; G S ) / =0.04(1)p,.

7. The I9'Ir moment: discussion

The ground state of Ig0Ir has been interpreted by Harmatz and Handley (1964) and Yates et a1 (1974) to have a 4 + {;+ [402]p-y'[615]n} configuration. The proton configuration appears as the ground state in "'3 189~19'9 1931r. Harmatz and Handley further suggest that the isomeric state at 26 keV in I9'Ir, which decays to the ground state by an M3 transition, is the 7 + { j + [402]p + y + [ 6 15]n} coupling of the proton and neutron states. The Nilsson- model prediction for the moment of the {;+ [402]p- y + [615]n} coupling is, however, ,U z -0.9 p,, which is considerably larger than that measured here. (In this estimate we have used the usual quenched neutron and proton spin g factors, g, = 0 . 6 g p , a rotational g factor g, =0.4, and the distortion is derived from the quadrupole moment of Murray et a1 (1 980).)

A second configuration of states with nearly appropriate energies which may be coupled to give both Z"=4+ and 7 + states is {?-[505]p F $-[512]n}. The proton state is found at 17 1 keV in I9'Ir, and the neutron state is the ground state of lS9Os and at 74 keV in I9'Os. The Nilsson model, however, predicts a moment of p = + 5 pN for the I n = 4 + state. Indeed, the only Nilsson configuration capable of giving a magnetic moment of the observed magnitude appears to be 4' {i-[541]p + 4 - [503]n}, although we note that the proton-state energy is unfavourably high and, further, it is not possible to account for a low-lying 7 + state using this configuration.

Whilst we are unable to suggest a satisfactory single configuration to account for the near-vanishing moment, an explanation might be sought in terms of mixing of the {;+[402]p- ?+ [615]nJ and {y-[505]p-j-[512]n} configurations.

A measurement of the magnetic dipole moment of the I n = 7 + isomer in Ir would clearly be of considerable value.

Acknowledgments

One of us (DWM) has profited from discussion with Dr P Vogel, and wishes to acknowledge the receipt of a Research Fellowship from the California Institute of Technology, where part of this work was performed. The research was supported by the Science and Engineering Research Council of Great Britain.

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