Nuclear structure study of the isomers of 102Rh by nuclear orientation

N&ear Physics A243 (1975) 309- 316; @ Nor&Holland Pa&&hing CO., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

NUCLEAR STRUCTURE

STUDY OF THE ISOMERS

OF *‘*Rh

BY NUCLEAR ORIENTATIOl’l E. SCHOETERS, R. GEERTS, R. E. SILVERANS + and L. VANNESTE ++ Iastituut Door Kern- en StralingsfysiJca, Leaven Uniuersity, 3530 Hetxrlee, Be&urn Received 23 December 1974 Abstract: The nucIear magnetic moments of the two isomers of rozRh have been measured using nuclear orientation at low temperatures. The results are 1~1= 0.4550.35 nm. for the 206 d isomer and bI = 4.11 kO.15 urn. for the 1057 d isomer. Strong evidence has been found for spin-parity assignments ZR = 2- for the former and In = 6+ for the latter. All results are interpreted following the jj coupling model and definite conclusions can be made about the nature of both states. E

RADIOACTIVITY lo2Rh, 102mRh [from Rh(p, d) and Ru(d, xn)]; measured y(f?, T) polarized nuclei; deduced i(, H, f. 3He-4He refrigerator, Ge(Li) detectors.

1. Iatruductfon

The isotope ‘*‘Rh has two isomeric states, one with a half-life of 206 d and one with a half-life of 1057 d, which we will designate henceforth as “““‘Rh and io2Rh respectively. The former is known to be a low spin state (Z = 0, 1 or 2), while for the latter spin values Z = 5 or 6 have been proposed ‘*“). The nucleus Rh possesses 45 protons, the odd proton involved being in the p, or g%shell according to a simpIe shell model. These proton states are known to have quite different g-factors. Therefore a measurement of the magnetic moment would be very conducive to the investigation of the structure of the Rh isomers. A nuclear orientation experiment suits this purpose very well and it will become clear in subsect. 3.3 that a careful analysis of the results may reveal valuable information about the spins too. 2. Experimental procedures 2.1. SOURCE

PREPARATION

Measurements have been done on two different sources. First natural rhodium powder was irradiated with 75 MeV protons for 6 PA - h. A mixture of 1*‘Rh and roZmRh, together with activities of 99Rh, l**Rh, ‘**Rh, loimRh, g’R~, 95Tc and 96Tc was formed. An iron sample containing both ‘*‘Rh and loZmRh was prepared by melting the powder together with a piece of high purity iron, rolling it to a thickness of 0.1 mm and annealing it in vacuum at 800 “C!for 10 h. The concentration of rhodium in iron was less than 2 at. %. t Aangestefd navorser NFWO. ++ Bevoegdverklaard navoner NFWO. 309

310

E. SCHOETERS

et al.

The activity for the second source was obtained in a (d, n) reaction on ruthenium and a chemical separation was carried out [described in ref. 3)]. It was allowed to decay for six years so that it contained only 1057 d ’ “Rh and three year “‘Rh at the time of the experiment. A “‘Rh(Ni) sample was then prepared in the same way. 2.2. APPARATUS

In two separate experiments the samples were soldered to the cold finger of a 3He-4He dilution refrigerator, which has been described previously 4), together with a “Co(Fe) sample which served as a nuclear thermometer. Two coaxially drifted germanium-lithium detectors, with volumes of 50 cm3 and 30 cm3, positioned at angles of 0” and 90” with respect to the external magnetic field, were used to record the spectra. The distance between source and detector was 14 cm. An external field of 3 kOe was used to polarize the Fe and Ni foils. All data registration was done automatically by a PDP 1l/20 minicomputer. 2.3. MAGNETIC

MOMENT

AND SPIN DETERMINATION

METHOD

The relevant parts of the decay schemes ‘) of ro2Rh and 102mRh are given in figs. 1 and 2.

lo2 Ru 44 50 Fig. 1. Relevant part of the decay scheme of lo2Rh.

The anisotropic radiation emitted by the oriented Rh nuclei may be described with the formula “) v = 2,4. with w(e) = 1 +~U&B,P,(cos e) (1) Y

311

lo2Rh ISOMERS 206d

Fig. 2. Refevant part of the decay scheme of iozmRh.

Here, W(0) denotes the normalized probabiity of emission in the direction defined by the angle 8 with respect to the quantization axis. The. F, functions are identical with the usual angular distribution functions, while the U, are a function of the angular moments of all transitions preceding the one observed. All these functions are tabulated “). The P,(cos 0) are the Legendre polynomials of order v. The orientation parameter Z3,of order v for the initial state I is defined as BY(Z) = C(2v+ l)~(ZvZfPnO)K(m). m

In this expression the population functions W(PPZ) for the magnetic sublevels m are a function of pH/IkT. As the hyperfine fields of Rh in Ni and in Fe have been measured before ‘I ‘), a measurement of 3, will yield a determination of ~1if Z is known. However, except at the lowest spin values, a change in angular momentum of one unit does not strongly influence B,. Only the factors U, and B, depend on the spin I of the parent state. The spin I can be determined unambiguously by using the I-dependence of B, in a combined nuclear orientation-nuclear magnetic resonance (NO-NMR) experiment. However, the preparation of a NO-NMR sample is very difficult due to the fact that only a low specific activity of ’ “Rh can be obtained. In a conventional nuclear orientation experiment one cannot sufficiently separate the dependence of .Z3,on p and I_ Therefore we suggest using the spin dependence of U,,. The factor U, can normally be measured with an accuracy of the order of 10 %. As the U, values calculated for spin Z = 5 and I = 6 differ by only a few percent, this is not sufficient. However, the ratio of two U, can often be determined with a much better accuracy, when combining the anisotropies of two y-rays in the following way:

( W@)--1Ivi (W(6)-

l)yt

= ZJ&&P, U;F;B,P,

_

u2F2

U;F;

_

(3)

In this equation the v = 4 term was neglected as may be done when B4 < B2. This method can be applied to the 697 keV and 767 keV y-rays in the decay of ro2Rh;

312

E. SCHOETERS

et al.

the F, coefficients of these E2 transitions are known exactly and the U,[Ui value differs 9 % for both assumptions: U,(697 keV)/Ui(767 keV) = UJU; = 0.94for I = 5 and U,/U,l = 1.03for I = 6. These values do not change significantly for reasonable Fermi contributions in the positon decay. As the error in the ratio (W(0) - 1)(697 keV)/( W(0) - 1)(767 keV) is primarily statistical, a definite spin determination must be possible. The applicability of this method strongly depends on the decay scheme and the magnitude of the anisotropies. For both reasons it is only applicable in the case of lo2Rh. 3. Results 3.1. THE SOURCES

L02Rh(Ni) AND la2Rh(Fe)

For the spin determination only the results at 8 = 0” were analysed. Furthermore only the “‘Rh(Ni) data were used in order to be able to neglect the v = 4 term. An example of the temperature dependence of W(0”) is given in fig. 3 for the 697 keV

Fig. 3. Temperature

dependence

of W(O’) of the 697 keV transition

in the decay of Io2Rh.

y-ray. Three separate runs were performed. The ratio U,lUiwas obtained each time for several temperatures and a mean value was calculated for each run. The data are listed in table 1. The experimental U,/U;value clearly indicates I = 6 for ’ “Rh. This spin value was introduced in the calculation of the hyperfine interaction constant. The results of the least squares fittings are summarized in table 2. For ’ “Rh(Fe) the ratio W(O’)/W(90”) was used. For the ’ 02Rh(Fe) source the 767 keV y-ray was omitted because of the 95Tc contamination. The hype&e field of Rh in Fe

313

l”*Rh ISOMERS

Experimental -__.

TABLE1 U2/u’2 values for $02Rh

No. run

UJUIZ

Weighted mean

1 2 3

1.06&0.04 1.05*0.07 1.04~0.06

1.05*0.03

TABLE 2

Experimsntaf Source

lo2Rh(Fe) loZRh(Ni) ““Rh(Ni)

results of nuclear orientation

measurements

in lo2Rh

Y-ray (kev)

b$H!

j&I

(n.m.. kG)

OrG)

(n.m.)

Weighted mean (n.m.)

697 697 167

2.492&140 8991 25 895+ 20

X9.6(16) “) 222(3) b, 222(3) b)

4.45 kO.30 4.05&0.20 4.03 10.20

4.11&0.15

IPI

“) Ref. ‘). b, Ref. 8).

was checked using the 307 keV y-ray of l”rmRh and showed excellent agreement with the quoted value. 3.2. THE SOURCE

lozmRh(Fe)

As the sample used for this measurement contained also “‘Rh, the 556 keV transition, which is not fed by the long-lived isomer, was chosen for the analysis. The result of a least squares fit for the ratio W(O”)/W(90”) was 1~1= 0.45+0.35 n.m. for I = 1 or 2. The error is rather large because of the small anisotropies, the unknown spin value and the involved uncertainty on the U, coefficient of the preceding /Iradiation. 4. Discussion 4.1. THE ISOTOPE

lozRh

The nucleus ‘*‘Rh contains 45 protons and 57 neutrons. The neutrons are 6lIing the d, and g3. orbitals. As the neighbouring odd-N Ru and Pd isotopes all have 3’ ground states, the neutron ~onfi~ration may be assumed to be ~v(d~-‘)~(g~‘)~~~ For the odd-A Rh isotopes the lowest energy levels are always 3-, 3’ or 4_+,indicating a close competition between the p+ and gq orbitals as predicted by the shell model. The 3’ state is interpreted as a (g+-3)t seniority three state. The large value of the experimental g-factor now is quite distinctive and definitively establishes the proton character as gp. The proton configuration might then have one of the following forms: (a) {“(P,“)O(gPS)tI~* (b)

Mp,“)o(g,-3),~,~

(e)

~~(P~“)*(g~-3)~~.~.

E. SCHOETERS

314

et 01.

The magnetic moment of an odd nucleus can be estimated using the formula “)

where g,,, ga,jP, j. are the g-factors and the spins of the odd proton or neutron and lis the total spin. For the g-factors of the odd-_4 groups we have used either Schmidt values (~schmidt),or empirical values from neighbouring nuclei (,u_,) or values Calculated using the Ml spin polarization theory of Arima and Horie lo) (P&. The results are summarized in table 3. The agreement with the calculated moments is

Comparison Proton config.

(a) (b) (c)

hcbmtdt

4.84 4.84 3.37

TABLE3 of experimental g value of lo2Rh with theory creak

kw

4.50~0.15 4.50*0.15 3.6020.12

4.85 4.11 3.25

4.11~0.15

reasonably good. Although the comp~ison seems to favour configuration (b), the other ones cannot be ruled out: a mixing of two or three configurations may occur. For odd nuclei spin values are predicted by Nordheim’s rules as revised by Brennan and Bernstein II). The predictions for the proposed configurations for “‘Rh are listed in table 4. A spin and parity value 7+ is not compatible with the observed TABLE4 Predicted spin values for different configurations Configuration

in “‘Rh

Predicted In

Applied rule

6+ (2+ or) 7+ (l+ or) 6+

R3 R2 R2

positon branch to the Sf level at 2219 keV which has a logft value as small as 6.7. Therefore the spin assignment 6+ is favoured. Taking into account the results for the magnetic moment, the observed crossing of the 3’ and 3’ Ievels and the spin value, one may conclude that a mixed con~guration is most probable for “‘Rh. 4.2. THE ISOTOPE

loZmRh

The small value of the experimental g-factor points to a p+ character for the odd proton. Consequently the configuration of lo2”Rhis probabIy z(p31)iv(dQ-1)3. The jj coupling rule then leads to possibIe spin parity values 2- and 3-. The latter is impossible due to the observed positon branchings: the former is also the one predicted by Nordheim’s strong rule ‘“).

315

to2Rh ISOMERS

Theoretical values for the magnetic moment have been calculated with formula (4) by the use of both Schmidt moments and empirical moments from neighbouring odd-A nuclei: the results are given in table 5. Our experimental value is reproduced very well using empirical g-factors. The deviation from the Schmidt value is apparently due to the quenching of the neutron g-factor. TABLE 5

Comparison

of the experimental ,u-value of tozmRh with theory ‘Gt,

-0.10 -0.65 -0.54

Ct.rr

-0.45Ifio.35

5. Conclusioa

The magnetic moments of lo2Rh and ro2”‘Rh have been measured. The results mainly suggest a g%character for the odd proton in ’ *‘Rh and a ps character for the odd proton in lo2”‘Rh. Experimental evidence was found also for a spin assignment Z = 6 for lozRh. All results were shown to agree with thejj coupling model for odd nuclei and, moreover, allowed for the derivation of the most probable colorations. This leads to a spin-parity assignment Z” - 2- for rozmRh. In conclusion we note that the magnetic moments also reveal that the isomerism in lo2Rh does not occur due to a recoupling of the proton and neutron angular momenta as is often the case in odd nuclei I’), but results from a differencein proton configuration. The authors wish to thank the cyclotron staff of the UniversitC Catholique de Louvain for the irradiation facilities and the Universitair Rekencentrnm KUL for the use of their IBM 370 computer. They are indebted to Prof. R. Gijbels of the Universitaire Instelling Antwerpen for providing them a six year old ‘02Rh source, Financial support by the Belgian Inte~niversi~ir Instituut voor Kernwetens~hap~n is gratefully acknowledged.

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316

E. SCHOETERS

et

of.

7) E. Matthias, D. A. Shirley, N. Edelstein, H. J. Kiirncr and B. A. Olsen, Hype&e structure and nuclear radiations, ed. E. Matthias and D. A. Shirley (North-Holland, Amsterdam, 1968) p. 878 8) R. C. Reno and C. Hohenemser, Hyperline interactions in excited nuclei, ed. G. Goldring and R. Kalish (Gordon and Breach, New York, 1971) p. 457 9) J. P. Elliott and A. M. Lane, Handb. Phys. 39 (1957) 241 10) A. Arima and H. Horie, Progr. Theor. Phys. 12 (1954) 623 11) M. H. Brennan and A. M. Bernstein, Phys. Rev. 120 (1960) 927 12) L. W. Nordheim, Phys. Rev. 78 (1950) 294; Rev. Mod. Phys. 23 (1951) 322