g-factor experiments on the first excited 2+ states in 102Ru, 106Pd and 110Cd

Nuclear Physics A188 (1972) 600-608;

@ North-Holland

Publishing

Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

g-FACTOR

K. JOHANSSON,

EXPERIMENTS ON THE FIRST EXCITED IN lo2Ru, lo6Pd AND “‘Cd E. KARLSSON, Institute

L.-O. NORLIN,

of Physics,

University

R. A. WINDAHL

of Uppsala,

2+ STATES

and M. R. AHMED +

Uppsala, Sweden

Received 17 February 1972 Abstract: The g-factors of the first 2+ levels in io2Ru, io6Pd and ir°Cd have been remeasured with increased accuracy, using the perturbed angular correlation method and the radio-active mother isotopes dissolved in ferromagnetic lattices. The results are g = &0.408+0.034, g = +0.399jcO.O29 and g = +0.35&0.07 respectively. Possible sources of error in the use of internal fields are discussed. E

RADIOACTIVITY

ro2Rh, lo6Rh, “OAg; measured rv(0, H). lo2Ru, io6Pd, “OCd first excited 2+ states deduced g.

1. Introduction Accurate values of the g-factors in the present isotopes are of interest not only for the direct comparison with various theoretical calculations of the vibrational states, but also to serve as a calibration in measurements of the IMPACT type. In the latter case the so-called transient field correction is determined with reference to g-factors obtained with PAC from radioactive sources. In several isotopes it seems to be possible to improve the existing radioactivity data, for instance in the case of 475 keV level in lo2Ru where the relative error in the published g-factor value ‘) is 23 %. 2. Experiments 2.1. SOURCE

on lo2Ru

PRODUCTION

The “‘Rh activity was prepared by irradiating natural ruthenium metal powder with 20 MeV deuterons during 20 h. Chemical separation was done 8 months later. After the separation the activity was dissolved in HCl (pH = 1.5) and dropped onto an iron foil. The foil was folded and melted to a small sphere, and was annealed for 50 h at 900°C before quenching to a low temperature. It is known that rhodium forms a continuous solid solution with y-Fe [ref. ‘)I. 2.2. PAC MEASUREMENTS

The source consisted of “‘Rh and ’ ““‘Rh with half-lives of 206 d and 1057 d with different decay schemes “). In fig. 1 is shown a small portion of the y-singles spectrum t On leave from Nuclear Research Centre, Bagdad, Iraq. 600

g-FACTOR

EXPERIMENTS

601

taken with a Ge(Li) detector. This part of the spectrum and the intensities given in the decay schemes were used to calculate the relative number of 206 and 1057 d decays in the source and it was found that at the time of the g-factor measurement 84 % of the activity originated from the 1057 d activity. With the single-channel analysers set on regions around 475 keV and 1047 keV, respectively, the relative number of coincidences from the different y-y cascades could be calculated from the decay schemes of Konijn et al. “) and the measured y-ray intensities involving the 475 keV level. The main contributions were from the 1047-475 keV (57,%) and 1113-(6313-475 keV (35 “%)cascades.

Fig. 1. A part of the y-ray spectrum of lo2Rh measured with a Ge(Li) detector.

-w--w OF all the -yT-cascactesirrwgate settings used in the g-factor experiment was measured with an automatic two-channel set-up and the result was A2 = -0.2364+0,0015 and A, = --0.0362+0.0037. The g-factor of the 475 keV level was determined by measuring the rotation of the angular correlation with the IPAC method “). The sample was polarized by application of an external magnetic field of 22 kG perpendicular to the plane of the four detectors. The temperature dependence of the magnetic hyperline field deviates in some cases from the temperature dependence of the bulk magnetization of the host material “)_ In order to avoid corrections for temperature dependence the measurement was done at liquid helium temperature. The four 3.8 cm x 5.1 cm NaI(T1) detectors were arranged in the angular configuration I(45”)II(9O”)III(135”)IV(9O”)I, which means that, e.g., the angle between detectors I and II was 45”. Coincidences obtained in the sequence of field directions

602

+-

IL JOHANSSON

-

+ etc., were combined

et al.

in the expressions y

1

p 2

The precession angle or of the magnetic the weighted mean of PI and P2 with p =

dipole moment

C Ui~i(l35’,

+B)

[ c a, Jq135”,

-B)

was obtained

by comparing

I’ 4

where Wi are the angular correlation functions and q the relative contributions from the different cascades in the total number of coincidences “). The value of P is 1.0743 +0.0042 and corresponds to an angular rotation or = - (0.0217+0.0012) rad. The effective field at the 1“Ru nucleus can be expressed as Beff = B,, + ($ -D) x M+ B,, where B, is the polarizing field, M the magnetization and D the demagnetization factor. With the values B,, = -(503 +9)kG [ref. ‘)I, B, = +22 kC, D= $(a sphere) and z = 23.1 k 1.4 ps [ref. ‘)I, the or observed here yields the result for the first 2+ level in lo2Ru g = +0.408+0.034.

3. Experiments

on lo6Pd

A g-factor determination with a non-magnetic source in an external field of 5 1. f kG has earlier been published by Johansson et al. “). Here will be reported some attempts to decrease the relative statistical error by using high internal fields. For judging the reliability of nuclear g-factors from time-integral PAC where hyperfine fields in ferromagnets are used, it is of interest to compare the results of precession measurements in different host materials. In such cases there may appear systematic errors of the following types: (a) The local magnetization in the vicinity of the impurity atom is not always saturated even in applied fields B, of the order of 10 kG [ref. ‘)I (probably due to magnetostricticn effects I”)) and the effective B,, may therefore fall below the value measured with methods which do not involve magnetic polarization. (b) The temperature dependence of the hyperfine field is different ‘*‘l) from that of the bulk magnetization usually used for extrapolating low-temperature Bhf values up to the higher temperatures where PAC experiments are most often performed. (c) The state of the alloy is critical if the solid solubility is small, which can lead to the segregation of an impurity-rich phase where B,, is zero or very small, meaning that only a fraction of the nuclei under study are subjected to the expected field II).

g-FACTOR

EXPERIMENTS

603

The fall of the hyperfine field when the impurity concentration is increased up to a few percent within the solubility range is, on the other hand, normally not a very steep function. Change of preparation conditions and heat treatments for the alloys can give indications of such effects. (d) For the evaluation of the g-factor using the tabulated B,, values one should similarly consider by which method and under which alloy conditions these values were obtained. Furthermore, fields determined by different nuclear probes of the same element in the same environment differ because of the hyperfine anomaly, which is expected to be especially large if s-electrons contribute to the fields “). In the present study of Pd in Fe, Ni and Co matrices it was known from earlier experiments “) that a polarizing field of more than 10 kG is needed for saturation of the Pd hyperfine field in iron. All present experiments were therefore carried out in fields of 20 kG or more. Effects of type (a) should therefore not be expected. The results of the precession measurements presented here in order to extract nuclear information are, in fact, part of a systematic investigation of temperature dependencies of impurity hyperfine fields ‘I). Such deviations as described under (b) were indeed found for T & 0.4T,. As a precaution against systematic errors of this type only data from low-temperature runs (T < 0.25TJ are considered in the following. In this region the o(T)/o(O) correction seems to be valid. Furthermore, the correction for decrease of local magnetization of the host around the impurity as considered by Lovesay and Marshall ’ 3, i4) seems to be small at such temperatures. TABLE 1 or/B for the lo6Pd 2+ state in different host material

Host Fe Ni co steel

wt (rad) corr. to 0°K -(1.737&0.021). -(0.524&0.013) -(1.261*0.013) +(0.173*0.011)~

lo-’

* lo-’ . lo-’ 1o-2

&rr (kG) -567415 -173& 5 -374+10 +51.1+0.5

tot/Ben (rad/kG)

(3.06+0.09) * lo- 5 (3.03&0.12). 1O-5 (3.37f0.10). 10-S (3.39+0.22) * 1O-5

The PAC experiment was carried out with the same equipment as described for lo2Ru using the 623-512 keV y-y cascade in io6Pd and the angles 1(52”)11(109”) 111(90”)1V(109”)1. The it results shown in table 1 refer to sources prepared in the following ways: electroplated, diffused 50 h at lOOO”C, annealed at 900°C for 50 h. Pd-Fe: Pd-Co: electroplated, melted, annealed at 900°C for 50 h. Pd-Ni : I The solubility of Ru in iron, cobalt and nickel is at least 10 at. % for each alloy at 900” C where the alloys were homogenized before quenching to room temperature ‘). The concentration of Ru in the alloys was estimated to be less than 1 at. %. We therefore assert that our samples represent dilute binary alloys of Ru with the transition

604

K. JOHANSSON

et al.

metals and that the atom formed in the B-decay Ru-Rh-Pd will experience a hyperfine field representative of a dilute Pd impurity in the respective matrices. From table 1 and fig. 2 it is found that individual ratios m/B,,, are in slight disagreeI

I

I

Host

20

j

I

I

material

1) Stainless steel

15

E P

3 10

5

B,ff

( kG)

Fig. 2. The precession angle as a function of the effective field in lo6Pd.

ment, since the result for the cobalt alloy is higher than the two others but in agreement with the stainless-steel result. Neglecting this unstatistical scatter the weighted result is m/B = (3.174kO.056) x lo-’ rad . kG_‘. We believe that errors of type (a) and (b) have been effectively eliminated by the present treatment. The remaining small inconsistencies are therefore probably due to either (c) imperfections in the alloys or (d) the fact that PAC and NMR methods measure slightly different quantities in a hyperfine field determination. The NMR determinations were made with the isotope “‘Pd (nuclear ground state of single-particle assignment d,) while the present measurement were performed on an excited state of “vibrational” character. Hyperfine anomalies A between such a pair of states have not - to our knowledge been studied, but can be expected to be of the order of 1 %, which would change the g-factor derived here by the same amount. The anomaly A for the same pair of states depends also on the relative contact term contributions to the hyperfine fields in the three alloys, and might in principle explain the variation of m/BefE mentioned above. In all three alloys s-electron densities are supposed to produce most of the hyperfine field. The total hyperfine field arises from conduction electron polarization (CEP)

g-FACTOR

EXPERIMENTS

605

and the rest from core polarization (CP). The CEP part is mainly due to s-electrons, and the CP part arises from polarized d-electrons which in turn polarize inner s-shells. The differencein contact term contribution to the hyperline anomaly for Co, Fe and Ni is therefore only a fraction of the total anomaly. The observed deviation seems therefore to be too large to be explained by hypertine anomaly variations. The magprobable that they were carried out in a sufficiently high polarizing field that the resonances occurred predominantly in the domains and not in domain walls, the latter being another possible reason for discrepancy between PAC and NMR data. Summing up the discussion on the reliability of hyperfine fields in ferromagnetic alloys we would conclude for the Pd case (where fairly accurate measurements are possible) that the preparation of the alloys seems to be critical and is the probable cause of variations between the different measurements, although all normal precautions have been taken in the preparation. Imperfect alloys generally show a lower average hyperfine field for the solute than well-prepared ones (except for a few cases where the solubility is very low and the interstitials have been found to have a higher field 16). It is therefore justified to assume that the highest cot/B,,, value observed here represents the best value, the others being reduced due to inhomogeneities, segregation, the presence of carrier material from the radioactivity separations, oxygen content etc. If the g-factor is calculated from the Pd-Co result alone we obtain for the first 2+ state in lo6Pd g = 0.399 kO.029, where z = 17.3k1.2 ps [ref. “)I and th e angular correlation coefficients A, = 0.2840f0.0022 and A, = 0.8049+0.0023 (uncorrected for solid angle) obtained in the same geometry have been used. The main contribution to the error of the g-factor is now the uncertainty in the lifetime (7 %). This g-factor which contains an additional uncertainty due to a possible hyperfine anomaly agrees well with the value reported earlier, g = 0.401 f0.034 obtained in the measurement with a diamagnetic source in an external field “). 4. Experiments on ‘l°Cd 4.1. SILVER

IN IRON

SOURCE

The hyperfine magnetic field acting on “‘Cd nucleus after the decay of ‘lomAg in Ag-Fe alloy was used by Keszthelyi et al. 18) to measure the g-factor of the 656 keV 2+ state in “‘Cd and the result was g = 0.30+0.12. As the statistical error is rather large in this case we decided to determine the g-factor more accurately. Suitable cascades to use simultaneously in the PAC measurement are 1504-656 keV and 1384-885-656 keV with the anisotropy A = 37 % (not corrected for solid angle). Four l1 ‘Ag-Fe sources with different concentrations were prepared by electroplating “OrnAg in AgNO, carrier solution onto an iron foil, which was then melted with an

K. JOHANSSON

606

et al.

electron gun. After the melting 90 ‘A of the activity had evaporated. Annealing was performed at 1000°C during 70 h followed by 800°C for 24 h. --The measured preen angh33f theme the same within limits of error and the weighted P-value in the g-factor measurement is P = 1.OOOf0.002 corresponding to g = O.OO+ 0.07. The 656 keV 2+ level is a vibrational state for which one expects g = 0.4 which is not in agreement with the present experimental value. Data concerning the solid solubility of silver in iron are somewhat confusing. The references in ref. “) have given different upper limit for the solid solubility (0.0-1.0 at. %). The most probable explanation for the small effect in the present experiment is that the solubility of silver in iron is very low and that the mean hyperfine magnetic field at the cadmium nuclei was cancelled by the polarizing external field (21 kG). This is also confirmed in experiments by Fox et al. 1“) who determined the hyperfine field on Ag in Fe using the NMR/ON technique. The concentration used was less than 10e3 at. %, which is about 500 times smaller than in our experiment. As such low concentration would give too low a coincidence counting rate it was decided to use the internal field at Cd in Gd measured at 77°K [ref. ““)I. 4.2.

SILVER

IN GADOLINIUM

SOURCE

Small amounts of silver are soluble in gadolinium metal which can be seen from the work on effective fields at 5s-5p impurities in gadolinium 21). A weak Ag-Gd

Lin.

scale

Fig. 3. Singles spectrum for ‘lomAg. Gate settings are indicated.

g-FACTOR

EXPERIMENTS

607

sample was prepared by placing a drop of “OrnAg in AgNOa solution onto a gadolinium foil, melting by an electron gun and annealing at 750°C during 20 d. The angular correlation of the y-y cascades accepted by the energy gates (fig. 3) were measured with the Ag-Gd source at room temperature, which is above the Curie point. The experimental values are A, = -0.2907~0.0007 and A, = -0.0246* 0.0016. In the IPAC measurement a total number of lo7 coincidences were collected with the source kept at 77°K. The result for the weighted P-value is P = 1.0123f0.0024 which gives wr = 3.2kO.6 mrad. Using r = 6.6kO.6 ps [ref. ‘“)I, Bbf= -(310f7) kG [ref. “)I and the applied field B. = + 22 kG, the present value of the g-factor for the lirst excited 2+ state in ’ 1‘Cd is g = +0.35+0.0s.

5. Comparisons with theory The g-factor of the excited 2+ states in ioZRu and lo6Pd agree with the estimated Z/A = 0.43. Greiner ‘l) h as d ed uce d a formula for the g-factors of vibrational nuclei basedonaeolle&emodel with the assumption that the proton distribution is Iess deformed than the neutron distribution. This is due to a larger pairing force between the protons than between the neutrons. The formula proposed is 9

= ;(l-zf)(l++j)

= +-),

-

j'= ;

(1/Z-1). ”

The factors G, and G, are the strengths of the pairing force for neutron and proton respectively. The experimental value G,/G, = 1.4 [ref. 24)] gives g = 0.37 for the first 2+ state in “*Ru and g = 0.38 for the first 2+ state in ’ 06Pd and “‘Cd, which is in good agreement with the experimental results. Our thanks are due to Dr. Z. Sziikefalvi-Nagy and Dr. V. R. K. Murty for their help in the final stage of the measurements.

References 1) K. Auerbach, K. Siepe, J. Wittkernper and H. J. Korner, Phys. Lett. 23 (1966) 367 2) Binary alloys, ed. M. Hansen (McGraw-Hill, New York, 1958) p. 702 3) J. Konijn, E. W. A. Lingernan, F. Diederix, B. J. Meijer, P. Koldewijn and A. C. Klaasse, Nucl. Phys. A138 (1969) 514 4) B. E. Karlsson, Ark. Fys. 22 (1962) 1; B. E. Karlsson, E. Matthias and C.-A. Lerjefors, Ark. Fys. 22 (1962) 27; K. Johansson, A. Karlsson and J. Kozyczkowski, Ark. Fys. 37 (1968) 251

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et al.

5) D. A. Shirley, S. S. Rosenbhun and E. Matthias, Phys. Rev. 170 (1968) 363 6) K. Johansson, S. Gustafsson and A. G. Svensson, Ark. Fys. 34 (1967) 97 7) Hyperfine structure and nuclear radiations, ed. E. Matthias and D. A. Shirley (North-Holland, Amsterdam, 1968) pp. 980, 1061 8) K. Jobansson, L.-G. Norlin~and G. Carlsson, Ark. Fys. 37 (1968) 445 9) K. Johansson, E. Karlsson, L.-O. Norlin, P. N. Tandon and H. C. Jam, Ark. Fys. 37 (1968) 453 10) A. Aharoni, HyperSne interactions in excited nuclei, ed. G. Goldring and R. Kalish (Gordon and Breach, London, 1971) p. 75 11) L.-O. Norlin, K. Johansson, E. Karlsson and M. R. Ahmed, Hypernne interactions in excited nuclei, ed. G. Goldring and R. Kalish (Gordon and Breach, London, 1971) p. 475 12)#;Kopfermann, ‘fzerrmRnnente (; Frankfur~amMair+1936) sect. 26 13) S. W. Lovesay and W. Marshall, Proc. Phys. Sot. 89 (1966) 613 14) S. W. Lovesay, Proc. Phys. Sot. 89 (1966) 625 15) M. Kontani, K. Asayama and J. Itoh, J. Phys. Sot. Jap. 20 (1965) 1737 16) L. C. Feldman, W. M. Augustyniak and E. N. Kaufmann, Hyperfine interactions in excited nuclei, ed. G. Goldring and R. Kalish (Gordon and Breach, London, 1971) p. 174 17) P. H. Stelson and L. Grodzins, Nucl. Data 1 (1965) 21 18) L. Keszthelyi, I. Demeter, I. D&szsi and L. Varga, Hyperfine structure and nuclear radiations, ed. E. Matthim andDz?hirley 7; Amsterdam, lpestpr 155 19) R. A Fox, P. D. Johnston and N. J. Stone, Phys. Lett. 34A (1971) 211 20) L. Bostrom, G. Liljegren, B. Jonsson and E. Karlsson, Phys. Scripta 3 (1971) 175 21) W. Greiner, Nucl. Phys. 80 (1966) 417 22) Hyperfhre structure and nuclear radiations, ed. E. Matthias and D. A. Shirley (North-Holland, Amsterdam, 1968) p. lO62 23) B. W. Marsden and N. J. Stone, Phys. Lett. 35A (1971) 35 24) S. G. Nilsson and 0. Prior, Mat. Fys. Medd. Vid. Selsk. 32, no. 32 (1961)