Measurement of the ground state spectroscopic quadrupole moments of 191Os and 193Os

Nuclear Physics A332 (1979) 41--60 ; © North-Holland Publlaklnp Co., Amsterdam

Not to be reprodueed'by photoprint or mlcroßlm without written permiwton fiom the publisher

MEASUREMENT OF THE GROUND STATE SPECTROSCOPIC QUADRUPOLE MOMENTS OF' 9 'Os AND "'Os H. ERNST, E. HAGN and E. ZECH Physik-Deportment, Technische Universitdt blt7nchen, D~GI6 Garching, West Germany Received 22 March 1979 (Revised 18 July 1979) Abstract : Radioactive "'Os and' 9 ~Os nuclei have been aligned in an Os single crystal at temperatures down to 4 mK . From the temperature deprndrnce of the y-anisotropy the quadrupole frequencies vQ = e 2 gQ/h have been determined as vQ("'OsOs) _ -27819 MHz and vQ(' 93 0sOs) _ -96115 MHz. With the known elxtric field gradirnt iôr OsOs of ey = (-4.5410.24) xÎO" V/cm= the ground state apecrttoscopic quadrupole moments arededuced to be Q(' 9 'Os) _ +2 .5310.16 b and Q(' 9 ~Os) _ +0 .8710 .15 b.

E

RADIOACTIVITY 'q' ~ "'Os [from 'q°~' °= Os (n, y)] ; measured 1,(0, t) of orirnted states. ' 9 'Os and "'Os deduced Q. Nuclear quadrupole relaxati°tt. Hyperfine enhanced nuclear cooling. Ge(Li) detxtors .

1 . Introdnctian The osmium nuclei are situated in a transition region between the well-deformed rare-earth nuclei and the spi~erical nuclei near Z °BPb . In addition, the quadrupole deformations change from prolate to oblate with increasing mass in the Os-Ir-Pt region. The existence of a prolate-oblate phase transition between Os and Pt has been established by the observation that the spectroscopic quadrupole moments of the first 2 + states in the even isotopes change sign . The current interest in the spectroscopy of the opium nuclei is due largely to the fact that, with increasing neutron number, a gradual transition is expected from well-deformed prolate shapes in the lightest Os isotopes to shapes which are alternatively described theoretically as spherical, prolate with a strong hexadecupole deformation, y - unstable, triaxial, or oblate in the region around mass number 19192. The electromagnetic moments ofthe even-A isotopes in this region have been the subject of several recent investigations, both eaperimeatal' -3) and theoretical`_e). Less information can be found in the literattue concerning the electromagnetic moments of the odd-A Os isotopes. Although the ground state nuclear magnetic m~lent of' 93 0s has bees determined experimentally ~, no conclusions on the shape of ' 9 'Os can be drawn from this experiment because of the unsensitivity of magnetic moments on the nuclear shape. The knowledge ofnuclear quadrupole moments, however, which are strongly depenat

42

H . ERNST et al .

dent on the nuclear shape, together with the data for the well-deformed isotopes, unambiguously yields the information about structural changes. This is the main reason why we have measured the ground state quadrupole moments of ' 9'Os ~~ = i - ; T.t = 15d) and 193OS V~ = i- ; T# = 31 h). The low-temperature nuclear orientation technique (NO) has become a standard method for the determination of the ground-state nuclear magnetic-dipole moments of radioactive nuclei . The application of this method to the measurement of nuclear electric-quadrupole moments, however, is in an initial state; only few experiments have been performed up to now'°- ' 6). This is mainly due to the fact that lower temperatures are necessary to get a considerable nuclear alignment as the typical quadrupole splittings in hexagonal metals, which provide the necessary electric field gradients, are smaller than typical magnetic splittings obtainable in ferromagnetic materials. Moreover, single crystals have to be used to establish a unique quantization direction with respect to which the nuclear alignment is observed via the anisotropy of the emitted y-radiation. To obtain the necessary low temperatures of T < 10 mK several techniques are being applied presently, the ordinary adiabatic demagnetization of paramagnetic salts, 'He-4He dilption refrigeration, and the rather new hyperfne enhanced nuclear cooling "). The lowest temperatures are obtained with the latter method. Using the van Vleck paramagnetic compounds PrCu6 or PrNi s as cooling materials temperatures below 1 mK have been reached' e). As the cooling capacity is also considerably high (in comparison ~to that of a "pure" nuclear demagnetization device) the hyperfine enhanced nuclear cooling technique is well suited for quadrupole nuclear orientation measurements. We have used PrCu6 in a two-stage demagnetization cryostat to cool sources of 1910sOs and 193 0sOs to temperatures of ~ 4 mK . Our measurements have shown that Os single crystals are well suited for quadrupole NO experiments because of their good low-temperature thermal and mechanical properties, and because of the relatively large electric field gradient. From Raghavan's universal correlation' ~ one can conclude that the electric field gradients of the neighboured elements as impurities in Os have similar values as that of the pure system . Thus, with the use of charged particle reactions as (d, xn), (a, xn), or (HI, xn) a wide field is opened for the determination of the ground state quadrupole moments of neutron deficient radioactive isotopes in the region Os-Pb. 2. Nuclear orientation In the presence of an axially symmetric electric field gradient eq the energy E~, of the m-substete of a nucleus with spin j is given by

where Q is the spectroscopic nuclear quadrupole momnat. For convenience the

QUADRUPOLE MOMENTS OF 'v' .'9aOs

43

quadrupole interaction frequency vQ is introduced which is defined as vQ = Q24Qlh. (2) For thermal equilibrium, the population probability a~, of the m-substate at a temperature T is given by the Boltzmann distribution a~, = exp (-E,~/kT)/ ~ exp ( -E~,,/kT) .

(3)

A reasonable population difference is obtained if the temperature is so low that hvQlkT ~ 1 is fulfilled. The angular distribution of y-rays emitted in the decay of oriented radioactive nuclei is most conveniently written as s°)

The different coefficients have the following meaning: The Bk describe the degree of orientation of the initial nuclear state. The connection with the a~, of eq. (3) is given by

They depend on the value ofj and on vQ/T. The Fk are the usual angular correlation coefficients, they depend on the spins between which the observed y-transition occurs, the multipolarity ofthe transition, and on the mixing ratio of different multipolarities if the y-transition is not pure. The Uk take into account the de-orientation effect of preceding unobserved y- and ß-transitions. They depend on the involved spins, multipolarities, and also on the mixing ratios of different multipolarities. In the case of a preceding ß-decay, the corresponding tensor rank and the mixing ratio of different tensor ranks, ifthe ß-decay is not pure, has to be taken. Tables ofthe most commonly needed Uk and Fk coefficients are given in ref. Z1). The Pk (cos B) in formula (4) are Legendre polynomials, 8 being the angle between the orientation axis, i.e. the direction of the electric field gradient, which coincides in the Os case with the c-axis of the crystal, and the observation direction of the yrays. The Qk coeffcients are dependent on the experimental set-up, as they take into account the solid angle of the detectors. The sum in eq. (4) runs on even k only, the maximum value of k being fixed by the spins and multipolarities which are involved in the decay cascade. In most cases, no higher terms than k = 4 are present, the k = 4 term being substantially smaller than the k = 2 term, normally. There are some special features in the context with quadrupole NO which will be outlined shortly. While the B2 term starts with (hv~,/kT) 2 in the case of magnetic interaction, it is proportional to hvQ/kT in the quadrupole case, i.e.

44

H. ERNST et al.

where c is a positive constant which is feed by the spin value. It has the decisive consequence that the sign of the y-anisotropy depends on the sign of vQ directly . This means that the sign of the quadrupole splitting can be determined unambiguously from a NO experiment. The linear dependence of W(B) on 1/T is a good approximation in a rather large temperature range, the slope being dependent on the quadrupole frequency vQ and on the specific properties of the decay cascade via the U2 and FZ coeflïcients. This means, that, in the case of y-transitions with mixed multipolarities, vQ and 8 cannot be determined simultaneously. This would be possible if one could extend the measurements to such low temperatures (T < 1 mK) that the anisotropy gets saturated, which, however, is not possible at the present state of low temperature technology . Thus, only y-transitions with pure multipolarity, or such y-transitions for which b is known with good accuracy, can be used for a precise determination of vQ. Generally, this is no restriction, as most decay cascades of radioactive nuclei have been investigated with y-y angular correlation or "standard" nuclear orientation, from which the necessary data on the mixing of different tensor ranks of the preceding ß-decays can also be taken. In order to get rid of several disturbing effects, such as the decrease ofthe counting rate due to the (mite half-life of the parent nuclear state, the anisotropy is measured at 0° and 90° with respect to the orientation axis. The quantity e

_ W(0) -1, W(90)

which is usually called the anisotropy, too, is then used for the further analysis . 3. Nuclear gaadrupde relaxation The applicability of eq . (4) for the y-anisotropy of oriented nuclei is based on the assumption that the impurity nuclei are in thermal equilibrium with the host lattice, i.e, that the corresponding spin temperature T, is equal to the lattice temperature TL. This assumption is not necessarily fulfilled, especially in the case of quadrupole interactions, where the nuclear spin-lattice relaxation times can become rather long at low temperatures . Therefore the consequences of the spin-lattice relaxation on the y-anisotropy will be discussed in subsect. 3.1 . For the interpretation of the yanisotropy of oriented 1910s a further complication exists, namely a possible reorientation in the 49 sec isomeric state i9imlr which is populated in the decay of i9iOs . These aspects will be discussed in subsect . 3.2. 3.1 . RELAXATION-DISTURBED NUCLEAR ORIENTATION

For the case of magn~ic hyperfine interaction, the theoretical description otr relaxation has been worked out in detail by Bacon et al. zs) . We will follow this

QUADRUPOLE MOMENTS OF `9` . "'Os

45

treatment, with the necessary modifications due to quadrupole interaction. The starting point is the master equation R

Here a~, is the time-dependent sub-level population ofstate gym) and W~ is the transition probability from state gym) to state fin). For relaxation processes with tensor rank 1 WM can be written as ZZ . z3) :

The strength of the relaxation is described by the reduced matrix element B. The E~, are the sublevel energies given by eq. (1) and T is the temperature of the host lattice. The stationary solution of eq. (8) is the Boltzmann distribution given by eq. (3). After a jump of temperature from T,, to TB the time dependence of the am is given by

The constants C,~,, and ~,, are calculated by diagonalizing the matrix of eq. (8), they are faced by the final temperature TB and the relaxation parameter B. The a,~(0) are the sublevel populations before the temperature change . The time dependence of the y-anisotropy is then given by

The constants co,(9) are calculated using eqs. (4), (S), and (10). The anisotropy ~ for a measurement interval dt is given by integration : dt)

r+er

- ér ,~

d~~

(12)

It is found that in most cases the anisotropy relaxation can be described in a fairly good approximation by an exponential relaxation with one time constant Ti (13) This time constant T~ can easily be observed in the experiment by measuring the time evolution of the y-anisotropy after a change of the temperature. Thecomparison of Tl' with typical time constants of the experiment (cooling-down timq warm-up

46

H. ERNST et al.

time) yields the information whether relaxation effects have to be included for the analysis of the anisotropy data 3.2 . RELAXATION-REORIENTATION IN THE INTERMEDIATE STATE "'°Ir

The relatively simple decay of t9t Os to levels in t9t Ir is illustrated in fig. 1 . The i_ -. ~- ß-decay is allowed; thus the tensor rank is fixed to L = 1 . No y-rays can be seen from the highly converted 42 keV E3 transition. The 129 keV E2/M1 transition is the only strong y-transition in this decay. As the E2/M 1 mixing ratio S strongly influences the magnitude ofthe y-anisotropy, an accurate value for 8 is necessary for

11/2 5/2' 1 /2'

191 77~ rlli Fig. 1 . Simplified decay scheme of '9 'Os.

3 /2'

Tna~ 1 Previously measured values of the 129 keV E2/M 1 mixing ratio Methad')

Value

Ref.

NO eME eeME eCE e average °)

-0 .28 f 0.06 0.395 f 0.015 -0 .36 ±ô:ôi 0.39 f0.02 0.39 f0.02 -0.398 ~0.020 0.37 f0.03 -0.46 f0.04 0.402 f0.005 -0.399 f0.004

za)

zs)

]6)

z~ ) :e )

29) 30) 3~) 32)

') NO : nuclear orientation; e- : Conversion coefficient; ME : MBBbauer-etFect; CE : Coulomb excitation . °) The NO value has been omitted for the calculation of the average because of a possibly incomplete reorientation of'9'°IrFe which influences the magnitude of the y-anisotropy . Taking not into account this effect the smaller y-anisotropy has to be described by a too small a.

QUADRUPOLE MOMENTS OF ' ° '~' 9 ~Os

47

a precise determination of the orientation of the levels preceding this transition . Table 1 lists the previously measured values of S, along with the average value taken for the present work. There is, however, a fundamental problem connected with the interpretation of the 129 keV y-ray anisotropy : Without the knowledge of the spinlattice relaxation time it cannot be anticipated a priori which state determines the degree of orientation. This is due to the relatively long lifetime of 4.9 sec of the 171 keV intermediate state 191mIr, during which a reorientation may take place. Immediately after the ß-decay the spin system is not iri thermal equilibrium with the lattice because of the different hyperfine splittings of ' 91 Os_Os and ' 91 mIrOs. This can be interpreted as a sudden change of the spin temperature, after which the system triestoreach the thermal equilibrium, the anisotropy relaxation beingdescribed by eq. (13). To discuss how the y-anisotropy of the 129 keV transition is determined the anisotropy relaxation time Ti has to be compared with the lifetime~z(~) of the state. There are three different possibilities which are discussed separately . (a) Ti ~ z(i): In this case no reorientation takes place in the intermediate state. The y-anisotropy is fixed by the orientation of the parent nuclear state, i.e, the quadrupole splitting of 1910~s can be determined. (b) Ti ~ z(~-) : A complete reorientation in the ~- state is expected according to the corresponding quadrupole splitting. The information on the quadrupole splitting of the parent state is lost completely . Thus it is vQ(191°'IrOs) which can be determined from the y-ray anisotropy . (c) Ti x z(~): The anisotropy is a function of vQ( 1910s_Os), vQ(191°'IrOs), and of Ti. It is expected that the interpretation of the y-anisotropy is complicated in this case. To find out which of these three possibilities is actually present Ti has to be determined experimentally . This caa be done by observing the time evolution of e(129) after a d~nite change of the lattice temperature. 4. Experimental detaüs The sample was prepared in the following way: From an osmium single aystal rod (purity > 99.99 ~) a disc of ~ 5 mm diameter and a thickness of ~ 0.4 mm was cut, the o-axis being oriented perpendicular to the disc plane. This disc was mechanically polished until a thickness of N 80 pm was reached. Attempts to make essentiâlly thinner samples were not successful as Os crystals are rather brittle. The sample was irradiated at the Munich research reactor FRM for a minute in a neutron flux of ~ = 8 x 10 1 ~ n/cm 2 sec to produce the radioactive isotopes 1910s (T~ = 15 d; ~~` _ ~-) and 1930s (T# = 31 h; ~~ _ ~-). After the irradiation the sample was annealed for ~ 1 h at a temperature of ~ 2300 °C under vacuum with a pressure of 10-' Torr . Special care was taken in slowly cooling down to room temperature. Hoth sides of the crystal were polished again, and then immediately wetted ultrasonically with Ga-In. The sample was then soldered to one side of the cold forger

48

H . ERNST et al.

worklnp salt for adiabatic dernapnetlzatbn ( Cr K alum )

radiation shield superconductlnp thermal switch

PrCu b Fig. 2. Main part of the two-stage demagnetization assembly . The second stage works on the basis of hyperFme enhanced nuclear cooling of the van Vleck paramagnetic compound PrCub . Final temperatures of 2 . . . . 3 mK caa be obtained with weak radioactive sources .

of the cryostat. For thermometry a e °CoNi foil was soldered to the other side of the

cold finger . A second thermometer, s'CoNi, was soldered to the outer side of the Os crystal. Such an arrangement is necessary, since a good thermal contact between theOs crystal and thecold forger is one of the necessary requirements in these experiments, and this can be checked via the temperature comparison of both thamo-

QUADRUPOLE MOMENTS OF iei . i9'Os

49

meters. That such precautions are actually necessary can be seen from the fact that in similar experiments with a Lu single crystal large temperature deviations between the cold finger and the sample have been observed tb). The sources, which had activities of 4 pC t 9'Os, 12 pC t930s, IS ~C s'Co, and 5 ~C e°Co, were cooled to temperatures as low as ~ 4 mK with a two-stage demagnetization cryostat, the lower part of which is shown schematically in fig. 2. Details ofthe cryostat are given in ref. ss). The first stage operates with CrK-alum as cooling salt and reaches a final temperature of ~ 12 mK . The second stage works on the basis of hyperfine enhanced nuclear cooling. The two stages are connected via a superconducting thermal switch . With the van Vleck paramagnetic compound PrCu 6 as cooling material temperatures of 2-3 mK have been obtained with weak radioactive sources. In this experiment a final temperature of ~ 4 mK was reached. A small external magnetic field of 4.5 kG, which is provided by superconducting split coils, was applied in order to orient the ferromagnetic domains and thus to establish a unique direction of the hyperfine field of the thermometer foils. Because of the demagnetization factor this field has to be applied parallel to the foil plane . Thus, the direction of the electric field gradient was perpendicular to the direction of the hyperfine field. For the y-ray detection two coaxial Ge(Li) detectors were used which were placed at 0° and 90° with respect to the direction of the external magnetic field. During the warm-up of the cryostat from 4 to 30 mK y-ray spectra were accumulated in a 2 x 4 K multichannel analyzer which was controlled by a PDP 8E computer. Every 1000 seconds the spectra were recorded onto magnetic tape . For normalization "warm" spectra were measured at He temperature before and after each cooling run. The low-energy part (E < 600 keV) of such a spectrum measured at 0° is illustrated in fig. 3. The final analysis of the data was performed with the PDP 10 computer of

CHANNEL NUMBER Fig. 3 . Low-eaergy part of a y-ray apednim measured at 0° with reapax to the direction of the eatanal magnetic t'idd .

H . ERNST et al.

50

the Munich accelerator laboratory. The peak intensities were determined by least squares fitting routines under the assumption of Gaussian line shape and a linear background. The anisotropies which were calculated according to eq. (7) were then used for further analysis. 250 200

ample

i

Temperature comparison

arrangement

,~~

-

~

~cos ;

150F

0 ' ~, 0

Os crystal

50

100

150

200

250

1/T (K - ~), g ~CoNi Fig . 4 . Taperature comparison of the two thermometers used to determine the overall temperature of the Os crystal . The experimental arrangement is shown in the inset . No temperature gradient is observed, even at the lowest temperatures of ~ 4 mK .

The teatperatures were determined from the anisotropies of the Co isotopes . Fig. 4 shows the reciprocal tanperature 1/T at the surface of the Os crystal, determined from the anisotropy of the 122 keV and 136 keV y-rays of s 'Co, versus 1/T of the cold finger which was determined from the anisotropy of the 1 .17 MeV and 1 .33 MeV y-rays of 6 °Co. The dashed line represents the ideal case, i.e. that both temperatures are equal. No significant deviations of the measured points from the ideal curve can be seen. For the further analysis the temperature of the e°Co theimometer was useä. 5. Reeolta 5 .1 . t"OsOs

Fig. 5 shows the time evolution of the 129 keV y-ray anisotropy after the demagnetization, together with 1/T of both thermometers. The time interval between two successive points is 1000 seconds, the accumulation period for one spectrum . The cad of the demagnetization step is marked with an arrow. It is obvious that e(129) rises more slowly than the 1/T values. T3~at this is not due to a slow cooling-

QUADRUPOLE MOMENTS OF '9' .'q'Os

51

Fig. 5. Time evolution of the y-anisotropies after the demagnetization of the second stage (PcCub). No time Iag is observed between the two thermometers . The anisotropy of the 129 keV y-ray of "'Os is clearly "delayed" which is ascribod to a spin-lattice relaxation time of'9'Os0_s which is of the order of the measurement intervals of 1000 sx.

down of the Os crystal because of its large specific heat can be seen from the fact that no delay between the 1/T values of the two thermometers is observed . As the proportionality e(129) ~ 1/T is expected to be fulfilled in a fairly good approximation the time lag of e(129) must be ascribed to relaxation erects, the corresponding time . constant Ti being of the order of 1000 seconds. Correctly, we should have taken into account the relaxation times of the thermometers, too. This has the consequearce that the estimated anisotropy relaxation time of the 129 keV transition is actually even longer. As this relaxation time Ti is of the same order of magnitude for Os_Os and Ir_Os [ref. 34)] we can conclude that the condition Ti ~ ~(~) is fulfilled. There is no relaxation-reorientation in the ~- state, and it is vQ (t 9t OsOs) which we can determine from the y-anisotropy of the 129 keV transition. To find out whether relaxation effects of the parent state ' 9' Os have to be taken into account, T~ has to be compared with the cooling-down time and the warm-up time of the cryostat. Fig. 5 shows that immediately after the demagnetization the system is clearly not in thermal equilibrium because of the largejump of temperature from T ~ 20 mK to T ~ 4 mK in a time interval of ~ 300 seconds. The temperature increase, however, takes plane during a time interval which is long in comparison to T~. The existence of thermal equilibrium is thus a fairly good approximation for the interpretation of the y-anisotropies which have bees measured during the watmup of the cryostat . Moreover, T~ is expected to become shorter at higher tempera-

52

H. ERNST et a!.

Fig. 6. Gamma anisotropy of the 129 keV y-transition of' 9 'Os versus reciprocal temperature.

tores. Fig. 6 shows s(129) versus 1/T, the solid line being the result of a least-squares fit, which yields vQ( t9 'OsOs) _ - (2 85±i2) MHz. The asymmetric error has been estimated in such a way that the uncertainty in the temperature assignment due to relaxation effects is included . The spin-lattice relaxation can be taken into account if the time dependence of the y-anisotropy is analyzed as described in subsect. 3.1 . The solid line in fig. 5 is obtained by a least-squares fit utilizing eqs . (8}{12) which yields vQ = - 278 f 9 MHz for the quadrupole . . slitting and B = (2 .6 t 1 .2) x 10-' Z for the parameter which describes the strength of the spin-lattice relaxation. There is some uncertainty in the theoretical description of the relaxation process because of the confinement to tensor rank 1 in eq. (9). As the corresponding uncertainty in vQ is expected to be significantly smaller than the quoted error, vQ(t9t OsOs) _ -278 f 9 MHz is adopted as final result . 5.2 . 19308

A simplified decay schane of t 930s is illustrated in fig. 7. As the ground state spin is i, only k = 2 terms are present in the anisotropy formula (4). Unfortunately, there is no y-transition for which all nuclear parameters of the decay cascade are known with good accuracy. Krane and Steyert ~ have performed a NO experiment on t930sFe. They have measured the anisotropies of 20 y-transitions at the constant temperature T = 192 f02 mK. Although they can determine the quantities UZF2B2 with good accuracy, large errors come in when doing the separation in U2FZ and

QUADRUPOLE MOMENTS OF _3l .5 h 19 76 5 117

'9`. '93 0s

53

2 1/2'

8

3/ I'

2 12

3/ 2' 5/ 2' 1/2`

19 5i 193 r 77I 116

3/2`

Fig. 7. Simplified decay scheme of ' 9'Os.

This is mostly due to the fact that there is a considerable mixing of different tensor ranks of the forbidden ß-transitions, and that the y-mixing ratios are not well known, too. This situation would be improved significantly, if the NO experiments on ` 930sFe would be extended to such low temperatures where the anisotropy gets saturated, as the UZFZ can they be determined directly from the saturation value of the anisotropy. Such an experiment is planned, but at the present state we have to use the U ZFZ values ofKrane and Steyert 9) for the interpretation ofour quadrupole data. We have analyzed the anisotropies of two strong transitions, namely those at 460 keV and 387 keV . The results are shown in figs. 8 and 9. The expected anisotropy can be expanded in powers of hvQfkT, the result, which is correct up to the quadratic term, is given by z ~Z~UzFZVQ)z e = ~~z~UzFzvQ) ' ~8) T + 4kZ_ Tz BZ.

where Bz is the saturation value of BZ. This shows that it is the product UZFzvQ which can be determined from our measur~eats. The least squares fit yields UZ FzvQ = 8S t 1.3 MHz for the 460 keV transition and UZFzvQ = 16.2 f 2b MHz

54

H. ERNST et a1. Q05

193~~ 460 keV

0 .04

,^ 0 .03 0

3

ô 3

0 .02

V

0.01

100 200 1/T (K -~)

Fig. 8. Gamma anisotropy of the 460 keV y-transition of ' 9 'Os versus reciprocal temperature .

for the 387 keV transition . No corrections for spin-lattice relaxation have been made as these would be small in comparison to the experimental uncertainty. Taking the U Z FZ values from ref. 9) the quadrupole frequency is deduced to be -109 (24) MHz and -87 (20) MHz, respectively. The mean value vQ = -96±15 MHz is adopted as final result. 6. Quadrupole moments of Os isotopes and field gradient of Oslps In order to deduce the quadrupole moments from our measured quadrupole frequencies, a value for the electric field gradient of Os_Os has to be available. It is obtained in the following way: Ernst et al. 3s) have determined the quadrupole frequency for the first 2+ state of' 860s in Os with a MöBbauer effect measurement as 179 f9 MHz. Hcehn et al . 3) have studied the X-ray spectra of muonic iae .ise" i9o.iv20s. With the use of model independent methods, they derive precise values for the quadrupole moments of the first excited 2+ states . These are listed in column 4 of table 2. Wagner et al. t) have performed MöBbauer-el%ct measureanents on the 2+ states of iae.tea " i9oOs and on the i_ ground state and the i- state at 69S keV of '890s. The quadrupole splittings which they found for Os compounds with a large 6e1d gradient, namely OsPz and OsO~, are listed in columns 5~. oftable 2. A least squares fit to the muonic data and the Mößbauer-ef%ct data yields more precise values for the'a 6 " tea" ie9" t 9oOs quadrupole moments, which are listed in

QUADRUPOLE MOMENTS OF

55

'91 " 193OS

Fig. 9. Gamma anisotropy of the 387 keV y-transition of' 930s versus reciprocal temperature.

column 7 of table 2. It should be noted, that the more precise value for the ground state quadrupole moment of'e 90s is obtained as a byproduct : Q~_(ta9ps) _ +0 .86t0.02 b. This is now in good agreement with the value of Himme1 36), who found Q = 091 f 0.10 b from optical hyperfine structure measurements. Taking the ratio t) Q~-('B 90s, 69 keV)/Q~-( te90s, g.s.) _ -0.735 f0.012, a more precise value for the i_ state of ta 90s is obtained : Q~_(te 90s) _ -0.63 f0.02 b. TAHIE

2

Results of a least-squares-fit

I' isb~

is°~

ie9~ i 90~ i9sOs

2+ 2+ }-

2+ 2+

E [keV] 137.2 155.0 g.s. 186.9 205.8

Q [b] Hoehn et al. a) -1 .65(4) -1 .47(4) -1 .18(3) -0 .99(3)

vQ [MHz] Wagner et al.') CsP=

OsO z

-1624(18) -1465(25) + 859(11) -1266(60)

+828(13) + 765(25) -446(9)

Q [b] average value -1 .63(3) -1 .47(3) +0 .86(2) -1 .20(3) -0 .99(3)

Combiningthe data of Haehn'et nl.') and Wagner et al .'), for' ° 90s a °ignificantly mare precisevalue is obtained.

56

H. ERNST et aJ.

With Q z " ( taeOs) _ -1.63±0.03 b and vQ(' 860sOs) = 179f9 MHz the electric field gradient of Os in Os is found to be which can now be used for the interpretation of our measurements . We fend for the ~- ground state of ' 9' Os and Q~_(1930s) _

+0.87 f 0.15 b

for the i- ground state of ' 930s % . D18CI1~0~

A comparison of experimental results for the spectroscopic quadrupole moments with values calculated on the basis of different theories may yield interesting information on the validity or breakdown of the different models in the transition region from deformed to spherical nuclei. In table 3 we present a summary of experimentally known quadrupole moments in the Os isotopes, together with the values predicted in the frame of the pairing-plus-quadrupole model (PPQ) a' s), the dynamic collective model (DCM) 6), the extended variable moment of inertia model (VMI)'), and the modified oscillator model (MOM) s). Teal,e 3

Quadrupole moments of Os isotopes Nucleus ~ s°Os ~e~~ ies~

is90s i9o~ ~9i~

iezO s i9sO s

` j

E[keV]

2*

Q [b] Theory

Experiment Q Cb]

Qo Cbl

PPQ ~)

DCM ~)

137.2

-1 .63(3)')

-1 .86

2*

155.0

-1 .47(3) ')

5.63(3) °) 4.7 (4) °) 5 .34(3) °)

}2*

69 .5 186.9 g.s. 205.8

-0 .63(2) b) -1 .20(3) ') +2 .53(16) °) -0 .99(3)')

2*

VMI

h)

MOM')

-1 .49

-1 .56

- 1 .71

-1 .53

-1 .29

- l .38

4.99(3) °)

-1 :18

-0 .38

-1 .13

4 .59(3) °)

-0.47

-0 .09

-0 .84

-1 .59 + 1 .05 -0 .37 -1 .35 +2 .50 -1 .27 +0 .83

') See table2. ") Calculated with Qa~s of table 2 and the ratio Qs~zlQan = -0.73510.012 of Wagrler et a1 . '). °) This work. °) Calculated with Qo = 4[s1rB(E2; 0 ~ 2*)]i~z from the experimental B(E2) values of ref.'); the ""rotational" Q= . quadrupole moments are then Riven by Qâ " _ -+jQo . ') Rd. a') . ~) Ref. °) . ~ Ref. 8). `) Calculated from experimental B(E2)'s') and the asymmdry paramders y from') . ') Calculated from Qo values of rd. s) under the aasumptioa of the validity of therotational model.

QUADRUPOLE MOMENTS OF '9' .'9aOs

57

A direct comparison ofthe spectroscopic quadrupole moment(SQM) is meaningful only for nuclear states with the same spin . The comparison can be extended to states with different spins, if the intrinsic quadrupole moments (IQM) Qo are used. In the frame of the rotational model the connection between Q and Qo is given by Q

-

Q°

3K2 -J(!+1) (j+lX2j+3)

(14)

For states with K = j eq. (14) reduces to 1(2~-1) Q = QoU+lX2j+3)

(15)

The top part of fig. 10 shows the behaviour of Qz " versus the mass number A (full circles). The triangles in fig. 10 represent the so-called rotational quadrupole moments Qi" which are connected with the B(E2) value via the relation QZ " _ -~{~B(E2 ; 0+ ~ 2 +)]#. The scale on the right-hand side is valid for the corrosponding Qo which is given by -3 .5 Q2 " according to eq. (14). It is obvious that the Qo which are calculated from Qi " represent an upper limit for the actual IQM, and that these values should be used for comparison with the odd-A data. It is evident from fig. 10 that all models overestimate the deviation from the rotational model with increasing A. This can be understood as theminimum ofthe calculated potential energy function, from which the deformation parameters are determined, becomes rather smooth for the heavier Os isotopes. The bottom part of fig. 10 shows the Qo which have been determined for the odd Os isotopes according to eq. (15) . The value for'e'Os has been taken from ref. "). At a first view the behaviour seems to be dit%rent from that of the eves isotopes. We will show, however, that this can be explained by Coriolis mixing, and that no significant even-odd staggering exists. Because of its high spin value, the i- [505] ground state of 19`Os is expected to be rather pure, as the states which could be admixed by~ the Coriolis interaction, have considerably high excitation energies. Thus its Qo value is more representative than those of 'a~ . ie9, i9sOs which are deduced Gom low-spin states, for which the Coriolis mixing can play an essential role. Fig. 10 shows that Qo (1910 s) fits exactly into the trend of the eves A isotopes. The ground state quadrupole moment of 890scan be explained ifa K = i admixture to the ground state is taken into account:

Taking Qo = 52 ~ which is obtained by an interpolation between iesOs and 19°Os, a2 ~ 0.1 has to be assumed. The quadrupole moment of the 69 keV ~- state of 'B90s provides further information on Coriolis mixing. The assumption of a pure

H . ERNST et al .

58

186

188 190 mass number

192

194

Fig. 10. Quadrupole moments of even (top) and odd (bottom) Os isotopes . The circles represent the experimental 2 + quadrupole moments (top, left scale), the triangles are intrinsic quadrupole moments deduced from experimental B(E2) values (top, right scale) . The squares represent intrinsic quadrupole moments which have been deduced under the assumption of pure configurations in the frame of the rotational model . Thecurves denoted with PPQ, DCM, VMI, and MOM show the predictions of different theoretical models (see text) .

[512] configuration for this state would imply Qo = 8.9 b, which is rather unrealistic. With the wave function ~- z

and Qo = 5 .2 b, a K = i admixture with a2 ~ 0.3 has to be assumed to reproduce the experimental value. No significant K = ~ admixture can be present because of the negative sign of Q,t - . This can be seen from table 4, which shows Q,t- for the dif%rent possible confïgurations. A similar situation holds for 1930s, but the relatively large experimental uncertainty of Q does not allow the prediction of details for the ground state wave function .

QUADRUPOLE MOMENTS OF '9'.'q'Os

59

Teams 4

Quadrupole moments of the }" ground state and the 69 keV }- excited state of's 90s fordifferent Nilsson configurations under the assumption of Qu = 5 .2 b j`

Configuration ~`K)

Q [b]

l .oa

I~ ~> I~ - }> 0.961~-~>+o .z91~ - }>

-1 .04 0.86

I~ ~> I~ }> I~ - ~> 0.881 }-}~+0.481 }- }~

-0 .37 - I .48 + 1 .85 -0 .63

Q~,P [b] ~.

-0.63

Thus we can conclude that the Os nuclei between A = 186 and A = 193 follow well the trend of a slightly decreasing deformation with increasing mass number. There is no evidence for a significant change of the nuclear shapes in this mass region. The authors want to thank Prof. E. Buches, J. Hufnagl, and the Deutsche Forschungsgemeinschaft for the preparation of the Os _crystal . This work , was supported by the Bundesministerium für Forschung und Technologie. Refere~es 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20)

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