1. Introduction The transient magnetic fields which act

r- 19

Hyperfine Interactions oo.(l9~ 387-399 © North-Holland Publishing Company

THE VELOCITY AND Z DEPENDENCE OF THE TRANSIENT

MAGNETIC FIELD IN IRON

J.L. EBERHARDT

*

Institute of Physics, University ofAarhus, DK-8000 .frhus C Denmark and Hahn Meitner Institut fur Kernforschung GmbH, D-l 000 Berlin 39. W. Germany

K.DYBDAL Institute of Physics, University ofAarhus, DK-8000 .frhus C Denmark

Received 7 February 1979

The velocity dependence of the transient magnetic field in iron has been investigated for 13 4 Ba at four initial velocities between Vi = 0.8vo and Vi = 3.6vQ (vQ = c/137). The present work confirms the linear v-dependence found for light ions (Z .;; 34). Existing data on transient fields were reanalyzed assuming a general validity of the linear v-depend· ence. The extracted Z-dependence shows a smooth, almost linear Z-dependence for ions with Z ;;. 12. From the present work, with the calibration of the transient field from syste­ matics, the g·factor of the first excited 2+ state in 134Ba is determined to be g = 0.41 (6).

1. Introduction The transient magnetic fields which act on nuclei moving in a magnetized ferro­ magnetic material have been utilized for g-factor measurements of short-lived exci­ ted nuclear states [1-4]. In the interpretation, the magnitude of the transient field was estimated from the adjusted Lindhard-Winther theory (ALW) [2,3,5]. In the last few years it has become increasingly evident from numerous experiments for light ions (6 .;;; Z';;; 26) recoiling into Fe that the transient field in many cases con­ siderably exceeds the ALW prediction [6-19] and follows a linear velocity depen­ dence, in contrast to the 1Iv dependence of the LW theory. The large fields were suggested [12] to arise from polarized half empty Is and 2s electron shells in the moving ion and such a model was shown to provide a qualitative understanding of measured transient field precessions. Since there is little hope that a microscopic model as proposed in [12] can explain quantitatively the transient field for heavy ion systems with many electrons it was decided to concentrate on the empirical relation suggested in [12] and investigate its validity in the heavier ion region.

* Present address:

Husarviigen 1G, S-23050 Bjiirred, Sweden. 387

388

I.I. Eberhardt, K. Dybdal / Transient magnetic field in Fe

So far very few data exist on the velocity dependence of the transient field for ions with Z > 26. In an early measurement for 196pt in Fe [20] an enhancement of the transient field over the ALW prediction was observed at an ion velocity of vi/vo = 2.3. Recent experiments on 82Se [21] in Fe and s6Fe [22], 82Se [21], and IS4,IS6,IS8, 160Gd [23] in Gd show velocity dependences which agree well with the prediction of the empirical relation. In the present work the velocity dependence of the transient field has been investigated for 134Ba recoiling into polarized Fe at four initial velocities between Vi = 0.8vo and 3.6vo. The first excited 2+ state of 134Ba is well suited for a transient field experiment since its mean life (T m = 7 ps) is short enough to ensure the integral precession due to the static magnetic field of B s = -7 .9( 1.4) T (see subsect. 3 and ref. [24]) to be small compared to the transient field contribution. The velocity dependence of the measured time-integral precession angles is found to be compa­ tible with a transient field being linear in v. Assuming a general validity of the linear velocity-dependence existing data on transient fields for ions with 6 ..;; Z..;; 80 have been reanalyzed (subsect. 4). The Z­ dependence obtained in this way enables a determination of the g-factor of the 2+ state in 134Ba (subsect. 5). 2. Experimental procedure Beams of 12C and 160 ions from the Aarhus 6 MV EN tandem Van de Graaff accelerator and 32S ions from the Niels Bohr Institute's 9 MV FN tandem Van de Graaff accelerator at energies of 30,45 and 80 MeV, respectively, were used to Coulomb excite 134Ba to the first excited J" = 2+ state at 0.605 MeV and subse­ quently implant the recoiling ions into Fe with velocities of vi/vo = 1.5, 2. I and 3.6, respectively. In a fourth experiment, ions recoiling after bombardment with 30 MeV 12C ions were slowed down in a 680 f.1g/cm2 thick copper moderator before entering the Fe backing. In a separate experiment on a target without Fe backing the exit energy from the moderator and the energy spread were determined to be E R = 2.2 ± 1.4 MeV (vi/vo = 0.8 ± 0.3) by detecting Ba ions in a solid state detector 0 at 21 with respect to the beam axis in coincidence with elastically scattered 12C particles at 225 0 • The 12C energy was chosen to give the same recoil energy as in the actual transient field experiment with a backscatter geometry. In all experiments the targets consisted of 300 f.1g/cm 2 BaCI 2, enriched to 86.2% in 134Ba, covered with 100-300 f.1g/cm2 Pb to prevent recrystallization of the hygroscopic target material. As a ferromagnetic backing a polycrystalline 1 mm thick iron window frame was used in the two intermediate velocity experiments, whereas in the high and low velocity experiments conventional 5 f.1m thick Fe foils * were used, magnetized ,. Manufactured by Goodfellow Metals Ltd.

p

p-

J.L. Eberhardt, K. Dybdal / Transient magnetic field in Fe

389

by the 0.1 T field of an external magnet. The properties of the window frames are described elsewhere [18]. At only 210 A turns, 72 ± 7% of full magnetization was reached for the frame used and stray fields, which give rise to beam bending effects were essentially zero. The experimental method is described in detail in refs. [3,4]. The time integral spin precession is determined from the change in 'Y-ray yield at a sensitive angle upon reversing (typically every minute) the magnetization direction of the Fe backings. In the three experiments performed in Aarhus 'Y·rays in coincidence with back­ scattered particles were detected in four gain stabilized 7.6 cm long by 7.6 cm diam NaI(Tl) detectors at ±69° and ±lll 0 with respect to the beam direction and 0 at a distance of 11 cm from the target. A 70 cm 3 Ge(Li) detector at 20 monitored the target condition and the occurrence of possible contaminating 'Y-ray lines which might not be resolved in the NaI(T!) spectrum. In the experiment at the Niels Bohr Institute two 60 cm 3 Ge(Li) detectors placed at ±11O° and at a distance of 6 cm from the target were used.

3. Results A summary of the measured effects and precessions, corrected for a precession due to the static hyperfine field of 4>5 = 0.90 ± 0.15 mrad (see below), is given in table 1. Where necessary (see subsect. 2) the data were corrected for small beam·

Table 1

Summary of measured integral transient field precessions tPt.f. for 134Ba(2i)

Bombarding E a) particle (MeV) 12C d) 12C 16 0 16 0

32S

,

".

30.2 30.2 36.0 45.4 80.0

(MeV) 2.2 ± 1.4 7.4 12.1 14.7 43.6

€

-

1 c)

€

+

1

(%)

0.8 ± 0.3 1.5 1.9 2.1 3.6

dW(IJ) _1_ dlJ W(IJ)

-tPtf = -t.1J + tPs

(rad- 1)

(mrad)

0.8(0.3) 3.41 2.9(0.5) g) 3.41 4.7(0.8) g) 3.43 10.3(1.0) 3.58

a) Bombarding energy. b) Vo = c/ 137. the Bohr velocity. c) For definition of € see text. d) Experiment with moderator between target and Fe backing. e) Recoil energy and velocity when entering the Fe backing. f) Corrected for 'Y·decay in the moderator. g) Corrected for incomplete magnetization of Fe frame (see subsect. 2). h) Result of ref. (24).

3.6(1.0) f) 9.3(1.5) 14.7(0.9) h) 14.8(2.3) 30(3)

J.L. Eberhardt, K. Dybdal / Transient magnetic field in Fe

390

bending and beam shift effects, calculated from the known stray field distribution between particle detector and target. An earlier experiment [24] on even Ba isotopes was reanalyzed with a lin.:ar velocity dependence for the transient field, taking into account decay in flight and small differences in the recoil energies of the different isotopes. The latter cor­ rection is negligible in the LW approach. The result for the transient field is also displayed in table 1 and the Larmor frequency due to the static magnetic field was fitted to be w = (1.5 ± 0.3) Xl 0 8 rad/s. The integral precession angles fle were determined from the ratios of coincident counts accumulated in the 'Y-ray detectors with magnetic field up and down and is given by fle

dW(e)

€-1

=-€ + 1 W(e)/-de'

(1)

where Wee) is the angular correlation function and the effect € is the average of the effects €12 and €34 for the two pairs of'Y-ray detectors with

.. =(N(ei)t N(e;H)I/2 elf

N(eiH N(e;)t

(2)

The angular correlation coefficients were calculated for a pure m = 0, 0 ~ 2 ~ 0 transition corrected for the finite solid angles of the 'Y-ray and particle detectors. The logarithmic derivative of Wee) at the 'Y·ray detection angle is displayed in column 6 of table 1. The cross ratios € 13 and €24, calculated as consistency check on the data, show no effect, as expected. Also the measured effects, analyzed in separate runs of a few hours duration show no systematic change as function of time. The measured transient-field precession angles are plotted versus the initial recoil velocity on entering the iron backing in fig. 1 together with the predictions from the LW theory with vp/vo = 0.78 (dashed curve) [5]. Also shown in fig. 1 are calculated precession angles using the empirical relation of Eberhardt et al. [12], in which the transient field is assumed to be linearly dependent on the velocity of the moving ions: Bu.

v

=aZR(Z) -

Vo

,

(3)

where Z is the atomic number of the recoiling nuclei and R(Z) = 1 + (Z/84)s/2 is a relativistic correction [5,12]. In the computations of the time-integral precession angles with the LW or empirical model the electronic stopping power data were taken from ref. [25] but scaled with recently measured a-particle stopping powers [26]. For the nuclear stopping power a universal expression, based on experimental observations [27] has been used. This expression gives nuclear stopping powers which are somewhat lower than those calculated by Undhard, Scharff and Schi~tt

[28]. In fig. 1 is shown a least squares fit to the data of time integral precessions for

J.I. Eberhardt, K. Dybdall Transient magnetic field in Fe

391

134 80 in Fe

't m -7ps

30

,.

/,~~~--------';'~'~;~J

" /

~/'

°0~=:-~---'--~~~-o-2~~~-!:3~~~---!4'-----~---.J

INITIAL VELOCITY (vi/vo)

Fig. I. Measured transient field precession angles as function of the initial recoil velocity in units of Vo (the Bohr velocity) for 134Ba recoiling into magnetized Fe. Predictions based on eq. (3) for a = 11.2 and g = 0.41 (full curve) and predictions based on the Lindhard-Winther theory with v p = 0.78 Vo (dashed curve) are also shown.

different initial recoil velocities calculated with the empirical relation with one free parameter, a proportionality constant being equal to the product of the parameter a and the nuclear g-factor. The quality of the fit (X 2 = 0.43) confirms the linear dependence of the transient field on the ion velocity as found for other ions.

4. The Z-dependence of the transient field in iron In order to be able to extract the Z-dependence of the transient magnetic field in iron from the available measured precession angles for different nuclei at differ­ ent initial recoil velocities assumptions about the velocity dependence have to be made. As shown in subsect. 3 transient fields proportional to the ion velocity describe the data well in many cases. Only for very light ions at recoil velocities comparable to the ions' Is electron orbital velocity ( 12C and 13C at v> 5vo) a decrease of the transient field with increasing ion velocity has been observed [15,18]. In terms of a microscopic model for the enhanced transient fields [12] the decrease is probably caused by the inability of the totally stripped ions to capture polarized electrons of the ferromagnetic medium into bound electron states. In the following analysis the linear velocity dependence is assumed to be a general feature of the transient field for ion velocities Vion < ZVo. Time-integral

392

J.L. Eberhardt. K. Dybdal / Transient magnetic field in Fe

transient-field precession angles for excited states of nuclei with atomic number 6 ~ Z ~ 80 have been computed using the best available stopping powers [25-27] (see also subsect. 3) and taking into account decay in flight and decay and energy loss in the target layer. The parameter a in eq. (3) was obtained for each Z from a fit to the experimental precession angles. Table 2 gives a summary of the available transient field precession data and the parameter a obtained for each case. The mean lifetimes of the nuclear states ob­ served in the experiments and the initial recoil velocity in units of the Bohr velocity Vo are given in the columns 2 and 3, respectively. In many cases precession angles have been measured for more isotopes of one element with different mean lifetimes 7 m for the nuclear states. The total precession 1::18 due to the static field B s and the transient field Bu. is given by 00

1::18

= tPu. + tPs - g~N {f Bu.(t) e- t / Trn dt + Bs 7 rn e- tS / Trn }

,

(4)

o

where g is the nuclear g-factor, fJ.N the nuclear magneton and t s the stopping time of the recoiling ion. From a simultaneous fit to the precession angles for all isotopes of an element tPu. and B s were determined, using g-factors, determined independently with other methods. In table 2 the longest mean life occurring in a sequence of iso­ topes has been given and the corresponding fitted transient field precession angle. Some remarks concerning the data in table 2 are given below. (i) The 20,22Ne experiments. Two inconsistent sets of data have been reported for 2~e and 22Ne recoiling into Fe, respectively. For the longer lived 22Ne(2~) state (7 rn =5 ps), however, a precession due to a large (unknown) positive static magnetic field might explain part of the discrepancy. (ii) The 56Fe experiments. Experimental precession angles, obtained with thick Fe backings (including static field contributions) and thin Fe backings were used in one simultaneous fit with a and the static magnetic field B s as free parameters. Values of B s = -21(2) T and a = 10.9(6) T were obtained with a normalized good­ ness of fit of X2 = 1.03. The static field was found to be only 63% of the value of -33 T obtained from NMR and Mossbauer experiments [40]. If B s is not considered as a free parameter but kept at B s = -33 T, a bad fit with X2 = 5.0 is obtained. Experimental precessions, corrected for a static contribution as obtained from the fit, are displayed in column 4 of table 2 for 56Fe recoiling in thick iron backings. (iii) The Mo-experiment. Only two experimental precessions are known. A transient field precession of tPu. = -37(28) mrad and an average g-factor for the "­ two states of g = 0.40(28) were fitted assuming the static field to be B s = -25.6 T

[1] . (iv) The Ru, Pd, Cd, and Te experiments. In order to extract the transient field precessions and the static magnetic fields from the data the g-factors for the differ­ ent isotopes of an element were supposed to be the same. Average g-factors, ob­ tained from radioactivity data (see ref. quoted in [1 D, of g =0.40(3), 0.34(1),

'­

J.L. Eberhardt. K. Dybdal / Transient magnetic field in Fe

393

Table 2

Summary of available transient field precession data and values for the parameter a (see text)

obtained from least squares fits. Nucleus

Tm

-(¢t.f,!g)exp (mrad)

Vi/VO

(ps)

I~C I~C I~N I~O I~F

10

loNe

0.065 U.8 7.0 2.9 0.86 1.0

I5Ne

5.0

~Mg

2.0

I~Si

~~S ~~Fe

0.7

0.23 10.1

1.0(5) a) 1.43(16) a,b) 5.9(1.1)

2.1 4.1 3.4 2.3 2.9 1.8 5.2

5.9(1.6) 9.3(8) 4.1(1.9) c) 4.6(9) 8.5(1.1) 3.6(9) 20(4) 2.8(4) 5(3) 8.6(1.6) 14.3(1.8) 1.1(8) 2.61(15) 5.9(9) 16(3) 2.0(4) d) _ 0.6(1.5) e) 0.8(1.3) e) 3.7(2.5) e) 11.7(3.5) e) 24.6(2.1) e) 30.8(3.0) e)

1.3

~Se

76.78,8O,~Se

98,I~Mo 98,loo,l02.I~Ru

0 0 0 0 0 0 0 0

16.3

3.2

16.1(2.8) 9.8(2.3) 15.3(3.0) 34(4) 27(4) 17(4) 12(4) 4(3) 26(10)

14.9 83.5

2.5 2.5

37(28) 25.4(7.3)

16.3

(T)

44(24) 29.9(3.3) 23.6(4.4) 32.6(8.2) 37.4(2.9) 29(13)

3.3(6)

5.9 7.8 2.1 6.7 2.3 3.7 5.1 7.7 0.9 2.1 3.4 6.7 1.7 0.4 0.5 1.2 4.1 6.2 6.2 ...... 3.0 6.2 ...... 4.4 6.9 ...... 3.8 5.1 ...... 2.0 5.1 ...... 2.8 5.1 ...... 3.3 5.1 ...... 3.8 5.1 ...... 4.5

Ref.

a

7.1(6)

16.1(2.6)

9.9(9)

12.4(8)

15.1(3.0)

10.9(6)

12.6(1.0)

14(11) 9.0(2.6)

[13] [14,15,16] [18] [7] [6,8] [29] [ 19] [19] [19] [12,30] [12,30] [3]

[19] [19] [19] [ 12] [12] [12] [ 12] [31] [2] [2] [2] [2] [9] [10] [10] [10] [33] [21] [21] [21] [21] [21] [1] [1] [1]

394

J.L. Eberhardt, K. Dybdall Transient magnetic field in Fe

Table 2 (continoled) Nucleus

12~Rh g) 104.106.108,I~Pd

1l0.1l2,1l4,ll~Cd

Tm (ps)

Vi/VQ

85 66.0 19.8

1.3 2.2 2.4 2.3

11.3(3.8) 28.2(2.0) 25.5(4.3) 26.8(5.3)

13.4 59.4

2.1 2.4

28.5(6.6) 56(15)

9.3(2.2) 14.2(3.8)

[ 1] [35]

81 52 43

1.8 ± 0.3

51(12) 78(36) h)

18(7)

1.3 1.1

13.7(1.8)

31.9

1.3 2.3 2.4 1.3

[36] [37] [20] [20]

14.5(4.3)

[20] [20] [39]

-(r[Jt.f.lg)exp (mrad)

Ref.

a (T)

11.1(8) 8.7(1.5) 9.0(1.8)

[34] [ 1] [1]

120,122,124

126,128,1~~Te

126,128,130.1~Xe

124,126

128,130,lll Xe 194, 196, 1~gPt

I~Pt

I~Hg

67(16) 75(14) 105(8) 123(8) 54(16)

a) For a g·factor of 0.56, pure P3h Pl/2 estimate.

b) Data from ref. [16] corrected to zero target thickness.

c) For ag-factor of g = 0.58, the pure d~/2 estimate.

d) For a g-factor of 0.53, from full sd space calculations [32].

e) Static field subtracted, see text.

f) Velocity range in the thin Fe foils.

g) With a static field B s = -54(1) T [40].

h) With g·factors and nuclear mean lifetimes as given in [38].

0.39(5) and 0.34(2) for the Ru, Pd, Cd, and Te isotopes, respectively, were used in the analyses. The fitted static magnetic fields, together with values obtained with other experimental methods (for a compilation see ref. [40]) are given in table 3. The static fields from the IMPAC experiments are 30-50% below those obtained from Mossbauer, NMR, spin-echo or DPAC experiments (see table 3). (v) The Xe experiments. Both the static and transient field are derived from the data of ref. [35]. The results of ref. [36] are more difficult to interpret since the 160 bombarding energies are not given unambiguously for the different isotopes and the target thicknesses of the solid Xe targets varied between 0.5 and 1.5 mg/cm 2 . For completeness also the transient field precession fitted from these data and the parameter a are given in table 2. The error in a reflects the uncertainty in the initial recoil celocity. The static field obtained from the data of ref. [35] shows a 41 % reduction (see table 3). In fig. 2 the parameter a is plotted versus the atomic number Z of the recoiling ion. Fig. 2 shows that a is about constant for Z ;;;;. 12, thus supporting the validity

J.L. Eberhardt, K. Dybdall Transient magnetic field in Fe

395

Table 3 Comparison between static magnetic hyperfine fields in Fe obtained from reanalyzed IMPAC data (present work) with those obtained with other methods [401 Element

IMPAC reanalyzed

Other methods

Ratio

(T)

(%)

- 33.2(2) - 50.3(7) - 59.3(9) - 34.6(2) + 67.0(3) +152(6)

63(6) 73(9) 73(5) 55(29) 46(24) 59(13)

(T)

, Fe Ru Pd Cd Te Xe

-21(2) -37(5) -43(3) -19(10) + 31(16) + 90(20)

of the Z-dependence of the empirical relation (3), but large deviations occur for Z < 12 (see subsect. 6). The best fit for a in the range 12 ~ Z ~ 80 gives a = 11.2(3) T (normalized goodness of fit X2 = 1.4) and is indicated in fig. 2. The quoted error on a is purely statistical and does not include possible systematic deviations from a Z-independent a.

5. The g-factor for 134Ba (2t) The calibration of the transient field obtained in subsect. 4 allows the extraction of the nuclear g-factor for the first excited 2+ state of 134Ba. A value of g = 0.41(6) I

40

E 30 Cl

0:::

W

~

~ 20

« o:::

~ 10

I

Btl •

fa

I

+A f

/

I'iTT

/

W

~

fl_

1

./' f

•

W

l R(ll

I

/

~

Q

~

~

~

ro

~

ATOMIC NUMBER l

Fig. 2. The parameter a of eq. 3 versus atomic number Z. The best fit to the data for 12.;; Z 0;; 80 is shown as a full line. The predictions from a microscopic model (see subsect. 6) are shown as dashed curves.

396

J.L. Eberhardt, K. Dybdal / Transient magnetic field in Fe

was obtained. The error reflects the statistical uncertainty, and estimated uncertain­ ties of 10% in the parameter a, 5% in the electronic stopping power and 20% in the nuclear stopping power for Ba in Fe. A preliminary account of a recent investigation by Brennan et al. on even Ba isotopes [41] gives a result for the g-factor of 134Ba (2i) of g =0.47(6), in good agreement with the present result. The measured g-factor is well described by g =Z/A, expected for rotations or vibra­ tions of a homogeneously charged fluid. A model proposed by Greiner [42], which has been successfull in.describing g-factors of nuclear states for nuclei with atomic numbers between 44 and 54 predicts a too low value of g = 0.35 for the g-factor. This hydrodynamic model uses the fact that the pairing force between protons is stronger than that between neutrons. This leads to estimates somewhat below Z/A. Microscopic dynamic calculations of collective states in neutron deficient doubly even Xe and Ba isotopes have been performed by Rohozinski et al. with reduced pairing forces to fit experimental energies [43]. The prediction of g = 0.25 for the g-factor, however, is far too low.

6. Discussion and summary

The linear dependence of the transient magnetic field on the ion velocity has been confirmed by the present experiment and it seems to be a general feature of the transient field. From fig. 1 it is obvious that the LW model describes the experimental data inadequately. Even at low velocities where it was expected to predict the magnitude of the hyperfine field well, the theory disagrees with exper­ iment. At an initial velocity of 0.8vo the LW theory gives an overestimation by a factor of two. The adjusted theory (v p = 0.40vo) used sometimes [2-4] would give an even larger discrepancy. There are no physical arguments to believe that the scattering of polarized Fe 3d electrons should not contribute to the total hyper­ fine field, but the present experiment indicates that its effect is overestimated by the LW theory. This might be caused by deviations from pure Coulomb scattering due to scattering on the electrons of the moving ion. Further, at velocities smaller than the orbital velocity of the Fe 3d electrons (v < vo) these might not be released and thus would not participate in the scattering process. However, to judge transient field theories it should be remembered that the effects on the calculated precession from the magnetic field and the stopping power can not be separated. Experimental nuclear stopping powers for Ba in Fe are not known and the simple scaling proce­ dure for the electronic stopping power (see subsect. 3) is not likely to be accurate at low ion velocities [44]. Further, the velocity dependence of the electronic stop­ ping powers might deviate from the assumed linear dependence, as seen for other ions [44]. Although subject to limitations due to incomplete knowledge of stopping powers (see above) and some nuclear g-factors and static fields (subsect. 4, table 2), the present analysis of older existing data, together with a similar analysis by

J.L. Eberhardt, K. Dybdal/ Transient magnetic field in Fe

397

FaWander et al. [22] for nuclei recoil implanted in magnetized gadolinium support a Z-dependence of the transient field for not too light nuclei, which is similar to the Z-dependence obtained from the Lindhard-Winther theory, Le. a linear depen­ dence, modified with a relativistic correction reaching a factor of two for nuclei with Z ~ 80. The parameters a (eq. 3) obtained for iron and gadolinium support the proportionality of the transient field to the density of polarized electrons in the ferromagnetic host material. From fig. 2 large fluctuations in a are seen to occur at low Z. The dashed curves in fig. 2 show a fit to the data for 6 ~ Z ~ 26 as proposed by Zalm et al. [19], assuming that for Z = 6-8, 10-14 and 26 the fields are due to unpaired polarized Is, 2s and 3s electrons in those ions, respectively. Their approach describes the Z­ dependence well for 6 ~ Z ~ 16, but deviates largely from the Z-independent a for Z between 16 and 26 where no experimental data are available at present. According to the interpretation of Zalm et al. similar fluctuations in a should be expected for higher Z. However, the available data do not reveal such oscillations in the investi­ gated Z-regions (Z ~ 12). For a better calibration of a experiments are needed in the unexplored Z-regions for well chosen cases where the nuclear g-factor can be determined with other methods. Furthermore, uncertainties in the low velocity stopping powers and in the static field contributions should be minimized by recoiling the ions through thin iron foils into a perturbation free backing [21] at not too low initial velocities. The simple features of the transient field for Z ~ 12 suggest some "collective" model description for the field, in which the highly excited cloud of electrons of the moving ion is polarized by interaction with the polarized electrons of the ferromag­ netic medium, however, no quantitative model for the transient field exists so far. For light ions, Le. few electron systems, such a statistical description would fail and electron shell effects might be observed. Indeed deviations from the linear Z- and velocity-dependence have been seen for light ions [15,18,19] and have been treated qualitatively within the framework of a microscopic model. Also recently deviations of the proportionality of the transient field with the polarized electron density in the host material have been reported and were explained by a molecular-orbital electron promotion mechanism [45]. In conclusion, the validity of the empirical relation (see subsect. 3) has been demonstrated in the present work for Z ~ 12 with Fe as a host material, thus enabling reliable measurements ofg-factors of very short-lived (0.1-10 ps) nuclear states. The authors wish to acknowledge the hospitality of the Niels Bohr Institute in Ris¢>, enabling the high velocity experiment. The technical assistance of F. Abildskov and O. Bank Nielsen is appreciated.

.,

398

J.L. Eberhardt, K. Dybdal / Transient magnetic field in Fe

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