l.E.3. I I Nuclear Physics A91 (1967) 633-643; @ North-Holland Publishing Co., Amsterdam

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

PRECESSION MEASUREMENTS FOLLOWING COULOMB EXCITATION

WITH OXYGEN IONS

(III). Gyromagnetic ratios of rotational states in W isotopes

P. GILAD, G. GOLDRING, R. HERBER 7 and R. KALISHtt

Physics Department, Weizmann Institute of Science, Rehovoth, Israel

Received 18 July 1966

Abstract: A measurement of the g-factor of the & state at 99 keV in ls3W is reported. Measurements are also described which make use of internal magnetic fields in saturated ferromagnetics. The value and sign of the internal fields acting on a tungsten nucleus in nickel, cobalt and iron have

been determined with the aid of these fields. Precession measurements have been carried out for the 4+ levels in ls2W, la4W and la6W. It is also established through the internal consistency of

the results that the internal fields are set up during a time shorter than 5 x IO-” sec.

NUCLEAR REACTIONS 18z~183,184,186W (laO, 160’y), E = 35, 41 MeV; measured E o(EY, 8, H). 182, 183j184,186W levels deduced g, internal fields in ferromagnetic material.

Enriched targets.

1. The gyromagnetic ratio of the g- level in ls3W

A precession measurement was carried out on the +- (99 keV) level in 183W,

similar to the previously reported measurements for 2+ states in a number of even

nuclei (refs. ‘3’) hereafter referred to as (I) and (II)). A special difficulty arose in this

case from the fact that the isotopically enriched la3W target +++ contained about 17%

of the even-mass number tungsten isotopes. With the NaI(TI) gamma counter used

in these experiments, the 99 keV +- --, +- radiation from 183W could not be resolved

from the 2+ -+ 0’ radiations from the even isotopes. The effect of the impurities on

the accuracy of the I8 3W measurement is magnified and aggravated by the relatively

high excitation probability of the 2+ levels compared to the 3- level, the longer life-

time of the 2+ states, and the fact that the $- level decays only partially by the ob-

served direct $- --f f- transition.

Measurements were therefore carried out on targets of enriched even isotopes as

well as the enriched ls3W and data from the former were then directly subtracted

(with the appropriate concentration factors) from the results of the latter, using the

scattered oxygen counts in the ring counter as a relative normalization. The measure-

ments on the 5- --$ :- transition in ls3W and the 2+ + O+ transitions in the even mass

tungsten isotopes were carried out with a beam of 35.4 MeV oxygen ions. The meas-

7 On leave of absence from Rutgers, The State University, New Brunswick, New Jersey, USA. 77 Present address: Laboratory for Nuclear Science, Massachusetts Institute of Technology,

Cambridge, Mass., USA. ttt Obtained from Oak Ridge National Laboratory.

633

634 P. GILAD t?t al.

urements on the 4+ -+ 2+ transitions in the even tungsten isotopes discussed below were carried out with oxygen ions of 41.3 MeV.

400 -

300 I t I , , “\:, I

0 IO 20 30 40 50 60 70 80 90 100

Counter Angle 0

Fig. 1. Angular distribution of the %- --f &- radiation of lS3W recoiled into copper. The curves show the computer fit to the lssW data corrected for isotopic contamination from data obtained on the

even-mass tungsten nucleides and suitably normalized.

0.90 1 G4

0.85 r

;-=

0.95 T1-

0.85 G2

B ( E2 &. 7’ (eZ lO-66 cm4 set’ 1

Fig. 2. Attenuation coefficients Gz, G, and G as a function of B(E2)t* for the tungsten isotopes.

PRECESSION MEASUREMENTS (III) 635

The angular distribution of the 3- + +- gamma radiation obtained in this proce- dure is shown in fig. 1 and compared with the calculated distribution (as given in (II), eq. (3) in the appendix)

IV(e) = 1 +$ P,(cos l9) -4 P,(cos e>

corrected for the finite apertures of the counters. This measurement was carried out only as a check since the angular distribution

of the $- --f +- radiation is determined unambiguously by the angular distribution measurements of the 2+ --f Of radiations. This can be clearly seen from fig. 2 which is a reproduction of fig. 2 of (II) indicating also the effective position of the ls3W level. The attenuation coefficients for the $- level are found by extrapolation to be: G2 = 0.95kO.02 and G, = 0.97kO.02. The +- + 3- radiation is therefore expected to be practically unperturbed.

The gyromagnetic ratio was measured as usual in a double ratio measurement with two counters, switching the field direction alternatively up and down. The change in counting rate E in each counter on application of the field is given by

obs.

The coefficient X was estimated from the various attenuation coefficients in fig. 2 as

X = 0.97 50.03.

As before, H had the value 16.6 kG. With the counters set at the angles of steepest change for the s- --* 4- radiation

(0 = + 114”20’) and after subtraction of the contributions from the even isotopes, one gets for the t- --f +- radiation; srs3 = 0.028+0.011, and from this an angular shift of dt7 = 0.019+0.009. The corrected angular shift is

0.X = 0.0174f0.009.

These values have been corrected for the angle of beam turning (cf. I) as well as for some small contributions to the gamma line from other transitions in ’ * 3W. These transitions are all short-lived and of low anisotropy and generate essentially a con- stant background in the precession measurements. The contributions from all these transitions was estimated to be about 13 % of the total counting rate.

The mean life of the 3- level has recently been measured at this laboratory 3, as 1.02 f 0.05 nsec.

Using this lifetime and the observed precession angle, the calculated gt- value is

gq- = 0.22AO.11.

A detailed analysis of the low-lying states of ls3W has recently been carried out 4), describing these states in terms of two mixed rotational bands with K = + and K = $.

636 P. GILAD et al.

With a certain set of parameters this constitutes an adequate description of all meas-

ured E2 and Ml transition probabilities.

On the assumption of gR = 0.4, the g-factor of the $- level is calculated in ref. “)

as g+- = 0.52 which is quite inconsistent with the measured value. Significantly the

g-factor of the ground state in this calculation is also about twice as large as the ex-

perimental value of 0.232 (ref. ‘)). S’ mce gR is the most sensitive parameter for the

two g-factors, the experimental evidence clearly suggests that gR in la3W has a value

close to 0.2. This makes gR in rs3W essentially identical to the g-factors in the neigh-

bouring isotopes lB2W and ’ 84W.

The analysis in ref. “) determines quantities of the form (gk-gR), and the present

evidence on gR suggests that all gk values in ref. “) have to be reduced by about 0.2.

This gives

gr+ = 0.2, g($_) = 0.2, g(t-) = 0.36.

In this way, the value g(+-) is brought appreciably nearer to the measured value.

The present measurements are unfortunately not quite accurate enough for a definite

conclusion about the consistency of the g-factors of the two levels in 183W.

2. Internal fields in ferromagnetic materials

In measurements of the type described here, the target material is deposited on a

ferromagnetic metal backing - nickel cobalt or iron - instead of the copper backing

employed in all measurements described earlier. The Coulomb excited recoil nuclei

are embedded in the bulk of the metal at a depth of some 0.5 mg/cm2. With the

application of an external field these nuclei experience large magnetic-fields aligned

along the direction of the applied field. These internal fields can be made use of in

precession measurements involving very short-lived nuclear states 6, ‘). In the appli-

cation of this technique one encounters two specific problems.

(i) The angular distribution of de-excitation gamma rays in the absence of an

applied field will often be perturbed by the very fields - in random orientation or

partially aligned - that form the raison d’etre of these measurements. For example

for 184W recoiling into demagnetized nickel, an attenuation G = 0.81+_0.01 was

found for the 2+ --+ O+ transition. This may be compared to G = 0.88kO.02 for

recoil into copper. Although a perturbation of this type will not in itself affect pre-

cession measurements in which the internal fields are completely aligned, a way has to

be found to ascertain that no other perturbations, e.g. quadrupole interactions, are

involved. The most straightforward way to accomplish this is to carry out an angular

distribution measurement with the internal fields aligned in the direction of the oxy-

gen beam or of the gamma counter. This method proved however inapplicable be-

cause of technical difficulties +. Instead, angular correlation measurements were al-

t The most serious problem is the difficulty of setting up a homogeneous saturation field close to a boundary surface of the material and perpendicular to it.

PRECESSION MEASUREMENTS (III) 637

ways carried out in a transverse field and analysed directly in terms of “precessed”

distributions. This type of measurement can also furnish information on perturbations;

however an added complication enters here in that if the magnetic field acting on the

nuclei is not strictly homogeneous, a general “smearing out” of the precessed distri-

bution will result, much in the same way as would be produced, say, by an isotropic

perturbation. This type of measurement can therefore be expected to yield meaning-

ful results only if the two conditions - the near homogeneity of the field and the ab-

sence of perturbations other than the precessing field - are simultaneously fulfilled.

(ii) The magnitude or even the sign (relative to the applied field) of the precessing

field is generally unknown. One can “calibrate” the field by carrying out a precession

measurement on some other level in the same nucleus or in another isotope, for which

the g-factor is known. (It is incidentally in such “calibrating” measurements that

the problem discussed in the preceding paragraph is most severely encountered).

This calibration level will however in general be relatively long-lived (as its g-factor

has of necessity been measured with the conventionally applied external fields) and

one is left with the problem of whether the effective fields are indeed identical for the

two levels, or in other words - the problem of how long after the nucleus settles in the

ferromagnetic lattice does the field establish itself at its equilibrium value. This prob-

lem by its very nature cannot be solved in a clear cut way, since one will always effec-

tively measure the product of an unknown field and an unknown g-factor. One can

only solve such a problem in a step-by-step procedure, establishing a general pattern

of internal consistency. The measurements reported here are considered as such a step.

The field acting on a W nucleus embedded in iron, cobalt and nickel was measured by

precession measurements on the 2+ level (cf. table 1) and subsequently precession meas-

TABLE 1

Summary of internal fields obtained from precession measurements of the 2+ + 0+ transitions in

ls4W and lasW

Nucleide t2+ (nsec)

Nickel Cobalt Iron _

WTz_ mtl+ (rad) (rad)

MW 1.85$-0.03 0.157~0.013 -5747 0.88+0.07 -320&38 1.21+0.10 -440+53

18f.W 1.46kO.06 0.161&0.013 -6418 0.85kO.07 -340+41 1.18kO.09 -47O,t56

The nominal target temperature is 295 4 5” K.

urements were carried out on the 4+ levels of 182W, ls4W, ls6W with mean lives of

89.1+ 10,63.2 k 7 and 36.7 &- 4psec, respectively. In a normal and pure rotational band

such as constitute the low-lying levels of the tungsten isotopes, one expects theg-factor

to be a constant of the band. As the precession measurements do indeed yield for the

g(4+) values, which within the experimental error are equal to the g(2+), we take this

not entirely as a proof but as a high probability indication that

, I 0% do ;00 40” 60” do”

I L__! 100” 120”

Angle B

Angle 8

PRECESSION MEASUREMENTS (III) 639

400( ‘n E 2 u

E ‘E 300(

200(

I OO( I

-20" I

0" I I I I I I

20” 40” 60” 80” 100” 120”

Angle 8

I Cd)

I000L---L -20”

Fig. 3. Angular

a)

b) c) d)

I

0" I I I I I I

20” 40” 60” 80” 100” 120” Angle 0

1

distribution of the 2+ + 0+ radiation of larW recoiled into various matrices. The solid line is the computer fit for a copper recoil catcher; the dashed line is the computer fit for a demagnetized nickel recoil catcher. Data for nickel recoil catcher, Data for cobalt recoil catcher, Data for iron recoil catcher.

In b, c and d, the recoil catcher domains were aligned in an external magnetic field. The solid line shows the computer fit for “field up”, the dashed line shows the fit for “field down” in

each case.

640 P. GILAD et al.

(i) the internal field in iron reaches its equilibrium value after recoil of the Coulomb

excited ion in a time short compared to 5. 10-l’ set and (ii) the g(4’) have the

values quoted, based on the equilibrium value for the effective field.

The use of precession measurements to obtain values for the internal field acting

on heavy nuclei recoiled into magnetic lattices has been discussed in detail by Gilad

et al. 8).

3. Measurement of the g-factors of the 4+ levels in W isotopes

Angular measurements in an applied transverse field + were carried out for the

2+ + o+ transition in 186W and ls4W after recoil into nickel cobalt and iron. The

measured distributions are shown in fig. 3.

The line drawn through the points represents a best fit with the parameter wr =

g(@H/A)r to the calculated distribution

W,(e) = T s

m e-(tir) W(O-wt)dt, 7 0

where W(0) is the angular distribution found in the recoil-into-copper measurements

(cf. fig. 3a).

In these evaluations the attenuation coefficients (G, = 0.900f0.027, G, = 0.947 +

0.019 for 186W and G, = 0.849f0.025, G, = 0.9OOkO.018 for 184W) found in the

copper-backing measurements were included as constant factors in the angular dis-

tribution coefficients. Such a procedure is strictly justified only for a sudden perturba-

tion; however in view of the smallness of the perturbation the exact nature of the

perturbation is not expected to have a strong effect on the angular distribution.

From the very good fits obtained in fig. 3 we conclude that the angular distributions

are not more perturbed in these cases than in copper-backing measurements and

furthermore - that the fields are reasonably homogeneous. This point is examined in

greater detail in ref. *).

Boehm et al. ‘) measured the angular distribution of the 2+ --f Of radiation in

ls2W after recoil into iron. In that case they found that the distribution could not be

fitted with a distribution of the type (1). The difference between ls2W on the one

hand and lg4W, 186W on the other hand is undoubtedly due to the much larger per-

turbation in lE2W (cf. II). It is noteworthy nevertheless that the value of Boehm and

Hagemann for the field in iron Hi,,, = 0.43 fO.10 MG is in good agreement with the

value found in our meaurements.

The angular distribution of 4+ + 2+ radiation from 184W after recoil into nickel

foils, the domains of which had been aligned with an external field is shown

in fig. 4. The solid line shows the calculated distribution W(0) = 1 +sP,(cos Q)-

+ It was established by repeating the measurements at various field strengths that the applied field is sufficient to ensure saturation.

PRECESSION MEASUREMENTS (III) 641

SP,(cos 0 (es. (5) in the appendix to II) appropriately modified to take into ac-

count the finite size of the particle and gamma counters.

IOO- - ~ ~

_~‘.L.!_~I_ I I -10" OkO" 20" 30" 40" 50" 60" 70" 80" 90" ' 100"

Counter Angle d

Fig. 4. Angular distribution of the 4+ + 2+ radiation of la4W recoiled into aligned nickel. The

solid line is the computer fit to the ‘Yield up” data.

Precession measurements were carried out for rs2W, rs4W and is6W on iron back-

ing at the angle of steepest change 0 = f 113”. The precession angles it observed

with application of the external field is given in table 2.

TABLE 2

Summary of s(4+) data for even-mass W isotopes

Nucleide D.R. WT4+ (rad)

=4+ (lo-” set)

s(4+)

ISZW 0.855+0.035 0.035f0.009 8.9Al.O 0.19$0.06 ISCW 0.843 +0.036 0.040*0.01 6.3 ho.7 0.30*0.09 186W 0.945 *0.030 0.0125&0.008 3.7kO.4 0.19iO.13(?)

The value of wr( ls2W) agrees well with the value found by Boehm 7, in a similar measurement.

The mean life of the 4+ levels has not been measured directly. However multiple

Coulomb excitation measurements 9, show that the relation of the B(E2) values for

the O+ -+ 2+ and 2f + 4+ transition is consistent to within an experimental un-

certainty of some 10 ‘A with the rotational model.

642 P. GILAD et al.

The values of the mean lives of the 4+ levels obtained in this way are given in table 2

as well as the g-factors obtained from the precession measurements with the assump-

tion of a field of H = 46Ok45 kG as derived from the measurements on the 2+ state

of la6W and ls4W.

gR

02

0.2

0.1

W 182

I I

W 184

W 186

Fig. 5. Comparison of g-factors for the 2+ level (solid points) and 4+ level (open points) in several

even-mass tungsten isotopes. The precessing field is Hint = 46Oh45 kG in the iron recoil catcher.

No definite conclusions can be reached concerning g(4+) in ls6W, the shortest-lived tungsten isotope

measured, see text.

A general comparison of the g-factors of the 2+ and 4+ levels is given in fig. 5, and

the g-factors for the two states are seen to be reasonably consistent in 18’W and rs4W.

The rather low value found for g( ‘s6W, 4+) may be considered as an indication

that at 3.5 x lo-” set, the field is not yet fully established. The measured value is

however not accurate enough to warrant a definite conclusion.

The best check on the consistency of the g-factors of the two levels can be obtained

by averaging over the measurements of the various isotopes. One finds in this way

g(4+) = 0.24kO.06, for l*‘W, 184W, ls6W,

g(2+) = 0.27&0.01,

where the 2’ values have been weighted in the same way as the 4+ measurements.

PRECESSION MEASUREMENTS (III) 643

If only the values for lB2W and rs4W are considered, one obtains

g(4+) = 0.25+0.06, for 182~ >

184~

g(2+) = 0.25+0.01,

As has been explained earlier, the fact that the g-factors for the 2+ and 4+ states

are found to be equal, as expected within a rotational band is now considered as a

confirmation of the assumption that the effective fields are the same in the two cases.

The values of the internal fields obtained with ls4W and ls6W are very close. This

provides a valuable check on the field measurements as well as an indirect but con-

vincing confirmation of the rather large difference in the g-factors of the 2+ states in

ls4W and ls6W.

4. Conclusion

The g-factor of the $- state of ls3W was found, within the rather limited experi-

mental accuracy, to be consistent with the g-factor of the ground state. Both are

consistent with a gR parameter which has the same value as the g-factors of ls2W

and is4W.

The examination of 4+ levels with internal magnetic fields leads to simultaneous

conclusions regarding the g-factors and the fields; namely that the g-factors of the 4+

levels of ls2W and is4W are within the limited accuracy of these measurements the

same as the g-factors of the 2+ levels, and that the internal fields are established within

less than 5 x lo-” sec. No definite conclusions can be drawn at this stage about the

g-factor of the 4+ level in ls6 W or about the value of the internal field acting on the

tungsten nucleus in iron at times shorter than 3 x 10-r’ after the recoiling tungsten

atom comes to rest.

The authors are indebted to Professors Boehm and Grodzins for communicating

their results prior to publication. The assistance of I. Ben Zvi with some of the

measurements and data analysis is gratefully acknowledged.

References

1) G. Goldring, R. Kalish and H. Spehl, Nuclear Physics 80 (1966) 33 2) P. Gilad, G. Goldring, R. Herber and R. Kalish, Nuclear Physics A91 (1967) 85 3) D. Ashery ef a[., private communication 4) R. T. Brockmeier, S. Wahlborn, E. J. Seppi and F. Boehm, Nuclear Physics 63 (1965) 102 5) P. B. Sogo and C. D. Jeffries, Phys. Rev. 98 (1955) 1316 6) L. Grodzins, R. Borchers and G. B. Hagemann, Phys. Lett. 21 (1966) 214 7) F. Boehm and G. B. Hagemann, Izv. Akad. Nauk USSR, in the press;

F. Boehm, G. B. Hagemann and A. Winther, Phys. Lett. 21 (1966) 217 8) P. Gilad, G. Goldring, R. Kalish and R. Herber, Phys. Rev., submitted 9) J. de Boer, G. Goldring and H. Winkler, Phys. Rev. 134 (1964) B1032