Partial lifetimes and g-factors of the first excited 5−2 states in 75,77As measured by means of time-differential perturbed angular correlations

Nuclear Physics AS00 (1989) 277-286 North-Holland. Amsterdam

PARTIAL ;- STATES

LIFETIMES AND g-FACTORS OF THE FIRST EXCITED MEASURED BY MEANS OF TIME-DIFFERENTIAL IN 75~77A~ PERTURBED ANGULAR CORRELATIONS

Received 16 December 1988 (Revised 20 March 1989) The half-life and the magnetic moment of the first excited $- state, and the EZ/Ml mixing ratio of the ground-state transition have been accurately measured in a time-differential PAC experiment. The results for 7’As are: T,,, = 273 (3) ps, @ = eO.918 (18) pN, 6jE2,‘Ml) = -0.48 (4), and for 17As: T,,, = 304 (3) ps, p = +0.736 (22) pN, S(EZ/Ml) = -0.8 (3). The magnetic moments are discussed in the framework of the core-excitation model.

Abstract:

E

RADIOACTIVITY

_~..

“Se [from ‘%e(n, y)],“Ge [from ‘“Ge(n, y)]; measured 71.77As levels deduced Tr,?, b, 6.

yy( t), yy( @,I);

-i

1. Intraduction

Several nuclear models have been proposed in order to explain the level scheme part of the and the electromagnetic properties of 75.77A~. Whereas the low-energy level scheme and the electrical properties could be satisfactorily reproduced ‘,‘) by considering the motion of an unpaired particle moving in a Nilsson orbit and coupled to the rotational motion of the core by a Coriolis force, the predictions for the static magnetic moments are off by more than a factor of two from the experimental values. The level scheme and the static maments predicted by the intermediate-coupling model “1 are reasonably close to the experimental data, but especially the E2 transition probabilities do not agree so well. So far, the static and transition moments have been most successfully evaluated in the framework of the coreexcitation

mode1 47s).Apparently,

precise experimental

values of the electromagnetic

moments are essential for testing the different models. New opportunities for investigating nuclear levels with lifetimes nanosecond range have been provided by the advent of the BaFz detector, which has timing properties comparable to that of ultra-fast the advantage of having an energy resolution and photo-peak efficiency to those of NaI(TI). ’ On leave from Ain Shams

University,

Cairo,

0375-9474/89/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

Egypt. B.V.

in the suhscintillation plastic with quite similar

278

M. Mohsen,

E Pleirer / Parfial Ijferimes and g:factors

In the present work, we have applied such detectors to measure the half-life and the g-factor of the first excited $- states in 7s*77A~ by means of the time-differential perturbed angular correlation (DPAC) technique. As will turn out later, it is essential for a correct analysis of the g-factor measurement that the anisotropy of the used y-ray cascade is accurately known. To determine this anisotropy, we used samples consisting of an aqueous solution of the radioactive material in order to eliminate the effects of extra-nuclear perturbations as much as possible. As an additional result, the multipole mixing ratios for the ground-state transitions were obtained. 2. Sample preparation Approximately 20 mg of natural SeO, and 80% enriched GeC&, respectively, were irradiated for 24 h in a thermal neutron flux of 2 x 1O’4n/s - cm”. For the g-factor measurements, the radioactivity was transferred into the ion source of the isotope separator. In the case of GeO,, a special ion source with a Ccl, gas inlet was used. The isotopes 7”Se (120 d) and 77Ge (11 hf were implanted at room temperature into iron foils (4N8) with a thickness of 25 pm that had been pre-annealed at 1000 K in a hydrogen atmosphere. The implantation energy was I IO keV and the implantation dose was about 2 x lO”“at/cm’. 3. Instrumental setup A conventional four-detector slow-fast coincidence system was used. The detectors consisted of 44 mm(ilx 30 mm BaF, crystals coupled to XP2020Q photomultipliers. With this arrangement up to four time spectra could be recorded simultaneously. The time resolution of the system was found to be about 500 ps FWHM for the ‘y-ray cascades of interest. The implanted iron foils used in the g-factor measurements were put in an external magnetic field B,,, = 0.215 (20) T oriented perpendicular to the plane of the detectors. Neglecting the demagnetization of the thin foil and the contributions due to diamagnetism and Knight shift, we can write the effective field at the nucleus as B = B&4.2) + A&,+ B,,, ,

(11

where B,,(4.2) = +34.394 (27) T is the known magnetic hyperfine tield of As in iron at 4.2 K [ref. “)] and d&r== -0.5 (1) T is the change in hyperfine field if the temperature is raised from 4.2 to 300 K [ref. ‘)I. 4. Data reduction and anaiysis Let C,,( 8, t) be the number of true coincidences registered by the pair of detectors i and j, positioned at a relative angle 0. Then C,,(@,t)=[CiiW(8,

t--l,j)l_l+(f-f,j)~~~’

e-“~‘~~“‘]~(~aii)‘~’

ew‘Jc”“,l”,

(2)

M. Mohsen, F. Pleiter / Partial i[fetimes nnd g-facrors

where

W( 0, t) is the directional

correlation

function

and

H+(t)

219

is the Heaviside

function; the gaussian describes the time resolution of the setup. If the directional correlation is not perturbed by extra-nuclear fields, the correlation function

can be expressed

in terms of Legendre

w(O) =

C

L=even

A~?~‘~{cos

polynomials

Pk:

(@)I,

(3)

where Akk is the anisotropy coefficient and Qk describes the attenuation of the directional correlation due to the finite angles subtended by the y-ray detectors. fit of the convolution The half-life, Tii2 = T In 2, was derived from a least-squares product in eq. (2) to the individual time spectra, treating the variables C,, tij, 0;; and T as adjustable parameters. To measure the anisotropy coefficients, four detectors were used, which were positioned at relative angles of 180” and 90”. The four time spectra were combined to form the conventional

four-detector R(t) =

ratio discussed

in ref. “):

C(Tr, t) - c&T, t) $C(Tr, t) + c&r, t) ’

(4)

C(r, t) = rG,(T f)C24(1T, t)l”2 c&r, The main advantage

2) = [C&r,

of forming

t)C,,(~-rr, ?)I”‘.

R

parameters

(6)

this ratio is that in this way all detector

can be factored out. In case the sum in eq. (3) extends expectation value of the four-detector ratio becomes

The right-hand

(5)

9

=

th

efficiencies kS4,

AzQ2 + i%&,Q, 1+6A44Q4 ’

side of eq. (7) was evaluated

using the Fk coefficients

over values

tabulated

(7)

as a function by Krane

the

of the multipole

mixing

et al. “) and the solid-angle

attenuation coefficients Qh that were calculated following the method outlined by Krane lo). For small values of Add, the experimental value R/Q2 approaches the anisotropy coefficient A,, , irrespective of the actual value of A,,. In the presence

of a magnetic

field B, the nuclear

spin direction

will change

to the magnetic hyperfine interaction. This causes the nuclear magnetic moment well as the directional correlation to precess with the Larmor frequency w,_: W(@, tf =

C AkkQ&{cos I,=eye*

(e - wLr)} ,

w=-ghbl/~,

due as

(8) (9)

where g is the nuclear g-factor. In order also to measure the sign of the magnetic moment, we used three detectors, positioned at angles of t135” and -135”. The two time spectra were combined to form the following three-detector ratio:

R(r)=

c,z(+$T,t) - C*3(-&-,f) C,z(+.&r,t) + C,,( -&T, t) .

(10)

280

M.

Mohsen,

Neglecting terms with ka4,

E

Heifer/ Partial1~fPiimes and g,facror.s

the expectation

Rrh( I) =

--$A22QZ 1 +;A2&:!

value of this ratio becomes

sin(2qt).

In the present ex~eriments~ the time resolution was comparable with the nuclear lifetime as well as with the period of the Larmor frequency. Evaluation of eq. (2) shows that this introduces a reduction of the modulation amplitude and an additional phase shift. It turns out that eq. (11) has to be replaced by

(12) This expression is vaiid for t 9 v’/T. The Larmor frequency was determined by a least-squares fit of eq. (12) to the experimental data. In the analysis of our experimental results we will accept the spin and parity assignments “*“) to the lower energy levels of 75A~and 77A~,

5. Experimental results for 7”As 5.t. HALF-LfFE

OF THE 280keV STATE

The half-life of the 280 keV, g- state in “As was measured using the 121-280 keV y-ray cascade to the ground state. The delayed component in the time spectrum could be well separated from the dominant prompt contribution arising from the strong 136-265 keV cascade (see ftg. 1, curve A). The half-life was found to be T ,,2 = 273 (3) ps. The error accounts for the statistical unce~ainty as well as for the uncertainty in the time calibration.

5.2. EZ/Ml

M~X~~~

RATIO

FOR THE

280keV y-RAY

TRANSITION

The anisotropy of the 121-280 keV y-ray cascade was determined from a dilute sohrtion of SeOz in 6 N HN03. The experimental four-detector ratio R(t) turned out to decrease slightly with time, with a relaxation rate of I x 10’ S-I (see fig. Za). After correction for the finite angles subtended by the detectors, we obtained the value R(O)/Q,== -0.431 (10). Since A 44 is essentially zero, this value equals the anisotropy coefficient A,:!. In order to derive the E2/Ml mixing ratio for the 280 keV y-ray transition, we must know the M2/El mixing ratio for the preceding 121 keV transition. The most accurate value, 6( M2/ El) = +6(5) x 10m3, follows from the b2 particle parameter obtained from the eK- y directional correlation ‘“%‘*f.Using this value, we find S(E2/MZ) = -0.51 (7) for the 280 keV transition. Note that a much more accurate

M. Mohsen, F. Pleiter / Partial Ilfefelimesand g-factors

281

IO8

IO6

g

A:

75As

8:

77As

IO4

8 % k

2 2

102

+2

0 delay Fig. 1. Decay

value,

curves

6(E2/Ml)

5.3. MAGNETIC

for A the 280 keV, f state in “AS and B the 264 keV, $ background has been subtracted.

= -0.48

121 keV transition

(4), is obtained

is assumed

MOMENT

The modulation

(ns)

if the M2 admixture

state in “As.

Random

in the preceding

to be zero.

OF THE

280keV

of the anisotropy

STATE

due to the nuclear

spin precession,

measured

with the implanted sample, is shown in fig. 3a. Eq. (12) was least-squares fitted to these data while fixing the value u7/r = 110 ps. Since it is known “) that all implanted “Se ions land on substitutional lattice sites, we put A2,Q2 = -0.31 being the maximum effective anisotropy under the actual experimental conditions. From the resulting Larmor frequency wL= -600 (11) mrad/s and the known effective field strength B = +34.11 (11) T we find a magnetic moment /.L= +0.918 (18) pN. We have omitted the diamagnetic correction and neglected the effect of a possible Knight shift. The quoted errors are mainly determined by the

282

M. M&en,

F. Plciter / Pnnial

lifetinm

and g-factors

4

2 delay tns)

Fig. 2. Time-differential anisotropy curves for (a) the 121-280 keV y-ray cascade in 7’As, and (b) the 2 I I-264 keV y-ray cascade in ” As. The distortion at t =O is due to prompt contributions and/or to the fact that the time+zsolution curves OF the different detector combinations are not equal,

I

I

I

I

Ll

4

2 delay (ns) Fig. 3. Modulation of the anisotropy due to the nuclear spin precession “As and (b) the 264 keV, $- state in “As. The eRective magnetic

for (a) the 280 keV, 3‘ state in field was B = +34.11 T.

assumed extent

uncertainty on statistics

of 4% in the effective anisotropy, and the accuracy

6. Experimental

6.1. HALF-LIFE

and depend

only to a minor

of the time calibration.

results for 77As

OF THE 264 keV STATE

The half-life of the 264 keV, $- state in 77A~ could be conveniently measured using the 211-264 keV y-ray cascade to the ground state (see fig. 1, curve Bf. The final result is TIit = 304 (3) ps.

6.2. E2/M1

MIXING

RATIO

FOR THE 264keV

y-RAY

TRANSITION

We determined the anisotropy of the 211-264 keV y-ray cascade by measuring the four-detector ratio R(t). Experiments on the as-irradiated GeO, powder and on a dilute solution of GeCl, yielded identical results. For neither source a perturbation of the anisotropy was observed. The averaged result is R/ Q2 = -0.202 (9), which value includes a 0.7% correction for Compton contributions of higher energy lines to the 211 keV energy window. We assume the 211 keV, z”-$-

transition

to be purely

M2. Analysis

of the four-

detector ratio with the aid of eq. (7) then yields a mixing ratio 6(E2/Ml) = -0.8 (3) for the 264 keV transition and an anisotropy coefhcient Az2 = -0.201 (9) for the 21 t-264 keV cascade. This value is close to the maximum possible anisotropy for this spin sequence.

6.3. MAGNETIC

MOMENT

OF THE

264 keV STATE

The magnetic moment was determined from a measurement on the implanted sample. To analyse the data with the aid of eq. (12), we used the values U~/T = 140 ps and AzzQz = -0.115

(see fig. 3bf. In doing so, we implicitly

assume a 100% substitu-

tional fraction. To our knowledge, no lattice-location experiments have been carried out on Ge implanted in iron. However, the large solubility of Ge [ref. ““)I and the large anisotropy observed in in-beam experiments on 67Ge in iron 17) may justify our assumption. In the analysis of the three-detector ratio we rather arbitrarily assumed an 8% uncertainty in the effective anisotropy. As in the case of “As, this determines the accuracy with which the Larmor frequency can be derived from the experimental data. The final value of the Larmor frequency is w,_= -481 (14) Mrad/s, from which we find a magnetic moment y = +0.736 (22) y,. No corrections for diamagnetism and Knight shift were applied.

284

M. Mohsen,

E Pleiter / Partial IUerimes and g:fac~orr

7. Discussion Our results The latter values

for T,,, and j_~ are close to the adopted

have been

determined

which themselves

scatter

by averaging considerably,

values

given in refs. “,‘*).

over a large number be it within

to point out that in several cases even the directly measured

of reported

limits of error. We want quantity,

wL7/B, deviates

notably from the corresponding values obtained in the present work (table 1). The present results should be considered to be more reliable because they were obtained in a time-differential experiment in which prompt, delayed and random events could be well separated. TABLE 1 Experimental

values of u/B measured excited $- states in “.“As

Level “As,

“As,

280 keV

264 keV

on the first

UN/B (mrad/T)

Ref.

6.6 (13)

IX

5.9 (9) 7.0 (8) 5.9 (9) 6.93 (15)

111 ) ?) present work

7.4 (7) 6.18 (19)

present

Iv1

c) work

We will now discuss the magnetic moments of the first excited $- states in 75.77A~ in terms of the core-excitation model in which the even-even core is assumed to couple to either a p3,* hole or an f_5,2 particle. Adopting the notation of ref. 4), we write the wave functions

of the t- ground

state and the first excited

$- state as

I;), = AlO;; ;)+Jl

-A* 122; 5))

(13)

I$), = BIO$; I) -Jl

- B2 125; ;) ,

(14)

where Ij,j,; J) denotes a state in which the core spin j, has been coupled to a particle (hole) spin j, to give a total angular momentum J. The magnetic moment follows from the expressions given by Braunstein and de-Shalit *‘) /.L($) = $( 1 - B*)(22g,+

13gi,2) +$B'g,,z

.

(15)

Here g, is the g-factor of the first excited 2+ state of the even-even core, and g3j2 and gs,* are the g-factors of the P~,~ and fslr single-particle states. We take g, = Z/A = 0.44. For 75As, Tandon and Chopra “) have derived B2 = 0.828 (6) from the ratio of B(M1) transition probabilities, and gX12= 1.076 from the ground-state magnetic moment. Substituting these values and the present result for ~(2) in eq. (15), we find g5,?=0.303 (8) which is close to the Schmidt value g$z =0.346.

M. Mohsen, E Pleifer / Partial liferimes and g-factors

In the case of “As, complete model

analysis.

not enough

However,

in the following

experimental

285

data are available

we may check the consistency

to carry out a

of the core-excitation

way. We assume

that the values of the intrinsic parameters g3,? and g5/2 for “As are equal to those for 75As. Using again eq. (15), we obtain B2= 1.02 (3). This relatively large value of B’ may be due to the larger energy

separation between the first and the second excited 2p state in “As as compared to “As. (Actually, the second excited $- state in “As has not yet been identified, but according to the known level scheme it must lie above 634 keV.) The occupation number ( NyP) of a particular single-particle orbital (l, j) follows from the summed spectroscopic strength observed in a pickup reaction, while the corresponding value from a stripping reaction may be interpreted as the number of holes (NEYP). Experimental results for the If,,, proton orbital obtained from (d, ‘He) reactions (ref. “)) and (jHe, d) reactions (ref. “)) on 72,74,76Geare collected in table 2*. In the latter case, only the transition to the lowest $- level in 73,75.77Asis taken value 2j + 1 = 6 for into account. The sum NY”+ N yp is close to the single-particle all nuclei.

However,

the If,,,

than one level, in apparent preceding paragraph.

strength

in “As

disagreement

seems to be distributed

with the conclusion

arrived

over more at in the

TABLE 2 Number of occupied (NY”) and empty ( NrP) states in the lf5,? proton orbital of “.“,“Cie as derived from (d, ‘He) and (jHe, d) reactions Isotope “Ge ‘+Se “Ge

1.34 2.20 2.44

4.92 3.32 2.05

6.26 5.52 4.49

“) from (d, ‘He) [ref. “)I. h, from (‘He, d) [ref. ‘?)I; only the transition to the lowest $- level in “.“,“As is taken into account.

The

authors

would

like to thank

Mr.

F.Th.

ten

Broek

for carrying

out the

radiochemical treatment of the irradiated materials, and Mr. J.J. Smit for performing the implantations. They are obliged to Dr. S.Y. van der Werf for valuable discussions. One of us (M.M.) gratefully acknowledges the financial support from the University of Groningen and the warm hospitality received in the Nuclear Solid State Physics Group of the Laboratorium voor Algemene Natuurkunde. l We did not use the (‘He, d) data reported summed to the spectroscopic strength observed value by almost 30%.

by Schrader er al. “) because their result for “Ge, if in the (d, ‘He) reaction I’), exceeds the single-particle

M. Mohsen, E Pleiter / Partial ljferimes and g,factors

286

This work was performed voor Fundamenteel the “Nederlandse

Onderzoek Organisatie

as part of the research der Materie”

(FOM)

voor Wetenschappelijk

programme

of the “Stichting

with financial Onderzoek”

support

from

(NWO).

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