The magnetic moment of the 8+ state in 212Rn

Artclear Physics A238 (1975) 141-148; @ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

THE MAGNETIC MOMENT OF THE 8+ STATE IN “‘Rn W. WITTHUHNt, 0. HiiUSSER, D. B. FOSSANtt, A. B. MCDONALD and A. OLINttt Chalk River Nuclear Laboratories, Atomic Energy of Canada Limited, Chalk River, Ontario, Canada KOJ lJ0 Received 29 August 1974 Abstract: The g-factor of the isomeric 8+ level of z12Rn (r+ = 1.0~s) was measured by the stroboscopic method. The result g = t-O.91 1 &to.012 indicates a small deviation from predictions based on core polarization blocking. E

NUCLEAR

REACTION 204Hg(12C, 4n), E = 70 MeV; measured ~(0, H, t). 212Rn level deduced g. Enriched target.

I

1. Introduction The low-lying excited levels in the N = 126 isotones 210Po, ‘llAt, ‘12Rn, 213Fr and 214Ra are expected to have predominantly an (h%)n proton shell model configuration. The levels of “‘PO and ‘“At have been studied by several authors ‘#2), while information on 212Rn, ‘13Fr and 214Ra has been given by Maier et al. “). All seniority u = 2 and 3 states with the highest spin (8’ for doubly even, y- for oddeven isotones) are isomeric states with half-lives between 50 ns (211At) and 67 ~LS (‘14Ra). The level schemes are shown in fig. 1. From single-particle additivity considerations, it follows that g-factors of (h,) states should have the same values, i.e., g((h$, J) = g(h%). Core polarization contributions are expected to be mainly of a renormalized character and thus additive except for a slight decrease in g for increasing n that results from the blocking of h+ + h, core excitations because of the filling of the h, orbital. Theoretical predictions “) yield a small blocking reduction of about 10 y. in the g-factor in going from the (h+)l, $- state in “‘Bi to the (h+)6, 8+ state in 214Ra. Additional effects might also make non-additive contributions; these effects, such as a core polarization state (J, u) dependence, are of considerable interest in the study of effective Ml operators. The experimental g-factor results for states in ‘OgBi(g.s.) [ref. ‘)I, 210Po(8+, T+ = 110ns) [refs. “-“)I, 211At(G-, T+ = 50 ns) [refs. 10*11)]and212Rn(8+, T+ = 1.0~s) [ref. “)I agree within the errors, indicating a significant deviation from the blocking predictions. Only the recently published g-factor of the 8+ state of 214Ra [ref. “)I shows a small difference of about 3 y0 compared to that of the “‘Bi ground state. t Present address: tt Present address: ttt Present address:

University of Erlangen-Niirnberg, Erlangen, Germany. State University of New York, Stony Brook, NY. University of Victoria, Victoria, BC. 141

142

W. WITTHUHN

et al. 8*6+-

8’ 6' 8+ 6* L'

"Ons

2'

1510 IL71 IL25

21/2-

-‘us

1585

6

L*-

-1637

2+-

-1381

4+ 21/2- 5Ons

1L17

17/2-

1321

I$-

1067

17/2-

IL10

'3/2_

1188

2f

1180

i

9l2-1

I 0+

2’oPo

9/2-1

0+

2rzRn

2’1At

-

o+-

213Fr

211

!a

Fig. 1. Low-lying levels of the (he)” proton configuration in N = 126 isotones. The schemes are taken from refs. I* 3).

Since the uncertainty of the g-factor result for the Sf state in “*Rn is of the same magnitude as the blocking prediction, a remeasurement of this *l*Rn 8+ state has been made with higher accuracy to gain further insight into core polarization blocking and possible cancellation from other non-additive effects. 2. Experiments and results 2.1. EXPERIMENTAL

PROCEDURE

The isomeric 8+ state of *l*Rn was populated and strongly aligned by the reaction 204Hg(‘2C, 4n)*‘*Rn with a 70 MeV ‘*C beam. The target was a droplet of liquid mercury (enriched > 80 % with *04Hg). It was placed in a small recess in a copper backing and kept in place by a thin mylar coating (about 100 pg/cm2)t. The Larmor precession frequency mL was determined by the stroboscopic method (SOPAD)14); the experimental set-up was similar to that described in ref. “). The ‘*C beam of the Chalk River tandem accelerator was chopped into pulses with a width of AT, = 40 ns and a repetition time of To = 800 ns. The y-ray intensity was detected by two NaI(T1) detectors Y and Z within two time windows 100 ns s t, =< 300 ns and 500 ns 6 t2 5 700 ns after the beam pulse. The detectors were placed symmetrically about the beam direction at angles 0 = 4 135”. The magnetic field, applied perpendicularly to the detector plane, was measured by a calibrated Hall probe. The uncertainty in the absolute value was 0.5 %. t The procedure of the target preparation

was similar to that described by Maier et al. 13).

212Rn 8+ MAGNETIC

143

MOMENT

In the present case only terms up to k = 2 are important in the multipole expansion of the angular distribution, i.e. only the expansion coefficient Azz is relevant. Thus the double ratio of the four counting rates Y1, Yz, Z1 and Zz is given by (for details see ref. ‘“)): Z,Y, oc 1 +4R do2cos(2d0)-2dw(o,-oLO)sin do2+4(0,-o,,)2 Z2Yl

(248)

,

(1)

with LT

3~422

R=

OLO =

1 +r/r,,,-t+AZZ

’

-

do

,

= A+‘. r

To

Ll

The quantity r is the mean life of the isomeric state, r,,, the relaxation time of the nuclear alignment and All is the deviation of the y-detectors from the symmetric position, mainly caused by beam bending (see fig. 1 of ref. ‘“)). 2.2. RESULTS

The stroboscopic resonance of the 1274 keV y-radiation is shown in fig. 2. The solid line is a least-squares fit of eq. (1) to the experimental data. All results are -

1

I

/

I

1

1

I

H, = 916.9 G g=O.894

I

I

I

400

,

I

I

I

1

I200

800

MAGNETIC

+ .008

FIELD

H

I

1600

[G]

Fig. 2. Stroboscopic resonance of the 1274 keV y-radiation following the reaction 240Hg(‘2C, 4n) 212Rn. The solid line is a least-squares fit of eq. (1) to the experimental data.

summarized in table 1. From the resonance field Ho and the beam pulsing frequency the uncorrected g-factor is determined to be g = +0.894+0.010.

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W. WITTHUHN

et al.

TABLE 1

Summary of the experimental y-transition

(keV)

CXP

.9""con-.

results

Line-width

A-P 22

AthOr.

b

22

AH(G) 4+ -+2+ 2++0+ average

227 1274

0.897&0.009 0.893&0.006 0.894&0.010 “)

85h-30 144&20 120&30

0.30f0.04 0.2850.03

0.36 0.26

“) The error includes the uncertainty of the magnetic resonance field Ho. complete alignment of the 8+ state.

b, Assuming

The experimental results show that the relaxation time z,,, is considerably greater than 7 (a relaxation time of greater than 100 psec is expected for the liquid mercury target 13,16)). If 1/7,,1 is << l/7, then the observed half-width of the resonance curve AH = 120+30 G corresponds to a half-life T+ = 1.3kO.3 ,us, which is consistent with the measured value of 1.0 ps [ref. “)I. Also the A”;,P values are very close to the A(2h2eo’ calculated for complete alignment of the 8+ state “) which again suggests 7,,1 > 7. 2.3. CORRECTIONS

TO THE g-FACTOR

The effective magnetic field He,, at the position of the nucleus differs from the external field because of the Knight shift K and the diamagnetic shift 6: He,, = H,, (l+K)(l+o).

Both corrections are of the order of a few percent in the lead region. However, the difference between the g-factors of 2o ‘Bi and 212Rn due to the blocking effect is predicted to be onjy about 5 %. Therefore the experimental data must b: corrected carefully for both shifts. We follow the procedure described in detail in refs. ‘s@“). The diamagnetic shielding factors are taken from a recent calculation by Feiock and Johnson ’ “) based on relativistic electron theory in Hartree-Fock-Slater approximation. The values of these corrections are listed in column 8 of table 2. The situation concerning the Knight shift is far more problematic because there are no experimental data on the Knight shift for PO, At, ,Rn and Ra. The only simple case is 20gBi: the g-factor was measured in an ionic environment (Bi3+), where the Knight shift vanishes, K(Bi) = 0. For all other nuclei we have estimated the Knight shifts K by extrapolating the available data. Extrapolating the Knight shifts in the liquid metals “) Cd, In, Sn, Sb, Te and Tl, Pb, Bi in connection with the systematic variation of the series Ga, In, Tl and As, Sb, Bi we estimate K(Po) = (l.Of0.3) %. Since the g-factor of the 8+ level in 210P~ was measured by the reaction 208Pb(a, 2n) 21‘PO the Knight shift has to be taken for dilute PO in Pb at an infinitesimally low conceitration. However, according to the experimental data for dilute metals in Pb given in ref. 22) the Knight shift is assumed to be the same within 30 %: K(Po in Pb) = K(Po).

2’2Rn 8+ MAGNETIC

MOMENT

145

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W. WITTHUHN

et al.

In a similar way (details are given in refs. Is, “)) the following Knight shifts are obtained: K(At in Bi) = (0.6f0.2)%, K(Rn in Hg) = (O.Of0.5)% and K(Ra in Pb) = (2.4+ 1.3)% (see column 7 of table 2).

3. Discussion The large anomaly in the h, proton g-factor in “‘Bi compared to the singleparticle value has stimulated several theoretical calculations 23-2*). The difference &Y = &cxp-gs.p. = 0.33 can be accounted for essentially by two contributions: (i) first-order core polarization 23) and (ii) mesonic exchange currents 2‘). In first-order perturbation theory core polarization contributions result from spin-flip excitations only, i.e. particle-hole excitations of h, + h, (proton) and i, + i, (neutron). Calculations have been made with different interaction potentials: Arima and Horie ‘“) used a simple interaction of the b-function type, Blomqvist et al. 24) chose Gillet, Kim-Rasmussen and Bruckner potentials, while Mavromatis et al. 2 ‘*2“) took a Kallio-Koltveit interaction as well as a Hamada-Johnston potential. I

I

,

I

I

3

L

5

I

0.95-

0.60 -

12 I

209Bi

I 2’0po

I

211At

I

2’2Rn

I

213Fr

6n I

21LRQ

nucleus

Fig. 3. Experimental g-factors of (ha)” proton states in N = 126 isotones compared with predictions from first-order core polarization. For refs. of the experimental points see table 2. (A) Mavromatis el al. 25), (B) Blomqvist et al. 24), (C) Mavromatis and Zamick 26), (D) Arima and HuangLin *‘), (E) Arita 32), (F) Arima and Huang-Lin, adjusted to *OgBi. (A), (B) and (C) have no mesonic corrections. 0: ref. 28), 0 : ref. **) including second-order terms; v : ref. *‘), A: ref. *‘) recalculated with 6g, = 0.16.

zt2Rn 8+ MAGNETIC

MOMENT

147

All calculations agree fairly well, resulting in 6g,+ = 6g,_,(h)-t6g,.,.(i) = 0.12 to 0.18 for the h, single-particle state in “‘Bi. The mesonic correction, which affects the orbital factor gl, was deduced experimentally by Yamazaki et al. “) to be 6g, = 0.1. The estimates given recently by Hyuga and Arima 30) including higher-order processes are about 6g, = 0.15. In recent letters *‘* *“) both the core polarization and mesonic effects were included in the calculations. The results for the *“Bi ground state moment are shown in fig. 3 (open symbols). In considering the core polarization for the (h%)nstates, the 6g,.,.(h) contributions to the g-factors (i.e., the corrections from the h, + h, proton excitations) are predicted to be proportional to the number of effective vacancies in the h, orbital. Thus, these spin-flip excitations should be blocked from 6g,.,.(h) = 0.140 for *“Bi to a value 6g,+(h) = 0.053 for *14Ra. In fig. 3 the comparison between predictions and the experimental data is shown. The measured g-factors for *“Bi to *l*Rn are the same within the experimental errors; the result for *14Ra is about 4 % smaller, which is still less than the predicted 10 o/oblocking reduction. The lack of a significant reduction in the experimental g-factors for the (hh)n states as n increases suggests that other non-additive effects perhaps cancel the blocking reductions. Any core polarization state dependence with respect to J or the seniority u are possible sources of these cancellations 31). Th e p resently available experimental information on the (h*)” g-factors represents an important challenge to the theoretical understanding of such non-additive effects. Arita 32) has estimated the effect of two-particle excitations (dotted line in fig. 3); they are shown to cancel the blocking of the first-order core polarization at least partly. We wish to thank J. L. Gallant for the preparation of the *04Hg target, J. C. Kiteley for technical assistance with the beam pulsing apparatus and R. L. Brown for his help in setting up the electronics. References 1) T. Yamazaki and G. T. Ewan, Phys. Lett. 24B (1967) 278; M. Ishihara, Y. Gono, K. Ishii, M. Sakai and T. Yamazaki, Phys. Rev. Lett. 21 (1968) 1814; T. Yamazaki, Phys. Rev. Cl (1970) 290; J. Blomqvist, D. Fant, K. WikstriSm and I. Bergstriim, Phys. Scripta 3 (1971) 9 2) I. Bergstriim, B. Fant, C. J. Herrlander, K. Wikstram and J. Blomqvist, Phys. Scripta 1 (1970) 243; K. H. Maier, J. R. Leigh, F. Piihlhofer and R. M. Diamond, Phys. Lett. 35B (1971) 401 3) K. H. Maier, J. R. Leigh, F. Piihlhofer and R. M. Diamond, J. de Phys. Suppl. 32 (1971) C6-221 4) S. Nagamiya, Proc. Int. Conf. on nuclear moments and nuclear structure, Osaka, J. Phys. Sot. Jap. Suppl. 34 (1973) 233; H. Horie, ibid., p. 463 5) C. P. Flynn and E. F. W. Seymour, Proc. Phys. Sot. 73 (1959) 945 6) T. Yamazaki, T. Nomura, U. Katou, T. Inamura, A. Hashizume and Y. Tendou, Phys. Rev. Lett. 24 (1970) 317 7) T. Yamazaki, T. Nomura, S. Nagamiya and T. Katou, Phys. Rev. Lett. 25 (1970) 547

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8) C. V. K. Baba, D. B. Fossan, T. Faestermann, F. Feilitzsch, P. Kienle and C. Signorini, Phys. Lett. 43B (1973) 483 9) S. Nagamiya, Y. Yamazaki, 0. Hashimoto, T. Nomura, K. Nakai and T. Yamazaki, Nucl. Phys. A211 (1973) 381 10) H. Ingwersen, W. Klinger, G. Schatz, W. Witthuhn and R. Maschuw, Proc. Int. Conf. on nuclear moments and nuclear structure, Osaka, J. Phys. Sot. Jap. Suppl. 34 (1973) 288 11) C. V. K. Baba, D. B. Fossan, W. Hering, D. Proetel, T. Faestermann, F. Feilitzsch and K. E. G. Lobner, Bull. Am. Phys. Sot. 17 (1972) 927 12) Y. Yamazaki, 0. Hashimoto, H. Ikezoe, S. Nagamiya, K. Nakai and T. Yamazaki, Proc. Int. Conf. on nuclear physics, Miinchen (1973) p. 226 13) K. H. Maier, K. Nakai, J. R. Leigh, R. M. Diamond and F. S. Stephens, Nucl. Phys. Al86 (1972) 97 14) J. Christiansen, H. E. Mahnke, E. Recknagel, D. Riegel, G. Weyer and W. Witthuhn, Phys. Rev. Lett. 21 (1968) 554; J. Christiansen, H. E. Mahnke, E. Recknagel, D. Riegel, G. Schatz, G. Weyer and W. Witthuhn, Phys. Rev. Cl (1970) 613 15) P. Heubes, H. Ingwersen, W. Klinger, W. Lampert, W. Loeffler, G. Schatz and W. Witthuhn, Phys. Rev. C7 (1973) 2128 16) K. H. Maier, J. R. Leigh and R. M. Diamond, Nucl. Phys. Al76 (1971) 497 17) T. Yamazaki, Nucl. Data A3 (1967) 1 18) N. Briiuer, A. Goldmann, J. Hadijuana, M. von Hartrott, K. Nishiyama, D. Quitmann, D. Riegel, W. Zeitz and H. Schweickert, Nucl. Phys. A206 (1973) 452 19) H. Ingwersen, W. Klinger, G. Schatz and W. Witthuhn, to be published 20) F. D. Feiock and W. R. Johnson, Phys. Rev. Lett. 21 (1968) 785; Phys. Rev. 187 (1969) 39 21) D. Kahan, Knight shifts at the melting point (NBS, Washington, October 1971) 22) L. H. Bennett, R. M. Cotts and R. J. Snodgrass, Proc. Colloque Ampere 13 (1964) 171 23) A. Arima and H. Horie, Progr. Theor. Phys. 11 (1954) 509; H. Noya, A. Arima and H. Horie, Progr. Theor. Phys. Suppl. 8 (1958) 33 24) J. Blomqvist, N. Freed and H. 0. Zetterstrom, Phys. Lett. 18 (1965) 47 25) H. A. Mavromatis, L. Zamick and G. E. Brown, Nucl. Phys. 80 (1965) 545 26) H. A. Mavromatis and L. Zamick, Nucl. Phys. A104 (1967) 17 27) A. Arima and L. J. Huang-Lin, Phys. Lett. 41B (1972) 435 28) F. C. Khanna and 0. Hausser, Phys. Lett. 45B (1973) 12 29) H. Miyazawa, Progr. Theor. Phys. 6 (1951) 801 30) H. Hyuga and A. Arima, Proc. Int. Conf. on nuclear moments and nuclear structure, Osaka, J. Phys. Sot. Jap. Suppl. 34 (1973) 31) A. Arima, ibid., p. 212; I. Tonozuka, K. Sasaki and K. Harada, ibid., p. 475; K. Arita, ibid., p. 516 32) K. Arita, Proc. Int. Conf. on nuclear physics, Mtinchen (1973) p. 264