Isospin mixing in 12C

Volume 62B, number 1

PHYSICS LETTERS

10 May 1976

ISOSPIN M I X I N G IN 12 C ~ E.G. ADELBERGER 1, R.E. MARRS 2, K.A. SNOVER 3 and J.E. BUSSOLETTI 3 Physics Department, University o f Washington, Seattle, WA 98195, USA and California Institute o f Technology, Pasadena, CA 91125, USA Received 25 March 1976 Gamma-ray decays of the 12.71 and 16.11 MeV states of 12C are mvestigated in a coincidence study of the l°B(r, P3') reaction, and using the 163 keV 11B(p, 3,) resonance. This information together with existing data on M1 transitions and stripping and pickup spectroscopic factors is used to determme the lsospin mixing between the 12.71 and 15.11 MeV levels. A charge dependent mixing matrix element of 110 -+ 30 keV is deduced.

The mixing of T = 0 and T = 1 levels in 8Be and 12C has attracted much attention because the off-diagonal matrix elements are believed to be about 150 and 250 keV, respectively [ 1 , 2 ] , while Coulomb forces apparently give matrix elements of only ~ 60 keV [ 1 , 3 ] . These examples seem to support Negele's analysis of &splacement energies which requires a sizable AT = 1 component of the short-range nuclear force [4]. The sigmficance of these results has led us to reexamine the mixing in 12C. The 15.11 MeV 1+, T = 1 and 12.71 MeV I + T = 0 levels form an interesting system for quantitative studies of lsospm violation [3]. Good wave functions are available and the levels are known to have a very simdar space structure. All previous analyses of the isospm impurities have assumed simple two-state mixing 115.1) = al 1) +/3t0)

(ltHcDI0) /3 = 2400 keV

a2 = 1 -/32.

t12.7)=--/311) + ctl 0) We examine the validity of this approximation in several applications below. In the three years since Bralthwaite, Bussoletti, Cecil and Garvey [2] (BBCG) reported a value (11HcD I0) = 250 --+50 keV a variety of experiments have been performed to check this result [ 5 - 8 ] . Un-

Supported m part by ERDA (Univ. Wash.), NSF (Caltech), and the A.P. Sloan Foundation (E.G.A.). 1 Visiting Associate, Caltech, 1975, permanent address University of Washington. 2 Present address: Caltech. a Present address: University of Washington.

fortunately the different approaches have yielded inconsistent results and none of the experiments by itself IS completely convincing. In this letter we report new experimental results wtuch bear upon the isospin mixing in 12C and then analyze electromagnetic and single-nucleon transfer data in A = 12 using the charge independent shell model calculation [9] of Cohen and Kurath (CK). Our ~trategy is first to estabhsh the correctness of the CK wave functions and then to use them to interpret radiative and single-parttcle transfer transitions revolving the 12.71 and 15.11 MeV states. We show that there is clear evadence for isospm mixmg m the 1 + doublet, but that the magnitude is much smaller than that reported by BBCG [2]. We begin with our measurements of the decay propertles of the 12.71 and 16.11 MeV levels of 12C (detads wdl appear elsewhere). Coincidence measurements of the 7-ray branching ratios of 12C(12.71) and 12C(16.11) were performed at the University of Washington using the 10B(z, PT) reaction at 4.1 MeV incident energy. Protons were detected m a counter telescope at 0 °. Gamma-rays were counted in a 25.4 cm × 25.4 cm NaI spectrometer, usually at 125 °. The singles and coincidence data were recorded simultaneously on magnetic tape and sorted later to obtain 7decay branching ratios. The system is designed so that dead time corrections to the branching ratios are negligible. The 7-ray detection efficiency was measured to -+3% as described in ref. [10]. From coincidence spectra we obtain F3,0/U = (1.93 -+ 0.12)%, F 3,1/F~'o = (0.t50 -+ 0.018), and Fa/F = (97.8 -+ 0.1)% for 12C(12.71), and F3,1/P = (2.42 -+ 0.29) × 10 -3 for 12C(16.11). Our branching ratios are in reasonable 29

Volume 62B, number 1

PHYSICS LETTERS

10 May 1976

Table 1 Comparison ofA = 12 observables with theory Transition

l'~t(eV) theory a) I',y(eV) exp.

Transmon

12B( 0.95~ 0.00) 12C(16.11~ 0.00) 12C(16.11-+ 4.44) 12C(16.11~12.71) 12C(15.11~ 0 )

1.71X 10 -3 0607 11.8 0.215 30.8

12C(15.11~ 4.44) 1.32 12C(15.1 ~ 1 2 . 7 ) 047 12C(12.71~ 0 ) 0.11 aaC(12.71~ 4.44) 0015

(2.19±0.24)× 10 - 3 b ) 0.50+0.11 c) 16.1 ±2.3 c) 0.23±0.05 c) 37.0 ± 1.1d)

State J, T

sPlCku p a) theory

sPlCku p g, h) exp.

12C( 0 ) 0+;0 12C(4.44) 2÷, 0 12C(12 71) 1+; 0 12C(15.11) 1÷, 1 12C(16.1 l) 2÷, 1

0.61 1.12 0.66 1.81 3.31

0.84 1.21 0 63 1.71 3.15

F~,(eV) theory a)

F,),(eV) exp. 0.92' ±0.36 d,e) 0.56 ±0.16d, e) 0.35 ±0.05 f) 0.053±0.010f, c)

pickup g, i) Sexp.

sstrippmg a) theory

sstrippmg g, j) exp.

0.67 1 98 2.85

5.70 1.10 0.79 0.83 0.56

6.09 1.41 0.86 0.76 0.56

a) Ref. [9j. b) Ref. [15] c) This work. d) Ref. [16]. e) Ref. [17]. f) Ref. [5]. g) Normahzatlon: (S(12.71) + S(15.11) + S(16.11))theory = (S(12.71) + S(15.11) + S(16.11))exp" h) Ref [141 , 13C(p, d). 1) Ref. [2] ; 13C(d, t). J) Ref. [181; 11B(r, d).

agreement with previous, less precise work (see ref. [I 1 ] ). Relatwe y-ray branching ratios of 12C(16.11) were also measured at Caltech using the 163 keV 11 B(p, 3') resonance. Water cooled 11B targets were bombarded with 1 0 - 1 5 / a A (electrical) of H~ ions. Gamma-rays were detected with a 15% Ge(Li) detector. From a spectrum on resonance with 0.1 C of integrated charge we deduce P~,0/F3,1 = (3.1 +- 0.5)%, Y,r(16.11 -+ 9.64)/P,rl = (2.0 +- 0.26)%, and F,r(16.11 12.71)/F3,1 = (1.45 + 0.25)%. Off-resonance y-ray yields were found to be neghgible. The efficiency of our detector was measured using the known decay schemes of 56Co and 23Na(p, 3') resonances at Ep = 1318 and 1416 keV [12]. In table 1 we present some experimental data on radiative widths in A = 12, along with the correspondmg values from the CK calculation [9]. We focus first on the y-ray results which give more rehable structure information than do reachon data. The CK calculation is m very good agreement with experiment for seven out of nine y-ray transitions, including all the lsovector M l's, with a maximum discrepancy between theory and experiment of 17%. On the other hand the "isoscalar" M1 transitions from the 12.71 MeV level are faster than expected by a factor of ~ 3. Since there is no reason why the CK isoscalar transition speeds should be less accurate than the isovector speeds, we follow ref. [5] and assume that the anoma3O

lously fast "lsoscalar" transitions contain an isovector component. This can arise from T = 1 impurities in either the lnihal or the final state. In the CK framework the M1 matrix elements are (01Ml112.71) = (0011Ml1101) ~ ( 1 liIHcD I 101 ) + t

E1 - Ei

(0011M1[11i)

(001 ]HcD 101,) + /Z-J E L S E / " (01/IMIII01) (4.441Mll 12.71) = (2011Mll 101) + ~ (1 ltlHcD1101)

t +

E1 - E t (2011HcD 1211)

/

E1 - El

(2011Mill lt)

(2111MII101)

where the CK states are labeled by IJTi). We evaluate the importance of the possible admixed CK states by making the reasonable assumption that no matrix elements of HCD are much greater than (1111HcDI 101 ). We take the energy denominators (when unknown experimentally) and the M1 matrix elements from CK. As expected the lsovector impurity m the 12.71 -~ 0 MeV transition is dominated by an admixture of the

b

V o l u m e 62B, n u m b e r 1

.050

PttYSICS LETTERS

o

1.2 1.0

10 May 1976

CK stripping and pmkup amplitudes are much largel for the 12.71 and 15.11 MeV levels than for any other 1 + states. We express this as

.02! 0.8 0,6

R = o(15.1)_ (m4~/2 +/3A03/2)2 +(a'4 {/2 +/3A1/2)2 o(12.7)

(aA3/2_~A~/2)2+(~A1/2 _/3A{/2)2

2.0 2.

1.8 1.6

1.0 -0.04

1.4 I

I

0.08

0.16

I

I

[

(3.00

0.08

0.16

B Fig. 1. E x p e r i m e n t a l ( s h a d e d area) versus c a l c u l a t e d (sohd line) q u a n t i t i e s as a f u n c t i o n o f t3. a - F ? o ( 1 2 . 7 1 / I ' ? 0 ( 1 5 . 1 1 ) ; b a n d c - S(12.71)/S(15.11) f r o m s t r i p p i n g a n d p i c k u p , res p e c t i v e l y ; d - S(12B(0)/S(15.11) f r o m p i c k u p . H a t c h e d

areas are from 13C(p, d). We assume relative errors of 10% for (d, r) and (d, t) and 15% for (r, d) and (p, d) spectroscopic factors. 15.11 MeV level into the 12.71 MeV state. This is due in part to the small energy denominator, but even more importantly because the 15.11 MeV level nearly exhausts the isovector M1 strength from the 12C ground state. Therefore this tranmion provides an excellent, nearly model-independent way to measure the 15.11-12.71 MeV mixing. By fitting the observed ratio 1'?(12.71 -+ 0)/P?(15.11 -+ 0) to that calculated from CK matrix elements we find/3 = +0.046 + 0.012 where we have included a 20% uncertainty in the theorencal lsoscalar rate (see fig. 1). The second solutmn to the quadratic equatmns, with negative/3, xs not consistent with transfer reactmn data. On the other hand the 12.71 -+ 4.44 MeV transition does not provide a good measure of/3 because our assumptions about (IHcD I)allow the lsospm impurity in this transition to have four significant components, due to admixtures into 12C(12.71) of the two lowest 1+ T = 1 levels and admixtures into 12C(4.44) of the two lowest 2 + T = 1 levels. (The admixtures with large energy denominators are important because of their large M1 matrix elements.) We now examine the 11B(r, d) proton stripping and 13C(d, t) neutron p]ckup spectroscopic factors for the 12.71 and 15.11 MeV levels. We expect these to prov]de an independent although less reliable measure of the 15.11-12.71 MeV isospin mixing. The two-state mixing approximation is vahd m this case because the

where A 0 a n d A 1 are the amphtudes for P3/2 and Pl/2 transfer associated with the lowest T = 0 and T = 1 levels, respectively. Isospm mlxang reduced by Coulomb forces causes the lower-lying member of an analog-antianalog doublet to have an enhanced parentage to l i B + p compared to l l c + n, while the upper member of the doublet is preferentially 11 C + n. Hence proton strippmg should preferentially populate the lower member of the doublet, and neutron pickup the higher member. This phenomenon Is well known from the celebrated case of the 16 MeV states m 8Be and follows from the fact that a proton particle-hole excitation has a lower energy than the corresponding neutron particle-hole excitation due to the Coulomb pairing energy. In table 1B we tabulate relatwe spectroscopic factors m A = 12. It can be seen that CK gwes a good account of those quantities not affected by 15.11--12.71 MeV mixing. The experimental ratio R is shghtly greater m 13C(d, t) and shghtly smaller m 11B(r, d) than the corresponding ratios calculated by CK, which is independent evidence for isospin mixing m the 1+ doublet. The values of the mixing parameters/3 reqmred to account for the pickup and stripping ratios are/3 = +0.020 -+ 0.025 and/3 = +0.038 + 0.37, respectively (see fig. 1). These values are m gratifying agreement with that extracted from the MI decays. It is hard for us to account for the large isospm violation found by BBCG m the ratio of 13C(d, t)12C(15.11) to 13C(d, r)12B(0) cross sections. However we note that there are discrepancies in the relatwe pickup spectroscopic factors deduced from different experiments. For example, the raUo of spectroscopic factors R s = S(15.11)/S(16.11) measured in a 13C(p, d) experiment at Ep = 55 MeV differs from the same ratio observed by BBCG m 13C(d, t) at E d = 28 MeV. The (p, d) ratio is equal to the corresponding (d, r) observed by BBCG which reqmres that/3 < 0.08. Even if the data were consistent, one might expect the BBCG rat]o to be a less rehable measure of/3 than our ratio R. The DWBA need only compensate for a Q31

Volume 62B, number 1

PHYSICS LETTERS

value difference m our case, while for BBCG it must also properly account for two different reactions. In addition the BBCG ratio deviates from the charge mdependent prediction by only ~2/3 while the ratio R deviates by ~ -+4/3. There does not seem to be enough " s l o p " in the CK calculation to reconcile the experimental M1 widths and (r, d) and (d, t) spectroscopic factor ratios with the BBCG values of/3 = 0.11. From fig. 1 we see that the ratios of predicted to experimental values of F~(12.71 ~ 0)/F~(15.11 ~ 0 ) , R ( 1 3 C ( d , t)) and R ~ l l B ( r , d)) would be 2.29 -+ 0.33, 0.69 + 0.07, and 1.32 -+ 0.20, respectively, if/3 = 0.11. Since these discrepancies are notably greater than those occurring in transitions not sensitive to the lsospin mixing, we conclude that t3 must be much smaller than 0.11. Although our result is model dependent, it is not especially sensitive to details of the model. It follows primarily from the fact that the 12.71 and 15.11 MeV levels have nearly identical space structure. We do not trust the large values of/3 estimated from other reaction data. These analyses assume that the cross sections of isospln forbidden reactions such as 12C(d, O')IEc(15.11) [2], 14N(d, o012C(15.11) [7], and I°B(~, d)12C(15.11) [8] are due entirely to a direct population of the small T = 0 component of the T = 1 state. Isospin violation in the reaction mechanism is Ignored which does not seem reasonable when one is talking about 1% effects (see ref. [13] for one possible isospin violation mechanism). The a-decay of 12C(15.11) almost surely does not provide a good "handle" on the admixture of 12C(l 2.71) because, as pointed out in ref. [6], the a-width of the latter state is so small (we obtain F~ = 17.7 -+ 2.8 eV) that very small admixtures o f higher lying 1+ T = 0 levels may not be ignored. Let us summarize. Based on a 300% effect in the relative 70 strengths of 12C(12.71) and 12C(15.11) when compared to the charge independent theory, we derive a matrix element (IIHcD[0) = 110 -+ 30 keV which is less than half that found by BBCG. Previously reported large values for the isospin mixing matrix element (11HcD 10) were derived from direct reaction

32

10 May 1976

studies which displayed 1% and 30% anomalies, when compared to charge independent predichons. However all other transfer reaction data are consistent with the matrix element deduced from the 7-rays. We conclude that, with the possible exception of 8Be, there is no evidence from isospin mixing for a sizable A T = 1 component o f the short-range nuclear force. EGA thanks G.T. Garvey for many enjoyable discussions on isospln mixing. We are grateful to D. Kurath for kindly sending us the CK matrix elements and to Prof. P.D. Parker for generous assistance in data taking at Caltech.

References [1] t~.C. Barker, Nucl. Phys. 83 (1966) 418. [2] W.J. Bralthwaite, J.E. Bussoletti, F.E. Cecil and G.T. Garvey, Phys. Rev. Lett. 29 (1972) 376. [3] F.D. Reisman, P.I. Connors and J.B. Marion, Nucl. Phys. A153 (1970) 244 14] J.W. Negele, Proc. Intl. Conf. Nucl. Structure and Spectroscopy, ed. H.P. Blok and A.E.L. Dleperink (Scholars Press Amsterdam, 1974) p. 618. [5] F.E. Cecil, L.W. Fagg, W.L. Bendel and E.C. Jones, Phys. Rev. C9 (1974) 798. [6] D.P. Balamuth, R.W. Zurmuhle and S.L. Tabor, Phys. Rev. C10 (1974) 975. [7] A. van der Woude, W.J. Ockels, P.J. Pasma and L.W. Put, Phys. Rev. C10 (1974) 952. [8] J. Spuller et al., Nucl. Phys. A248 (1975) 276. [9] S. Cohen anal D. Kurath, Nucl. Phys. 73 (1965) 1; A101 (1967) 1. [10] R.E. Marrs, E.G. Adelberger, K.A. Shover and M D. Copper, Phys. Rev. Lett. 35 (1975) 202. [11] F. Ajzenberg-Selove, Nucl. Phys. A248 (1975) 1. [12] B.P. Smgh and H.C. Evans, Nucl. Instr. 97 (1971) 475. [13] F. Iachello and P.P. Singh, Phys. Lett. 48B (1974) 81. [14] H. Taketam, J. Muto, H. Yamaguchi and J. Kokame, Phys. Lett. 27B (1968) 625. [15] J.W. Olness and E.K. Warburton, Phys. Rev. 166 (1968) 1004. [16] B.J. Chertok et al., Phys. Rev. C8 (1973) 23. [17] D.E. Alburger and D.H. Wilkinson, Phys. Rev. C9 (1972) 384. [18] P.D. Miller et al., Nucl. Phys. A136 (1969) 229.