Beta-ray angular distributions of spin aligned 8Li and 8B

Nuclear Physics A 746 (2004) 681c–684c

Beta-ray angular distributions of spin aligned 8 Li and 8 B T. Sumikamaa , T. Iwakoshia , T. Nagatomoa, M. Oguraa , Y. Nakashimaa , H. Fujiwaraa , K. Matsutaa , T. Minamisonoa , M. Miharaa , M. Fukudaa , K. Minamisonob and T. Yamaguchic a

Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan

b c

TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T 2A3, Canada

Gesellschaft f¨ ur Schwerionenforschung, Planckstrasse 1, D-64291 Darmstadt, Germany

The alignment correlation terms in the β-ray angular distributions from spin aligned 8 Li and 8 B have been measured precisely. The difference of these terms between the mirror pair is compared with the prediction. As a result, the G-parity violating induced tensor term is found to be small. The significant contribution from the second-forbidden matrix elements is shown by comparing with the β-α correlation coefficients. 1. INTRODUCTION The β-α angular correlation coefficients of the mirror pair 8 Li and 8 B were measured in 1975 and 1980 by Tribble et al. [1] and McKeown et al. [2] to test the conserved vector current (CVC) hypothesis and the existence of the G-parity violating induced tensor term. The results were consistent with non existence of the induced tensor term. While strong interaction induces only the G-parity conserved current into the weak nucleon current, a small but finite G-parity irregular current may be caused by the asymmetry between the up and down quarks such as the mass difference. To set more accurate limit to the induced tensor term, other approaches are necessary in the mass A = 8 system. Due to the contribution from the second-forbidden matrix elements, it is difficult to extract the induced tensor term only from the β-α angular correlation coefficients. In the present study, the alignment correlation terms in the β-ray angular distributions of spin aligned 8 Li and 8 B have been determined precisely. Since some of forbidden matrices have the opposite sign between the two correlation experiments, we have a chance to determine these forbidden matrices and the induced tensor term at the same time. 2. β-RAY ANGULAR DISTRIBUTION The β-ray angular distribution from spin oriented nuclei 8 Li or 8 B is given by [3]




dW B1 (E) B2 (E) ∝ F∓ (Z, E)pE(E − E0 )2 B0 (E) 1 + PP1 (cos θ) + AP2 (cos θ) , dEdΩ B0 (E) B0 (E)

(1)

where F∓ (Z, E) is the Fermi function, E and E0 are the β-ray total energy and the end-point total energy, respectively. θ is the angle between the β-ray direction and the 0375-9474/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2004.09.050

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T. Sumikama et al. / Nuclear Physics A 746 (2004) 681c–684c

orientation axis. Pi (cos(θ)) are Legendre polynomials. With magnetic substate popula tions am , where am = 1, the spin polarization and the spin alignment for the spin I = 2   case are defined as P = 1/2 mam and A = 1/2 m2 am − 1, respectively. Note that Eq. (1) is slightly modified from the one in Ref. [3]. Here, the alignment correlation term B2 (E)/B0 (E) is described as 

E 1 dI ± dII b 3 f B2 (E) =− − ± ±√ ± B0 (E) 3Mn A Ac Ac 14 Ac



3 g E0 − E 28 A2 c Mn 

3 j3 E 3 j2 E0 − 2E −√ +√ , (2) 14 A2 c 2Mn 35 A2 c Mn where Mn is the nucleon mass, A is the mass number, b is the weak magnetism matrix element, c is the Gamow-Teller matrix element, dI includes the time component of the axial-vector current, dII is the G-parity violating induced tenser matrix elements. f and g are the second-forbidden matrix elements in the vector current, and j2 and j3 are the second-forbidden matrix elements in the axial-vector current. The upper and lower signs indicate β − and β + decay, respectively. Here, we neglect the broad distribution of the final state for simplicity, but this distribution have to be taken into consideration for the weak magnetism b/Ac [5]. Rather large nuclear structure dependent dI term is cancelled in the difference δ between B2 (E)/B0 (E) of 8 Li and that of 8 B as 

δ=

B2 (E) B0 (E)





B2 (E) − B0 (E) 8 Li





8B

dII 3 f 2E  b − +√ + =− 3Mn Ac Ac 14 Ac





3 g E0 − E  . (3) 28 A2 c Mn

The induced tensor term dII /Ac can be determined from the δ. Since the signs of the three terms, f , g and j2 , are inverted in the expression of the β-α angular correlation coefficient, these terms can be separated from the other terms in principle by comparing these data from two different correlation experiments. 3. EXPERIMENTAL PROCEDURE The experimental setup and procedure are essentially the same as those used in the previous work on the mass A = 12 system [4]. The 8 B and 8 Li nuclei were produced through the nuclear reactions 6 Li(3 He, n)8 B and 7 Li(d, p)8 Li, respectively. A 4.7-MeV 3 He (3.5-MeV deuteron) beam provided by the Van de Graaff accelerator at Osaka University was used to bombard an enriched metal 6 Li (natural LiO2 ) target. The recoil angle of 8 B (8 Li) was selected to produce the polarized nuclei. The 8 B (8 Li) nuclei were implanted in a TiO2 (Zn) single crystal placed in an external magnetic field H0 = 2.3 kOe (600 Oe) to maintain the polarization and to manipulate nuclear spins by use of the RF magnetic field. The crystal c axis was set parallel to H0 . The resonance frequencies are split by the quadrupole coupling eqQ between the electric quadrupole moment Q of 8 B (8 Li) and the electric field gradient q in TiO2 (Zn). The initial polarization produced through the nuclear reaction was converted into the positive and negative alignments using two different methods in the NMR technique, as shown in Fig. 1. The one is the Adiabatic First Passage (AFP) method to interchange the populations between neighboring magnetic substates. The other is the depolarization method which equalizes the substate populations. Fig. 1-(b) shows the procedure to produce,

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T. Sumikama et al. / Nuclear Physics A 746 (2004) 681c–684c

(a)

A-2 -1 0 +1+2

(b) +

A

Count 0 2 -1 1

-2 -1 0 +1+2

Cycle 1 + Beam A Section A Section Cycle 2 + Beam A Section A Section

0 -1

1 0 -1 0 -1 -2

t

-2 -1 0 1 2

t

: Depolarization : AFP

0 -1

A-

-1 0 1 -2 -1 2

Figure 1. Timing program of the spin control for alignment production. (a) Alignments of both signs (A− , A+ ) were produced in the same beam-count cycle. (b) The procedure of the β-NMR technique is shown for a negative alignment production.

±

Polarization (%)

for instance, the negative alignment. The 0 alignment was converted back into the po± A A larization to check the spin manipulation. Section -2 Section The substate populations and thus the alignments were determined from the polarization observed before and after the -4 Cycle 1 (A- A+) alignment sections. As shown in Fig. 1Cycle 2 (A+ A-) (a), alignments of both signs are produced -6 in the same beam cycle to reject a system0 400 800 1200 atic error caused by the beam fluctuation. Time (ms) The polarization changes in the count sections of the timing program are shown in 8 Fig. 2 in the case of 8 B. The pure align- Figure 2. Polarization change of B as a funcments with no residual polarization were tion of time. successfully created. The β-ray angular distributions were observed by two sets of plastic-scintillation-counter telescopes placed above and below the catcher relative to the initial polarization. The alignment correlation terms were detected by comparing the energy spectra of the positive and negative alignments. 4. RESULTS AND DISCUSSION The preliminary result of the alignment correlation terms B2 (E)/B0 (E) was obtained as a function of the β-ray energy as shown in Fig. 3. The β-α angular correlation coefficients p∓ (E) in Ref. [2] are also plotted in the same figure, after multiplied by −2/3 to compare with the alignment correlation terms. Both of these correlation terms have large E 2 contributions from the second-forbidden matrix elements. The significant deviation is found between the alignment correlation terms and the β-α correlation coefficients as expected

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T. Sumikama et al. / Nuclear Physics A 746 (2004) 681c–684c

6

0

B

8

-2

2

-4 0

d (%)

B 2(E) / B 0(E) (%)

4

-2

Li

-8

Preliminary

-10

8

-4 -6 -8 0

-6

12 8 4 b-Ray Total Energy (MeV)

Figure 3. Alignment correlation terms. The full circles are the present data and the crosses are the data from the β-α angular correlation coefficients [2].

-12 0

Preliminary

4 8 12 b-Ray Total Energy (MeV)

Figure 4. The difference of the alignment correlation terms. The full circles and the crosses are from the present result and from the β-α correlation coefficients [2], respectively. The lines shows the weak magnetism term with ±1σ bands [5].

from the finite values of the f , g and j2 terms. Among these 3 terms, the contribution of j2 is unique, since the j2 terms of the alignment correlation term and the β-α correlation coefficient are proportional to +j2 E(E − E0 /2) and −j2 E(E − E0 /2), respectively. In higher energy region (E > E0 /2) of Fig. 3, the contribution of j2 term is negative for the alignment correlation terms and positive for the β-α correlation coefficients, so that j2 itself is found to be negative. The differences δ are shown together with the experimental weak magnetism b/Ac [5] in Fig. 4. Significant deviation between δ for alignment term and that for β-α correlation coefficients is due to the contribution from the f and g terms. Since the difference δ is mainly reproduced by b, the induced tensor term dII /Ac is found to be very small. Figure 4 shows the contributions from f and g are small, i.e. about 10 % of b at 10 MeV. Detailed analysis is in progress. REFERENCES 1. 2. 3. 4. 5.

R.E. Tribble and G.T. Garvey, Phys. Rev. C 12 (1975) 967. R.D. McKeown, G.T. Garvey and C.A. Gagliardi, Phys. Rev. C 22 (1980) 738. B.R. Holstein, Rev. Mod. Phys. 46 (1974) 789. K. Minamisono, K. Matsuta, T. Minamisono et al., Phys. Rev. C 65 (2001) 015501. L. De Braeckeleer, E.G. Adelberger et al., Phys. Rev. C 51 (1995) 2778.