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Isoscalar and isovector spin-flip M1 strengths in 11B

The 11B(3He, t) and 11B(d, d′) reactions were measured at forward scattering angles to study the isoscalar and isovector M1 strengths in 11B. Combining the experimental results from the two reactions, the excitation strengths for the isoscalar and isovector spin-flip M1 transitions were successfully determined for the low-lying states in 11B. The obtained strengths were compared with the shell model calculations.

The M 1 transition strengths provide important information on the nuclear structure because they could be a good measure to test theoretical nuclear models. Recently, the M 1 transition strengths are of interest from a view of not only the nuclear physics but also neutrino astrophysics because the spin part of the M 1 operator is identical with the relevant operators mediate neutrino induced reactions. Raghavan et al. pointed out that the 11 B isotope can be used as a possible neutrino detector to investigate stellar processes [1]. High-energy neutrinos from the stellar processes like the proton-proton fusion chain in the sun and the supernova explosions excite low-lying states in 11 B and 11 C by M 1 and Gamow-Teller (GT) transitions via the neutral-current (NC) and chargedcurrent (CC) processes. Such neutrinos can be detected by measuring emitted electrons from the CC reaction and γ rays from the de-excitations of the low-lying states. Because there is one excess neutron in 11 B nucleus, the low-lying states in 11 B are excited by both the isovector and isoscalar transitions. Therefore, both the isoscalar and isovector spin-flip M 1 strengths must be measured to estimate the CC and NC cross sections for the neutrino induced reactions.
The cross sections of hadronic reactions provide a good probe for the weak interaction response since the relevant operators in the hadronic reactions are identical with those in β-decay and neutrino capture processes. Thus, we recently measured cross sections for the 11 B( 3 He, t) and 11 B(d, d ) reactions to determine the isovector and isoscalar spin-flip M 1 strengths in 11 B.
The experiment was performed at Research Center for Nuclear Physics, Osaka University using 450-MeV 3 He and 200-MeV deuteron beams. The detailed explanations for the experimental procedures have been given in Ref. [2]. The measured cross sections were shown in Figs. 1 and 2. Since the ground state of 11 B has non zero spin, the cross sections for the 11 B( 3 He, t) and 11 B(d, d ) reactions are described by an incoherent sum over the cross sections of the different multipole contributions as dσ/dΩ = ∆J π dσ/dΩ(∆J π ). In order to determine the spin-flip M 1 strengths by the multipole decomposition analysis, the angular distribution of the cross section for each ∆J π transition must be given to extract the ∆J π = 1 + contribution.
For the 11 B( 3 He, t) analysis, the cross section for each ∆J π transition was calculated by the distorted wave impulse approximation as seen in Fig. 1. Since the GT strength B(GT) for the ground-state transition is known to be 0.345 ± 0.008 from the β-decay strength, the cross sections for the ∆J π = 1 + transitions to the excited states in 11 C can be related to the B(GT) values by assuming the linear proportional relation. The GT strengths are easily related to the isovector spin-flip M 1 strength B(στ z ) under the assumption that the isospin symmetry is conserved. Although the isospin-symmetry breaking changes this ratio, the variation is usually small. Therefore, the GT strengths obtained from the charge exchange reaction are still useful to study the isovector spin-flip M 1 strengths.   For the 11 B(d, d ) analysis, the cross section for each ∆J π transition was calculated by using the deformed potential method. As shown in Fig. 2, the cross section for the 11 B(d, d ) reaction was successfully explained by the calculation. The isoscalar spin-flip M 1 strength B(σ) for the transition to the 2.12-MeV (1/2 − 1 ) state is 0.037 ± 0.008, which is obtained from the γ-decay widths of the mirror states and the B(GT) value [3]. Using this value, the cross section for the ∆J π = 1 + transitions to the other excited states except the 5/2 − 1 state at E x = 4.44 MeV can be related to the B(σ) values. Since the observed ∆J π = 2 + transition strength for the 4.44-MeV state is much larger than the expected ∆J π = 1 + strength, the ∆J π = 1 + component of the transition strength can not be reliably extracted. Thus, the isoscalar spin-flip M 1 strength for this state was determined from the measured B(GT) value and the relative strength of the isoscalar transition to the isovector transition calculated by using the Cohen-Kurath wave functions (CKWF) [4].
The obtained B(GT) (B(στ z )) and B(σ) values are compared with the shell model predictions using the CKWFs in Fig. 3. The CKWFs reasonably explain the experimental result except the quenching by a factor of 0.5-0.7. The present result will be useful in the measurement of the stellar neutrinos using the NC and CC reactions on 11 B.