Neutrino-nucleus reactions and muon capture inC12

Abstract

The neutrino-nucleus cross section and the muon capture rate are discussed within a simple formalism which facilitates the nuclear structure calculations. The corresponding formulae only depend on four types of nuclear matrix elements, which are currently used in the nuclear beta decay. We have also considered the non-locality effects arising from the velocity-dependent terms in the hadronic current. We show that for both observables in 12 C the higher order relativistic corrections are of the order of ∼ 5% only, and therefore do not play a significant role. As nuclear model framework we use the projected QRPA (PQRPA) and show that the number projection plays a crucial role in removing the degeneracy between the proton-neutron two quasiparticle states at the level of the mean field. Comparison is done with both the experimental data and the previous shell model calculations. Possible consequences of the present study on the determination of the ν µ → ν e neutrino oscillation probability are briefly addressed.

Nuclear structure and neutrino-nucleus interaction

“…energies and pairing strengths v pair s (p), and v pair s (n) were varied in a χ 2 search to account for the experimental spectra of odd-mass nuclei 11 C, 11 B, 13 C, and 13 N, as explained in Ref. [6]. This method, however, is not applicable for the space S 6 which comprises 21 s.p.…”

“…(2.3)], and for the hadronic current operator J α ≡ {J, iJ / 0 } we use the nonrelativistic form. In spherical coordinates (m = −1, 0, +1), and when k is taken to be along the z axis, it reads [6,7] …”

“…The leptonic current l α ≡ {l, il / 0 } is given by [6,Eq. (2.3)], and for the hadronic current operator J α ≡ {J, iJ / 0 } we use the nonrelativistic form.…”

“…and L / 00 are defined in [6]. The exclusive cross-section (ECS) for the state |J π n , as a function of the incident neutrino energy E ν , is…”

Pairing correlations in odd-mass carbon isotopes and effect of Pauli principle in particle–core coupling in 13C and 11Be

“…This, in turn, can be circumvented through the particle-number projection procedure [21,22], i.e., in the framework of the projected BCS (PBCS) approximation. In fact, recently it has been found [23,24] that the low-lying energy spectra in 13 C can be described quite well in the context of the PBCS approximation for the pairing force among the valence neutrons. Moreover, in this study it was shown that the projection procedure is very important to account for the weak decay observables around 12 C.…”