Neutrino and antineutrino charge-exchange reactions onC12

Abstract

We extend the formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, both for neutrino-nucleus reactions and muon capture. Explicit violation of CVC hypothesis by the Coulomb field, as well as development of a sum rule approach for the inclusive cross sections have been worked out. We have done a thorough study of exclusive (ground state) properties of 12 B and 12 N within the projected quasiparticle random phase approximation (PQRPA). Good agreement with experimental data achieved in this way put in evidence the limitations of standard RPA and the QRPA models, which come from the inability of the RPA in opening the p 3/2 shell, and from the non-conservation of the number of particles in the QRPA. The inclusive neutrino/antineutrino (ν/ν) reactions 12 C(ν, e − ) 12 N and 12 C(ν, e + ) 12 B are calculated within both the PQRPA, and the relativistic QRPA (RQRPA). It is found that the magnitudes of the resulting cross-sections: i) are close to the sum-rule limit at low energy, but significantly smaller than this limit at high energies both for ν andν, ii) they steadily increase when the size of the configuration space is augmented, and particulary for ν/ν energies > 200 MeV, and iii) converge for sufficiently large configuration space and final state spin. The quasi-elastic 12 C(ν, µ − ) 12 N cross section recently measured in the MiniBooNE experiment is briefly discussed. We study the decomposition of the inclusive cross-section based on the degree of forbiddenness of different multipoles. A few words are dedicated to the ν/ν-12 C charge-exchange reactions related with astrophysical applications.

Inclusive and pion production neutrino-nucleus cross sections

“…At large angles the contribution of the collective states is suppressed by form factor effects [22]. Several studies have been made on the excitation of low energy collective states in neutrino interactions [22][23][24][25][26][27][28] but specific work is needed to assess their role in the present type of data where forward bins offer favorable conditions to display their contribution.…”

Nuclear structure and neutrino-nucleus interaction

“…In the PQRPA calculations we were not able to use spaces lager than S 6 because of numerical difficulties. Thus all results that follow were done with the RQRPA where such calculations are feasible [7].…”

“…The GT sum rule limit SR GT [7] and several previous RPA-like calculations, namely: RPA [12], CRPA [17], and RQRPA within S 20 for two-quasiparticle cutoff E 2qp =100 MeV [9], PQRPA within S 2 , S 3 , and S 6 [7], as well as the shell model result [12], are also exhibited.…”

“…A few of them are exhibited in the left panel of Fig. 3, namely: a) SM and RPA [12], with g A = 0.88, and S 3 , b) CRPA [17], with g A = 1.26, and S 4 , c) RQRPA [9], with g A = 1.23, S 20 , and E 2qp =100 MeV, and d) PQRPA [7], with g A = 1.0, S 2 , S 3 , and S 6 . In spite of very significant differences in g A , and the 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] …”