Weak transitions inA=6and 7 nuclei

Abstract

The 6 He beta decay and 7 Be electron capture processes are studied using variational Monte Carlo wave functions, derived from a realistic Hamiltonian consisting of the Argonne v 18 two-nucleon and Urbana-IX three-nucleon interactions. The model for the nuclear weak axial current includes one-and twobody operators with the strength of the leading two-body term-associated with ∆-isobar excitation of the nucleon-adjusted to reproduce the Gamow-Teller matrix element in tritium β-decay. The measured half-life of 6 He is under-predicted by theory by ≃ 8%, while that of 7 Be for decay into the ground and first excited states of 7 Li is over-predicted by ≃ 9%. However, the experimentally known branching ratio for these latter processes is in good agreement with the calculated value. Two-body axial current contributions lead to a ≃ 1.7% (4.4%) increase in the value of the Gamow-Teller matrix element of 6 He ( 7 Be), obtained with one-body currents only, and slightly worsen (appreciably improve) the agreement between the calculated and measured half-life. Corrections due to retardation effects associated with the finite lepton momentum transfers involved in the decays, as well as contributions of suppressed transitions induced by the weak vector charge and axial current operators, have also been calculated and found to be negligible. 23.40.Bw, 23.40.Hc Typeset using REVT E X

Muon capture on deuteron andHe3

“…[52], and has been used widely in studies of weak processes [21,22,34,48]. The second one, g A =1.2695 (29), is the latest determination quoted by the Particle Data Group (PDG) [53].…”

“…In the present work, we consider two different models, both of which have been used in studies of weak pp and hep capture reactions in the energy regime relevant to astrophysics [20][21][22]. The first model has been developed within the so-called "Standard Nuclear Physics Approach" (SNPA) and has been applied also to study weak transitions for A = 6 and 7 nuclei [48], and magnetic moments and M 1 widths of nuclei with A ≤ 7 [49,50]. It will be discussed in Sec.…”

Precision measurement of the6He half-life and the weak axial current in nuclei

“…Table VII lists the shifts that have occurred in M GT arising from (a) an improvement in the Q-value determination, (b) an improvement in the calculation of the nucleus-dependent radiative correction, and (c) the inclusion or not of the shape-correction function in the statistical rate function calculation. The benchmark experimental f t-value that has been used by theorists [4,[13][14][15] up until now dates back to Ref. [58] and a statistical rate function obtained from the tabulated values of Wilkinson and Macefield [59].…”

“…[4,13] and later [14,15] have shown that, using the case of 3 H to fix nucleon-delta excitations, the f t-value for 6 He can be calculated to within a few percent. These two decays, then, can play an important role in testing the accuracy of nuclear wave-function calculations [4,13,14], or as suggested in Ref. [15], in fixing low-energy constants in effective-field theory calculations [1].…”

Effects of Three-Nucleon Forces and Two-Body Currents on Gamow-Teller Strengths

“…For the transition operator, the focus is on the role of meson-exchange currents [4] and two-body currents (2BCs) from chiral effective field theory (χEFT). Twobody currents are related to three-nucleon forces (3NFs) [5,6] because the low energy constants (LECs) of the latter constrain the former within χEFT.…”