Charge dependence of one-boson exchange potentials

Abstract

The Fermi nuclear matrix elements M F for the ΔJ = 0, ΔT = ±1 β-decays of 41Ar, 44Sc and 52Mn are calculated theoretically in the jj-coupling shell model using in addition to the usual Coulomb potential one-boson exchange potentials with the mass splitting of the ρ-meson, δρ = ρ ±− ρ 0, as a variable parameter. These results are compared with those obtained by using the Blin-Stoyle-Le Tourneux charge-dependent potential which contains parameters p and r that measure the deviation of nuclear forces from exact charge symmetry and q and s that measure the deviation of nuclear forces from exact charge independence. Comparison yields 3 r− p ≈ 0.1 % whereas 3 s− q is dependent on δρ. Using the well-attested relation of 3 s− q ≈ 1%, we obtain δρ in the range, −1 1 2 to – 5 MeV , which are consistent with experimental values todate. With δρ = −3 MeV it is found that the theoretical values of M F are consistent with the experimental ones for the decays under consideration.