Fermi nuclear matrix elements and charge dependence of nuclear forces

By assuming the validity of the conserved vector current theory, the Fermi nuclear matrix elements Msub(F) for the beta decay of F20, Na24, A41, So44, Mn52 and Co56 which violate the ΔT=O selection rule are calculated theoretically in the jj-coupling shell model. In addition, Nilsson's wave functions are used for the Na24 decay, as the jj-coupling shell model wave functions with the lowest symplectio representation do not give a good description to this rather deformed nucleus. In these calculations, the Msub(F) is obtained by considering a short-range, charge-dependent, internucleon potential in addition to the usual Coulomb potential. Experimental values of Msub(F) are obtained by measuring the asymmetry parameter A appearing in the β-γ circular polarisation correlation. Comparison between the theoretical and experimental values yields the result that the deviation of nuclear forces from exact charge independence is about a few per cent, while the deviation from charge symmetry is consistent with a value an order of magnitude smaller. If the conserved vector current is not valid, additional contributions to the Fermi nuclear matrix elements can arise from mesonic exchange currents. However, it is found that such effects would be between one and two orders of magnitude smaller and can be neglected. Thus, the results are consistent with the conserved vector current theory. (author)