Search for pseudoscalar interaction in 1 2 + → 1 2 - β-decay transitions. (II) On the calculation of the longitudinal polarization of β^--particles emitted in 1 2 + → 1 2-transitions and the relative contribution of the pseudoscalar interaction

A relation between the longitudinal polarization of the β^--particles emitted in 1 2+ → 1 2 - transitions and the relative contribution of the pseudoscalar interaction to β decay is obtained. Lepton conservation, time reversal invariance, C_S = C_T = 0 and the validity of the two-component neutrino theory with a left-handed neutrino were assumed. The non-relativistic nuclear matrix elements as well as the relativistic ones were taken into account and the importance of the latter mentioned. The combinations of electron radial wave functions were calculated by taking into account the finite size of the nucleus and carried out using a surface as well as a uniform distributed nuclear charge. Some considerations on the sensitivity of other ΔJ = 0, yes, transitions to the detection of the pseudoscalar interaction are also made.