Density matrix approach to the atomic nuclei: Anomalous E1 transitions, para- and orthostates, isobaric analogue states

Abstract

The matrix elements of single-particle and collective transitions have been expressed in terms of time-even ϱ + and time-odd ϱ − components of a density matrix variation in the external field. ϱ + and ϱ − obey a rather simple system, which has the same mathematical form in superfluid and non-superfluid nuclei. We have demonstrated the importance of the energy gap variation in the external field for the electric single-particle transitions. In particular the anomalous E1 transitions in deformed nuclei cannot be explained without taking into account the energy gap variation processes. A striking analogy exists between collective nuclear states and the hydrogen molecule. We have shown that the former can be characterized, to a good accuracy, by values of the intrinsic spin of either 0 or 1. Some experiments capable of displaying nuclear orthostates are proposed. The collective state equations have been solved exactly analytically in the case of isobaric analogue states. The nuclear Coulomb potential has been accounted for explicitly and no approximations have been made for the nuclear self-consistent field and the residual interaction. In this way we have obtained an exact formula for the allowed Fermi β-decay matrix element which accounts for all the isobaric spin impurities due to the nuclear Coulomb potential. Formulas for the ground-state isobaric spin impurity and the Coulomb shift have been also derived. For the sake of completeness a method for exclusion of spurious states has been developed. It is applicable for any nuclear self-consistent potential and residual interaction radial dependences.