Two-step mechanisms of two-proton decays of nuclei

Abstract

A formalism for describing two-step two-proton decays of nuclei is developed on the basis of the multiparticle theory of deep-subbarrier one-proton decays of nuclei that employs integral expression for the decay widths in question. This formalism relies on the idea that the interaction between the emitted protons has but a slight effect on the widths with respect to the two-proton decays being considered. It is shown that such a decay is naturally broken down into the sequential one-proton decays of an (A, Z) parent nucleus and an (A − 1, Z − 1) intermediate nucleus, these decays being related by the Green’s function G(A − 1, Z − 1) that describes the intermediate nucleus with allowance for its real and virtual states, which give rise to, respectively, the sequential and the virtual two-step two-proton decay of the parent nucleus. It is also shown that the widths with respect to sequential two-step two-proton decays coincide with the analogous widths constructed within the R-matrix theory of nuclear reactions leading to the production of unstable particles and with their counterparts obtained with the aid of solving the set of kinetic equations for the chain of nuclei undergoing radioactive decays. It is found that the widths with respect to virtual two-step two-proton decays are close in structure to the widths constructed for the simultaneous two-proton decays of nuclei by using integrated formulas within a simplified model of the method of three-particle hyperspherical polynomials.