Theory of two-step two-proton decays of nuclei
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CLEI Theory
Theory of Two-Step Two-Proton Decays of Nuclei S. G. Kadmensky* and Yu. V. Ivankov Voronezh State University, Universitetskaya pl. 1, Voronezh, 394036 Russia Received January 13, 2014
Abstract—A general theory of many-body diagonal and nondiagonal one-proton decays of spherical and deformed nuclei is developed on the basis of an approach not employing R-matrix theory in describing deep-subbarrier alpha and one-proton decays of nuclei but relying on integral formulas for the widths with respect to these decays. With the aid of this theory and by means of a diagram technique, a formalism is developed for describing two-step two-proton decays of a (Z, A) parent nucleus, which proceed as two successive time-separated one-proton decays of the parent and intermediate [(Z − 1, A − 1)] nuclei, these decays being related by the Green’s function for the intermediate nucleus, G(Z − 1, A − 1). It is shown that, upon taking into account, in this Green’s function, intermediate-nucleus states that are on- and offshell states for the decaying system, there arise, respectively, sequential and virtual two-proton decays of parent nuclei. Expressions for the widths with respect to sequential and virtual two-proton decays from the ground and excited states of spherical and deformed nuclei and for the angular and energy distributions of emitted protons are obtained. DOI: 10.1134/S1063778814120096
1. INTRODUCTION Deep-subbarrier one-proton decays have been studied to date for a large group of nuclei in the case of transitions from their ground and isomeric states (for an overview, see [1]). The properties of these decays were successfully described on the basis of the many-body theory of one-proton decays that employs integral formulas for the widths with respect to these decays and which relies on the results obtained from an analysis of the alpha decay of nuclei [2, 3] and their diagonal and nondiagonal one-proton decays [4–7]. After Goldansky predicted [8, 9] the existence of a new form of the two-proton radioactivity of nuclei, vigorous experimental and theoretical investigations (see the review article of Grigorenko [10]) into twoproton decays of spherical and deformed nuclei began. Those investigations were performed for transitions not only from their ground states but also from their excited states, including isomeric states. From the point of view of the theoretical approaches developed for describing two-proton decays, the whole set of the aforementioned two-proton decays can be partitioned into two subsets: that of sequential decays [10] and that of true two-proton decays. Sequential two-proton decays proceed as the time-separated independent real one-proton decays of the parent [(Z, A)] and intermediate [(Z − 1, A − 1)] nuclei, the respective decay energies Q1 and *
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Q2 [8] being positive. The independence of the decays in question is ensured by the possibility of disregarding the interaction between the two emitted protons. Sequential two-proton decays are successfully described wit
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