Yu. V. Ivankov

Two-step mechanisms of two-proton decays of nuclei

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.

Theory of two-step two-proton decays of nuclei

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 off-shell 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.

A consistent description of the successive two-proton decay of nuclei using the diagram technique, the R-matrix theory of nuclear reactions, and kinetic equations for the decay of radioactive nuclei

Using the results from the many-particle theory of deep subbarrier single-proton decays (SPDs) of nuclei, which is based on integral formulas for SPD widths, a general theory of successive two-stage two-proton decays (TSTPDs) from the ground and excited states of both spherical and deformed nuclei is developed. Such decays represent a pair of actual sequential SPDs of the parent (Z, A) nucleus and the intermediate (Z − 1, A − 1) nucleus that are associated by Green’s function G(Z − 1, A − 1) for an intermediate nucleus. It is demonstrated that virtual TSTPDs with widths at positive but fairly low heat values Q1 of the parent nucleus SPD (potentially being much greater than the corresponding widths of successive TSTPDs) appear when the virtual states (lying outside the mass surface of the decaying system) of the intermediate nucleus in the above Green’s function are considered. It is shown that the formulas for the widths of successive TSTPDs obtained using this theory agree with those for similar widths constructed in the theory of nuclear reactions, which includes the production of unstable particles, and with systems of kinetic equations for a chain of nuclei undergoing radioactive transformation. The conditions under which these systems of kinetic equations are generalized by including processes related not only to successive decay but to virtual decays of nuclei as well are studied.

Mechanisms and widths of two-proton decay

A method for calculating the widths of two-proton decay of nuclei with regard to its deep subbarrier character is proposed. The structure and coupling of the channels of facilitated two-proton decay of spherical nuclei are considered for the diproton and uncorrelated mechanisms of two-proton decay.

Magnon mechanism of defect reactions in solids

A phenomenological theory is developed that describes the effect of a magnetic field on the defect reactions in a solid. The theory is based on a concept regarding the lattice magnetism according to which a defect induces a magnetoactive (magnon) branch in the spectrum of elementary excitations of a crystal lacking a magnetic structure in the absence of defects. The probability of a defect complex disintegrating in a magnetic field is calculated in terms of the magnon mechanism of the reaction.

Phenomenological features of two-proton virtual decay of the 45 Fe nucleus

On the basis of the theory of diagonal two-proton two-step virtual decays of spherical nuclei that was developed earlier and the superfluid model of the nucleus, the total and partial widths for the two-proton decay of the 45Fe parent nucleus in the ground state to the ground state of the 43Cr daughter nucleus were calculated along with the angular distribution of protons emitted in this decay. The calculated features of this mode of 45Fe decay were shown to be highly sensitive to the choice of form for nucleon shell potentials. It is also shown that there exists a potential such with which one can construct a successful simultaneous description of the experimental total width and the angular distribution of emitted protons for the aforementioned two-proton mode of decay of the 45Fe nucleus.

Effect of periodically time-dependent magnetic fields on a population of spin states of radical pairs

The time dependences for a population of radical pair spin states and the amplitudes of the transitions between them are calculated for magnetic fields of complex configuration. The abovementioned values are derived directly from the solution to the Liouville equation for the components of a spin density matrix for a radical pair. The oscillating mechanism of the relaxation of partial populations of spin levels upon the monotonous reduction of the full population was established in the course of our calculations.

Influence of weak magnetic fields on radical-pair reactions

The time dependences of the populations of radical-pair spin states and transition amplitudes between them have been calculated for constant and pulsed magnetic fields, with allowance for hyperfine interaction. The above-mentioned characteristics have been found directly by solving the Liouville equation for the radical-pair spin density matrix. It is established that the relaxation of spin-level partial populations oscillates with a monotonic decrease in the total population.