Abstract

The present article deals with detailed theoretical studies of pairing correlations between nucleons in the potential approach in the context of the adiabatic three-particle model of nucleus. In the mentioned model the even-even spherical (or deformed) nucleus has been considered as a system of the corresponding core and two valence nucleons which are moving in the static field of the core. The model is based on the assumption that the valence nucleons motion consists of two components in the R⁶ space: rapid angular nucleons motion within the S⁵(Ω) sphere and adiabatic (slow) motion of nucleons along hyperradius R. Stationary states of deformed even-even nuclei whose mean self-consistent field being simulated by anisotropic Woods-Saxon potential, are described in the framework of the adiabatic three-particle model. An algorithm and relevant software applications are elaborated in order to obtain numerically the energy spectrum of axially symmetrical deformed nuclei. The efficiency of the adiabatic approach is illustrated for the example of the numerical calculation of spectra of the axially symmetrical deformed even-even nuclei ⁶⁴Zn and ⁷⁴Se which have two valence nucleons in the outer unfilled shells. The calculated energies of excited states are in agreement with the experimental data for the region of lightweight nuclei while for the region of middle and heavy nuclei the effect of polarization of the even-even core must be taken into account. The thin structure of the energy spectrum by total angular momentum of the nucleus was found and was explained due to the residual interaction of valence nucleons. The results of this work will be first of all of a fundamental character and will give new information on the mechanisms of formation of low-lying even-even nuclei states

Keywords: even-even nucleus, nuclear core, Schrödinger’s equation, adiabatic approximation, hyperspherical adiabatic approach, correlations of nucleons

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