Nucleon density distribution in description of nuclear decays
Introduction
The challenge of nuclear theory is to find a unified approach suitable for describing nuclear structure and nucleus-nucleus interaction. Though ab initio approaches are promising for this, they can presently be used only to describe relatively light nuclei. So, we often use the partially ab initio microscopic approach [1], in which the energy density functional (EDF) is constructed based on the interaction of nucleons and several phenomenological parameters are introduced. With the EDF one can calculate self-consistently the nucleon distributions in nuclei. As shown in Refs. [1], [2], [3], [4], [5], the radius and diffuseness parameters calculated with the partially ab initio EDF are smaller than those in the phenomenological approach. The nucleon-nucleon interaction in the surface region of nucleus should be consistent with the density profiles. The smaller the diffuseness, the stronger the nucleon-nucleon attraction is in the surface region of nucleus. The interaction between the nucleons in the surface region is mainly responsible for the nucleus-nucleus attraction, while the nuclear structure is mainly defined by the nucleon-nucleon interaction inside the nucleus. The density profiles of two nuclei can be fold with the nucleon-nucleon interaction to calculate the nucleus-nucleus potential.
The nucleus-nucleus potential is required in the analysis of nuclear collisions, dinuclear system (DNS) dynamics, alpha-decay, cluster radioactivity (CR), and spontaneous fission (SF). The CR and SF can proceed quite a long period of time, which complicates their experimental observation. Therefore, the theoretical prediction of half-lives is important but is supposed to be sensitive to the nucleus-nucleus potential used. The CR and SF will be considered here with the cluster approach in which the nucleus-nucleus potential is a crucial ingredient. Previously we have calculated the nucleus-nucleus potential with the phenomenological nucleon density profiles and nucleon-nucleon interaction in the surface region. As the first step, one can use the self-consistently calculated nucleon density and check if the interaction of nucleon in the surface region, which corresponds to a good description of the Coulomb barrier, is consistent with the EDF used.
In Sect. 2, we discuss the nucleon density distributions obtained in the self-consistent calculations presented in Ref. [2]. In Ref. [2], we have microscopically calculated the nucleon distributions and showed how the phenomenological nucleon-nucleon interaction is modified for these densities to obtain a good description of the position and height of the Coulomb barrier, which are the measurable objects. In Sect. 3, we check if this potential is suitable for simultaneous description of half-lives for alpha-decay, CR, and SF. As shown in this section, the mass parameter for the cluster model depends on the surface diffuseness and is calculated either phenomenologically or microscopically. It worth to justify microscopically the phenomenological mass parameter used for the DNS [6]. The cluster configurations considered are formed in charge asymmetry coordinate [7], [8], [9], [10]. The results are summarized in Sect. 4.
Section snippets
Nucleon density distribution in the partially ab initio EDF
There are partly ab initio microscopic approaches in which the main part of the EDF parameters is found starting from the free nucleon-nucleon interaction and only several phenomenological parameters are introduced. The self-consistent non-relativistic Hartree-Fock-Bogoliubov approach with D3Y interaction has been suggested in Ref. [1]. This approach includes the low density free nucleon-nucleon scattering as close as possible. The phenomenological parameters are fit to the ground-state nuclear
Calculations with phenomenological and self-consistent nucleon distributions
In the DNS model [13], the nucleus just before the fission or cluster emission is presented as a system consisting of two daughter nuclei (clusters). Under assumption of fast –equilibrium, the system is described by two coordinates: the distance R between the centers of mass of the clusters and the charge asymmetry where and are the charge numbers of heavy and light DNS nuclei, respectively. The DNS evolves in the charge asymmetry coordinate and can decay in the R
Summary
The self-consistently calculated nucleon density distributions have been analyzed. The use of these distributions allows us to describe the Coulomb barrier in the nucleus-nucleus interaction potential if the parameter of external nucleon-nucleon interaction is consistent with the nuclear diffuseness. The smaller the diffuseness, the stronger the nucleon-nucleon attraction is in the surface region (smaller ). The right description of the Coulomb barrier heights is a good verification of the
CRediT authorship contribution statement
I.S. Rogov: Investigation, Writing - original draft. G.G. Adamian: Methodology. N.V. Antonenko: Conceptualization, Writing - review & editing. T.M. Shneidman: Methodology. H. Lenske: Methodology.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work was partly supported by RFBR (17-52-12015, 20-02-00176) and DFG (Le439/6-1). I.S.R. and N.V.A. were supported by the Tomsk Polytechnic University Competitiveness Enhancement Program. T.M.S. acknowledges Russian Government Subsidy Program of the Competitive Growth of Kazan Federal University.
References (23)
- et al.
Nucl. Phys. A
(2000) - et al.
Nucl. Phys. A
(1995) - et al.
At. Data Nucl. Data Tables
(1988) Theory of Finite Fermi Systems and Applications to Atomic Nuclei
(1982)(1967)- et al.
Z. Phys. A
(1986) - et al.
Phys. Rev. C
(1998) - et al.
Phys. Rev. C
(2016) - et al.
Sov. J. Nucl. Phys.
(1988) - et al.
Phys. At. Nucl.
(2010) - et al.
J. Phys. G
(1975)
Z. Phys.
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