Self-consistent methods for structure and production of heavy and superheavy nuclei

Abstract

Self-consistent methods for the structure of heavy and superheavy nuclei are reviewed. The construction and application of energy-density functionals are discussed. The relationship between the self-consistent methods and microscopic-macroscopic approaches is considered on the mean-field level. The extraction of single-particle potentials from the energy-density functional is described. The isotopic dependence of nucleon distributions and its influence on the nucleus-nucleus interaction is analyzed. As a new additional condition we introduce that the energy-density functional must describe the heights of the Coulomb barriers in nucleusnucleus interaction potentials, thus imposing constraints on the properties of the functional at low matter densities. The self-consistent methods are applied to describe the quasiparticle structure, cluster radioactivity, and fission of the heaviest nuclei. These methods are used to predict the probabilities of β-delayed multi-neutron emission and half-lives of β-decays and electron captures in heavy and superheavy nuclei. The predicted properties of superheavy nuclei are used to estimate the production cross-sections of superheavy nuclei in complete fusion reactions. Contents

Competition between weak and alpha-decay modes in superheavy nuclei

“…Despite the large number of SHN already synthesized with different types of cold and hot fusion reactions, there is a limitation in these reactions that produce neutrondeficient isotopes, far away from the predicted location of the most stable SHN, which is unreachable by fusion reactions with stable beams. Predictions of shell closures from macroscopic-microscopic models based on deformed liquid drop models with shell corrections [9][10][11][12] agree with predictions from self-consistent non-relativistic [13][14][15] and relativistic [16,17] mean-field models with effective nuclear interactions that produce shell closures at (Z, N ) = (114, 184), (120, 172), and (126, 184), depending on the effective interaction used. The sensitivity of the shell closures to the properties of the underlying nuclear forces, makes it possible to use SHN as a laboratory to investigate the nuclear force.…”

Pairing and nonaxial-shape correlations in N=150 isotones

“…In the present paper, I fix the pairing parameters to reproduce reasonably the data of 244 Cm which are 0.63 and 0.57 MeV for neutrons and protons, respectively. The resultant pairing gaps are 0.65 and 0.59 MeV with V ν 0 = −270 and V π 0 = −310 MeV fm 3 . For the SLy4 functional, I find that the strength V ν 0 = −310 and V π 0 = −320 MeV fm 3 produces the pairing gap as 0.67 and 0.53 MeV for neutrons and protons, respectively.…”

“…Recent developments in experimental technology and theoretical modeling have significantly advanced the study of exotic nuclei. The existence of superheavy nuclei in the limit of a great number of protons has long been a subject of interest in nuclear physics [1][2][3]. The shell effect is a key to define their stability.…”

Model for independent particle motion

“…[4]). It turns out that the existence of the heaviest nuclei with Z > 104 is primarily determined by shell effects due to the quantum-mechanical motion of protons and neutrons inside the nucleus [70,71,72,73,74]. In these nuclei the heights of fission barriers are entirely determined by the shell corrections and they would not exist without shell effects.…”

“…Although state-of-the-art theoretical models provide a reasonable description of many aspects of the physics of superheavy nuclei, they face substantial challenges in the prediction of the location of next spherical shell closures [31,32,72,73,74,75]. These challenges are illustrated in Fig.…”