On deformability of atoms—comparative study between atoms and atomic nuclei

Abstract

Atomic nuclei can be spontaneously deformed into non-spherical shapes as many-nucleon systems. We discuss to what extent a similar deformation takes place in many-electron systems. To this end, we employ several many-body methods, such as the unrestricted Hartree-Fock method, post-Hartree-Fock methods, and the density functional theory, to compute the electron density distribution in atoms. We show that the electron density distribution of open-shell atoms is deformed due solely to the single-particle valence orbitals, while the core part remains spherical. This is in contrast to atomic nuclei, which can be deformed collectively. We qualitatively discuss the origin for this apparent difference between atoms and nuclei by estimating the energy change due to deformation. We find that nature of the interaction plays an essential role for the collective deformation.

Sub-barrier fusion reactions

“…To this end, the barrier distribution extracted from the quasi-elastic scattering for the 24 Mg+ 90 Zr system was analyzed with the Bayesian statistics. From this analysis, the hexadecapole deformation parameter of 24 Mg, β 4 = −0.11 ± 0.02, has been determined precisely for the first time (see Fig. 13).…”

“…13 The barrier distribution for the 24 Mg+ 90 Zr system extracted from quasi-elastic scattering at backward angles. The right panel shows the posterior probability distribution for the Bayesian analysis for the quadrupole and the hexadecapole deformation parameters of 24 Mg. Taken from Ref. [41].…”

“…Using such sensitivity of the barrier distribution to the deformation parameters, the quadrupole and the hexadecapole deformation parameters of the 24 Mg nucleus have been extracted recently [41]. To this end, the barrier distribution extracted from the quasi-elastic scattering for the 24 Mg+ 90 Zr system was analyzed with the Bayesian statistics.…”

Analysis of a Skyrme energy density functional with deep learning

“…In a electron system without phonons, the only interaction between electrons is the repulsive Coulomb force, which causes two electrons to distribute as far as possible. In marked contrast, nucleons tend to get closer to each other due to a short-ranged attractive nuclear force, and thus the mechanism which determines the density distribution is quite different between electron and nucleon systems [28]. In addition, for electron systems, the KS-EDFs, which are inspired by the Hartree-Fock method, works well in general.…”