Tetrahedral shape of $^{110}$Zr from covariant density functional theory in 3D lattice space

TL;DR

This paper introduces a new computational method for covariant density functional theory in 3D lattice space, revealing a tetrahedral shape in the ground state of $^{110}$Zr and analyzing deformation effects on the energy surface.

Contribution

The paper develops an efficient PCG-F method for covariant density functional theory and applies it to identify tetrahedral deformation in $^{110}$Zr.

Findings

Ground state of $^{110}$Zr exhibits tetrahedral shape

Deformations $eta_{31}$ and $eta_{33}$ soften the potential energy surface

Single-particle levels evolve microscopically with deformation

Abstract

Covariant density functional theory is solved in 3D lattice space by implementing the preconditioned conjugate gradient method with a filtering function (PCG-F). It considerably improves the computational efficiency compared to the previous inverse Hamiltonian method (IHM). This new method is then applied to explore the tetrahedral shape of $^{110}$Zr in the full deformation space. The ground state of $^{110}$Zr is found to have a tetrahedral shape, but the deformations $\beta_{31}$ and $\beta_{33}$ greatly soften the potential energy surface. This effect is analysed with the microscopic evolution of the single-particle levels near the Fermi surface driven by the deformation.