Single particle in a reflection-asymmetric potential

Abstract

Single particles moving in a reflection-asymmetric potential are investigated by solving the Schrödinger equation of the reflection-asymmetric Nilsson Hamiltonian with the imaginary time method in 3D lattice space and the harmonic oscillator basis expansion method. In the 3D lattice calculation, the ${\mathbf{l}}^2$ divergence problem is avoided by introducing a damping function, and the$⟨{\mathbf{l}}^2{⟩}_N$ term in the non-spherical case is calculated by introducing an equivalent $N$-independent operator. The efficiency of these numerical techniques is demonstrated by solving the spherical Nilsson Hamiltonian in 3D lattice space. The evolution of the single-particle levels in a reflection-asymmetric potential is obtained and discussed by the above two numerical methods, and their consistency is shown in the obtained single-particle energies with the differences smaller than 10${}^{-4}[\hslash {\omega }_0]$.

arXiv comment8 pages, 5 figures, 1 table

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