Searching for single-particle resonances with the Green's function method

TL;DR

This paper employs the Green's function method within the relativistic-mean-field model to accurately identify and analyze single-particle resonances in exotic nuclei, demonstrating the approach's reliability and slight dependence on coordinate space size.

Contribution

It introduces a Green's function approach to directly determine resonance energies and widths, confirming its effectiveness compared to previous density of states methods.

Findings

Resonance energies and widths are consistent with previous methods.

Results are minimally affected by the size of the coordinate space.

The Green's function extremum method reliably identifies both wide and narrow resonances.

Abstract

Single-particle resonances in the continuum are crucial for studies of exotic nuclei. In this study, the Green's function approach is employed to search for single-particle resonances based on the relativistic-mean-field model. Taking $^{120}$Sn as an example, we identify single-particle resonances and determine the energies and widths directly by probing the extrema of the Green's functions. In contrast to the results found by exploring for the extremum of the density of states proposed in our recent study [Chin. Phys. C, 44:084105 (2020)], which has proven to be very successful, the same resonances as well as very close energies and widths are obtained. By comparing the Green's functions plotted in different coordinate space sizes, we also found that the results very slightly depend on the space size. These findings demonstrate that the approach by exploring for the extremum of the Green's function is also very reliable and effective for identifying resonant states, regardless of whether they are wide or narrow.