Probing neutron-emission resonances of kaonic nuclei with the complex momentum representation method

Abstract

We systematically investigate the resonant states of kaonic nuclei using the relativistic mean-field complex momentum representation (RMF–CMR) method. Validation with different integration contours confirms that the RMF–CMR method is effective and reliable for calculating resonant states in kaonic nuclei. The strong \(K^-\)-nucleon attraction in light kaonic nuclei induces a pronounced core compression effect and a sharp increase in nuclear potential depth; this effect weakens as the nucleon number increases. A new \(1d_{5/2}\) resonant state is identified just above the neutron continuum threshold in \(^{13}_{K^-}\) C; its single-particle density is strongly extended at finite distances, exhibiting a halo-like spatial distribution in the light kaonic nucleus. We also find that nuclear matter softening shifts d-orbital resonant levels closer to the continuum threshold and generally weakens their coupling to the continuum, and the \(1d_{5/2}\) state, lying much closer to the continuum threshold than the \(1d_{3/2}\) state under the common \(\ell =2\) centrifugal barrier owing to the spin-orbit splitting, retains an extremely narrow width over the whole investigated parameter range and is more sensitive to nuclear matter softening. The widths discussed in this work refer to the neutron-emission widths of single-particle shape resonances; the mesonic \(\bar{K}N\) decay of the kaonic nucleus itself is not included.