Spectroscopic factors of resonance states with the Gamow shell model

We provide an investigation of the spectroscopic factor of resonance states in $A =5-8$ nuclei, utilizing the Gamow shell model (GSM). Within the GSM, the configuration mixing is taken into account exactly with the shell model framework, and the continuum coupling is addressed via the complex-energy Berggren ensemble, which treats bound, resonance, and non-resonant continuum single-particle states on an equal footing. As a result, both the configuration mixing and continuum coupling are meticulously considered in the GSM. We first calculate the low-lying states of helium isotopes and isotones with the GSM, and the results are compared with that of \textit{ab initio} no-core shell model (NCSM) calculations. The results indicate that GSM can reproduce the low-lying resonance states more accurately than the no-core shell model. Following this, we delve into the spectroscopic factors of the resonance states as computed through both GSM and NCSM, concurrently conducting systematic calculations of overlap functions pertinent to these resonance states. Finally, the calculated overlap function and spectroscopic factor of $^6$He$(0_1^+)$ $\otimes \nu p_{3/2} \to $ $^7$He$(3/2_1^-)$ with GSM are compared with the results from \textit{ab initio} NCSM, variational Monte Carlo, and Green's function Monte Carlo calculations, as well as avaliable experimental data. The results assert that wave function asymptotes can only be reproduced in GSM, where resonance and continuum coupling are precisely addressed.