  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.
