arXiv2024
$^7$Li and $^7$Be play an important role in Big Bang nucleosynthesis and nuclear astrophysics. The $^3$H($^4$He,$γ$)$^7$Li radiative capture reaction is crucial for the determination of the primordial $^7$Li abundance. In nuclear astrophysics, lithium isotopes have attracted a great interest because of the puzzled abundance of $^6$Li and $^7$Li. Purpose: In this work we study spectra of $^7$Be, $^7$Li and elastic scattering cross sections $^4$He($^3$He, $^3$He), $^4$He($^3$H, $^3$H) within the Gamow shell model (GSM) in the coupled-channel formulation (GSM-CC). The evolution of channel amplitudes and spectroscopic factors in the vicinity of the channel threshold is studied for selected states. Methods: GSM provides the open quantum system formulation of nuclear shell model. In the representation of GSM-CC, GSM provides the unified theory of nuclear structure and reactions which is suited for the study of resonances in $^7$Be, $^7$Li and elastic scattering cross-sections involving $^3$H and $^3$He projectiles. Results: The GSM-CC in multi-mass partition formulation applied to a translationally invariant Hamiltonian with an effective finite-range two-body interaction reproduce well the spectra of $^7$Be, $^7$Li and elastic scattering reactions: $^4$He($^3$He, $^3$He), $^4$He($^3$H, $^3$H). Detailed analysis of the dependence of reaction channel amplitudes and spectroscopic factors on the distance from the particle decay threshold allowed to demonstrate the alignment of the wave function in the vicinity of the decay threshold. This analysis also demonstrates the appearance of clustering in the GSM-CC wave function in the vicinity of the cluster decay threshold.