Description of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Be</mml:mi><mml:mprescripts/><mml:none/><mml:mn>7</mml:mn></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Li</mml:mi><mml:mprescripts/><mml:none/><mml:mn>7</mml:mn></mml:mmultiscripts></mml:math> within the Gamow shell model
J.P. Linares Fernandez, N. Michel, M. Płoszajczak, Alexis Mercenne
Abstract
Background: $^{7}\mathrm{Li}$ and $^{7}\mathrm{Be}$ play an important role in big bang nucleosynthesis and nuclear astrophysics. The $^{3}\mathrm{H}(^{4}\mathrm{He},\ensuremath{\gamma})^{7}\mathrm{Li}$ radiative capture reaction is crucial for the determination of the primordial $^{7}\mathrm{Li}$ abundance. In nuclear astrophysics, lithium isotopes have attracted great interest because of the puzzling abundance of $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$.Purpose: In this work we study spectra of $^{7}\mathrm{Be}$ and $^{7}\mathrm{Li}$ and elastic scattering cross sections $^{4}\mathrm{He}(^{3}\mathrm{He},^{3}\mathrm{He})$ and $^{4}\mathrm{He}(^{3}\mathrm{H},^{3}\mathrm{H})$ 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 the 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 $^{7}\mathrm{Be}$ and $^{7}\mathrm{Li}$ and elastic scattering cross sections involving $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ projectiles.Results: GSM-CC in the multimass partition formulation applied to a translationally invariant Hamiltonian with an effective finite-range two-body interaction reproduces well the spectra of $^{7}\mathrm{Be}$ and $^{7}\mathrm{Li}$ and elastic scattering reactions $^{4}\mathrm{He}(^{3}\mathrm{He},^{3}\mathrm{He})$ and $^{4}\mathrm{He}(^{3}\mathrm{H},^{3}\mathrm{H})$. Detailed analysis of the dependence of reaction channel amplitudes and spectroscopic factors on the distance from the particle decay threshold allowed us 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.Conclusions: We demonstrated that GSM formulated in the basis of reaction channels including both cluster and proton/neutron channels allows us to describe both the spectra of nuclei with low-energy cluster thresholds and the low-energy elastic scattering reactions with proton, $^{3}\mathrm{H}$, and $^{3}\mathrm{He}$ projectiles. Studying dependence of the reaction channel amplitude and spectroscopic factor in a many-body state on the distance from the threshold, we showed an evolution of the $^{3}\mathrm{He},^{3}\mathrm{H}$ clustering with increasing separation energy from the cluster decay threshold and demonstrated a mechanism of the alignment of many-body wave function with the decay threshold [J. Oko\l{}owicz, M. P\l{}oszajczak, and W. Nazarewicz, Prog. Theor. Phys. Suppl. 196, 230 (2012); J. Oko\l{}owicz, W. Nazarewicz, and M. P\l{}oszajczak, Fortschr. Phys. 61, 66 (2013)], i.e., the microscopic reorganization of the wave function in the vicinity of the cluster decay threshold which leads to the appearance of clustering in this state.