The Gamow Shell Model: a theoretical tool unifying nuclear structure and reaction frameworks
1 November 2016
Theory Trailer Conference Room
Nicolas Nicolas Michel
The Gamow Shell Model (GSM), a configuration interaction model where many-body states are constructed from the one-body Berggren basis, bearing bound, resonant and scattering states, has been shown to be a powerful tool to describe the structure of drip-line nuclei as loosely bound and resonant many-body states can be efficiently calculated therein. In order to avoid center of mass excitations, GSM has been defined in the Cluster Orbital Shell Model (COSM) frame, using a core and valence nucleons. The lack of exact antisymmetry in laboratory frame of COSM wave functions will be discussed and shown to be very small, by comparing COSM and Jacobi-coordinate calculations. In order to deal with very large matrices, where the Lanczos or Davidson methods can no longer be used, the Density Matrix Renormalization Group (DMRG) has been introduced within GSM. Its fundamental idea is to build a basis of increasingly correlated many-body states, so that matrices bear tractable dimensions. Applications of GSM and GSM-DMRG will consist of the study of 6He and 8He charge radii, of the single-particle and collective motion in unbound deformed 39Mg, and of the isospin triplet 6He, 6Li and 6Be. GSM-DMRG has also been successfully applied to realistic interactions in the context of no core GSM, with the examples of 4H, 4Li, 5He and 6Li.
GSM has been extended to a reaction framework using the Resonating Group Method (RGM). In the RGM method, a basis of channels is constructed from target states and projectile states, which generate compound many-body basis states. Target states and projectile states are calculated in GSM, as they consist of bound or resonant eigenstates of the GSM Hamiltonian matrix. Scattering many-body states are solutions of the Hamiltonian coupled-channel equations, from which reaction observables such as scattering and radiative capture cross sections can be calculated. GSM-RGM has been used to calculate the 18Ne(p,p) and 14O(p,p) reaction cross sections, where the proton-rich 19Na and 15F nuclei are unbound and thus are nuclei of choice for GSM-RGM. The 6Li(p,p) scattering reaction, and 6Li(p,)7Be, 6Li(n,)7Li, 7Be(p,)8B and 7Li(n,)8Li radiative capture reaction cross sections, of astrophysical interest, will also be presented using GSM-RGM. GSM-RGM applications have been considered for the moment with one-nucleon projectiles only. Hence, the future inclusion of many-nucleon projectiles in GSM-RGM will be discussed.