Spectral-shift and scattering-equivalent Hamiltonians on a coarse momentum grid
Gómez Rocha, María
Ruiz Arriola, Enrique
Lippmann-Schwinger equation
Phase shifts
Momentum grid
Equivalent hamiltonian
Scattering (Physics)
The solution of the scattering problem based on the Lippmann-Schwinger equation requires in many cases a discretization of the spectrum in the continuum which does not respect the unitary equivalence of the S-matrix on the finite grid. We present a new prescription for the calculation of phase shifts based on the shift that is produced in the spectrum of a Chebyshev-angle variable. This is analogous to the energy shift that is produced in the energy levels of a scattering process in a box, when an interaction is introduced. Our formulation holds for any momentum grid and preserves the unitary equivalence of the scattering problem on the finite momentum grid. We illustrate this procedure numerically considering the non-relativistic NN case for 1S0 and 3S1 channels. Our spectral shift formula provides much more accurate results than the previous ones and turns out to be at least as competitive as the standard procedures for calculating phase shifts.
2020-01-24T08:31:50Z
2020-01-24T08:31:50Z
2019-11-21
info:eu-repo/semantics/article
Gómez-Rocha, M., & Arriola, E. R. (2020). Spectral-shift and scattering-equivalent Hamiltonians on a coarse momentum grid. Physics Letters B, 800, 135107.
http://hdl.handle.net/10481/59101
10.1016/j.physletb.2019.135107
eng
http://creativecommons.org/licenses/by/3.0/es/
info:eu-repo/semantics/openAccess
Atribución 3.0 España
Elsevier BV