Adaptive mesh grading for finite element solutions of an integral equation in quantum scattering

Eyre, D.; Wright, C. J.

doi:10.1016/0021-9991(88)90069-1

Cited by 2 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A relevant question is the choice of the particular grid (see e.g. [21] for consideration of adaptive mesh). We will take Gauss-Chebyshev grid whose energy eigenvalue problem corresponds to diagonalizing in a Laguerre basis [22].…”

Section: Introductionmentioning

confidence: 99%

Spectral-shift and scattering-equivalent Hamiltonians on a coarse momentum grid

Gómez-Rocha

Arriola

2020

Physics Letters B

View full text Add to dashboard Cite

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 1 S 0 and 3 S 1 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.

show abstract

Section: Introductionmentioning

confidence: 99%