Modified variable phase method for the solution of coupled radial Schrödinger equations

Abstract

A modified variable phase method for the numerical solution of coupled radial Schrödinger equations, which maintains linear independence for different sets of solution vectors, is suggested. The modification involves rearrangement of coupled equations to avoid the usual numerical instabilities associated with components of the wave function in their classically forbidden regions. The modified method is applied to nuclear structure calculations of halo nuclei within the hyperspherical harmonics approach.

Non-relativistic pair annihilation of nearly mass degenerate neutralinos and charginos III. Computation of the Sommerfeld enhancements

“…To avoid the matrix inversion (100) we seek a method where the inverse of U defined in (99) follows directly from the solution of a differential equation system. This can indeed be found by an adaptation of the reformulation of the Schrödinger problem described in [44].…”

“…for every ai [44]. The condition reduces the N second-order differential equations (102) to a system of 2N coupled differential equations of first order for α ai (x) and β ai (x).…”

“…For leading-order scalar boson and photon exchange, the coefficient b e 1 e 2 e 4 e 3 vanishes. For Z-and W -boson exchange the spin-dependent part of the potential arises from the axial-vector coupling, see (41), (44).…”

Self-interacting inelastic dark matter: a viable solution to the small scale structure problems

“…We follow and slightly modify the procedure of ref. [85] to solve the more general problem where there are N scattering channels of which our problem is the N = 2 special case. First, we write the wave function in component form as…”

“…Using these substitutions, one can show that the original Schrödinger equation (A.9) reduces to two first order differential equations, one of which is (see ref. [85]):…”