Jost function method on a Lagrange mesh

Abstract

particular nature. The complex momentum of the virtual state is purely imaginary with a negative sign, while that of the bound states is also purely imaginary but with a positive sign. Hence, the virtual states and bound states give the same negative sign for the energy eigenvalue. Under the condition that the potential vanishes faster than the Coulomb one, the two-body Schrodingerequationbecomessimpleintheasymptoticregion.Therefore,onecandefinetheasymp- totic solution, and the scattering wave is constructed as the distortion by the presence of the potential. The S-matrix can be represented by using the distortion from the asymptotic solution. The Jost function method (JFM) has been developed in order to obtain the S-matrix accurately using the properties of functions, which become constant in the asymptotic region and equal to the Jost functions. In Refs. (1,2), a practical formalism is given to calculate the Jost functions by using thetechniqueofthevariable-constantmethod.Themethodhasbeendevelopedandappliedtodiscuss the partial decay widths in the coupled-channel problem (3), the property of the virtual states of the 4 He+n and 9 Li+n systems (4), and the application to the orthogonality condition model (5). Based on the above success, we found that the JFM approach is very useful in studying unstable systems. The Lagrange-mesh method is one of the efficient ways to perform an approximate variational calculation for the Hamiltonian with expressions discretized on mesh points. The calculation is sim- plified with the help of the basis of Lagrange functions. The essential point is that the basis functions are orthogonal to each other and vanish at all mesh points except one, the associate mesh point. The