Modified Variational Method for Scattering

In the variational approach to scattering, one traditionally adopts a trial function of the form ${\mathcal{I}}_t\mathrm{}\left(r\right)={\Sigma }_i{C}_i{\varphi }_i+j_l\mathrm{}\left(r\right)+{\lambda }_{t}g\left(r\right)\mathrm{}{n}_l\mathrm{}\left(r\right),$ where the ${\varphi }_i$ are square-integrable functions, ${\lambda }_t$ is the tangent of the trial phase shift, $j_l\mathrm{}\left(r\right)\mathrm{}$ and $n_l\mathrm{}\left(r\right)\mathrm{}$ are, respectively, the regular and irregular Riccati-Bessel functions, and $g\left(r\right)\mathrm{}$ cuts $n_l\mathrm{}\left(r\right)\mathrm{}$ off at the origin. A modified form for the trial function is suggested and used in the determination of phase shifts in the static-exchange hydrogen problem.