scattering database
Low energy module hex-main computes a precise two-electron wave function from the non-relativistic Schrödinger equation,
\[ (E - H) \Psi_{\mathrm{sc}}^S = H_{\mathrm{int}} \Psi_{\mathrm{inc}}^S \ . \]
The wave function \( \Psi_{\mathrm{sc}} \) is expanded into bipolar spherical functions,
\[ \Psi_{\mathrm{sc}}^S(\mathbf{r}_1,\mathbf{r}_2) = \sum_{\ell_1 \ell_2 L M} \psi_{\mathrm{sc},\ell_1 \ell_2}^{LMS}(r_1,r_2) \mathcal{Y}_{\ell_1 \ell_2}^{LM} (\hat{\mathbf{r}}_1,\hat{\mathbf{r}}_2) \ , \]
and the radial part into the product base of B-splines,
\[ \psi_{\mathrm{sc},\ell_1\ell_2}^{LMS}(r_1,r_1) = \sum_{ij} \psi_{\mathrm{sc},\ell_1\ell_2ij}^{LMS} B_i(r_1) B_j(r_2) \ . \]
The Schrödinger equation is then transformed into a matrix equation for sufficient amount of coupled angular momentum states \( (\ell_1,\ell_2) \) . The ECS (exterior complex scaling) method is used to avoid specifiying a specific outgoing boundary condition. Every \( \{LMS\} \) partial wave is solved independently.
For details see the Doxygen documentation.
External links
[1] Bartlett P.; PhD Thesis (2005).
[2] McCurdy, Martín; J. Phys. B: At. Mol. Opt. Phys. 37 (2004) 917–936.
Jakub Benda © 2017