Hex
scattering database
Hex-ecs
Low energy module hex-ecs 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