scattering database
This program computes the T-matrix from the first second order of the distorted wave Born approximation. The distorted wave Born approximation of the first order (DWBA-1) is similar to the well-known plane wave Born approximation. However, to speed up the convergence of the Born series (of which we are using just a single term in the first-order computation), part of the potential is excluded from the perurbative description and solved precisely. The spliting is the following \[ V = W + U \, \] where \(V\) is the full potential felt by the projectile, \(U\) is the so called "distorting potential" that will be solved precisely as mentioned above and explained below. This splitting has two consequences:
First of all, the free states are no longer free, so we cannot use the plane waves. Instead, one receives a distorted waves as a solution of the modified equation for partial waves \[ \left( -\frac{1}{2}\frac{\mathrm{d}^2}{\mathrm{d}r^2} +\frac{\ell(\ell+1)}{2r^2} +U(r) \right)\chi_{k\ell}(r) = E_{k}\chi_{k\ell}(r) \ . \]
Secondly, the T-matrix receives two contributions now -- one from the scattering term and one as a correction due to the redefinition of the potentials. The result is the two-potential formula \[ T = (N+1) \left<\chi_f^{(-)}\psi_f\right|V-U_f\left|\mathcal{A}\Psi_i^{(+)}\right> + \left<\chi_f^{(-)}\psi_f\right|U_f\left|\psi_i\beta_i\right> \ . \]
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Jakub Benda © 2017