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Hex

(Hydrogen-electron collisions code)

Jakub Benda, MFF UK (c) 2014

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Hex is a package of several programs used for computation of T-matrices and derived scattering quantities of a collision of electron with atomic hydrogen. The method used is the non-relativistic quantum mechanics with different approximations depending on the energy of the projectile.

Hex-ecs

Hex-ecs is the most complex and computationally demanding package of the four. It is used for solving the scattering problem in the low-energy regime, which means situations when the projectile energy is not considerably larger than the ionization threshold of the atom. With thinkable resources, the program can produce valid results for energies up to, say, 100 eV but certainly not higher. Moreover, this optimistic number holds just for scattering on the ground state. Excited states require much, much larger temporal and memory requirements.

The implemented method is the discretization of the Schrödinger equation in a B-spline basis. The whole equation is solved for every global angular symmetry as a set of linear algebraic equations, i.e. using a LU-decomposition. Umfpack library was chosen for this task. The results are the partial T-matrices for every outgoing particle partial wave.

Hex-dwba

This is the high-energy program. The T-matrices are sought using the distorted wave Born approximation of the first order. To evaluate perturbation contributions, a lot of integration is necessary. That is implemented using the Clenshaw-Curtis algorithm assisted by discrete cosine transform computed by FFTW.

High-energy region (> 100 keV) can be satisfactorily described by the primitive first-order plane wave Born approximation, which, if the exchange is disregarded, is nothing more than a Fourier transform of the potential.

Hex-db

The last pillar Hex-db is a name of the database interface. All above mentioned programs output partial T-matrices that can be easily stored in a common SQLite database. Hex-db then serves as an easy and script-friendly way of retrieving these numbers. In addition to that, several common derived scattering quantities (like cross sections and collision strengths) are implemented in the code and can be computed on request from the basic data.

Hex-db also has a simple HTML form interface for deployment on servers. An example, and official presentation of the results, is on the UTF web page.