Atomic X-sections

Quantemol is now offering access to world leading expertise in calculation of atomic electron and photon cross sections. 

Quantemol is collaborating with Dr. Oleg Zatsarinny from Drake University, USA. Over several years Dr Zatsarinny has developed a new suit of programs (BSR) to model electron and photon interaction with atoms and ions based on the B-spline R-Matrix method. The programs can be used to calculate elastic, inelastic, ionization, differential and momentum transfer electron-impact cross sections, along with photoionization cross sections what is important for CORINF collaboration. Additionally, the codes can be used for atomic-structure bound-state calculations, including the accurate calculations of oscillator strengths for a wide range of levels. Distinguish feature of the code is employing B-splines as universal basis for bound and continuum atomic orbitals that guarantees the high numerical accuracy of computations. The most important new feature of the method is the ability to use flexible non-orthogonal radial functions for both the target and scattering wavefunctions. Along with the multi-configuration Hartree-Fock method it allows one use much more accurate target state as employed before. Last years the code was extended with new fully-relativistic version based on the Dirac-Coulomb Hamiltonian.

Quantemol can now offer atomic consultancy projects which deploy the B-Spline R-Matrix method, both in the non-relativistic scheme suitable for light atoms or in fully-relativistic
approach which is necessary for accurate treatment of heavy atoms.

Precise cross sections data produced by B-spline R-matrix provides an invaluable source of data on atomic spectrum and a theoretical base for measurements in optical spectroscopy and mass spectrometry as well as exploration of new sources of light.

The B-Spline R-Matrix (BSR) Method
[O. Zatsarinny, Comp. Phys. Commun. 174, 273 (2006)]

• The method is based on the non-perturbative close-coupling expansion.
• The close-coupling equations are solved using the R-matrix method.
• Atomic-structure calculations − frozen-core approximation

Distinctive feature: Allows for non-orthogonal orbital sets to represent both bound and continuum radial functions

  • independent generation of target states – much more accurate target representation (term-dependence, relaxation effects, correlation)
  • no artificial orthogonality constraints for continuum orbitals – more consistent treatment of N-electron target and (N+1)-electron collision system −> (no pseudo−resonances, improved convergence)


Experimental comparison

atome electron collisions


metastable production


Ionisation complex targets
Total cross sections


More example can be found in the topical review: J. Phys. B: At. Mol. Opt. Phys. 46 (2013) 112001