Relativistic analogues of nonrelativistic integrals in R-matrix calculations

Relativistic analogues of integrals are applied to the nonrelativistic R-matrix code to demonstrate the possibilities of the method. An expression for the relativistic analogue of the multipole integral is obtained. Energy levels and electron impact excitation cross sections for transitions in C 2+ ,F e 22+ and W 70+ , calculated with different codes, are compared. It is found that the relativistic analogues of integrals method shows good agreement with results calculated using a relativistic code. Resonance structure is a prominent feature in the electron excitation collision cross sections for low and intermediate energies of the incident electron, due to the formation of doubly excited states during the collision processes. The accuracy of close-coupling calculations, in many cases, is determined by the number of closely spaced energy levels of the target included to couple with the incident electron. R-matrix calculations can become time consuming, or even beyond the capabilities of available computational resources, since the size of (N +1 )-electron Hamiltonian matrix that must be diagonalized in the inner region depends on the number of channels that are formed from the target levels. To deal with this problem, close-coupling calculations can be performed in pure LScoupling employing nonrelativistic wavefunctions, and later adopting various methods [1–4] to generate K-matrices (essential in cross-section calculations) for the fine-structure levels. However, relativistic effects that are important for heavy elements and high-ionization stages are not included in such calculations.