A general program for computing matrix elements in atomic structure with nonorthogonal orbitals Original Research Article

To solve some problems concerning the atomic structure and transition probabilities, one needs to evaluate the matrix elements of various operators with respect to the configuration wave functions formed from the nonorthogonal one-particle orbitals. The program presented performs the angular integration necessary for expressing such matrix elements as weighted sums of radial integrals. Any amount of nonorthogonality between the orbitals may be presented leading to overlap integrals for the matrix elements. The calculations follow the method based on the representation of configuration wave functions through the Slater determinants. The program, therefore, can also be used for obtaining the corresponding vector-coupling coefficients. A distinguishing feature of the present procedure is the preliminary generation of vector-coupling coefficients for the individual subshells, which reduces considerably the amount of calculations. The operators included in the present version of the program are the one- and two-particle electrostatic interaction along with the one-particle tensor operator and simple overlap. Matrix elements of these operators provide the basis for studying the formation or decay of the inner-shell vacancies.