Numerical calculation of soft-X ray transition probability for the muffin-tin potential

The matrix elements of the coordinate, the momentum and the gradient of the potential were used to calculate the optical transition probability between the valence and core states, obtained for the muffin-tin model of the crystal potential. It has been found that gradV is the most suitable form for the numerical calculation while the other forms can yield substantial errors for both transition and simple metals when the core energy amounts few Rydbergs and the amplitude of the core function reaches at the muffin-tin radius 10^–3-10^–2 of its maximum value.