TY - JOUR

T1 - Direct matrix elements of spin–other-orbit interaction in configurations with p- and h-electrons in outer shells

AU - Anisimova, G. P.

AU - Dolmatova, O. A.

AU - Krylov, I. R.

AU - Tsygankova, G. A.

PY - 2023

Y1 - 2023

N2 - The direct matrix elements of the energy operator for the spin–other-orbit interaction of the npnʹh and np5nʹh confi gurations are determined. The direct matrix elements together with exchange elements are intended for further numerical calculation of fi ne-structure parameters and other characteristics of atoms such as gyromagnetic ratios. The coeffi cients for radial integrals are calculated in the single-confi guration approximation, in the formalism of irreducible tensor operators, and in two representations, i.e., LSJM and uncoupled angular momentum. A formula has been derived for calculating the direct matrix elements of the considered confi guration in the uncoupled angular momentum representation and has been tested on small rank matrices with M = ±7 (1 rank) and M = ±6 (4 rank). All other direct matrix elements have been calculated for a matrix with M = 0 (12 rank). The obtained values have been transformed into the LSJM representation using the matrix of Clebsch–Gordan coeffi cients and compared with an independent calculation in the LSJM representation. The complete agreement of the direct matrix elements of the interaction considered in two diff erent calculation schemes indicates that the obtained results are reliable.

AB - The direct matrix elements of the energy operator for the spin–other-orbit interaction of the npnʹh and np5nʹh confi gurations are determined. The direct matrix elements together with exchange elements are intended for further numerical calculation of fi ne-structure parameters and other characteristics of atoms such as gyromagnetic ratios. The coeffi cients for radial integrals are calculated in the single-confi guration approximation, in the formalism of irreducible tensor operators, and in two representations, i.e., LSJM and uncoupled angular momentum. A formula has been derived for calculating the direct matrix elements of the considered confi guration in the uncoupled angular momentum representation and has been tested on small rank matrices with M = ±7 (1 rank) and M = ±6 (4 rank). All other direct matrix elements have been calculated for a matrix with M = 0 (12 rank). The obtained values have been transformed into the LSJM representation using the matrix of Clebsch–Gordan coeffi cients and compared with an independent calculation in the LSJM representation. The complete agreement of the direct matrix elements of the interaction considered in two diff erent calculation schemes indicates that the obtained results are reliable.

KW - energy-operator matrix

KW - SPIN–OTHER-ORBIT INTERACTION

KW - LSJM Representation

KW - uncoupled angular momentum representation

M3 - Article

VL - 90

SP - 1

EP - 8

JO - Journal of Applied Spectroscopy (English Translation of Zhurnal Prikladnoi Spektroskopii)

JF - Journal of Applied Spectroscopy (English Translation of Zhurnal Prikladnoi Spektroskopii)

SN - 0021-9037

IS - 1

ER -