The effective operator for atomic level widths due to l1N1l2N2→l1N1+1l2N2−2εl3 Auger transitions

Abstract

The effective operator AΓ for the Auger l1N1 l2N2→ l1N1+1 l2N2- 2εl3 transitions was determined in the nonrelativistic approximation in the second quantization representation in the case of normal ordering of electron creation and annihilation operators. The matrix element of AΓ yields a partial Auger width of a level. The specific transitions when l2=1, 2 and l1> 0 were considered in detail. The general formula for a matrix element of AΓ was derived when a wavefunction with open-shells was presented in normal coupling. Compact expressions for the matrix elements of AΓ in the case l1N1 l22 when N1=1, 2, 4l1+1 and 4l1 were obtained. The selection rules for matrix elements of AΓ are discussed by using the quasispin technique.