Scalar Two-Electron Single Operator in J-Space

Scalar two-electron operators in j-space are composed of the single tensor operators in j-space of k rank formed from the operators of electron creation and annihilation. They form a complete system of simplest scalar operators in j-space. This makes it possible to express by them any complex scalar operators in j-space. General formulas are obtained for the matrix elements of these scalar two-electron operators in j-space in the case of a subshell of equivalent electrons. Simpler algebraic formulas are derived in different special cases from these general formulas. Recurrent relations for matrix elements of operators are obtained. It is shown that obtaining these relations is most easier if we use the quasispin formalism. It is shown that the consideration of the matrix elements of operators is greatly simplified if we use Casimir operators for unitary U(2j+1) and symplectic Sp(2j+1) groups. In this case, it is possible to express the matrix elements of operators through the precedence numbers , which simplifies the obtained formulas for the matrix elements of operators. For example, the matrix elements of operators with odd k ranks do not depend on the number of electrons N.

j-представление, single tensor operator, scalar two-electron operator, electron creation operator, electron annihilation operator, secondary quantization, quasispin, Casimir operators, j-representation, antisymmetric wave function, seniority number, highly charged ions

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