Single Tensor Operator in J-Representation
https://doi.org/10.25587/SVFU.2019.73.39428
Abstract
In the article, tk single tensor operator of k rank is formed in j-space from the creation and annihilation operators of electrons in jm states. The given operator represents a complete system of (2j+1) operators in j-space. Its submatrix element is equal to δ - Kronecker symbol. Tk operator can be formed from this single tensor operator and act on all electrons of the considered system (nuclei, atoms). The submatrix element of Tk operator is expressed in terms of submatrix elements of the creation and annihilation operators of electrons or through coefficients of fractional parentage with one detached electron. The creation and annihilation operators of electrons in j-space can be represented as a single operator of a change in the number of electrons in two spaces, which are quasi-spin and of angular momentum. This makes it possible to obtain simpler formulas for calculating the submatrix elements of Tk operator in the cases of one jN-subshell of equivalent electrons that do not contain summation over possible states of intermediate multielectron systems. Simple algebraic expressions have been obtained for the submatrix element of T0 and T1 operators for any number of electrons. Recurrence relations have been achieved for the submatrix elements of Tk operator (k takes any value equal to or less than (2j + 1)) for any number of electrons in the subshells . The calculated values of the submatrix elements of Tk operators for are given in the ables.
About the Authors
I. S. Kychkin
M. K. Ammosov North-Eastern Federal University
Russian Federation
Russian Federation
V. I. Sivtsev
M.K. Ammosov North-Eastern Federal University
Russian Federation
Russian Federation
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Review
For citations:
Kychkin I.S., Sivtsev V.I. Single Tensor Operator in J-Representation. Vestnik of North-Eastern Federal University. 2019;(5):44-56. (In Russ.) https://doi.org/10.25587/SVFU.2019.73.39428
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