Theoretical Investigation of fine structure and wavefunctions of Tantalum atom for 5d³6s² and 5d²6s²6p configurations.

Wave function contains all the information of electrons and defines the probability of a particle to be in various Energy Eigenstates. The ground state wave function of the quantum many-body system is a complicated task to calculate. Tantalum belongs to d block element, and it has open d shell configuration. This study is an attempt to determine two electron shell configurations of Ta I, 5d36s2 and 5d26s26p. Term symbols, fine structure, total angular momenta, coefficient of fractional parentage and coupled wave functions for two configurations of 5d36s2 and 5d26s26p of Ta I have been investigated. Russell-Saunders coupling scheme or LS coupling scheme has been used to obtained 39 term values and 95 fine levels. The minimum value of total angular momentum J is 1/2 and maximum 11/2 for both configurations. Total 120 microstates are determined for configuration 5d36s2.81 coupled wave functions along with their coefficient of fractional parentage are reported for Ta I. These wave functions are important to calculate several spectroscopic quantities i.e., probability density, lifetime, energy, etc.