Length and velocity matrix elements in quadrupole transition calculations (for transitions in He and Li+)

Abstract

Electric quadrupole multiplet strengths have been calculated for a large number of transitions in He and Li⁺ using analytical orbital wavefunctions of frozen core type. Very good agreement between length and velocity forms of the transition matrix element is obtained when the orbitals have the correct asymptotic form. The velocity form is far less sensitive to small changes in the orbitals than is the length form. The bound-state contributions to the quadrupole polarizabilities of the ions He through B⁺³ have been estimated from ¹S-¹D multiplet strengths, and it is concluded that the continuum contributions are very large.