Transition amplitudes in length and velocity forms in the photoionization of intermediate subshells of high Z atoms

Chandrasekar's work is one of the earliest in which photoabsorption matrix elements were determined in length, velocity, and acceleration forms [1]. Out of the three forms, the length and velocity form calculations are commonly discussed [2–4]. Non-local potentials typically cause non-equivalence of length and velocity forms [5]. Relativistic and correlation effects also play important roles in the inequality of length and velocity forms [4]. In the present work, we attempt to identify the conditions, causes, and consequences for the non-equivalence between length and velocity forms of transition matrix elements in the intermediate subshells of atomic mercury. The matrix elements are calculated using the RRPA [6] and the RRPA-R [7]. Truncation of the RRPA impacts the equivalence of the different gauges, but to varied extents in different energy regions. [1] S. Chandrasekhar, Astrophys. J. 102, 223 (1945). [2] A. F. Starace, Phys. Rev. A 3, 1242 (1971). [3] I. M. Savukov and W. R. Johnson, Phys. Rev. A 62, 052506 (2000). [4] G. Aarthi et al., J. Phys. B 47, 025004 (2014). [5] I. P. Grant, J. Phys. B 7, 1458 (1974). [6] W. R. Johnson and C. D. Lin. Phys. Rev. A 20, 964 (1979). [7] V. Radojevic, et al., Phys. Rev. A 40, 727 (1989).