Curious behaviour of Cooper minima in relativistic channels of ns subshells in high-Z atoms

Cooper minima (CM) in dipole photoionization channels refer to a zero in the matrix element which lead to minima in the cross section [1] and intriguing features in the angular distribution asymmetry parameter β. Furthermore, it is well known that the CM is extremely sensitive to relativistic and correlation effects [2]. A systematic survey of CM in the relativistic channels, with comparisons to nonrelativistic results were studied in earlier [3-5]. The present work highlights and provides explanations for some of the curious behaviours of  CM in the ns→εp_1/2 and ns→εp_3/2 dipole channels such as (1) movement of CM in the relativistic split channels in opposite directions of energy and (2) resurgence of CM in the ns→εp_3/2 channel which had moved in the discrete region as a function of Z. To demonstrate these behaviors, we consider the dipole matrix elements of the ns subshells of Hg (Z=80), Rn (Z=86), Ra (Z=88), No (Z=102), Cn (Z=112), and Og (Z=118) and find that these curious behaviours are result from the competition between Coulomb attraction and spin-orbit forces. [1] J. W. Cooper, Phys. Rev. 128, 681 (1962); [2] W. R. Johnson and K. T. Cheng, Phys. Rev. A 20, 978 (1979); [3] R. Y. Yin and R. H. Pratt, Phys. Rev. A 35, 1149 (1987); [4] P. C. Deshmukh, B. R. Tambe, and S. T. Manson, Austral. J. Phys. 39, 679 (1986); [5] S. T. Manson, Phys. Rev. A 31, 3698 (1985).