Unusual behavior of Cooper minima of ns subshells in high- Z atoms

Abstract

A study of Cooper minima (CM) arising from the photoionization of $6s$, 5s, and $4s$ subshells of high-$Z$ atoms has been performed using Dirac-Fock (DF), two-channel relativistic-random-phase approximation (RRPA), and fully coupled RRPA. The results show huge splittings between $ns\ensuremath{\rightarrow}\ensuremath{\varepsilon}{p}_{3/2}$ and $\mathrm{ns}\ensuremath{\rightarrow}\ensuremath{\varepsilon}{p}_{1/2}$ CM which increase with $Z$ owing primarily to the relativistic interactions (spin orbit) that are attractive for the $\ensuremath{\varepsilon}{p}_{1/2}$ final state but repulsive for the corresponding $\ensuremath{\varepsilon}{p}_{3/2}$. In addition, it was found that correlation in the form of interchannel coupling (essentially configuration interaction in the final continuum states) plays a huge role in determining the location of the CM. For $6s$ photoionization, the $6s\ensuremath{\rightarrow}\ensuremath{\varepsilon}{p}_{3/2}$ and $6s\ensuremath{\rightarrow}\ensuremath{\varepsilon}{p}_{1/2}$ CM behave completely different as a function of $Z$. It was also found that for $5s$ and $4s$ photoionization, the CM move below the threshold, with increasing $Z$, and, at high enough $Z$, the $5s\ensuremath{\rightarrow}\ensuremath{\varepsilon}{p}_{3/2}$ and $4s\ensuremath{\rightarrow}\ensuremath{\varepsilon}{p}_{3/2}$ CM re-emerge into the continuum. The calculations have been carried out for the $ns$ subshells of Hg ($Z=80$), Rn ($Z=86$), Ra ($Z=88$), No ($Z=102$), Cn ($Z=112$), and Og ($Z=118$).