Tunneling ionization of the F4 and D6 states of vanadium: Exchange blockade

Abstract

Using time-dependent density functional theory (TDDFT) calculations, we compare tunneling ionization of the $a\phantom{\rule{0.16em}{0ex}}^{4}F$ ground state and the $a\phantom{\rule{0.16em}{0ex}}^{6}D$ first excited state of vanadium in laser fields of intensities between 1.4 and $4.0\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. The calculated ionization yields of the ground state of vanadium were already shown to agree well with experimental results [Chu and Groenenboom, Phys. Rev. A 94, 053417 (2016)]. We find that the tunneling ionization rate of the sextet state is lower than that of the quartet state. This is surprising, since the ionization potential of the sextet is lower than that of the quartet state. This finding, however, is consistent with the experimental observation that niobium, whose ground state is $a\phantom{\rule{0.16em}{0ex}}{}^{6}{D}_{1/2}$, has a much smaller ionization yield than vanadium ($a\phantom{\rule{0.16em}{0ex}}{}^{4}{F}_{3/2}$), even though their ionization potentials are extremely close [Smits et al., Phys. Rev. Lett. 93, 213003 (2004)]. Our calculations demonstrate the existence of exchange blockade for the higher spin state. It arises from a strong field dynamic effect that mixes the highest and second highest electrons in the same set of unoccupied spin orbitals, which causes an isotropic attractive potential that confines the electrons close to the core.