Atomic distortion and ac-Stark shifts of H under extreme radiation conditions

According to a general nonperturbative theory that describes atomic behavior in intense, high-frequency radiation fields, the atom becomes stable against decay by multiphoton ionization in the limit of high frequencies if the parameter ${\alpha }_0$=(I${/2)}^{1/2}$ ${\omega }^{\mathrm{-}2}$ (a.u.) (with I the intensity and ω the frequency of the field) is kept constant, although otherwise unrestricted. We show that, under this condition, in the subsequent limit of strong fields (${\alpha }_0$ large), the Schrödinger equation describing the structure of the hydrogen atom in a laser field of circular polarization is separable in toroidal coordinates. Explicit asymptotic expressions are given for its energy eigenvalues and its eigensolutions. They correspond to a rapid decrease of the ionization potential and a drastic increase of the size of the atom with ${\alpha }_0$. For the binding energy of the ground state we find: ‖$E_0$‖ =(1/2π${\alpha }_0$) (ln${\alpha }_0$+2.654284) (a.u.). A dramatic distortion of the shape of the atom is found, which in the strong field becomes a torus-shaped object. Furthermore, we introduce a classification of its states by strong-field quantum numbers. We show how the levels at low ${\alpha }_0$, characterized by the weak-field quantum numbers introduced earlier, and the levels at high ${\alpha }_0$, characterized by the strong-field quantum numbers, are correlated. We find that the energy spectrum in strong fields displays a multiplet structure. A comparison is made between our analytical results and those of a numerical calculation carried out earlier.