Multiply charged negative ions of hydrogen in linearly polarized laser fields

Motivated by the prediction of the appearance of atomic multiply charged negative ions (AMCNI) of hydrogen, induced by a linearly polarized laser field, we present an analytical quantum mechanical treatment of the appearance and structure of AMCNI in a linearly polarized field, based on high-frequency Floquet theory (HFFT). For the simplest AMCNI of hydrogen, H^2- and H^3-, the values of a₀ at which the first bound state appears are a₀= 1.62x 10² and a₀= 1.02x 10⁴, where a₀ =I^1/2/w² is the amplitude of the oscillation of a free electron in the field with frequency w and intensity I (unless stated otherwise, we use atomic units throughout this paper). Whereas in vacuum at least one of the electrons of an AMCNI autodetaches, an intense highfrequency field can change the character of the ion dramatically, such that bound states of AMCNI can appear. Due to the interaction with the field, the electrons of the AMCNI oscillate in phase along the polarization axis. This "quiver" motion enables the electrons to be spatially separated over distances of order a₀, reducing the repulsive e-e interaction as a₀ increases. In other words, for a₀ large enough, the field enables a configuration in which the electrons, while widely separated, are bound to one proton. For the prediction of bound states of H^N- with N>3, however, a relativistic description or low-frequency theory is required.