R-matrix Floquet theory of molecular multiphoton processes: II. Multiphoton ionization of H₂

Abstract

Multiphoton ionization rates for H2 immersed in an intense linearly polarized laser field are calculated using the recently developed R-matrix Floquet theory of molecular multiphoton processes. We assume that the H2 molecule is aligned along the laser polarization direction and we adopt the fixed-nuclei approximation, in which the motion of the target electrons is calculated in the laser field and in the field of the nuclei, which are assumed to be fixed in space. An accurate multi-state wavefunction is employed to calculate one-, two- and four-photon ionization rates for H2 at several internuclear separations over a range of frequencies and intensities. Analysis of the ionization rates reveals the important role played both by resonances corresponding to Rydberg bound states converging to the H2+ ion ground state and by doubly excited states converging to the H2+ ion first excited state. These resonances give rise to resonant enhanced multiphoton ionization peaks in many of the ionization rates studied in this paper, and their possible role in controlling the vibrational population of the final H2+ ion is discussed.

Lippmann-Schwinger description of multiphoton ionization

“…With the help of the formulas (28) and (29) we calculated the integrals a, n + p|Ĥ int |b, n . In the case of hydrogen atom the atomic states |a are characterized by energies and angular momenta.…”

“…In this development we are inspired by a series of works by Burke and collaborators who combined the Floquet description of the laser field with the R-matrix scattering theory. Following the seminal work [24], this approach has been successfully implemented for calculating the total MPI rate and the level shift in atomic hydrogen [25], helium [26], the negative hydrogen ion [27] and molecular hydrogen [28]. Most recently the R-matrix Floquet theory was combined with the basis spline technique to describe the twoelectron MPI from the helium atom in the ground [29] and excited states [30].…”

Molecular ionization and dissociation using synchrotron radiation and ultrashort laser pulses

“…Notice that, in order to perform the integral over R in equation (1), this wave function must be obtained at different values of R. Several accurate methods have been successfully developed to evaluate ψ 0+ αlαǫα (r, R). Among them, it is worth mentioning (i) the discretized close-coupling (DCC) method [12,[17][18][19] and the convergent close-coupling (CCC) method [20][21][22], in which the electronic wave function is written as a combination of products of target and scattering electronic wave functions with the appropriate boundary conditions, (ii) the exterior complex scaling (ECS) method [23][24][25], in which the electronic coordinates are scaled in the complex plane beyond a certain (usually large) distance r 0 thus ensuring the correct asymptotic behavior for r i < r 0 , and (iii) the Rmatrix method (and its many extensions, see, e.g., [26][27][28] and references therein), in which the problem is first solved within a sphere of finite size and then the asymptotic behavior is switched on later from outside the sphere. In principle, all these methods can be implemented by using different basis sets and/or grid methods.…”

Multiphoton Selective Excitation and Analytical Control of Small Molecules in Intense Laser Fields: an Algebraic Model

“…Some theoretical and computational methods have been developed for improvements in experiment, such as the Coulter transformation method, the Floquet theory method, and dressed molecule picture etc. (Colgan et al, 2001;Chang et al, 1985;Chu & Telnov, 2004;Leforestier & Wyatt, 1985;1983;Dibble & Shirts, 1991 ). Much of the work, however, has studied the problem by numerically solving the time-dependent Schrödinger equation (TDSE) as an initial value problem in Hilbert space.…”

“…The development of generalized Floquet formalisms allows the reduction of the periodical or quasiperiodical time-dependent Schrödinger equation into a set of time-independent coupled equations or Floquet matrix eigenvalue problem. The Floquet method has also been employed to study the problem of molecules in intense laser fields, but it has usually been used to discuss the atomic problems (Leasure et al, 1981;Burke et al, 2000;Colgan et al, 2001;Chu & Telnov, 2004). In this chapter we present the algebraic approach on a different background.…”