Extraction of the absolute value of the photoelectron spectrum probability density by means of the resolvent technique

Abstract

In this work we consider the theoretical treatment of the interaction of a laser pulse with an atom and focus on the methodology used to extract the quantity that is observed experimentally, i.e., the electron probability density. We solve the time-dependent Schrödinger equation (TDSE) using two techniques: the spectral method, which makes use of an expansion of the wave function onto the field-free atomic eigenstates, and the wave-function method, where the TDSE is numerically solved on a grid. In this work we show that the electron probability density can be extracted from the final wave function, obtained by the wave-function method, by using the resolvent technique with a proper choice of the energy resolution. The advantage of this approach is that it does not require the calculation of the field-free atomic eigenstates. As an illustration of this method we compare the spectral and wave-function methods in the case of atomic hydrogen interacting with a linearly polarized mid-IR laser pulse. The comparison shows excellent agreement.

Molecular resolvent-operator method: Electronic and nuclear dynamics in strong-field ionization

“…We have extended the ROM from atoms [37,38] to molecules [16]. For this, we solved the TDSE, by using a grid method, in a (1+1)D model for the H 2 + molecule with one degree of freedom for the electron and another one for the nuclei.…”

“…The resolvent operator extracts from the wave function a particular region of the energy spectrum centered around E with an energy width δ. The definition of this operator is then similar to the atomic case and all properties associated with this resolvent can be applied to the molecular case [38]. By defining…”

“…The use of the Green's operator transforms the resolvent into an operator which depends linearly on the Hamiltonian [37,38]. The application of the Green's function on the final wave function is then reduced to an inversion problem (see more details in Appendix A).…”

“…which is independent of δ if the latter is chosen properly, i.e., close to the density of states in the continuum defined by the discretization [38]. In practice, the resolvent (R) is defined by the Green's functionĜ such that…”

“…In Eq. (3), E refers to the total energy and δ to a parameter associated with the energy resolution [38]. The resolvent operator extracts from the wave function a particular region of the energy spectrum centered around E with an energy width δ.…”