# Analysis of atomic and molecular negative ions in a constant electric field using a resolvent method

## Abstract

We use a resolvent method to study atomic and molecular negative ions in a constant electric field potential which is linear. When a linear potential is applied, it makes the shape of the original potential of the system slanted into one side and thus changes the time evolution of the system. In particular, a bound state can be changed into a state, so called 'quasibound' state, which is not bound anymore and decays into the continuum due to the presence of the linear potential. For an atomic system, we use an attractive delta function fixed at the origin for the interaction potential and solve the single particle Schrodinger equation. For an actual system, we choose the Hydrogen negative ion, and determine the strength of the delta function so that the bound state energy can simulate the electron affinity of the Hydrogen. We find the resolvent of the system and the poles of the resolvent in the analytically continued region. From the patterns of the location of the poles, we can view the one delta function system as a combination of three simple systems. Though they are not exactly the same, this view gives some insight on the system. From the residue at each pole, complex eigenstates are constructed and used for the calculation of the survival probability of an initial state. For the same initial state, we calculate the photodetachment rate when a time-periodic potential is applied. The plot for the photodetachment rate shows peaks at certain incident photon energies. These are compared with an experimental data and give a good agreement although our model is just one dimensional. For a molecular system, two delta function model is suggested by us as an extension of the one delta function model. We find the resolvent of the system and the pole structure from the resolvent. The complex eigenstates are constructed from the residue of the resolvent at each pole. We try to model Oxygen molecular negative ion and determine the strength of the delta function and the distance between the delta functions so that they are consistent with the electron affinity and the internuclear distance of the Oxygen molecule. We also calculate the survival probability and the photodetachment rate of an initial state and find that the plot of the photodetachment rate has similar shape to that of the one delta function model.