Ionization in a 1-Dimensional Dipole Model

Costin, O.; Lebowitz, J. L.; Stucchio, C.

Ionization in a 1-Dimensional Dipole Model

Authors

Costin, O.

Lebowitz, J. L.

Stucchio, C.

Description

We study the evolution of a one dimensional model atom with $δ$-function binding potential, subjected to a dipole radiation field $E(t) x$ with $E(t)$ a $2π/ω$-periodic real-valued function. Starting with $ψ(x,t=0)$ an initially localized state and $E(t)$ a trigonometric polynomial, complete ionization occurs; the probability of finding the electron in any fixed region goes to zero. For $ψ(x,0)$ compactly supported and general periodic fields, we construct a resonance expansion. Each resonance is given explicitly as a Gamow vector, and is $2π/ω$ periodic in time and behaves like the exponentially growing Green's function near $x=\pm \infty$. The remainder is given by an asymptotic power series in $t^{-1/2}$ with coefficients varying with $x$.
Corrected proof, extensive changes. 39 pages, 1 figure