On the validity of an approximation method for two-colour photodetachment

Abstract

The validity of an approximation method used by Bivona et 01 for two-colour photodetachment is investigated. It is found that while their approach may be valid for some S-matrix elements, in others, contributions neglected in the scheme are much larger than the terms that are retained. In aAdition. an explanation is suggested for Ihe linear dependence found for the transition probability on final-state energy.Recently, Bivona er a1 (1994) reported on a calculation of two-colour photodetachment in a model negative ion located in a strong magnetic field. In the model, a single electron interacts with a static spherically-symmetric binding potential V ( r ) , as well as low-intensity radiation at high frequency RH, high-intensity radiation at low frequency S22~ and a DC magnetic field.The authors use the familiar formalism in which an exact expression for the S-matrix element connecting the initial (bound) to a final (free) state is given by Sjf = -i dt(a~(T,I)IV(T)[a+)df (1)

The effect of nonanalyticities in coupling potentials on transition probabilities in two-level systems

“…In those cases, the coupling causes some population to be transferred to |2 while V is on, but then the atom returns to state |1 with 100% probability when the pulse has passed. These restoring A 2 have been (Robinson 1981(Robinson , 1984(Robinson , 1985a(Robinson , b, 1993(Robinson , 1995 designated as pulse area eigenvalues (EV), A 2 n , and the solutions, b 2n , as their eigenfunctions (EF). The EV need not be real and positive.…”

“…The EV need not be real and positive. (They are real if V is a symmetric function of time (Robinson 1981).) The eigenvalues are also given by…”

A comment on the validity of an approximation method for two-colour photodetachment

“…Recently, Robinson (1995) investigated the validity of an approximation method used by Bivona et al (1994) for two-colour photodetachment in the presence of a static magnetic field B, raising serious doubts on the reliability of the cross section obtained by its application. The starting point of the criticism of Robinson is the approximate form of the S-matrix element connecting the initial (bound) state of a negative ion to a final (free) state dressed by a low-frequency (LF) electromagnetic field.…”

“…By choosing the LF field parameters equal to the ones used by Bivona et al (1994) and Robinson (1995), arguments of the Bessel functions are obtained that allow us to approximate these functions by taking the leading terms resulting from the expansion in terms of their arguments. Then the transition amplitude of the process in which a single HF photon along with two laser photons are absorbed is found to be…”

“…We observe that this law could be obtained by crossing out the leading term of ( 8). Equivalently, it could be obtained by considering the time-oscillating function entering the term denoted by δ in (5) of Robinson (1995) to be time-independent. Since the conclusion drawn by Robinson is clearly unfounded, as it is based on an incorrect calculation, we cease doing any further comparison with his result and turn our attention to the more interesting question pointed out by this author, which concerns the reliability of the photodetachment cross sections obtained by describing | i through the unperturbed wavefunction of the ground state.…”