The theory of resonant reactions, in the projection-operator formulation of Feshbach, is generalized to account for the presence of an external electromagnetic field. The theory is used as the basis for the construction of low-frequency approximations for the transition amplitude. Results obtained here for scattering in a laser field confirm earlier versions of the low-frequency approximation when the resonances are isolated. However, if there are several closely spaced resonances additional terms must be included (their importance magnified by the appearance of near singularities) which account for the effect of radiative transitions between pairs of nearly degenerate resonant states. The weak-field limit of this result yields a low-frequency approximation for single-photon spontaneous bremsstrahlung which, through the inclusion of correction terms associated with closely spaced resonances, provides an improvement over the Feshbach-Yennie version derived some time ago. A separate treatment is required to deal with the limiting case of a static external field and this is worked out here in the context of a time-dependent formulation of the scattering problem. Linear and quadratic Stark splitting of the resonance positions, and resonance broadening due to the tunneling mechanism, are expected to play a significant role in the static limit and these effects are included in the approximation derived here for the transition amplitude.
The theory of resonant reactions, in the projection-operator formulation of Feshbach, is generalized to account for the presence of an external electromagnetic field. The theory is used as the basis for the construction of low-frequency approximations for the transition amplitude. Results obtained here for scattering in a laser field confirm earlier versions of the low-frequency approximation when the resonances are isolated. However, if there are several closely spaced resonances additional terms must be included (their importance magnified by the appearance of near singularities) which account for the effect of radiative transitions between pairs of nearly degenerate resonant states. The weak-field limit of this result yields a low-frequency approximation for single-photon spontaneous bremsstrahlung which, through the inclusion of correction terms associated with closely spaced resonances, provides an improvement over the Feshbach-Yennie version derived some time ago. A separate treatment is required to deal with the limiting case of a static external field and this is worked out here in the context of a time-dependent formulation of the scattering problem. Linear and quadratic Stark splitting of the resonance positions, and resonance broadening due to the tunneling mechanism, are expected to play a significant role in the static limit and these effects are included in the approximation derived here for the transition amplitude.
The effect of a low-frequency laser field on photoionization and radiative recombination processes is studied theoretically, with particular attention paid to the combined influence of the electron-ion Coulomb interaction and the laser field on continuum states of the system. A procedure for representing the asymptotic states of the system, with both long-range interactions properly accounted for, is described. The transition rates are strongly affected by the existence of a Rydberg series of resonances. Methods developed for describing similar resonant processs that occur in the field-free case are generalized here to include the effects of the external laser field. A simple model, based on parametrizations of the type employed in quantum-defect theory, is used to study the modification of resonant structures in the cross section introduced by the external field. In the weak-field limit, a low-frequency approximation for bound-state Compton scattering is obtained, with resonance effects accounted for.
A modified perturbation theory is developed for the calculation of the time-dependent wave function describing the propagation of an atom in a two-mode laser field. With the mode frequencies nearly equal, a first approximation is obtained that reproduces and extends known results, for both resonant and nonresonant transitions. This lowest-order solution sums terms that describe the absorption of a photon from one mode and emission into the other, leaving the total number of photons unchanged and shifting the momentum of the atom accordingly. Corrections are generated by expansion of a resolvent from which the nearly degenerate states have been projected out. These approximate solutions are used to construct asymptotic states in a formulation of atom-atom scattering in the two-mode field. In close analogy with the soft-photon approximation, a ``soft-pair'' approximation is developed based on the dominance of those asymptotic interactions in which the transfer of energy from the field to the atom is small, allowing one to relate the scattering amplitude in the presence of the field to the field-free amplitude. When the atomic ground state and an excited state are closely coupled by the field, the asymptotic wave function can have mixed parity allowing for long-range contributions to the effective potential. In addition to an enhancement of forward-scattering probabilities, this leads to a threshold anomaly that is analyzed here, in the resonant case, with the aid of a modified effective-range theory.
We study collision of two atoms with formation of Feshbach resonance at combined interaction with the external magnetic field and laser radiation. In cases of one- and two-photon resonances of laser radiation with two discrete vibrational molecular levels, we show that Feshbach resonances appear at interaction of external magnetic field with dressed states formed via Autler-Townes effect. In addition, in case of one-photon resonance the lower vibrational molecular state is coupled by laser radiation with the continuum of the elastic channel and forms laser-induced Feshbach resonance via both Autler-Townes effect and LICS mechanism. We study the combined process of formation of Feshbach resonances; this enables the control of Feshbach resonance by varying the magnetic field and intensity and frequency of laser radiation. We obtain the cross-sections of elastic and inelastic scattering and show that quenching of resonance occurs at the energy equal to that of the systems ground state. Dependence of the cross-sections on the magnetic field and laser intensity is examined in detail. In all considered cases, the scattering length is obtained depending on the magnetic and laser fields are studied. In the absence of magnetic interaction if the hyperfine substates of the quasibound state in the closed channel and those of individual colliding atoms in the open channel are the same, Feshbach resonances may arise via weak interaction between nuclear and electronic motions, which leads to transitions between electronic states. The obtained results can be employed in new studies of collisions of cold atoms, e.g., of alkali metal atoms and for interpretation of new experiments in BECs.
A set of coupled equations for the particle scattering by a two level atom in a strong near resonant radiation field is derived from the time dependent Schrodinger equation. This set of equations is discussed in a first and second order approximation. The result can be visualized in terms of a scheme in which the two well separated (nondegenerate) atomic states split, each into two energy levels. The splitting depends on the strength of the field and on the difference between the resonance frequency and the frequency of the incident light and is typically a few meV. In this scheme all possible elastic, quasielastic, inelastic and superelastic transitions between the four levels can be induced by collision processes. In addition, multiphoton processes may occur if the scattered particle remains long enough in the interaction region. Estimates of the two photon gain process for electron and heavy particle scattering by sodium atoms in a dye laser field are given. It is suggested that the superelastic processes may play an important role in laser induced gas breakdown, even if the laser frequency does not coincide with any atomic transition. Spontaneous emission of atoms in laser fields is also treated. The results are similar to the particle scattering processes.
A critical examination of the theory of resonance radiation has been carried through, employing the mathematical technique of Laplace and Stieltjes transforms. Particular attention has been devoted to the question of the temporal behavior of the excited state. With no restrictions on the interaction between atom and radiation field other than that it be real, and that processes of sufficiently high frequency contribute only negligible effects, one can prove that the probability amplitude of the excited state cannot decay according to the general law ${\ensuremath{\Sigma}}_{\ensuremath{\mu},\ensuremath{\nu}}{C}_{\ensuremath{\mu}\ensuremath{\nu}}{t}^{{\ensuremath{\lambda}}_{\ensuremath{\mu}}}{e}^{\ensuremath{-}{\ensuremath{\beta}}_{\ensuremath{\nu}}t},$ where the ${\ensuremath{\lambda}}_{\ensuremath{\mu}}$ and ${\ensuremath{\beta}}_{\ensuremath{\nu}}$ are complex constants lying in the right half-plane and the ${C}_{\ensuremath{\mu}\ensuremath{\nu}}$ are arbitrary complex coefficients. The deviation from the law just cited can be termed a straggling phenomenon since exact analysis shows that the probability amplitude, for sufficiently long times, is greater than that defined according to the radioactive decay law.Rigorous analysis of the source of this apparently anomalous behavior reveals the following explanation. Although the probability amplitude of the excited state is, strictly speaking, a functional of the interaction between the transition current in the atom and the photon states of the electromagnetic field, the essential features are determined principally by those states lying near the resonance frequency. Three elementary observations are immediately apparent. First, a particularly tractable analytical approximation for the interaction can be made such that the value of the actual interaction is reproduced at the resonance frequency and such that the behavior for high and low frequency photon states is at least qualitatively correct. Exact solutions in closed form can be obtained for this interaction. Second, in terms of the preceding representation it is possible to show that, associated with the transition between two atomic states, one is presented with a concomitant picture of a damped oscillation of charge describable in purely classical terms. Third, this classical motion can be interpreted as forming a source function for a continuous stochastic process in terms of which one finally derives the representation of the probability amplitude of the excited state. The straggling phenomenon previously cited is therefore that associated with all diffusion processes. The consideration of the exact interaction leads to more involved diffusion phenomena but does not in any case permit a radioactive decay law.
In the first paper of this series a formal theory of atomic scattering of electrons in the presence of an intense electromagnetic field was given. Cross sections, near the forward direction, between atomic states (modified by the laser) were obtained. However, it was assumed that the atom could not emit spontaneous radiation. In this paper the effect of spontaneous radiation is included, and it is shown that in most cases the measured cross section will be a weighted average of the two different cross sections starting from the two different initial states which are those atomic states resonantly linked by the laser. The Born approximation for the scattering is obtained, and it is shown that for the simplest description of the spontaneous radiation field the effect of the laser on the cross sections is simply to multiply them by a factor which depends upon the laser detuning.