A tetradic scattering matrix formalism is proposed as a comprehensive framework for describing scattering and relaxation processes of both stationary and non-stationary systems. In the latter case (realized by the scattering of the molecular-maser beam) ordinary dyadic T-matrix formalism involving on-the-energy-shell scattering amplitudes is inadequate, the introduction of off-the-shell elements being required. Expressions are given relating the tetradic T-matrix elements to various scattering and attenuation rates (or cross sections). The relation to the tetradic level-shift operator in relaxation (linear response) theory is discussed. Photon absorption is presented as the successive occurrence of a scattering and a relaxation process, from the point of view of this formalism.
A tetradic scattering matrix formalism is proposed as a comprehensive framework for describing scattering and relaxation processes of both stationary and non-stationary systems. In the latter case (realized by the scattering of the molecular-maser beam) ordinary dyadic T-matrix formalism involving on-the-energy-shell scattering amplitudes is inadequate, the introduction of off-the-shell elements being required. Expressions are given relating the tetradic T-matrix elements to various scattering and attenuation rates (or cross sections). The relation to the tetradic level-shift operator in relaxation (linear response) theory is discussed. Photon absorption is presented as the successive occurrence of a scattering and a relaxation process, from the point of view of this formalism.
The resonant response of a multilevel atomic system to strong coherent radiation is analyzed using an extension of the methods of time-independent scattering theory, adapted to the density-matrix formalism in order to include thermal bath effects. General steady-state expressions are derived for self-attenuation and resonance scattering rates in strong saturating fields, as functions of the coupling strengths, relaxation parameters, and frequency detunings. Formal expressions are given for radiative-damping and collision-broadening relaxation parameters, relating the latter to scattering amplitudes. Modifications of collision-broadening parameters by the presence of very strong fields are discussed. The Bloch equations are derived by transformation to the time domain, under specified conditions.
The quantum theory can be formulated in the language of positive functionals on Weyl or Clifford algebra (L-functionals). It is shown that this language gives simple understanding of diagrams of Keldysh formalism (that coincide in our case with the diagrams of thermo-field dynamics). The matrix elements of the scattering matrix in the formalism of L-functionals are related to inclusive cross-sections, therefore we suggest the name “inclusive scattering matrix” for this notion. The inclusive scattering matrix can be expressed in terms of on-shell values of generalized Green functions. This notion is necessary if we want to analyze collisions of quasiparticles.
A theoretical study is presented of the effects of collisional perturbations on the time-resolved resonant and near-resonant photon scattering from a molecular system. The photon counting rate is formulated in terms of tetradic Green's functions in Liouville space. The collisional and radiative damping effects are handled by an effective-Liouvillian formalism. The formal expressions are disentangled by invoking a series of successive approximations, assuming short correlation times of the thermal bath, neglecting relaxation processes in the ground electronic state, considering rotational relaxation as providing the dominant damping mechanism in the excited electronic manifold, specializing to weak electromagnetic fields, neglecting some off-resonance processes and disregarding collision-induced radiative processes. The photon counting rate is expressed as a triple convolution of the photon counting rate for the free molecule with the Doppler Gaussian profile and with a Lorentz profile. The latter incorporates purely collisional effects due to intrastate cross relaxations and proper T2 processes. The theory accounts well for the recent experimental data of Williams, Rousseau, and Dworetsky on collisionally perturbed I2 molecules.
We present a general microscopic theory for near resonance light scattering (RLS) from collisionally perturbed atoms and molecules. The theory is based on the tetradic scattering formalism of Fano and Ben-Reuven. We perform a systematic density expansion and show that the four-time, many-body, dipole correlation functions necessary for the evaluation of the RLS cross section may be rigorously expressed (to lowest order in pressure) in terms of three single-particle, two-time, correlation functions, two of which are associated with the absorption and emission line broadening and the third is a cross correlation function. Our most general expressions are valid for an arbitrary value of the bath correlation time (relative to the broadening), and interpolate smoothly all the way from the static limit of inhomogenous broadening up to the reverse, the Markovian (homogenous) limit. The stochastic Gaussian model of Takagahara, Hanamura, and Kubo is obtained also as a special case of the present formulation.
A study has been carried out on the relationship between formal scattering theory and the density matrix formalism. The density operator is developed in terms of the scattering operator S and the observable square modulus matrix elements of S are shown to be equivalent to elements of the density matrix. The Møller wave operators are similarly treated and subsequently used in obtaining the density matrix expression for the transition matrix. Finally, using the latter, it is shown that the hierarchy of approximations to the density matrix yields equivalent results to those obtained from the Born series.
The theory of optical birefringence is discussed from the point of view of the scattering of polarized photons by molecules using the framework of formal scattering theory and quantum electrodynamics. In Part One, those features from noncovariant quantum electrodynamics relevant to the molecular scattering of photons are reviewed. Chapter One contains an outline of classical electrodynamics in the Coulomb gauge, including the Stokes parameter and density matrix formulations of polarization. Chapter Two deals with the quantization of the radiation field, and the occupation number representation is defined. The quantum mechanical description of polarized light is outlined in Chapter Three: operator equivalents of the density matrix and Stokes parameters are invoked, the parameters themselves being obtained from the expectation values of the Stokes operators with the state vector of the photon. The Stokes parameter and density matrix are then applied to the polarization of a general beam containing an arbitrary number of photons, and some new methods are developed. The interaction of the electromagnetic field with bound electrons is formulated in Chapter Four in terms of a canonically transformed interaction Hamiltonian in which the multipole terms are explicit. Since each term is then gauge-invariant, this Hamiltonian is particularly suited to the application of diagrammatic perturbation theory which follows from the iteration of the scattering matrix in the interaction representation (Chapter Five). Also the extension of the theory to multiphoton processes is facilitated "because the field strength is explicit in the transformed Hamiltonian. The S-matrix connects the initial and final asymptotic states of the scattering system, and in Chapter Six the state vector and density operator of the scattered photon beam are obtained from those of the incident beam. Part Two contains the application of the above methods to a variety of linear and nonlinear optical birefringence effects in the absence or presence of external fields. In Chapter Seven, general equations are obtained for the polarization changes imposed on a forward scattered photon in terms of matrix elements of the reaction operator between plane polarized photon base states; whereas Chapter Eight extends this treatment to an n-photon beam, thereby encompassing the hyperpolarizability contributions to the polarization changes of the forward scattered beam. It is then demonstrated that the fundamental process in optical birefringence can be interpreted as an infinitesimal unitary transformation of the polarization spinor. Also the S-matrix approach to birefringence is compared with the methods used in crystal optics, and with the classical treatments of the scattering of polarized light by molecules. The general equations obtained for the polarization changes of the forward scattered beam are subsequently interpreted in the light of the physical circumstances appropriate to the bire- fringence effect of interest. In Chapters Nine, Ten, and Eleven, diagrammatic perturbation theory is used to obtain explicit expressions, in terms of molecular polarizability and rotation tensors, for the linear and nonlinear contributions to the polarization changes involved in natural optical activity, and in birefringence phenomena induced by static and optical electric and magnetic fields. The nonforward scattering of polarized photons by molecules is discussed in Part Three. General equations are calculated in Chapter Twelve for the azimuth, ellipticity, and depolarization ratio of the Rayleigh beam at any scattering angle and for any polarization of the incident beam. Explicit expressions in terms of molecular quantities are then obtained for the polarization at scattering angles of 90° and almost zero from both optically inactive and optically active molecules. It is demonstrated that a determination of the precise polarization state of the scattered beam can provide useful molecular information additional to that obtained from depolarization ratios alone. This is because the depolarization ratio depends on only the diagonal elements of the polarization density matrix and so does not convey all the information about the system. Raman scattering processes are contained in the formulation and the polarization of the Raman light at any scattering angle can be obtained. This is shown to be particularly useful for predicting the polarization of stimulated Raman light for any Raman-active liquid placed within a laser cavity. By extending the nonforward scattering formulation to incorporate multiphoton processes, equations are obtained in Chapter Thirteen for the ellipticity, azimuth, and depolarization ratio of the second harmonic wave at any scattering angle as a function of the incident polarization. Several specific situations are subsequently investigated. Finally, it is shown in Chapter Fourteen that the near-forw- ard Rayleigh and Raman scattering formulations provide an explanation for the observed polarization, as a function of the initial polarization, of the self-trapped filaments that arise from the self-focusing of an intense laser beam.