Theory of Collision Effects on Line Shapes Using a Quantum-Mechanical Description of the Atomic Center-of-Mass Motion—Application to Lasers. II. The Pseudoclassical Collision Model and Steady-State Laser Intensities

Abstract

Pressure effects in gas lasers are studied within the framework of a theory that treats the center-of-mass motion of the active and perturber atoms quantum mechanically. Such a theory considers the perturber-induced energy-level variations and the velocity changes of the active atom caused by collisions on an equal basis. The calculation is carried out assuming that the active atom undergoes many binary collisions before it decays. As such, this paper represents a generalization of our previous work, which was valid only if the active atom underwent, on the average, at most one collision in its lifetime. The transition from the "one-collision" to the "many-collision". domain is achieved by use of a pseudoclassical collision model. This model enables one to incoporate the results of a rigorous quantum-mechanical treatment of the one-collision problem intdy standard classical procedure for handling many (binary) collisions. The result is a quantum-meqhanical theory of collision effects valid in the many-(binary-)collision pressure region. Using this theory, expressions for the laser intensity profile are derived employing a collision model which, although quite elementary, should prove to be rea.sonably accurate for lasers operating slightly above threshold at pressures where both the collision-broadened linewidth and cavity detuning are much smaller than the Doppler width associated with the laser transition. A comparison of theory and experiment is made, and the signHIcance of their relatively good agreement is discussed. the collision interaction in the two radiative levels is comparable, we offer a calculational model in Appendix A.In Secs. II and Ill we review QMI and outline the philosophy of the present calculation, including a detailed exposition of the pseudoclassical model in Sec. III. The mathematical development of the problem is presented in Secs. IV-VI, with expressions for the gain, linear pulling, saturation, and nonlinear pushing parameters of the laser, as we11 319