Influence of Resonant and Foreign Gas Collisions on Line Shapes
P. R. Berman, Willis E. Lamb
In the limit of a dipole-dipole interaction between neutral atoms and the binary-collision approximation, we present a theory of pressure broadening in which the multiplet structure of the atomic levels is considered. The appropriate Schr\"odinger equations for the collision problem are numerically integrated to obtain solutions for both resonant and foreign gas broadening. The presence of radiation fields is neglected in the first half of the paper, where the collisional time rate of change of the density matrix is found. The pertinent collisional decay parameters are extracted from these equations. The ratios of the parameters of the average magnetic dipole to electric quadrupole moment obtained were 1.21\ifmmode\pm\else\textpm\fi{}0.02 for the relaxation of the entire ensemble in resonant broadening, 0.966\ifmmode\pm\else\textpm\fi{}0.012 for the relaxation of the initially excited atoms in resonant broadening, and 1.12\ifmmode\pm\else\textpm\fi{}0.02 for the relaxation of the initially excited atoms in foreign gas broadening. In the second half of the paper, the collisional broadening results are incorporated in a systematic evaluation of (i) spectral profiels (effects arising from the velocity and recoil of the emitting atom are neglected), (ii) Hanle-effect line shapes, and (iii) laser phenomena. For the case of resonant broadening, the radiation trapping process is reviewed and its influence on line shapes discussed. Finally, a detailed comparison of the theory with experimental findings as well as with previous theoretical results is made. We conclude that the dipole-dipole interaction is sufficient to explain most cases of resonant and some cases of foreign gas broadening.
Physical Review•Nov 5, 1969•155 citations