Transmission of a Lorentzian Spectral Line Through a Layer of Lorentzian Absorbers. Part I

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Abstract
This paper is concerned with the evaluation of the integral that represents the total transmitted intensity. We consider the general case in which the thin-absorber linewidth ΓA is allowed to be different from the linewidth ΓS of the source. The introduction of the parameter γ = ΓA/ΓS has made it possible to expand the integral in an infinite series, each term of which is a rational algebraic expression. Our formulation avoids the tedium of numerical integration and lends itself readily to programming in FORTRAN. The application to Mössbauer spectroscopy is discussed. The results are valid in the case of a split source even if the spacing between the emission lines is less than their linewidth.