An approach to the theory of pressure broadening of spectral lines

Abstract

An attempt has been made to give a rigorous treatment of pressure or Stark broadening under the following assumptions:

• 1) the perturbating particles move independent of each other on straight lines with constant velocity v. The particles are distributed in the space with mean density n, the directions of their velocities are uniformly distributed on the unit sphere.

• 2) We neglect at all interactions of particles whose impact parameter is bigger than some constant ρ and we neglect interactions of particles with impact time t_p at times t with |t − t_p|⩾τ/2 where τ is another constant. Under these assumptions we get two formulae for the line profile I(ω) or its Fourier transform R(t)= = ∫ I(ω)e^iωtd, Part II, Theorem 3 and 4. Both formulae are very similar in character. They consist of terms which are sums of one-particle-interactions, two-particle-interactions and so on. The first formula holds for any value of n, v, τ and ρ whereas the second one can only be proven for nπρ² v τ < log 2. But the second formula is independent of τ and its one-particle approximation even of ρ. A detailed discussion of the second formula has been made in I. It clearly shows the nature of impact approximation.

For ω²I(ω) there can be established another very similar type of formulae (cf. II.5.). This type seems to be very useful for the discussion of the line-wings (cf. the end of I.).

The mathematical techniques are mainly the well-known methods of nearly elementary probability theory. New seems to me the calculus of many-particle-interactions developped in II.2. and applied in II.3.

The research reported herein has been sponsored in part by the United States Government.