Line Strengths for Noble-Gas Maser Transitions; Calculations of Gain/Inversion at Various Wavelengths

Abstract

Relative line strengths for s-p, p-d, and d-f transitions of Ne, A, Kr, and Xe are derived by the method of Koster and Statz, under the assumption of the j-l coupling scheme of Racah. When the relative strengths are given a common denominator, a set of rules for strong lines becomes apparent, similar to rules which have been noted for L-S coupling. For comparison with experiment, we consider several sets of Ne lines, each set having one specific initial, and one final configuration. For the higher l values (p-d and d-f) the lines found to give oscillation are almost exclusively the lines with large relative strengths. The absolute line strengths S are then calculated in the Coulomb approximation of Bates and Damgaard; we consider only transitions between two excited states. There is the following simple relation between (gain constant/volume density of inversion) and S:α/(N2/g2−N1/ g1)=1.76×10−13 (mass number)1/2S. The units of α are cm−1. N1 and N2 are in cm−3. S is in atomic units, a02e2. The linewidth is taken to be determined by Doppler broadening at 400°K. For several lines upon which measurements of α have been made, we give the corresponding values of (N2/g2−N1/g1). This inversion quantity is a population difference between elementary quantum states.