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

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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/(N 2/g 2−N 1/ g 1)=1.76×10−13 (mass number)1/2 S. The units of α are cm−1. N 1 and N 2 are in cm−3. S is in atomic units, a 0 2 e 2. 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 (N 2/g 2−N 1/g 1). This inversion quantity is a population difference between elementary quantum states.

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