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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/(*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.

© 1964 The American Institute of Physics

Received 15 August 1963
Revised 20 December 1963
Published online 20 July 2004