Level-Crossing Signal Line Shapes and Ordering of Energy Levels

Abstract

Theory and experiments are presented to show that, when correctly interpreted, the sign of the dispersion-shaped term which describes a part of the change in resonance scattering at level crossings can be used to determine the energy ordering of the crossing levels, and hence, in some cases, to obtain the sign of the nuclear magnetic moment. Because of a discrepancy in the literature in the theoretical prediction for the sign of the dispersion-shaped term, we have made a recalculation. The result is borne out by our experiments.Colegrove, Franken, Lewis, and Sands 1 introduced the use of the "level-crossing" effect in atomic resonance fluorescence as a very fruitful technique for the measurement of fine and hyperfine structures. 2 The experiments have relied largely on the study of the Lorentz-shaped term that describes a part or, for certain geometries, all of the variation of the resonance scattering at level crossings. We wish to show that if the dispersion-shaped term is used, in addition to obtaining the level-crossing magnetic fields, we can determine the energy ordering of the crossing levels which may be of importance in the analysis of the level structure. In particular instances this can serve to obtain the sign of the hfs interaction constant, and hence that of the nuclear magnetic moment. Since the sign of the dispersion-shaped term is crucial we call attention to the fact that our calculations show that this sign is opposite to that obtained by Franken, 3 whose result is used in much of recent levelcrossing literature. In contrast, our result -which was corrobated by our experiments-is in agreement with early work of Weisskopf, whose result also appears in the review article by Breit, and with that of Rose and Carovillano and of Lassila. 4 We have calculated in a manner analogous to that of Franken 3 the rate R at which photons of polarization f are absorbed from ground-state levels with magnetic quantum numbers ra, m', and are re-emitted with polarization g from excited-state levels M, M'-We find Roz y f f *g *cr A-4/ ixm J \x'm 6 m'M m'\. m m M /A'where f^m, g^m f , etc. are the appropriate electric dipole matrix elements, T is the excited-state decay constant, and E M and E^' are the

Hanle effect in the singlet excited states of the alkaline earths

“…An error of sign in the denominator of wave function of the excited states, transition Franken's formula was corrected by Stroke et 01. probabilities, oscillator strengths, and collision (4). For transitions J = 0 + J = 1 + J = 0 and with cross sections.…”

Hyperfine Structure of the3P2and4PIsler1, Marcus2, Novick3 1969Phys. Rev.23040View full textAdd to dashboardCite

“…The Sternheimer 24 correction for distortion of the electron core in lithium increases Q by about 11% over the value obtained directly from Eq. (8).…”