Bardeen's Theory of Superconductivity and thef-Sum Rule

Abstract

T HE atmospheric bands of oxygen result from an intercombination magnetic dipole transition with a probability of only 0.14 sec -1 . 1 Although well known in the solar absorption spectrum, this system was not observed in emission until 1947, when Kaplan 2 reported the (0, 0) and (0, 1) bands in an oxygenenriched nitrogen afterglow. Subsequently, the bands have been produced in emission in 3 in He discharge with a trace of O2, 4 and in a high pressure glow discharge in pure O2. 5 In addition the (0, 1) band is a prominent feature of the infrared spectrum of the night air-glow. 6 -7 Under appropriate conditions a sealed-off glass vessel containing spectroscopically pure O2 at about 1-cm pressure will afterglow very strongly in the infrared. The afterglow spectrum from 3000 to 9100A contains only the (0, 0) and (0, 1) atmospheric bands (with heads at 7593.7 and 7685A, respectively) and a weak continuum. The rf electrodeless discharge which precedes the afterglow produces these forbidden bands with much greater intensity. This spectrum contains members of the Av -0 progression up to v f ==4, as well as O I lines. OI 8446.8A and the OI triplet at 7772A are very strong, indicating a high degree of dissociation of the O2. The (0, 0) band of the direct discharge, photographed in a net exposure of about 30 minutes on a Baird two-meter grating, is shown in Fig. 1. >%]k#lK*ft*^^FIG. 1. The (0, 0) *2 -3 2 band of the forbidden oxygen atmospheric system produced in emission. The "rotational temperature" is 710°K.The spectral composition and pressure requirement suggest that the energy producing the afterglow is stored in the high degree of dissociation and is released by three-body volume recombination. The "active oxygen'* of the afterglow is also capable of heating to incandescence tiny flecks of metal for as long as 10 seconds in the afterglow. Because of the high probability of this metallic surface recombination, an electrodeless discharge is propitious for afterglow production.The rotational and vibrational "temperatures" were measured in both the afterglow spectra and the direct discharge. The rotational distribution in the direct discharge follows very closely the Boltzmann formula with a "temperature" of 710°±10°K. The vibrational " temperature" is approximately the same, 670° db80°K. 8 In the afterglow spectra the (1, 1) band does not appear on our plates, placing an upper limit on the vibrational "temperature" of the afterglow of about 450°K. Since the rotational "temperature" computed from the profile of the unresolved (0, 0) band in the afterglow is approximately room temperature (roughly 310°K), the excited oxygen molecules in the afterglow appear to attain thermal equilibrium before radiation, as would be expected from the low transition probability and the moderately high pressure.The agreement between vibrational and rotational temperatures in the discharge and afterglow shows that many collisions occur before the excited molecule radiates. In excitation by molecule formation in three-body collisions, up to...