The Infrared Spectrum of Active Nitrogen

Abstract

The equations can be simplified by the introduction of two new parameters:.6 A = f dxp{x)e-™<-xa \ 0=0(6, a)- J aIn terms of these, Eqs. (28) and (29) become <t>R (b) = Ma)e ie + <t>L(a)Ae ie , Mb) = <t>L(a)e-ie +<t>R(a)A*e-i°. (30) (31) (32)B is the phase shift per cell given by the ordinary WBK method. | A | 2 is the probability that the particle changes its direction of motion in going through one cell.Floquet's theorem tell us that the solutions to the wave equation for a periodic potential can always be written in the form u(x) exp[ijuof], where u(x) has the periodicity of the lattice and M is either purely real or purely imaginary. It is real for the energy levels corresponding to allowed levels, and imaginary for the stop bands between them. Equations (31) and (32) represent a linear transformation whose characteristic values are X=exp[±i/ix]. The secular equation obtained from Eqs. (31) and (32) isThe roots of this equation areWhenever the quantity in parentheses is negative, the equation has two imaginary roots, complex conjugates of each other. In this case \=cos0±i(sin 2 0-|,4| 2 )*which to first order in |i| satisfies |X| = 1. Whenever the quantity in parentheses is negative, we will be in an allowed energy range. As the energy is varied, for a given potential, sin0 will repeatedly go through zero. When sin0 comes close enough to zero, the term in parentheses in Eq. (34) becomes positive and both roots will be real. The roots, when real, will have their extreme values (i.e., farthest removed from unity) when sin0=O. For that value of energy, we have |x| = i±U|~*fc»-to first order in | .4 |. The zone boundaries occur when the quantity in parentheses is negative, we will be in an sin0=±|.4|. The fact that we have taken into account only the first-order correction makes our solution an approximate one, which is valid only if the coefficient | A j is small compared with unity. The method is therefore valid only when the region between bands is narrow. This condition is not as restrictive as the one applicable to the usual perturbation theory approach.It is possible that | A \ can be zero. In this case a particle can travel through the lattice without being reflected. The reflections caused by different parts of the cell must cancel in such a case. If | A | vanishes at an energy for which sin0=O, the spacing between adjacent bands vanishes and they touch each other.The author wishes to thank Professors Furry and Brillouin for helpful discussions, and the Atomic Energy Commission for a Predoctoral Fellowship.Thirty-one bands, including the (0, 0) band at 10,440A, of the N2 first positive system have been photographed in the Lewis-Rayleigh afterglow of active nitrogen. There is no indication that the v-0 level of the B 3 U state is preferentially populated as required by the "resonance" theory of atomic re-association using D(Ni) = 7.383 volts. The analogy between the Lewis-Rayleigh glow and the spectrum of the airglow is discussed briefly.

The Reactive Components in Active Nitrogen and the Role of Spin Conservation in Active Nitrogen Reactions

“…This theory was based on analogous processes that were thought to occur in the emissioil of the spectrum of the night slry, and on the very large energies transferred to metal foils in some experiments made by Lord Rayleigh (54). I t has since been found that the interpretation of the atmospheric spectrum in terms of Nz+ was wrong (7) and that Rayleigh's results were due to bombardment by electrons from the exciting discharge (2). Mitra has therefore suggested recently (45) that the activity of active nitrogen is due to nitrogen atoms.…”

“…represent ethylene and acetylene in electronically excited triplet states and N.C2Hd is a collisio~l complex. From quenchi~lg experiments with excited metal atoms, reaction [7] is known to occur when the excitation energy is sufficiently high and it has already been pointed out (41) that this is a good example of spin con~ervation. ?~ Reaction [6] would have to compete with the energetically more favorable reaction Both reactions [6] ancl [9] are spin-allowed.…”