Electron Density and Light Intensity Decay in Cesium Afterglows

Abstract

nucleus by observing the angular correlation of the emitted particles as a function of time. 2 One would expect a correlation to persist to times of the order of the total spin relaxation time T 2 of the intermediate nuclei j in the sample, perhaps milliseconds or better. 8 We show here how the theoretical delayed coincidence correlation function describing the effect of the magnetic field is to be obtained from the usual correlation function.The equations of the Weisskopf-Wigner treatment of the decay 4 can be made to yield a function W(Qi\ Q 2 ; t-f) which can be interpreted as the rate (steradian -2 sec -1 ) at which particles of the second transition are emitted at time / with direction O2 555 #2, <P2 when the preceding particle in the cascade was emitted at time /' with direction Qisstf!, <p lf the initial nuclei /1 being randomly oriented at time zero. As indicated, this rate comes out to be a function of /-/' only, and we refer to it as the delayed coincidence angular correlation function. 5 If wo is the circular Larmor frequency of the intermediate nucleus j in the external magnetic field (along the s-axis), then the delayed coincidence correlation is given bywhereIn Eq. (1), n and T are the lifetimes of the initial and intermediate nuclei, respectively, and in Eq.(2), S is the invariant summation over the spin coordinates <n and c 2 of the emitted particles, and pi and p 2 are densities-in-energy of the states of the emitted particles. The usual instantaneous angular correlation 6 isnormalized to fW(di, tp\\ 0 2) <p 2 )(dQi/4:T)dtt 2~l . It is actually a function only of the angle 6 between Qi and Q 2 , of course. The transformation properties of the nuclear matrix elements 7 can be used to obtainfor rotations of Q 2 by angle a around the z-axis. If this is substituted into Eq. (1) with a=coo/, one discovers that W{0 h <pi;0 2} <p 2 ;t) = (l/r) exp(-t/r)W(0 h <PI;02, *>2+o>oO-WThe delayed coincidence angular correlation pattern is just the instantaneous pattern precessing with the intermediate nucleus around the external field. 8 If the instantaneous correlation is given as a power series in cos0, the corresponding delayed coincidence correlation is obtained as a fourier series in (#4 by transforming the instantaneous correlation to a Legendre series: 9 W(0) = 27JP/(COS0), and then applying the spherical harmonic addition theorem 9 to Pj(o>s0) =Pj(cos0i cos0 2 +sin0i sin0 2 cos(^i-^2)).For example, the instantaneous correlation W(0) = 1+r cos 2 0 = l-f-(r/3)-|-(2f/3)P2(cos0) gives the delayed coincidence correlation (omitting the decay and normalization factors):Wifii, <pi; 02, <P2; /) -14-(r/3) 4-(r/6) (3 cos 2 0i -1) (3 cos 2 0 2 -1) + (r/2) sin20i sin20 2 cos(^?i~ <p 2~c uoO +(r/2) sin 2 0i sin 2 02 cos2(<pi-<p 2 -a> 0 t). (5)In general, the odd harmonics of coo/ drop out if either counter is in the equatorial plane, 0i or 02=90°; and there are no oscillating terms at all if either counter is on the axis, 0i or 02-0° or 180°. The relative amplitudes of the various harmonics are complicated functions ...

Microwave cavity studies of ionization decay in caesium vapour

“…From the results presented in figures 11 and 13 it can be seen that the loss rate is characteristic of a recombination process involving two charged particles, that the magnitude of the coefficient (10-7-10-6 cm3 s-1) is in approximate agreement with the values obtained by Dandurand and Holt (1951) and that there is a dependence of recombination coefficient on pressure. All these factors are consistent with dissociative recombination having been the principal loss mechanism.…”

“…The results of these workers together with the atomic beam measurements of Hammer and Aubrey (1966) all indicate values in the range 10-9-10-11 cm3 s-l, in reasonable agreement with the values predicted by the collisional radiative model and of the twoelectron three-body process. On the other hand, the measurements by Dandurand and Holt (1951), at a pressure of about 1 torr using a cavity technique, gave large values of about 10-7 cm3 s-1. Loeb (1960) has pointed out that their suggested recombination mechanism, C S Z ~ + e+Csz + h v is unsatisfactory and has indicated that the large value of the recombination coefficient is indicative of a dissociative recombination process of the form CSZ+ + e+Cs~*+Cs + Cs.…”

“…Loeb (1960) has pointed out that their suggested recombination mechanism, C S Z ~ + e+Csz + h v is unsatisfactory and has indicated that the large value of the recombination coefficient is indicative of a dissociative recombination process of the form CSZ+ + e+Cs~*+Cs + Cs. Dandurand and Holt (1951) have reported that the light emitted during the discharge indicates a predominance of Cs+ ions : hence the dissociative recombination rate will be dependent on the production rate of CSZ+. Loeb (1960) has suggested that the formation of C s 2 ~ may result from a three-body process such as Csf + Cs+Csz+ + c s when the production rate of CSZ+ could be strongly dependent on pressure and the recombination process would reflect this.…”

Study of Electron Generation by Solid Propellant Technique

“…The rate constant for cesium ion recombination has been measured by various investigators at pressures from 10"3 to I mm Hg (6,7,8);…”

Research on Ionisation Characteristics of Easily Ionisable Chemicals

“…One experiment which is of interest in this work is the measurement of electron-ion recombination coefficients in caesium. This has been carried out by two observers, Mohler (1937) and Dandurand and Holt (1951).…”