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Additional resources for Advances in Electronics and Electron Physics, Vol. 15
39) yields for - a 5 s 5 a, and I(s) = 0 for s 5 -a. These equations apply when s, is positive. The intensity distribution is (ideally) symmetrical about s = 0. Figure 11 shows the intensity distribution for various vplues of s,. It is evident from the curves that the maximum intensity occurs at a point considerably less than s,. The probability of an atom emerging from the source slit is proportional to the velocity. 22a. oven. In fact, the most probable velocity in the beam is m The deflection of atoms in the beam will generally be less than s, The values of Is] at the maxima of the curves occur at about (s,1/3 for large s, (s, 10a or greater).
B. The Beam Intensity and Intensity Distribution (6, '7) Evidently, from Eq. (34), the point at which an atom crosses the detector plane depends upon its velocity and its substate. Consider first the case when no forces are applied to the atoms of the beam, that is, when the deflecting magnets are switched off. The number of atoms striking the detector per unit time with velocities in the range v to v dv is given approximately by + dN=I . TZ (2)" ~kT v8 exp (g) dv. (35) This can be rewritten as dN = I(v)dv = 3 va exp a4 (- -$)dv, where lo = NoaAE 47rrs (37) is the total number of atoms striking the detector per unit time, No is the number of atoms per unit volume in the oven, a is the oven slit area, A is the area of the detector, T is the total distance between the oven slit and the detector, e' is the average speed of an atom inside the oven (5 = d m , and a is the most probable speed inside the oven (ff = d W .
The analysis has not been made for u-transitions which are of particular interest in atomic beam standards. The significance of these frequency shifts predicted by Salwen can be demonstrated by looking for a displacement of the resonance peak as a function of radiation field intensity. If a shift is not observable within the precision of measurement over a range of oscillator field intensity, then the frequency shifts are not significant in the measurements. Of course, radiation field dependent frequency 44 RICHARD C.
Advances in Electronics and Electron Physics, Vol. 15