VELOCITY DISTRIBUTIONS IN K AND TI BEAMS 1315 lector. a similar helical velocity selector has also where v lies between the limits vmax and vmin. Over the been used in a study of the characteristics of thin limited range of o allowed in the present case, the admit metal films as a function of the incident velocity of the tance is very nearly triangular in terms of v. The resolu- deposited atoms. tion calculated in the usual way at A=0.5 is Av/vo=y The notation used in a discussion of the selector is If it is assumed the velocity distribution incident on shown in Fig. 1 as are the dimensions of the rotor used the rotor, Iodm, does not change significantly over the in the present work. The cylinder was made of Dural range of velocities admitted for a given a, then the because this material allowed the cutting of slots to the transmitted intensity is necessary depth and at close intervals without signi ficant distortion of adjacent slots. The ends of the slots I,=-Iovo In(1-y2EIovor occur at 0.5 intervals on the end faces. To allow ad- to powers of y through ?. Iodv is the modified Max- justment of the line connecting the source slit and the wellian distribution detector parallel to the cylinder axis, it is necessary to have at least one slot parallel to the axis. Actually, two such slots were cut to avoid dynamical imbalance where a=m/2kT, and the distribution has been nor- The resolution properties of the velocity selector will malized to unity. Then Eq. (4)becomes be derived under the assumption that both source and detector have infinitesmal dimensions. All molecules I,=2yaD exp(-a2vo?) which are ultimately detected then travel in a plane Equation(5)becomes exact as the slot width becomes ontaining the cylinder axis, oven slit, and detector. infinitesimal. It will be shown that this expression is The validity of this assumption will be discussed in sufficiently close to the much more cumbersome exact more detail later. A molecule of velocity vo which goes expression so that it can be used as the theoretical through the slot without changing its position relative distribution to the sides of the slot will satisfy the equation To obtain an exact expression for I the variation of (1)the incident distribution, Io over the admittance must in which o and L are fixed, and w is the angular velocity. I=(Y1-1)exp[-x2/(1-)2] Since the slots have a finite width, a range of veloci transmitted by the rotor for a fixed w. The limiting 21exp(-30)+x:01 velocities correspond to molecules which enter the slot at one wall and leave the slot at the opposite wall, dx max=20(1-y)-1 and vmi=0(1+y)2,(2) erey=l/(ropo)and ro is the mean radius. In the present apparatus, y=0.05033, a fixed property. A variation of the radius by a few percent will have a where avo=xo. This expression is unwieldy and gives no negligible effect on the limiting values of D and thus, insight into the general nature of Io. Table I contains the mean value, ro, may be used. The admittance A, TABLE I, A comparison of the intensity distribution after analysis the ratio of the effective slot aperture for the velocity y the rotor as calculated in several approximations. v to that for the velocity vo is A=1-|(0/)-1l/, Exact hs0. 318 cm FIG. 1. Schematic diagram of velocity selector 38909850 切=都 25.40cm