Electron-Alkali-Metal Inelastic Recoil Experiments with Spin Analysis: Experimental Method and the Small-Angle Behavior of the $4{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to 4{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ Excitation of Potassium

The use of the atom-beam recoil technique in the study of differential inelastic electron-atom collisions with spin analysis is discussed. The general theory of the experimental method is presented. It is shown how to relate the observable $R$, the fractional depolarization of a polarized atom beam, to the several direct and exchange scattering amplitudes. A linear momentum-transfer analysis, required to connect the atomic and electron scattering angles, is also given. Some observations of the change of spin state of potassium, resulting from small-angle excitations of $4{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\to 4{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2},\frac{3}{2}}^{}{}_{}{}^{}$ transitions are discussed, and are related to the threshold laws.