Non Adiabatic Treatment of Elastic Scattering of Electrons By Atomic Hydrogen
Non Adiabatic Treatment of Elastic Scattering of Electrons By Atomic Hydrogen
Kazem Omidvar
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9) tan 5^ = + + + + + a" sin 5. + C'aJ sin 5_, + + + + + a" cos 67 + qTa" cos 8" ^1 /l ^i'2 ^2 Equations (^-5) and {h. G) can be integrated from the origin with 2k + proper boimdary values. C~ is then calcxolated by means of (^. 7). Using ■^ + + the asymptotic anrp3j. Tudes of U~ (x) and U^ (x) together with their phase + -''1 ^2 + shifts and the values of c7, we obtain the phase shifts of ur(x) from ('^-. 9)- To find the total elastic scattering cross section we note that 5/^ of all the incide...nt electrons have spins parallel to the bound electron spin and the remaining l/k have antiparallel spins ^ ^ . The ri2l total elastic cross section is then given by*- -• . Oo (4. 10) S =^XI (2i+l) k"^ i-o o 1. 2^+ 5. 2- j^ sin 5^ + ^ sm ^ In this paper the numerical integration ha^ been carried out for j?= 0, 1, 2. + The integration cannot be started without the values 'of UJ (x) and + ^1 U/, (x) at the origin. These have been calculated in Appendix III. The results are (4. 11) u; (x) = b;x^-*-i ^ 1 x->o ^ 1 + iop p5,
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