The collision of slow electrons with atoms. III.—The excitation and ionization of helium by electrons of moderate velocity

Abstract

functions of the various helium lines for electron energies up to, and in certain cases greater than 400 volts. In this paper we have extended the calculations in this way and have considered also ionizing collisions. Since the probability of ionization by electrons can be measured with considerable accuracy we can apply a very satisfactory test of the theory in this direction. In addition to the probabilities of ionization of hydrogen and helium the velocity and angular distributions of ejected and scattered electrons are also computed. The comparison of calculated and observed results is discussed in detail and it is found that Born's approximation is valid for electrons with energies greater than 200 volts. Section I. ExcitationHelium. § 1. Method of Calculation. -Employing throughout the sam that used in paper A we see that the differential cross-section l n ( §)d<o corre sponding to excitation of the state from the ground state by an electron which is scattered through an angle S into the solid angle dco is given by where I B(S)d<o = | \ f -9 \*do>,T 0, are the wave functions for the initial and final states respectively, k j2 n being the wave number of the electron incident in the direction of the unit vector n 0 and k' /2tz th at of the electron scattered in the direction of the unit vectorWe may use for the wave functions V F0, T*n the same forms as those given in paper A for the P and D states. If we write (Z |y) for the wave function of a single electron in the nlm state in the field of a charge Ze, the approximation used in paper A corresponds to a wave function for the nlm state of helium of the formf

Theoretical analysis of the relativistic first order Born approximation for inner shell (e, 2e) processes

“…In the theory of nonrelativistic (e, 2e) processes, the classical first Born result of Massey and Mohr [16] has long been known to give a reasonable first estimate of TDCS, in particular for asymmetric ''Ehrhardt'' type geometries (see, e.g., [17]). Therefore quite naturally, the first studies of relativistic (e, 2e) processes considered relativistic extensions of this work [4,6,9,10].…”

Semirelativistic model for ionization of atomic hydrogen by electron impact

“…This model gives good results if the condition Zα ≪ 1 is fulfilled. Before turning to the analytical calculation of the integral J(λ) proper, let us recall how the integral I(λ) [16] can be obtained. This is explained without any detail in [20].…”

“…The origin of this shift stems from the fact that the main contribution to the TDCS comes from the term H 1 (q) given by Eq. (16). This term contains a dominant integral I 1 .…”

“…Indeed, in the non relativistic Coulomb Born Approximation (NRCBA), a well known integral occurs [16] and is usually denoted by I(λ). In this article, we show that the main contribution to the unpolarized triple differential cross section (TDCS) in the SRCBA corresponding to the ionization of atomic hydrogen in its ground state by electron impact comes from this term added to relativistic corrections valid to first order in Z/c.…”

Total ionization cross section in electron-hydrogen scattering

“…Here, we calculate the total ionization cross section in e--H scattering. First work on the e--H ionization problem using the quantal method was performed by Massey and Mohr [4]. They employed the first Born Approximation (FBA).…”