Total cross-sections for inelastic scattering of charged particles by atoms and molecules—VIII. Systematics for atoms in the first and second row

Abstract

The Bethe theory gives an asymptotic formula for the total cross-section σ tot for inelastic scattering of fast charged particles. For a (structureless) particle of charge ze and (non-relativistic) velocity v, it is written as σ tot = 4 πa 0 2 z 2( R/ T) M tot 2 ln (4 c tot T/ R), where R is the Rydberg energy, a 0 is the Bohr radius and T= 1 2 mv 2 , m being the electron mass. Two quantities, M tot 2 and ln c tot, depend upon the internal dynamics of the atom. We have performed comprehensive calculations of these quantities for neutral atoms He through Ar by use of independent-particle models, and also have studied the influence of electron correlations for several atoms. Our calculations reveal certain systematics of M tot 2 and ln c tot as functions of the atomic number Z. Because M tot 2 is expressed as the ground-state expectation value of the squared sum of atomic-electron coordinates, the trend of M tot 2 follows the size of the atom, governed by its shell structure. The quantity ln c tot also varies with the atomic size, but within a fairly modest range. Hence, the variation of σ tot at fixed v from one atom to another is chiefly governed by M tot 2.