Classical and Quantum Mechanics in the Theory of Charged-Particle Stopping

A quarter of a century ago the author stepped into Jens Oddershede s office and asked for support on a problem involving computation with atomic wave functions in connection with a new theoretical scheme to treat stopping of charged particles at intermediate speed. This visit resulted in two related publications, two joint papers and a number of follow-up studies by Jens and several others. In 1989 a Sanibel Symposium was devoted to aspects of the penetration of charged particles through matter, and since then, quite a few quantum chemists have joined the community of theoreticians dealing with particle penetration. 

Niels Bohr, a pioneer in both disciplines, emphasized the significance of classical vj. quantal arguments in particle penetration. Not the least in view of the complexity of ab initio computations in this area, such considerations keep being relevant. This note adds new points to an old discussion based on recent developments. 

ADVANCES IN QUANTUM CHEMISTRY, VOLUME 48 ISSN 0065-3276 DOT I0.I0I6/S0065-3276(05)48007-7 

Since the cross section for nonrelativistic Coulomb scattering is the same in classical and quantum mechanics, equation (2) must contain much of the essential physics in the slowing-down process. However, it also contains an undetermined minimum energy transfer rmin which is nominally zero and hence leads to an infinite stopping force. 

Bohr [4], using purely classical arguments, found a solution to this problem which turned out to survive the emergence of quantum mechanics. To see what is going on, consider first Thomson s formula 

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Interplay of Classical and Quantum Mechanics in the Theory of Charged-Particle Stopping... 

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