Abstract
Quantum physics is undoubtedly the most successful theory of the microscopic world, yet the complexities which arise in applying it even to simple atomic and molecular systems render the description of basic collision probabilities a formidable task. For this reason, approximations are often employed, the validity of which may be restricted to given energy regimes and/or targets and/or projectiles. Now we have found that the lognormal function, widely used for the probability distribution of macroscopic stochastic events (as diverse as periods of incubation of and recovery from diseases, size of grains, abundance of species, fluctuations in economic quantities, etc.) may also be employed to describe the energy dependence of inelastic collisions at the quantum level (including ionization, electron capture and excitation by electrons, positrons, protons, antiprotons, etc.), by allowing for the relevant threshold energy. A physical interpretation is discussed in this article by analogy with the heat capacity of few-level systems in solid state physics. We find the generality of the analysis to extend also to nuclear reactions. As well as aiding the description of collision probabilities for quantum systems, this finding is expected to impact also on the fundamental understanding of the interface between the classical and quantum domains.
Highlights
Ionization, excitation and electron capture are elementary processes in atomic and molecular collisions, important in applications ranging from the modelling of the propagation of fast charged particles through matter to damage-control in medical dosimetry
We have found that the lognormal distribution, extensively employed in economics, industry, biology, ecology, geology, astrophysics (e.g.9–11), may provide, to a good level of accuracy, the energy dependence of the probability for collision processes on the quantum scale for a variety of targets and projectiles, including electrons, positrons, protons and antiprotons
A physical interpretation of its significance in quantum systems is discussed and its applicability found to extend into the realms of nuclear reactions and solid state physics
Summary
Quantum physics is undoubtedly the most successful theory of the microscopic world, yet the complexities which arise in applying it even to simple atomic and molecular systems render the description of basic collision probabilities a formidable task For this reason, approximations are often employed, the validity of which may be restricted to given energy regimes and/or targets and/or projectiles. Ionization, excitation and electron capture are elementary processes in atomic and molecular collisions, important in applications ranging from the modelling of the propagation of fast charged particles through matter (such as in plasmas and the atmosphere) to damage-control in medical dosimetry The description of their energy dependence using quantum, classical and semi-classical approaches remains challenging, even in the case of simple atomic targets and structureless projectiles (e.g.1–3). A physical interpretation of its significance in quantum systems is discussed and its applicability found to extend into the realms of nuclear reactions and solid state physics
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
