A statistical description of scattering at the quantum level

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.

Detection of low-energy charged particles by channel electron multipliers

“…A log-normal energy dependence of the detection efficiencies of 𝑒 + , 𝑒 − , protons and ions has been established. The ratio of the 𝑒 + and Ps detection efficiencies has been extracted using a log-normal fit to current and previous CEM 𝑒 + detection efficiency measurements in combination with the equivelocity relationship [9,10,19] and with typical voltages applied to the CEM [18], that such a statistical function may also describe the energy dependence of inelastic collisions at the quantum level.…”

“…Seah et al [4], in their model approach, scaled by the energy of maximum efficiency. Here, for 𝜀 𝑑 + , we are guided by recent findings regarding the log-normal distribution as a description of inelastic collisions as a function of the excess energy 𝐸 = 𝐸 − 𝐸 th , where 𝐸 th is the threshold energy for the process under consideration [18]. In the present case, 𝐸 = 𝐸 eff and the threshold for detection is the work -4 - + for biased grids of figure 3 with the work function of the detector surface deducted (bullets).…”

“…Following a brief description of the apparatus, new experimental determinations of 𝜀 𝑑 + are presented and compared with previous work [15][16][17] for incident energies between 0-1400 eV. Systematic effects are understood with the aid of simulations, allowing the data to be reconciled into a single curve that shows a clear log-normal energy dependence [18]. 𝑅 𝑑 is extracted by first fitting a log-normal function to current and previous 𝜀 𝑑 + in combination and then implementing the equivelocity relationship to determine 𝜀 𝑑 Ps [9,10,19].…”

Laser-induced inner-shell excitations through direct electron re-collision versus indirect collision

“…After deriving the ionization rate, we now calculate the re-collision time t r and the velocity of the electron v r at the re-collision time by calculating the electron classical trajectories ì r(t) under the influence of the laser field with the assumption of zero velocity at the tunneling time t i and the requirement that ì r(t r ) = 0 [20,29]. For the wavepacket spread w r we set w r (t i , t r ) = 2m e w(t i ) (t r − t i ) [30], and for σ(v) we used the Bethe formula σ [31][32][33], where E i is the binding energy of the inner-shell electron and m e is the electron mass. Since we are only interested in the ratios between the different fluorescence yields, we can set A = 1 (in the case that different channels are involved, we still assume that their cross sections are within the same order of magnitude).…”

Differential positronium-formation cross sections for Ne, Ar, Kr, and Xe

“…Following the work of [29] in which the lognormal function was found to describe the energy dependence of a variety of inelastic collisions by allowing for the relevant threshold energy, we plot in Fig. 3(a) the values of dQ Ps d versus ( E E th ), i.e., the total energy (E = E + − E th ) scaled by the corresponding Ps formation threshold energy.…”