https://biblio.ugent.be/publication/685594/file/1130605.pdf

Review of Particle Physics

The stopping and range of ions in matter is physically very complex, and there are few simple approximations which are accurate. However, if modern calculations are performed, the ion distributions can be calculated with good accuracy, typically better than 10%. This review will be in several sections: 

a)

A brief exposition of what can be determined by modern calculations.




b)

A review of existing widely-cited tables of ion stopping and ranges.




c)

A review of the calculation of accurate ion stopping powers.

The stopping and range of ions in solids

CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecu- lar simulation program. It has been developed over the last three decades with a primary focus on molecules of bio- logical interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estima- tors, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numer- ous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983.

/pdf/charmm-the-biomolecular-simulation-program-4kexem0xkx.pdf

CHARMM: the biomolecular simulation program.

One of the simplest, and most completely treated, fields of application of quantum mechanics is the theory of atoms with one or two electrons For hydrogen and the analcgous ions He+, Li++, etc, the calculations can be performed exactly, both in Schrodinger’s nonrelativistic wave mechanics and in Dirac’s relativistic theory of the electron More specifically, the calculations are exact for a single electron in a fixed Coulomb potential Hydrogen-like atoms thus furnish an excellent way of testing the validity of quantum mechanics For such atoms the correction terms due to the motion and structure of atomic nuclei and due to quantum electrodynamic effects are small and can be calculated with high accuracy Since the energy levels of hydrogen and similar atoms can be investigated experimentally to an astounding degree of accuracy, some accurate tests of the validity of quantum electrodynamics are also possible Finally, the theory of such atoms in an external electric or magnetic field has also been developed in detail and compared with experiment

Quantum Mechanics of One- and Two-Electron Atoms

Transport, Collective Motion, and Brownian Motion

The quantum theory of radiation

Das Kraftespiel zwischen neutralen Atomen zeigt eine charakteristische quantenmechanische Mehrdeutigkeit. Diese Mehrdeutigkeit scheint geeignet zu sein, die verschiedenen Verhaltungsweisen zu umfassen, welche die Erfahrung liefert: Bei Wasserstoff z. B. die Moglichkeit einer homoopolaren Bindung, bzw. elastischer Reflexion, bei den Edelgasen dagegen nur die letztere — und zwar dies bereits als Effekte erster Naherung von ungefahr der richtigen Grose. Bei der Auswahl und Diskussion der verschiedenen Verhaltungsweisen bewahrt sich das Pauliprinzip auch hier, in Anwendung auf Systeme von mehreren Atomen.

Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik

The stopping power of matter for fast particles is at present believed to be due to three different processes: (1) the ionization; (2) the nuclear scattering; (3) the emission of radiation under the influence of the electric field of a nucleus. The first two processes have been treated in quantum mechanics by Bethe, Moller, and Bloch in a very satisfactory way. A provisional estimation of the order of magnitude to be expected in the third process has been given by Heitler. The result obtained was that the cross-section ϕ for the energy loss by radiation for very fast particles (if the primary energy E ≫ mc 2) is of the order ϕ ∽ Z2/137 ( e 2/ mc 2)2, (1) Where Z is the nuclear charge. It is the aim of the present paper to discuss in greater detain the rate of loss of energy by this third process and its dependence on the primary energy; in particular we shall consider the effect of screening . The results obtained for very high energies (> 137 mc 2) seem to be in disagreement with experiments made by Anderson ( cf . 7).

On the Stopping of Fast Particles and on the Creation of Positive Electrons

Quantum theory of radiation

It is well known that according to relativistic quantum mechanics, electrons and positrons with energy large compared with their rest mass have a very large probability when passing through the field of a nucleus of losing a large fraction of their energy in one process by emitting radiation. Hard quanta have a correspondingly large probability of creating electron pairs. Until recently it was believed that the direct measurements of Anderson and Neddermeyer on the energy loss of fast electrons showed that though this energy loss by radiation existed, it was much smaller for energies greater than about 108 e-volts than that theoretically predicted, and it was therefore assumed that the present quantum mechanics began to fail for energies greater than about this value. More recent experiments by Anderson and Neddermeyer (1936) have, however, led them to revise their former conclusions, and their new and more accurate experiments show that up to energies of 300 million e-volts (the highest energies measured in their experiments) and probably higher, the experimentally measured energy loss of fast electrons is in agreement with that predicted theoretically. In fact, one may say that at the moment there are no direct measurements of energy loss by fast electrons which conclusively prove a breakdown of the theory. This is particularly satisfactory, inasmuch as the theoretical reasons for expecting a breakdown of the theoretical formulae at energies greater than about 137 mc 2, namely the neglect of the classical “radius” of the electron, have been shown by v. Weizsacker (1934) and Williams (1934) to be unfounded. Under these circumstances, and in view of the experimental evidence mentioned above, it is reasonable as a working hypothesis to assume the theoretical formulae for energy loss and pair creation to be valid for all energies, however high, and to work out the consequences which result from them. It is our aim to deduce results which can be compared directly with cosmic ray experiments and which will then allow one to decide whether or not the theory fails for extremely high energies, and in the latter case, at what point the failure begins.

W. Heitler

Papers

The quantum theory of radiation

Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik

On the Stopping of Fast Particles and on the Creation of Positive Electrons

Quantum theory of radiation

The Passage of Fast Electrons and the Theory of Cosmic Showers