In 1938, Stueckelberg introduced a scalar field which makes an Abelian gauge theory massive but preserves gauge invariance. The Stueckelberg mechanism is the introduction of new fields to reveal a symmetry of a gauge--fixed theory. We first review the Stueckelberg mechanism in the massive Abelian gauge theory. We then extend this idea to the standard model, stueckelberging the hypercharge U(1) and thus giving a mass to the physical photon. This introduces an infrared regulator for the photon in the standard electroweak theory, along with a modification of the weak mixing angle accompanied by a plethora of new effects. Notably, neutrinos couple to the photon and charged leptons have also a pseudo-vector coupling. Finally, we review the historical influence of Stueckelberg's 1938 idea, which led to applications in many areas not anticipated by the author, such as strings. We describe the numerous proposals to generalize the Stueckelberg trick to the non-Abelian case with the aim to find alternatives to the standard model. Nevertheless, the Higgs mechanism in spontaneous symmetry breaking remains the only presently known way to give masses to non-Abelian vector fields in a renormalizable and unitary theory.

The Stueckelberg Field

A new version of the classical over-barrier model for multiple-electron capture in slow collisions between ions and atoms is described. This version accounts for the different ways in which an exchange of a certain number of electrons can occur. Since no adaptable parameter is involved this model has predictive power. Model predictions of absolute multiple capture cross sections are compared with experiment and are found to be in good agreement. Some dynamic effects are accounted for by introducing a velocity-dependent minimum energy uncertainty. Predicted widths of energy gain spectra and of the spectra of autoionisation electrons are found to be in reasonable agreement with experiment.

https://iopscience.iop.org/article/10.1088/0022-3700/19/18/021/pdf

A classical model for multiple-electron capture in slow collisions of highly charged ions with atoms

An introduction to the basic ideas and methods of chiral perturbation theory is presented. Several phenomenological applications of the effective Lagrangian technique to strong, electromagnetic and weak interactions are discussed.

/pdf/chiral-perturbation-theory-3wrq1sp814.pdf

Chiral perturbation theory

Interaction of slow multicharged ions with solid surfaces

The authors attempt to give a comprehensive discussion of observations of atomic negative-ion resonances throughout the periodic table. A review of experimental and theoretical approaches to the study of negative-ion resonances is given together with a consideration of the various schemes that are used for their classification. In addition to providing, where possible, tabulated data for the energies, widths, and symmetries of these states, the authors also attempt to highlight regularities in their behavior both within groups of the periodic table and along isoionic sequences.

Atomic negative-ion resonances

Cross sections for K-shell ionization, x-ray production, or auger-electron production by ion impact

We report measured cross sections for the collisional production of highly charged low-velocity Ne recoil ions resulting from the bombardment of a thin Ne gas target by highly charged 1-MeV/amu C, N, O, and F projectiles The measurements were made using time-of-flight techniques which allowed the simultaneous identification of the final charge state of both the low-velocity recoil ion and the high-velocity projectile for each collision event For a given incident-projectile charge state, the recoil charge-state distribution is very dependent upon the final charge state of the projectile Single- and double-electron capture events by incident bare nuclei and projectile K-shell ionization during the collision cause large shifts in the recoil charge-state distributions toward higher charge states A previously proposed energy-deposition model is modified to include the effects of projectile charge-changing collisions during the collision for bare and hydrogenlike projectiles and is used to discuss the present experimental results

Charge-state correlated cross sections for the production of low-velocity highly charged Ne ions by heavy-ion bombardment

We have used a secondary ion recoil source to study electron capture and ionization in collisions of ${\mathrm{Ar}}^{+q}$ with He, Ne, Ar, and Xe at projectile energies between 250 and 660 eV per charge. By analyzing outgoing projectiles and target ions in coincidence we have measured cross sections for ionization of the system with and without simultaneous electron capture, as well as for normal electron capture only. Cross sections for direct ionization (no electron capture) are found to be small, whereas those for ionization accompanied by electron capture are often quite important.

Coincidence Measurements of Electron Capture and Ionization in Low-Energy Ar +q + (He, Ne, Ar, Xe) Collisions

Experimental cross sections are reported for electron capture and transfer ionization for Ne, Ar, Kr, and Xe projectiles on He for charge states ($q$) between 2 and 13 and for projectile energies between $(250 \mathrm{and} 1000 \mathrm{eV})q$. The double-electron capture is found to be typically an order of magnitude weaker than single-electron capture, and to be dominated in most cases by the transfer ionization channel. While gross features of the cross sections can be qualitatively understood, quantitative agreement with available theoretical model calculations is poor.

Total cross sections for electron capture and transfer ionization by highly stripped, slow Ne, Ar, Kr, and Xe projectiles on helium

/pdf/k-shell-ionization-cross-sections-for-elements-se-to-pd-0-4-3bxrvh3lgn.pdf

Tom J. Gray

Papers

Cross sections for K-shell ionization, x-ray production, or auger-electron production by ion impact

Charge-state correlated cross sections for the production of low-velocity highly charged Ne ions by heavy-ion bombardment

Coincidence Measurements of Electron Capture and Ionization in Low-Energy Ar +q + (He, Ne, Ar, Xe) Collisions

Total cross sections for electron capture and transfer ionization by highly stripped, slow Ne, Ar, Kr, and Xe projectiles on helium

K-shell ionization cross sections for elements Se to Pd: 0.4 to 2.0 MeV