Binary theory of antiproton stopping

Enhancing trappable antiproton populations through deceleration and frictional cooling

“…Recently, data on stopping powers for protons and antiprotons traveling through solid foils have been measured for light, moderate, and heavy elements, namely carbon (Z ¼ 6), aluminum (Z ¼ 13), nickel (Z ¼ 28), and gold (Z ¼ 79) [16], and have been shown to be in good agreement with a binary collision theory of Sigmund and Schinner [17][18][19][20].…”

“…However, straggling is also subject to a Barkas effect [22], with straggling of low-energy antiprotons typically reduced by up to a factor of 2 compared to protons at the same energy and in the same material. At low velocities, straggling is reduced from the Bohr values in a way which is not fully understood: an electron gas model implies / 2 (where ¼ jvj=c is the normalized particle speed), while a binary collision model [18] predicts / 6=5 . Recent observations [22] are in reasonable agreement with the latter, with a least-squares fit across several materials yielding an estimate of / 0:9AE0:2 .…”

Geant4 Model for the Stopping Power of Low Energy Negatively Charged Hadrons

“…Recent experimental measurements of antiproton stopping powers unambiguously support a velocity-proportional for energies - [21]. However, at lower energies the situation is less clear: for instance, measurements of in molecular hydrogen and helium provided some evidence for an increase of the antiproton stopping power with decreasing velocity below - [22], [23]; this behaviour might be attributed to the sizeable contribution of nuclear stopping, but the issue is still under debate [24], [25].…”

“…Alternative approaches, such as the dielectric formalism (local-density approximation) [20] or the kinetic theory [30], share similar difficulties; therefore they are not easily implementable in a general-purpose Monte Carlo code. Other recent theoretical calculations of antiproton stopping powers require extensive computations [24], [31], [32], [25].…”

“…These parameters are then obtained by means of shell-wise integration of available (experimental or theoretical) oscillator strength data in the form of optical or dielectric response functions. This is nevertheless a laborious procedure, and has only been carried out for a few selected materials, mainly metals; tabulated values of and for some elements can be found in [25]. The outlined method for the determination of the and parameters is still too complex to be of practical use in a generalpurpose Monte Carlo code; further simplifications are thus necessary.…”