Charge-exchange Straggling Research Articles

Energy-loss straggling of helium in elemental solids: The importance of the charge-exchange and bunching effects

In this study, we extend to Helium (He) ions the analysis of the energy-loss straggling of protons in simple materials as presented in NIMB 497 70 (2021). Our findings show that the excess of energy-loss straggling for both protons and He ions is highly correlated to the inhomogeneous distribution of electrons over the unit cell, referred to here as bunching effects, and that charge-exchange straggling has a minor impact, although it can compete with bunching effects for light targets. The Convolution approximation for swift Particles program was used to demonstrate that the bunching effect is a significant contributor to the straggling for both protons and He ions. In addition, we show that packing effects, a special form of bunching is of minor importance. The Yang-O’Connor-Wang formula for He was refined in this work to account for recent experimental data.

Energy loss straggling of energetic ions in varying thicknesses of Titanium foils

Energy loss straggling of energetic Li, C and O ions in varying thicknesses of self-supporting Titanium foils is measured, in the fractional energy loss limits (ΔE/E) ~ 5–50%. For these measurements, transmission technique is utilized and recorded energy spectra are estimated through Gauss fitting function. The measured straggling values are compared with the prediction of most commonly used collisional (Bohr, Lindhard-Scharff, Bethe-Livingston, Titeica) and collisional plus charge-exchange (Yang et al.) straggling formulations. Titeica theory, which is considering collisional straggling only, shows lesser deviations with the measured values. Based on the present measurements, the fitted relations for charge-exchange straggling is developed.

A theoretical and experimental investigation of Bragg's rule for energy-loss straggling in low mean energy loss regime in air and its constituents

A theoretical and experimental investigation of Bragg's rule in low energy loss region where charge exchange straggling can be ignored is presented. Energy-loss straggling of 5.486 MeV alpha particles in air and 5N purity constituent gases was measured using high-resolution alpha spectroscopy system. Measured values are compared with Bohr, Bethe-Livingston and Yang et al. formulations. An experimental investigation of Bragg's rule to estimate the energy-loss straggling in air using the experimental data of constituents is discussed.

Systematics of heavy-ion charge-exchange straggling

The dependence of heavy-ion charge-exchange straggling on the beam energy has been studied theoretically for several ion-target combinations. Our previous work addressed ions up to krypton, while the present study focuses on heavier ions, especially uranium. Particular attention has been paid to a multiple-peak structure which has been predicted theoretically in our previous work.For high-Z1 and high-Z2 systems, exemplified by U in Au, we identify three maxima in the energy dependence of charge-exchange straggling, while the overall magnitude is comparable with that of collisional straggling. Conversely, for U in C, charge-exchange straggling dominates, but only two peaks lie in the energy range where we presently are able to produce credible predictions. For U–Al we find good agreement with experiment in the energy range around the high-energy maximum.The position of the high-energy peak – which is related to processes in the projectile K shell – is found to scale as Z12, in contrast to the semi-empirical Z13/2 dependence proposed by Yang et al.Measurements for heavy ions in heavy targets are suggested in order to reconcile a major discrepancy between the present calculations and the frequently-used formula by Yang et al.

Anatomy of charge-exchange straggling

We have studied charge-exchange straggling theoretically for swift krypton and silicon ions and five target gases in the MeV/u energy regime. We find a pronounced two-peak structure for all ion-target combinations. The peak at the highest energy appears around the velocity where the bare ion and the one-electron ion are equally abundant in the equilibrium charge distribution. Correspondingly, the low-energy peak appears near the cross-over between the charge fractions of the two- and the three-electron ion. The possibility of further peaks at lower energies is discussed. Our findings are compared with recent experimental results on straggling of krypton beams.

Energy loss straggling in thick mylar polymeric foils for swift heavy ions in fractional energy loss limits Δ E/ E ∼ 5–80%

The energy loss straggling in thick mylar (monomer composition: C 10H 8O 4) polymeric foils has been measured for swift heavy ions covering Z = 3–22, in the fractional energy loss limits Δ E/ E ∼ 5–80%. These measured straggling values have been compared with the most commonly used Bethe–Livingston collisional straggling formulation after modifying it suitably for thick targets. Further, the charge-exchange straggling values have been extracted from the measured values and were found to be consistently higher than the corresponding values deduced from Yang’s et al. formulation. Finally, an analytical expression has been developed for charge-exchange straggling for ion–polymer combinations, considered in the present study.

Charge-exchange straggling in equilibrium

A general expression has been derived that allows computation of charge-exchange straggling of swift heavy ions when many charge states are involved. Charge exchange is found to hinge on the variation of the stopping cross section with the ion charge and on the transient behavior of the charge population as a function of traveled pathlength. These effects appear factorized in the final formula. The focus of this paper is on straggling in charge equilibrium. The case of MeV/u sulfur ions in carbon has been used as an illustration. Charge-exchange straggling is found to be dominating straggling over a considerable range of beam energies.

Energy-loss straggling of (200–1000) MeV/u uranium ions

The charge-exchange contribution can dominate the energy-loss straggling of partially stripped heavy ions depending on the charge-changing cross sections and the partial stopping powers. We have studied the energy-loss straggling of few-electron uranium ions in different solids in the energy range of (200–1000) MeV/u. Our experimental data are compared with a new model taking into account realistic screening for relativistic scattering of target electrons at close impacts to derive partial stopping powers. Screening of the projectile nucleus by inner-shell electrons reduces the charge-exchange straggling compared to that pertaining to a point-like charge distribution.

Stopping of relativistic hydrogen- and heliumlike heavy ions

The stopping power for hydrogen- and heliumlike heavy ions penetrating matter at energies of 100–1000 MeV/u is calculated. For hydrogenlike ions the difference in d E/d x for an extended and a collapsed electron distribution is at the level of 1% and nonperturbative effects easily account for half of the difference. Differences of this magnitude have drastic effects on charge-exchange straggling. The theoretical results lead to good agreement with experimental values when applied in simulations.

Statistics of energy loss and charge exchange of penetrating particles: Higher moments and transients.

Recent work on mean energy loss and straggling of ions in the presence of charge exchange has been extended to higher moments. The transient behavior of charge-exchange straggling has been determined as well as the skewness of the energy-loss profile. Formulas have been found for the two- and three-state cases where terms that have been well known in principle could also be written in a way that illustrates their respective origin. In addition to the frequently analyzed case of negligible energy loss in charge-changing events, we also mention explicitly the opposite situation where all energy loss is associated with charge exchange. The role of transients and skewness is very different in the two extremes. As in a previous paper by one of us, the notation has been kept general such as to allow for both collisional and spontaneous events, and no distinction needs to be made between charge exchange and change of excitation state. Finally we compare our calculations to recently obtained experimental results.

Statistical theory of charged-particle stopping and straggling in the presence of charge exchange

General expressions have been derived for the mean energy loss and straggling of a heavy charged particle penetrating through a thin slice of matter. The main input parameter is a differential energy loss rate that allows for transitions within an arbitrary number of projectile states. Both spontaneous and collision-induced events are potentially induced, but different events are assumed statistically independent. Asymptotically, the mean energy loss is shown to approach a linear dependence on time or path length. The slope is given by the equilibrium energy loss rate, and the intercept at zero path length depends on the incident projectile state. Energy-loss straggling can be split into a collisional part and a contribution from variations in projectile state. The latter turns out to be related to the intercept in the mean energy loss for the pertinent projectile states. Previous results applying to a two-state system have been generalized to an arbitrary number of states. A full evaluation has been presented for a three-state system. A procedure is outlined that allows to empirically determine the magnitude of charge-exchange straggling.

Energy loss and energy loss straggling of N, Ne, and Ar ions in thin targets

We have measured the energy loss and energy loss straggling of N, Ne, and Ar ions in He, N 2, SF 6, and Ar windowless gas targets and in carbon foils at energies of 5–15 MeV. The experimental results of the energy loss straggling are approximately a factor of 1.5 and 2.0 larger than the straggling calculated from the collision straggling for Ne and Ar ions, respectively. Charge exchange straggling has to be taken into account in order to explain the experimental findings. The measured energy loss agrees very well with the Bethe formula if the meaured averaged squared charge state q 2 in gaseous targets is being used. Deviations to the tables of Northcliffe are of the order of 10–30%.