A large set of experimental charge-state distributions is analyzed in this work. Two fit formulas are presented for mean equilibrium charge states of projectiles ranging from protons to uranium. One formula is given for all ions in gas targets and another one for solid targets. The deviation from the experimental data is reduced by roughly a factor of two in comparison with the widely used formula by Nikolaev and Dmitriev as well as with the Bohr stripping criterion as revised by Northcliffe. Finally, the influence of the projectile charge state on the prediction of stopping powers for fast projectiles in carbon is shown and comparison is made with experimental energy-loss data.

Improved charge-state formulas

Equilibrium charge fractions of ions of Z = 4–92 emerging from a carbon foil

Binary stopping theory has been developed to characterize the electronic stopping of swift heavy ions in matter. It is an extension of Bohr’s classical theory of 1913 incorporating screening, higher-order-Z1 and shell corrections, high-speed quantum and relativity corrections as well as projectile excitation and ionization. The main numerical input comes from optical properties. The computation of shell corrections involves orbital velocity distributions of target and projectile electrons. Calculated stopping parameters depend on ion charge. Equilibrium stopping forces may be computed by adoption of a suitable model for the equilibrium charge state. This paper summarizes the current status of the theory, in particular the sensitivity of its predictions to pertinent input. Charge-dependent stopping forces have been calculated for selected systems and compared to experimental results. Equilibrium stopping forces calculated for a wide variety of ion–target combinations are compared with experimental data from the literature spanning over 6 decades in ion energy.

Binary theory of electronic stopping

The article describes the main achievements of the NUMEN project together with an updated and detailed overview of the related R&D activities and theoretical developments. NUMEN proposes an innovative technique to access the nuclear matrix elements entering the expression of the lifetime of the double beta decay by cross section measurements of heavy-ion induced Double Charge Exchange (DCE) reactions. Despite the fact that the two processes, namely neutrinoless double beta decay and DCE reactions, are triggered by the weak and strong interaction respectively, important analogies are suggested. The basic point is the coincidence of the initial and final state many-body wave functions in the two types of processes and the formal similarity of the transition operators. First experimental results obtained at the INFN-LNS laboratory for the 40Ca(18O,18Ne)40Ar reaction at 270MeV give an encouraging indication on the capability of the proposed technique to access relevant quantitative information. The main experimental tools for this project are the K800 Superconducting Cyclotron and MAGNEX spectrometer. The former is used for the acceleration of the required high resolution and low emittance heavy-ion beams and the latter is the large acceptance magnetic spectrometer for the detection of the ejectiles. The use of the high-order trajectory reconstruction technique, implemented in MAGNEX, allows to reach the experimental resolution and sensitivity required for the accurate measurement of the DCE cross sections at forward angles. However, the tiny values of such cross sections and the resolution requirements demand beam intensities much larger than those manageable with the present facility. The on-going upgrade of the INFN-LNS facilities in this perspective is part of the NUMEN project and will be discussed in the article.

https://hal.archives-ouvertes.fr/hal-01806968/document

The NUMEN project: NUclear Matrix Elements for Neutrinoless double beta decay

In the search to develop tools that are able to modify surfaces on the nanometre scale, the use of heavy ions with energies of several tens of MeV is becoming more attractive. Low-energy ions are mostly stopped by nuclei, which causes the energy to be dissipated over a large volume. In the high-energy regime, however, the ions are stopped by electronic excitations1,2,3, and the extremely local (∼10 nm3) nature of the energy deposition leads to the creation of nanosized ‘hillocks’ or nanodots under normal incidence4,5,6. Usually, each nanodot results from the impact of a single ion, and the dots are randomly distributed. Here we demonstrate that multiple, equally spaced dots, each separated by a few tens of nanometres, can be created if a single high-energy xenon ion strikes the surface at a grazing angle. By varying this angle, the number of dots, as well as their spacing, can be controlled.

Creation of multiple nanodots by single ions.

Equilibrium charge distributions have been measured for 18 kinds of ions passing through a carbon foil in the energy region of 1\char21{}6 MeV/u for light ions and of 0.2\char21{}1 MeV/u for heavy ions. By combining the data obtained at present with those reported for other energies or ion species, an attempt is made to find the systematics for charge fraction F(q), mean charge q\ifmmode\bar\else\textasciimacron\fi{}, and distribution width d over the wide range of ion species Z and energy E. Strong correlation has been found between the shell structure of ions and the variation of q\ifmmode\bar\else\textasciimacron\fi{} or d with Z or E. The analysis for this correlation enables the evaluation of rather reliable values of q\ifmmode\bar\else\textasciimacron\fi{}, d, or F(q) for ion species 4\ensuremath{\le}Z\ensuremath{\le}92 in carbon foils from 0.02 to 6 MeV/u.

Systematics of equilibrium charge distributions of ions passing through a carbon foil over the ranges Z=4-92 and E=0.02-6 MeV/u.

Equilibrium mean charges q-bar of ions passing through a carbon foil were observed to oscillate vs projectile atomic number Z at ion energies 0.55, 1, and 2 MeV/u. The maxima of the oscillation take place for closed-shell ions having the electrons in mean number Z-q-bar = 10 and 28.

Noriyoshi Kuno

Papers

Equilibrium charge fractions of ions of Z = 4–92 emerging from a carbon foil

Systematics of equilibrium charge distributions of ions passing through a carbon foil over the ranges Z=4-92 and E=0.02-6 MeV/u.

Z oscillation of mean charges of energetic ions emerging from a carbon foil: Correlation with the shell structure of ions.

Z1-and Z2-Oscillation of Mean Charges of Ions (Energy~1MeV/u) Emerging from a Thin Foil

Equilibrium charge fraction of ions of Z=4-92 (0.02-6 MeV/u) and Z=4-20 (up to 40 MeV/u) emerging from a carbon foil