Precise charge state distribution of projectile ions through solid targets

The charge state distribution (CSD) of the projectile ions through solid targets in the intermediate energy range (1 MeV/u $<$ E $<$ 4 MeV/u) has a major impact on the collision of the ion atom and accelerator physics. We explore the mean charge states taken from the empirical formula [Schiwietz $et~al.$, Nucl. Inst. Meths. {\bf 225}, 4(2004)] are only good for projectile ions with $Z_1 \le 16$. To solve this issue, we develop a model in which instead of a single formula, if we employ four formulae, the comparative picture between experimental and empirical data becomes impressive. Furthermore, the CSDs with the mean charge state so obtained and the Gaussian distribution function having distribution width given by [Novikov and Teplove, Phys. Lett. {\bf378}, 1286(2014)] compare well with the experimentally measured CSDs for the entire range of projectile ions. We believe that precise CSDs will be highly useful in both ion-atom collision and accelerator physics.