Semi-empirical formulas for heavy-ion stripping data

2014 All available charge state measurements for heavy ions in dilute gases and carbon foils at equilibrium or near-equilibrium conditions have been analyzed to improve semi-empirical formulas for the distribution parameters. Each experimental distribution was fit to an asymmetric function Fq = Fm : exp {2014 0.5 t2/(1 + 03B5t) }, where t = (q 2014 q0)/03C1 and q0 is the maximum intensity charge value. Subsequent fits of the resultant distribution parameters q0, p, and 03B5 to empirical functions of projectile charge and velocity yielded rms deviations of about 0.5 for q0, 4 % for q0/Z, 5-7 % for p, and 0.03 for 03B5/03C1. The asymmetric distribution gives substantial improvement over previous expressions for prediction of small Fq values for heavy ions in dilute gases. REVUE DE PHYSIQUE APPLIQUÉE TOME 12, OCTOBRE 1977, PAGE Accurate predictions of charge state distributions for heavy ions in gaseous and solid media are particularly of interest for the design of new accelerators and for estimation of output beam intensities. Five years ago a comprehensive review [1] ] of charge-changing processes for heavy ions in gases and solids and two extensive compilations [2, 3] of equilibrium charge state distribution measurements appeared. In the review by Betz [ 1 ] several semi-empirical formulas for the mean charge, q and width, d, of the distribution were discussed. In the past five years several new experimental results for highly stripped ions have been reported, but there has been relatively little development of new empirical representations of the data. We have utilized recent experimental measurements and data from previous compilations [2, 3] to obtain improved semi-empirical formulas for the distribution parameters. Inspection of the data reveals differences of 0.51.0 unit in the values of mean charge reported by different experimenters for identical projectile energies and target materials. These variations may be attributed to effects such as the angular acceptance of the apparatus, insufficient target thickness for equili(*) Operated by Union Carbide Corporation for the U.S. Energy Research and Dcvclupmcnt Administration. brium and the density effect in gases. Such ambiguities make it difficult to develop completely general formulas and consequently only the two most commonly used types of stripping media, carbon foils and dilute light gases, will be considered here. Each experimental charge state distribution was fit to an asymmetric function Fq = F m . exp { 0.5 t2/ (1 + Et) }, where t = (q q.)Ip and qo is the maximum intensity charge value. Values of Fq 0.1 % were excluded from the fits. When the asymmetry parameter 82013>’0, the distribution function reduces to the usual Gaussian of width p, qo q, p d and F mp 1 / dTi The moments T n = f dt t "F9 / f dt Fq may be evaluated numerically with integration limits chosen so that Et > l . Then q = qo + p Tl ; (d/ p) 2 = T 2 T12; and (d/ p) 3 s = T 3 3 T2T 1 + 2 T13, where d and s are parameters defined by Betz [1]. Fits with asymmetric and Gaussian distributions to experimental Fq values [3] for 15 MeV 127I ions in dilute Ar gas are presented in figure 1. Clearly the inclusion of thé 8 parameter produces a significantly better fit, although small Fq values at high q are still underestimated somewhat. In figure 2, F9 values for 58 experimental distributions for heavy ions (Z 5 16) in dilute gases are compared with the asymmetric fit values by plotting (Fq jF m) 1 + E ‘ versus t. The curve Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:0197700120100154300