Parameter-free calculation of charge-changing cross sections at high energy

Charge-changing cross sections at high energies are expected to provide useful information on nuclear charge radii. No reliable theory to calculate the cross section has yet been available. We develop a formula using Glauber and eikonal approximations and test its validity with recent new data on carbon isotopes measured at around $900A$ MeV. We first confirm that our theory reproduces the cross sections of ${}^{12,13,14}\mathrm{C}+{}^{12}\mathrm{C}$ consistently with the known charge radii. Next we show that the cross sections of ${}^{12-19}\mathrm{C}$ on a proton target are all well reproduced provided the role of neutrons is accounted for. We also discuss the energy dependence of the charge-changing cross sections.

Figure 1

Total reaction (or interaction) and charge-changing cross sections of ${}^{12}\mathrm{C}$ on a ${}^{12}\mathrm{C}$ target as a function of incident energy. Calculations are performed with the HO densities that give $r_p=r_n=2.326$ fm. Results with the zero-range profile functions are also drawn for comparison. References for the experimental data on ${\sigma }_R$ (open circle) and ${\sigma }_I$ (open rectangle) are quoted in Ref. [24]. The ${\sigma }_{\mathrm{cc}}$ data are taken from Ref. [8] for diamond, Ref. [25] for inverted triangle, Ref. [26] for closed triangle, and Ref. [27] for open triangle.

Figure 2

Charge-changing cross sections of carbon isotopes on a proton target at about $900A$ MeV.

Figure 3

Energy dependence of charge-changing cross sections of (a) ${}^{12}\mathrm{C}$ and (b) ${}^{19}\mathrm{C}$ on a proton target. The data are taken from Ref. [25] for open inverted triangles and from Ref. [26] for closed triangles.

Figure 4

Impact-parameter dependence of the direct and indirect charge-changing probabilities for ${}^{12}\mathrm{C}$ and ${}^{19}\mathrm{C}$ on a proton target at (a) $1000A$ and (b) $100A$ MeV.