Abstract
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 $^{12\ensuremath{-}19}\mathrm{C}$ 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.
Highlights
Charge-changing cross sections at high energies are expected to provide useful information on nuclear charge radii
We show that the cross sections of 12−19C on a proton target are all well reproduced provided the role of neutrons is accounted for
The measurement of the charge-changing cross section (CCCS) newly appears as a potential means to extract the proton radius since it has the great advantage that the cross section can be measured for almost all nuclei by the same setup as the total reaction or interaction cross section that plays a decisive role in determining the nuclear matter radius [3]
Summary
We show that the cross sections of 12−19C on a proton target are all well reproduced provided the role of neutrons is accounted for. Isotope shift measurement allows us to precisely deduce the charge (proton) radius for some limited unstable nuclei. The CCCS has recently been measured to get information on the proton radii of light unstable nuclei [4,5,6,7,8]. Where b is a two-dimensional (2D) impact parameter vector perpendicular to the beam (z) direction, |0 = |0P 0T is a product of the projectile and target ground-state wave functions, and, e.g., χ p is a sum of the phase-shift functions χpN between the projectile’s proton (p) and the target’s nucleon (N ): χp =.
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