Relativistic heavy ions measure the momentum distribution on the nuclear surface

Abstract

In fragmentation reactions of the type $^{16}\mathrm{O}+ \mathrm{target}\ensuremath{\rightarrow}^{15}\mathrm{O}+X$, the momentum distribution of the outgoing fragment $^{15}\mathrm{O}$ reflects the momentum distribution of the nucleon which is removed from the surface of the projectile nucleus. We derive a relation using Glauber's multiple scattering theory and the Wigner transform of the one-body density matrix. The experimental cross section at 2 GeV/nucl is analyzed with the following result: The uniform and local Fermi-gas models fail to reproduce the momentum distribution on the surface. The shell model with harmonic oscillator wave functions is correct for momenta below the Fermi momentum. Hartree-Fock wave functions describe the data up to 350 MeV/c.NUCLEAR REACTIONS Heavy ions, relativistic energies; fragmentation reactions; relation to nuclear momentum distribution on the surface.