Experimental results from high energy proton-nucleus interactions, critical phenomena, and the thermal liquid drop model of fragment production

In an inclusive experiment, isotopically resolved fragments, $3\le Z\le 13$, produced in high-energy proton-nucleus collisions have been studied using a low mass time-of-flight, gas $\Delta E$-silicon $E$ spectrometer and an internal gas jet. Measurement of the kinetic energy spectra from 5 to 100 MeV enabled an accurate determination of fragment cross sections from both xenon and krypton targets. Fragment spectra showed no significant dependence on beam energy for protons between 80 and 350 GeV/c. The observed isobaric yield is given by $Y\alpha A_f^{-\tau }$, where $\tau \sim 2.6$ for both targets; this also holds for correlated fragment data. The power law is the signature for the fragment formation mechanism. We treat the formation of fragments as a liquid-gas transition at the critical point. The critical temperature $T_c$ can be determined from the fragment isotopic yields, provided one can set an energy scale for the fragment free energy. The high energy tails of the kinetic energy spectra provide evidence that the fragments originate from a common remnant system somewhat lighter than the target which disassembles simultaneously via Coulomb repulsion into a multibody final state. Fragment Coulomb energies are about $\frac{1}{10}$ of the tangent sphere values. The remnant is characterized by a parameter $T$, obtained from the high energy tails of the kinetic energy distributions. $T$ is interpreted as reflecting the Fermi momentum of a nucleon in this system. Since $T\gg T_c$, and $T$ is approximately that value expected for a cold nucleus, we conclude that the kinetic energy spectra are dominated by this nonthermal contribution.