Ab initio Glauber-theory calculations of high-energy nuclear scattering observables using variational Monte Carlo wave functions

Abstract

Experiments using intermediate- to high-energy radioactive nuclear beams present numerous findings. Extracting important properties of physical observables relies on a firm theoretical analysis. Though Glauber theory is believed to work well, no convincing calculation has so far been done. We perform ab initio Glauber theory calculations of both elastic differential cross sections and total reaction cross sections for p+12C, 12C+12C, and 6He+12C systems. The wave functions of both 6He and 12C are generated by variational Monte Carlo calculations with spatial and spin-isospin correlations induced by realistic two- and three-nucleon potentials. Glauber's phase-shift function is computed by Monte Carlo integration up to all orders of nucleon-nucleon multiple scatterings. We show an excellent performance of the Glauber description to the selected data on the above systems. We also find that the cumulant expansion of the phase-shift function converges rapidly up to the second order for the above systems. This finding will open up interesting applications for the analysis of high-energy nuclear experiments.

Figures (4)

• Figure 1: $p+^{12}{\rm C}$ elastic differential cross sections at 300, 500, 800, and 1000 MeV as a function of the momentum transfer. The cross sections of three higher incident energies are drawn by multiplying a factor 10$^3$ successively. The data are taken from Meyer85Okamoto10 (300 MeV), Hoffmann90 (500 MeV), Blanpied81 (800 MeV), Palevsky67Alkhazov72 (1000 MeV).
• Figure 2: Energy dependence of the total reaction cross sections of the $^{12}$C$+^{12}$C collision. The data are taken from (inverted triangles) Takechi05 for $\sigma_R$; (circles) Ponnath24 and (triangles) Ozawa01 for $\sigma_I$.
• Figure 3: Rutherford ratios of the $^{12}{\rm C}+ ^{12}$C elastic differential cross sections at 80 and 120 MeV/nucleon as the momentum transfer $q$. The cross section at 80 MeV/nucleon is drawn by multiplying a factor 10$^2$. The data are taken from Buenerd81 for 86 MeV/nucleon and from Hostachy87 for 121 MeV/nucleon.
• Figure 4: Energy dependence of the total reaction cross sections of the $^{6}{\rm He}+^{12}$C collision. The datum is taken from Tanihata85b.