Three-nucleon interaction in heavy-ion collisions at intermediate energies

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The effect of a three-nucleon ($3N$) interaction is studied for the production of high energy protons in heavy-ion collisions in the incident energy range of 44 to $400\phantom{\rule{0.16em}{0ex}}A\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$. The $3N$ interaction is incorporated into the antisymmetrized molecular dynamics transport model of Ono [A. Ono, Phys. Rev. C 59, 853 (1999)] as a $3N$ collision term, following a diagram of three consecutive binary collisions. For the theoretical $^{40}\mathrm{Ar}+^{51}\mathrm{V}$ reaction studies, no contribution from the $3N$ collisions is observed for high energy proton production at the incident energy of $44A\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$. However when the incident energy increases, the contribution increases gradually. At $200A\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ and above, the contribution is observed as distinctly harder energy slopes in the proton energy spectra. The model is applied to the available Bevalac data for $^{40}\mathrm{Ar}+^{40}\mathrm{Ca}$ at $42,92$, and $137\phantom{\rule{0.16em}{0ex}}A\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$. The experimental proton energy spectra are reasonably well reproduced at angles $\ensuremath{\theta}\ensuremath{\ge}{70}^{\ensuremath{\circ}}$ for all three incident energies, showing negligible $3N$ contributions at $42A\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ and significant contributions at $137A\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ at the large laboratory angles. Good agreement at these large angles, where the $3N$ collision is a major mechanism to produce such protons, strongly indicates for the first time the importance of the $3N$ interaction in intermediate heavy ion reactions in a full transport calculation. The possible relation between the $3N$ collision term and the short range and the tensor interactions is suggested.