Comparison of nonequilibrium processes in $p+\mathrm{Ni}$ and $p+\mathrm{Au}$ collisions at GeV energies

The energy and angular dependence of double differential cross sections $d^2\sigma /d\Omega \mathit{dE}$ were measured for $p,d,t$, ${}^{3,4,6}\mathrm{He}$, ${}^{6,7,8}\mathrm{Li}$, ${}^{7,9,10}\mathrm{Be}$, ${}^{10,11}\mathrm{B}$, and C produced in collisions of 1.2, 1.9, and 2.5 GeV protons with a Ni target. The shape of the spectra and angular distributions almost does not change whereas the absolute value of the cross sections increases by a factor $~$1.7 for all ejectiles in this beam energy range. It was found that energy and angular dependencies of the cross sections cannot be reproduced by microscopic models of intranuclear cascade including coalescence of nucleons coupled to statistical model for evaporation of particles from excited, equilibrated residual nuclei. The inclusion of nonequilibrium processes, described by a phenomenological model of the emission from fast and hot moving sources, resulting from break up of the target nucleus, leads to very good reproduction of data. Cross sections of these processes are quite large, exhausting approximately half of the total production cross sections. Due to good reproduction of energy and angular dependencies of $d^2\sigma /d\Omega \mathit{dE}$ it was possible to determine total production cross sections for all studied ejectiles. Results obtained in this work point to the analogous reaction mechanism for proton induced reactions on Ni target as that observed previously for Au target in the same beam energy range.

Figure 1

Ratio of the total production cross sections from the present experiment to those obtained in independent experiment of NESSI Collaboration [8] for $p+\mathrm{Ni}$ at $T_p=1.2$ GeV.

Figure 2

Upper panel: comparison of the total production cross sections from the present experiment on $p+\mathrm{Ni}$ collisions at $T_p=2.5$ GeV (full dots) and those for Li, Be, and B ejectiles obtained by Raisbeck et al. [9] for the same nuclear system but at $T_p=3.0$ GeV (open squares). Lower panel: the data from present experiment at $T_p=1.2$ GeV (full dots) and total production cross sections measured by NESSI Collaboration [8] at the same energy (open squares).

Figure 3

Typical spectra of ${}^4\mathrm{He}$, ${}^7\mathrm{Li}$, ${}^9\mathrm{Be}$, and ${}^{11}\mathrm{B}$ ejectiles (upper left, upper right, lower left, and lower right parts of the figure, respectively) measured at ${35}^{ˆ}$ for three energies of the proton beam; 1.2, 1.9, and 2.5 GeV, impinging on to the Ni target. Open circles represent the lowest energy, full squares—the intermediate energy, and the open triangles show the data for the highest energy.

Figure 4

Typical spectra of selected lithium, beryllium, and boron isotopes from $p+\mathrm{Ni}$ collisions measured at ${35}^{ˆ}$, ${80}^{ˆ}$, and ${100}^{ˆ}$ (left, middle, and right columns, respectively) for 2.5 GeV proton beam impinging on to the Ni target. The detected particles are listed in the central panel of each row of pictures. Open circles represent the experimental data, and solid lines correspond to intranuclear cascade followed by evaporation of particles, respectively.

Figure 5

Typical spectra of lithium, beryllium, and boron ejectiles from $p+\mathrm{Ni}$ collisions measured at ${35}^{ˆ}$, ${50}^{ˆ}$, and ${100}^{ˆ}$ (left, middle, and right columns, respectively) for 2.5 GeV proton beam impinging on to the Ni target. The detected particles are listed in the central panel of each row of pictures. Open circles represent the experimental data, dashed, dot-dashed, and solid lines correspond to slow emitting source, fast emitting source and the sum of both contributions, respectively.

Figure 6

Ratio of production cross section determined at 1.2 (open circles) and 1.9 GeV (full dots) to the cross sections found at 2.5 GeV beam energy. The lower panel presents cross sections for slow sources, panel in the middle for fast sources, and upper panel for sum of both contributions. The horizontal lines depict values of the ratios averaged over IMFs; the solid lines for the 1.9 GeV and the dashed lines for 1.2 GeV.

Figure 7

Typical spectra of protons, deuterons, and tritons (upper, middle, and lower rows of the figure, respectively) measured at ${20}^{ˆ}$, ${65}^{ˆ}$, and ${100}^{ˆ}$ (left, middle, and right columns of the figure, respectively) for 2.5 GeV proton beam impinging on to the Ni target. Open circles represent the experimental data, dashed, dot-dashed, and solid lines correspond to the two-step model, the emission from the fireball and the sum of both contributions, respectively.

Figure 8

Same as on Fig. 7 but for ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$. The dotted line for ${}^4\mathrm{He}$ denotes the contribution of an additional, slowly moving source.

Figure 9

In the lower panel of the figure the apparent temperature of the moving sources, averaged over beam energies is drawn as a function of the ejectile mass. Open circles and full dots represent values of temperature parameters $T_2$ and $T_1$ for fast and slow source, respectively. Full squares indicate temperature $T_3$ of the fireball. The solid and dashed lines were fitted to the points representing the IMF’s and ${}^4\mathrm{He}$. The dash-dotted line was fitted to points representing the LCP’s. In the upper panel the dependence of the beam energy averaged velocity of the sources is drawn versus the mass of ejectiles. The symbols and lines have the same meaning as for the lower part of the figure with one exception: The full dots are not shown because the velocity of the slower source was fixed during the analysis (at velocity ${\beta }_1=0.005$ of heavy residuum of target nucleus after intranuclear cascade) and it is represented by a solid line.

Figure 10

Energy dependence of the production cross section of ${}^7\mathrm{Be}$ ejectiles in proton induced reactions. The lines show results of a compilation of ${}^7\mathrm{Be}$ production cross sections [4], the symbols represent experimental data of the present experiment (open squares) for a Ni target and the data published by Budzanowski et al. [2] (full squares) for an Au target. The solid and dashed lines depict the excitation functions from Ref. [4] for Au and Ni targets, respectively.

Figure 11

Energy dependence of various reaction mechanisms for protons (open squares), deuterons (full squares), tritons (open triangles), and ${}^3\mathrm{He}$ (full triangles). The relative contribution of the fast stage of the reaction, i.e., intranuclear cascade and coalescence of nucleons into LCPs ${\sigma }_{INCL}/\sigma$ is presented in the upper panel of the figure, evaporation contribution from the equilibrated residuum of the intranuclear cascade ${\sigma }_{GEM}/\sigma$ is shown in the middle panel, whereas the contribution of fireball emission ${\sigma }_3/\sigma$ is depicted in the lower panel.