Non-equilibrium emission of complex fragments from $p+\mathrm{Au}$ collisions at 2.5 GeV proton beam energy

The energy and angular dependence of double differential cross sections $d^2\sigma /d\Omega \mathit{dE}$ was measured for reactions induced by 2.5 GeV protons on Au target with isotopic identification of light products (H, He, Li, Be, and B) and with elemental identification of heavier intermediate mass fragments (C, N, O, F, Ne, Na, Mg, and Al). It was found that two different reaction mechanisms give comparable contributions to the cross sections. The intranuclear cascade of nucleon-nucleon collisions followed by evaporation from an equilibrated residuum describes the low energy part of the energy distributions whereas another reaction mechanism is responsible for the high energy part of the spectra of composite particles. A phenomenological model description of the differential cross sections by isotropic emission from two moving sources led to a very good description of all measured data. Values of the extracted parameters of the emitting sources are compatible with the hypothesis claiming that high energy particles emerge from preequilibrium processes consisting in a breakup of the target into three groups of nucleons; small, fast, and hot fireball of $\sim 8$ nucleons, and two larger, excited prefragments, which emit light charged particles and intermediate mass fragments. The smaller of them contains $\sim 20$ nucleons and moves with a velocity larger than the CM velocity of the proton projectile and the target. The heavier prefragment behaves similarly as the heavy residuum of the intranuclear cascade of nucleon-nucleon collisions.

Figure 1

Typical energy spectra of ${}^4\mathrm{He}$ (left column) and ${}^7\mathrm{Li}$ particles (right column) measured in the present experiment (open circles) and published in Ref. [12] (full dots) for corresponding emission angles. The lines show prediction of evaporation of ${}^4\mathrm{He}$ and ${}^7\mathrm{Li}$ evaluated by means of GEM program of Furihata [17, 18] from excited residual nuclei of the first stage of the reaction with properties extracted from BUU calculations.

Figure 2

Open circles represent experimental energy spectrum of ${}^7\mathrm{Li}$ particles measured at $35°$ in the current experiment. The lines present result of phenomenological model described below; the short-dashed line shows the contribution of the slow emitting source, the long-dashed line depicts the contribution of the fast source, whereas the solid line presents the sum of both contributions. Please note, that the shape of this experimental energy distribution as compared with spectra shown in right part of Fig. 1 also confirms the monotonic change of the exponential slope with the scattering angle.

Figure 3

Open circles represent typical spectra of various ejectiles obtained in the present experiment. Hydrogen isotopes detected at $65°$ are shown in the upper-left part of the figure. Data for He, Li, and Be isotopes detected at $35°$ are depicted in the upper-right, the lower-left and the lower-right parts of the figure, respectively. The dashed lines show contribution evaluated by means of the BUU and Generalized Evaporation Model whereas the full lines correspond to phenomenological model of two emitting sources described below.

Figure 4

Typical spectra of boron ions ${}^{10,11,12}$B measured in the present experiment by telescope consisted of silicon semiconductor detectors placed at scattering angle of $35°$ in respect to the proton beam—open circles. The lines have the same meaning as in Fig. 3.

Figure 5

Typical spectra of carbon, nitrogen and oxygen ions measured in the present experiment without isotopic separation by telescope consisted of silicon semiconductor detectors placed at scattering angle of $35°$ in respect to the proton beam—open circles. The lines have the same meaning as in Fig. 3

Figure 6

Examples of energy spectra for heavier, elementally identified IMF's obtained in the current experiment by means of Bragg curve ionization chambers. The open circles represent experimental data and the solid lines show results of phenomenological model analysis obtained with assumption of only one moving source.

Figure 7

Parameters of the phenomenological model found from the fit to the experimental spectra of isotopically identified particles are presented in the figure as functions of mass of registered particles. (a) The ratio of the cross section for emission from the slow source ${\sigma }_1$ to the sum of cross sections for both sources ${\sigma }_1+{\sigma }_2$. The solid line depicts average value of the ratio (0.560 ± 0.044). (b) The apparent temperature of the slow source (full squares and solid lines) and that of the fast source (open squares and dashed lines) is given versus mass number of the ejectiles. The lines were fitted separately for light charged particles (${}^1\mathrm{H}$-${}^4\mathrm{He}$) and intermediate mass fragments (A${}_F\ge 6)$. (c) The ejectile mass number dependence for the factor scaling the Coulomb barrier of two touching spheres to the actual height—necessary for a good description of the data. Full squares represent the slow source and open squares show results for the fast source. The line $k=1$ is also depicted to facilitate interpretation of the figure. (d) The velocity of the fast source is shown as a function of emitted fragment mass number—open squares. Thin solid line ${\beta }_2=0.018$ represents the velocity of the common center of mass of the proton projectile and the target, and thick solid line ${\beta }_1=0.002$ shows velocity of the slow source—fixed at velocity of heavy residuum of the intranuclear cascade.

Figure 8

The squares present experimental total production cross section, i.e., the sum of the contribution ${\sigma }_1$ from the slow source and ${\sigma }_2$ from the fast source as a function of the atomic number $Z$ of ejectiles. The solid line shows result of the fit of the $\sigma \sim Z_F^{-\tau }$ formula to the data.