Percolation-fission model study of the 1 GeV proton-induced reaction on ${}^{208}\mathrm{Pb}$ targets

The 1 GeV proton-induced reaction on ${}^{208}\mathrm{Pb}$ targets is analyzed by using the percolation model combined with the Atchison fission model. The fragment mass distribution and the isotopic production cross sections obtained from our model are compared with the experimental data. The trends of the fragment mass distribution for the 1 GeV proton-induced reaction can be reproduced by our calculation in some degree. The order of magnitude for the calculated isotopic production cross sections at the calculated peak positions is similar to that of the experimental peak values. The calculated peak positions of the isotopic production cross sections are shifted to the heavier region than those of the experimental data.

Figure 1

Geometry of predecay nuclei.

Figure 2

Fragment mass distribution for the 1 GeV proton-induced reaction on ${}^{208}\mathrm{Pb}$ targets. The solid and thin-solid histograms are the results obtained from the PF model with the hexagonal lattice and the simple-cubic lattice, respectively. The dotted histogram is the result of the simple percolation model without the fission process. The open circles are the experimental production cross sections, which are taken from Fig. 18 of Ref. 2.

Figure 3

Isotopic production cross sections for the 1 GeV proton-induced reaction on ${}^{208}\mathrm{Pb}$ targets as a function of neutron numbers. The solid and thin-solid histograms are the results obtained from the PF model with the hexagonal lattice and the simple-cubic lattice, respectively. The open circles are the experimental isotopic production cross sections [2].

Figure 4

Comparison of the isotopic production cross sections for the 1 GeV proton-induced reaction on ${}^{208}\mathrm{Pb}$ targets between two parameter sets listed in Table . The thin-solid histograms are the same as those described in the legend to Fig. 3. The dotted histograms are the results obtained by the simple-cubic lattice with the parameters labeled “hexagon” in Table .