New empirical formula for nucleon-induced nonelastic cross sections based on two physical effects

A simple universal parametrization of nucleon-induced nonelastic cross sections is presented for a wide range of targets that is valid for the entire energy range from zero to a few gigaelectronvolts. We review several early studies by Letaw et al., Pearlstein, Shen, Niita et al., and Tripathi et al., and our proposed approach differs completely from the formulas therein. The present formula is constructed based on recently discovered physical effects involving Coulomb repulsion and the discrete-level constraint and is based on the assumption that cross sections are continuous in both incident energies and targets. Our formula is given by a set of smooth functions of the mass number, which differs from the best formula to date by Tripathi et al. To compare our formula precisely with that by Tripathi et al., we proposed the relative error index, which indicates the relative error between experimental data and predicted values. For the ${}^{12}\mathrm{C}, {}^{27}\mathrm{Al}, {}^{56}\mathrm{Fe}, {}^{\mathrm{nat}}\mathrm{Ag}, {}^{\mathrm{nat}}\mathrm{Cd}, {}^{\mathrm{nat}}\mathrm{Sn}, {}^{197}\mathrm{Au}$, and ${}^{208}\mathrm{Pb}$ targets used in this paper, the corresponding relative error indices show clearly that our formula is superior to that by Tripathi et al.

Figure 1

Comparison between formula-predicted values by the three formulas and data of neutron-induced nonelastic cross sections for ${}^{12}\mathrm{C}$ (red), ${}^{27}\mathrm{Al}$ (blue), ${}^{56}\mathrm{Fe}$ (green), and ${}^{208}\mathrm{Pb}$ (brown) below 100 MeV. The solid red lines indicate our simulation results, the dashed blue lines indicate those by Tripathi et al. and the dotted green lines indicate those by Pearlstein. Note that for ${}^{12}\mathrm{C}$ the experimental error bars are present but are covered by the plotting symbols.

Figure 2

As in Fig. 1 but with incident energies in the range of 0–2000 MeV for neutron-induced nonelastic cross sections.

Figure 3

Comparison between formula-predicted values and data for neutron-induced nonelastic cross sections for ${}^{\mathrm{nat}}\mathrm{Ag}, {}^{\mathrm{nat}}\mathrm{Cd}, {}^{\mathrm{nat}}\mathrm{Sn}$, and ${}^{197}\mathrm{Au}$ below 100 MeV. The solid red lines indicate our simulation results, the dashed blue lines indicate those by Tripathi et al., and the dotted green lines indicate those by Pearlstein.

Figure 4

As in Fig. 3 but with incident energies in the range of 0–2000 MeV for neutron-induced nonelastic cross sections.

Figure 5

Comparison between formula-predicted values and data for proton-induced nonelastic cross sections for ${}^{12}\mathrm{C}$ (red), ${}^{27}\mathrm{Al}$ (blue), ${}^{56}\mathrm{Fe}$ (green), ${}^{208}\mathrm{Pb}$ (brown) below 100 MeV. The solid red lines indicate our simulation results, the dashed blue lines indicate those by Tripathi et al., and the dotted green lines indicate those by Shen.

Figure 6

As in Fig. 5 but with incident energies in the range of 0–2000 MeV for proton-induced nonelastic cross sections.

Figure 7

Comparison between the predicted values by the three formulas and data of proton-induced nonelastic cross-sections for ${}^{\mathrm{nat}}\mathrm{Ag}, {}^{\mathrm{nat}}\mathrm{Sn}$, and ${}^{197}\mathrm{Au}$ below 100 MeV. The solid red line indicates the result by our simulation, the dashed blue line indicates the result by Tripathi et al., and the dotted green line by indicates the result Pearlstein.

Figure 8

As Fig. 7 but with incident energies in the range of 0–2000 MeV for proton-induced nonelastic cross sections.

Figure 9

Singular behavior of original formulas. The solid blue lines indicate the results using the formula by Pearlstein, the dashed green lines indicate those by Niita et al. for the $n$ injection, and the dotted red lines indicate those by Shen for the $p$ injection.

Figure 10

Comparison between two calculations of neutron-induced nonelastic cross sections. The solid blue lines indicate the results of full calculations with the DLC effect, and the dashed green lines indicate those without the DLC effect.

Figure 11

Comparison between three calculations of proton-induced nonelastic cross sections. The solid blue lines indicate the results of full calculations with DLC and Coulomb effects, the dotted red lines show those without the Coulomb effect but with the DLC effect, and the dashed green lines show the bone structure resulting from neither DLC nor Coulomb effects. The difference between the dotted and the solid lines indicates the extent of the effect of Coulomb repulsion.