Empirical formula for total inelastic cross-section of proton-nucleus scattering

Abstract

We propose a generic empirical formula for total inelastic cross-sections for various target nuclei scattered by a proton at different energies, which is applicable over a wide range of energy from $15 ~MeV$ to $1~ TeV$. The proposed model is parameterized based on the fitting of extensively studied experimental cross-section data for the Aluminium and Carbon nucleus targets, considering factorization over high-energy and low-energy regimes. The parameters in high-energy formula are determined by the fitting of the high-energy saturation value of the inelastic scattering cross-section data with mass numbers. The universality of the empirical formula is investigated by comparing the model prediction with the experimental data of inelastic proton-nucleus scattering over a wide range from light elements such as Deuterium to heavy elements such as Uranium. A detailed comparison with the existing models and GEANT4 simulation is also presented.

Figures (11)

• Figure 1: The left figure is high-energy correction Eq.(\ref{['eq:highour']}) fitting with experimental dataBobchenko:1979hp.In the right figure, the green dashed line represents the power-law model, the blue dashed line corresponds to the Letaw $\textit{et. al.}$ model, and the red solid line indicates the proposed model. The shaded gray region denotes the experimental uncertainty band.
• Figure 2: This figure shows the fitting of proton scattering with $^{12}$C and $^{27}$Al experimental data carlson1996Bobchenko:1979hpdenisov1973absorptionfumuro1979dependenceGrchurin1985 using the least chi-square method using machine learning.
• Figure 3: Model results and comparison for the inelastic scattering cross-section of target (a) $^2$H and (b) $^4$He with configuration $1s$ shell.
• Figure 4: Model results and comparison for the inelastic scattering cross-section of target (a)$^6$Li, (b)$^9$Be, (c)$^{10.8}$B, (d)$^12$C, (e)$^{14}$N with configuration $1p$ shell.
• Figure 5: Model results and comparison for the inelastic scattering cross-section of target (a)$^{19}$F, (b)$^{20}$Ne, (c)$^{23}$Na, (d)$^{24}$Mg, (e)$^{28}$Si, (f)$^{40}$Ar, and (g)$^{40}$Ca with configuration $2s+1d$ shell.