Nucleus-nucleus cross sections
The simulation of nucleus-nucleus interactions and the corresponding cross sections is required by accelerator experiments, cosmic ray studies and medical applications, and in other applications. An important input for simulations of this process is the total reaction cross section, which is defined as the total (\(\sigma_{T}\)) minus the elastic (\(\sigma_{el}\)) cross section for nucleus-nucleus reactions:
With increasing energy electromagnetic dissociation (EMD) becomes dominant, especially for the collisions of heavy nuclei. At low and intermediate energies EMD does not play an essential role, while the nuclear break-up and multi-particle productions dominate. Currently, EDM cross secction is not used in reference Physics Lists.
The strong interaction cross sections can be calculated in the Glauber approximation [SYuSZ89, Shu03] at high (\(>\) 1 GeV) energies. The description of the cross sections at low and intermediate energies is the challenging component.
A first simple expression was proposed in [BP50]: \(\sigma_{1,2}=\pi (R_1+R_2-c)^2\), where \(R_1\) and \(R_2\) are the radii of the two interacting nuclei (\(R=r_0\ A^{1/3}\)), \(r_0\simeq\) 1.36 fm, and \(c\sim\) 0 – 1.5 fm, depending on a projectile energy (following [SBV74, SBV75] and the further refinements of [STS+93] \(c \propto (A_1^{-1/3}+A_2^{-1/3})\)).
In order to extend the parameterization to the intermediate energy range [eal87] \(\sigma_{AB} = \pi R_{int}^2\ (1-B/E_{CMS})\) can be used, where \(R_{int}\) is composed of two terms, energy dependent and independent, \(B = Z_A Z_B e^2/r_C(A^{1/3}+B^{1/3})\) is the Coulomb barrier of the projectile-target system, and \(E_{CMS}\) is center-of-mass system energy.
- BP50
H.L. Bradt and B. Peters. Physical Review, 77:54, 1950.
- eal87
S. Kox et al. Trends of total reaction cross sections for heavy ion collisions in the intermediate energy range. Phys. Rev. C, 35:1678–1691, 1987.
- SBV74
C.B. Dover S. Barshay and J.P. Vary. Physics Letters, 51B():5, 1974.
- SBV75
C.B. Dover S. Barshay and J.P. Vary. Physical Review C, 11():360, 1975.
- SYuSZ89
V.V. Uzhinskii S.Yu. Shmakov and A.M. Zadorozhny. Computer Physics Communications, 54:125, 1989.
- Shu03
P. Shukla. Physical Review C, 67():054607, 2003.
- STS+93
L. Sihver, C. H. Tsao, R. Silberberg, T. Kanai, and A. F. Barghouty. Total reaction and partial cross section calculations in proton-nucleus (Zt≤26) and nucleus-nucleus reactions (Zp and Zt≤26). Physical Review C, 47(3):1225–1236, mar 1993. URL: https://doi.org/10.1103%2Fphysrevc.47.1225, doi:10.1103/physrevc.47.1225.