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, to name a few domains.
Because nuclei are charged, total and elastic cross sections are
infinite due to Coulomb interaction. In reality, they are restricted by
the screening of the atomic electrons. This interaction leads to a
small-angle scattering which can be ignored in a first approximation.
Thus, inelastic cross sections are the most important ones. 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.
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.
In the “Sihver”, “Kox” and “Shen” parameterizations
[STS+93][eal87][SWF+89] are used, with
the Shen parameterization recommended for all physics lists.
| [BP50] | H.L. Bradt and B. Peters. Physical Review, 77:54, 1950. |
| [eal87] | (1, 2) 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. |
| [SWF+89] | W.-q. Shen, B. Wang, J. Feng, W.-l. Zhan, Y.-t. Zhu, and E.-p. Feng. Total reaction cross section for heavy-ion collisions and its relation to the neutron excess degree of freedom. Nuclear Physics A, 491:130–146, 1989. |
| [Shu03] | P. Shukla. Physical Review C, 67():054607, 2003. |
| [STS+93] | (1, 2) L. Sihver, C. H. Tsao, R. Silberberg, T. Kanai, and and A. F. Barghouty. Total reaction and partial cross section calculations in proton-nucleus ($zt \leq 26$) and nucleus-nucleus reactions ($zp$ and $zt \leq 26$). Phys. Rev. C, 47:1225–1236, 1993. |