An analytic model for nucleus–nucleus reaction cross sections

Abstract Nucleus–nucleus reaction cross sections are a key component of radiation transport simulations, with applications from particle beam cancer therapies to radiation shielding for space. For use in Monte Carlo codes, universal, reliable and highly efficient models are required. Here we describe an Glauber-based analytic density-folding model for nucleus–nucleus reaction cross sections, applicable to projectiles and targets with mass number $$A\ge 12$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:math> . The model uses spherical, Gaussian-shaped matter densities that are optimised to describe the surface of density distributions from spherical Hartree–Fock calculations (surface-optimised Gaussian approximation, SGA). A phenomenological reaction barrier correction ( $$1-V_B/E_{cm}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>B</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mi>cm</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) is included to improve performance of the model at low energies. Whilst the Gaussian densities are not normalised, the good description of the density near the nuclear surface results in reaction cross sections that match those from numerical density folding calculations with Hartree–Fock densities typically to within 2% between 10 and 2000 MeV/nucleon for colliding nuclides from $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>12</mml:mn> </mml:mmultiscripts> </mml:math> C to $$^{238}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>238</mml:mn> </mml:mmultiscripts> </mml:math> U. Comparisons are made to experimental data for stable nuclides at $$E=30$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>=</mml:mo> <mml:mn>30</mml:mn> </mml:mrow> </mml:math> to 2000 MeV/nucleon and show good agreement for a wide range of systems. For chains of neon, sodium and magnesium isotopes interacting with carbon at 240 and 950 MeV/nucleon, the general trend with proton-neutron asymmetry is reasonably described, but specific effects of nuclear structure such as deformation and neutron skins lead to experimental measurements being underestimated. The assumption of spherical symmetry and the use of matter densities may therefore limit the accuracy of the model for exotic nuclides. Calculations for $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>12</mml:mn> </mml:mmultiscripts> </mml:math> C+ $$^{16}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>16</mml:mn> </mml:mmultiscripts> </mml:math> O and $$^{12}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>12</mml:mn> </mml:mmultiscripts> </mml:math> C+ $$^{48}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>48</mml:mn> </mml:mmultiscripts> </mml:math> Ti show the model performs reasonably well at energies near $$V_B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:math> , but further work is required to benchmark the parameterization of $$V_B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>V</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:math> used and to extend the parameterization of the nucleon–nucleon cross sections and ranges used within the model.