Low Energy Charged Particle Interactions

Introduction

The low energy charged particle transport class library described here simulates the interactions of protons, deuterons, tritons, He-3 and alpha particle with kinetic energies up to 200 MeV. The upper limit is set by the comprehensive evaluated neutron scattering data libraries that the simulation is based on. It reuses the code of the low energy neutron interactions package, with some small modifications to take into account the change of incident particle.

Only the inelastic interactions are included in this model, while the elastic interaction is treated approximately by other Geant4 models, and the interference between Coulumb and nuclear elastic is neglected.

Physics and Verification

Inclusive Cross-sections

Cross-section data is taken from the ENDF/B-VIII.0 [Gro91] and JENDL/DEU-2020 [JENDLDEU2020SNO21] evaluated data libraries for those few elements where data exist. As these isotopes are only a few, most of the isotopes data are taken from the TENDL data library (version TENDL-2019) which uses the TALYS nuclear model. The format is exactly the same as for the low energy neutron data libraries. While the energy of the TENDL files goes up to 200 MeV, in the case of ENDF it only reaches 150 MeV for most isotopes and for some is even less.

The treatment of this data is done with the same code as for the low energy neutron package. It should be mentioned that for all except a few low Z isotopes in the ENDF data library, there is no information about individual decay channels, but only about the total cross section plus particle yields. Therefore the same remark as for the neutron package holds: there is no event-by-event conservation of energy, nor of atomic or mass number.

The absence of treatment of the correlation between inelastic and elastic interactions affects the emission of charged particles, while it does not for neutron and gamma emission. The effect is expected to increase with incident energy and modify the secondary particle spectra.

Neutron-induced alpha production reactions on carbon

Some breakup reactions are only partially described or not described at all by G4ParticleHP, either because of incomplete or missing information in the evaluated neutron data library, or an incomplete implementation of the model itself.

The base class G4ParticleHPInelasticBaseFS and its derived classes in G4ParticleHP are devoted to describing reactions that involve more than one particle and a residual nucleus in the final state. These classes use, when available, evaluated energy-angle distributions to sample the final state of the reaction products, otherwise, the n-body phase space distribution. Reactions involving only one particle and a residual nucleus in the final state are described in G4ParticleHPInelasticCompFS and its derived classes instead. The description is however incomplete when it comes to breakup reactions proceeding in multiple steps, as they are not considered to their whole extent but only to the first step, leaving an intermediate nucleus in an excited state that is forced to decay to the ground state without any particle emission. This can be the case of the 12C(n,n\(^{\prime}3\alpha\)) reactions, which are important in many applications.

G4ParticleHPInelasticCompFS incorporates the 12C(n,n\(^{\prime}3\alpha\)) multistep breakup model from NRESP7.1: a Monte Carlo simulation code developed at the Physikalisch-Technische Bundesanstalt (PTB), Germany, to study the response of organic scintillation detectors to fast neutrons between 0.02 and 20 MeV [DK82] . Two different mechanisms are considered:

  1. \(n+^{12}\)C \(\rightarrow\) \(\alpha+^{9}\)Be\(^{*}\) \(|\) \(^{9}\)Be\(^{*}\) \(\rightarrow\) \(n^{\prime}+^{8}\)Be \(|\) \(^{8}\)Be \(\rightarrow\) \(2\alpha\)

  2. \(n+^{12}\)C \(\rightarrow\) \(n^{\prime}+^{12}\)C\(^{*}\) \(|\) \(^{12}\)C\(^{*}\) \(\rightarrow\) \(\alpha+^{8}\)Be \(|\) \(^{8}\)Be \(\rightarrow\) \(2\alpha\)

Both end up with the \(2\alpha\) decay of 8Be from its ground state but differ in the first and intermediate steps. Each mechanism comprises one or more reaction channels associated with excited well-defined or pseudo-states of the intermediate nucleus. The model samples the direction of the outgoing neutron from an isotropic distribution in the center-of-mass system and the alpha particles are emitted conserving energy and momentum. Relativistic kinematics is applied at each step.

Beware that angular distributions for the \(^{12}\)C(n,n\(^{\prime}3\alpha\)) reactions in the neutron data library are ignored in this model. The \(^{12}\)C(n,\(\alpha\))\(^{9}\)Be reaction, on the other hand, has a strong anisotropy in the center-of-mass system and there is no angular distribution data for this reaction in the neutron data library G4NDL whatsoever. Hence, for a complete description of neutron-induced alpha production reactions on carbon, the angular distributions for the \(^{12}\)C(n,\(\alpha\))\(^{9}\)Be reaction in NRESP7.1 are also incorporated (hard coded) in G4ParticleHPInelasticCompFS.

To invoke this model, the user needs to use the UI command:

/process/had/particle_hp/use_NRESP71_model true

A detailed description of the model and its verification and validation are published in A. R. Garcia et al, NIMA 868, 73-81 (2017) [GMCO+17] . The authors would appreciate the citation of their work by users of this model in the publication of their results.

Data Format

A detailed description of the data format used for the charged particle files available is described in an extensive note available for download <https://geant4-userdoc.web.cern.ch/ContributionFromUsers/UsefulNotes/particleHPFormat.pdf>`__.

Bibliography

DK82

G. Dietze and H. Klein. Nresp4 and neff4: monte carlo codes for the calculation of neutron response functions and detection efficiencies for ne213 scintillation detectors. Technical Report PTB-ND-22, Physikalisch-Technische Bundesanstalt (PTB), Braunschweig, Germany, 1982.

GMCO+17

A.R. Garcia, E. Mendoza, D. Cano-Ott, R. Nolte, T. Martinez, A. Algora, J.L. Tain, K. Banerjee, and C. Bhattacharya. New physics model in GEANT4 for the simulation of neutron interactions with organic scintillation detectors. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 868:73–81, Oct 2017. URL: https://doi.org/10.1016/j.nima.2017.06.021, doi:10.1016/j.nima.2017.06.021.

Gro91

ENDF/B-VI: Cross Section Evaluation Working Group. Endf/b-vi summary document. Technical Report BNL-NCS-17541 (ENDF-201), Brookhaven National Laboratory, Upton, NY, USA, 1991. edited by P.F. Rose, National Nuclear Data Center.

JENDLDEU2020SNO21

Y. Watanabe JENDL/DEU-2020: S. Nakayama, O. Iwamoto and K. Ogata. Jendl/deu-2020: deuteron nuclear data library for design studies of accelerator-based neutron sources. Technical Report 58(7), J. Nucl. Sci. Technol., 2021. 805-821.