Low Energy NeutronInteractions in Geant4

Jacek M. HoleczekInstitute of Physics, University of Silesia, Katowice,

Poland[Adam Konefał’s results also presented.]

[Talk based on the Geant4 Physics Reference Manual.]

Varian Clinac-2300 in Geant4

Geant4 visualizations of the whole setup (left) and of the accelerator head alone (above).

”All inclusive” Geant4 simulation (i.e. all relevant accelerator components and the concrete accelerator bunker, with the maze and the door, simulated). Neutrons originate from photonuclear and electronuclear reactions, caused by the therapeutic beam (the components of the accelerator head particularly strongly activated), A. Konefał et al., 2006.

Varian Clinac-2300 @ 20 MV

Scheme of the accelerator bunker with the numbered locations where neutron fluences were determined; calculated and measured thermal and epithermal neutron fluences presented; fast neutron fluences, total flunences and the effective dose calculated only; all values normalized to Dmax (central axis maximum X-ray dose @ 100 cm SSD); fluences determined as the number of neutrons per square centimeter; mean neutron energy presented, too,A. Konefał et al., 2006.

Introduction

• The neutron kinetic energies in Geant4 from thermal up to about 20 MeV (A. Konefał –> 18 to 19 MeV, depends on Z and A), the upper limit set by the comprehensive evaluated neutron scattering data libraries that the simulation is based on.

• A. Konefał -> Geant4.7 (and later?) needed (previous versions deliver incorrect results).

• High Precision and Low Energy Parameterized Models exist.• Interactions of neutrons split into four parts (in analogy to the other

hadronic processes): radiative capture, elastic scattering, fission, and inelastic scattering; each part considered as a separate model.

• No neutron-spin electron-spin interactions (i.e. no magnetic moments’ interaction) -> very weak interaction (about 10 eV neutron energy loss), possibly important only in ferromagnetic medium (macroscopic collective effects appear) -> MCNP – A General Monte Carlo N-Particle Transport Code (can be used for neutron, photon, electron, or coupled neutron/photon/electron transport; thermal neutrons are described by both the free gas and S(α,β) models).

Why Low EnergyParameterized Models?

• High precision data library not complete (no data for several key elements -> users should develop their detectors using only elements which exist in the high precision library).

• Low Energy Parameterized neutron Models cover the same types of interaction as the High Precision Models (elastic and inelastic scattering, capture and fission).

• Results not as precise as they would be if the relevant library data existed; however, the simulation is much faster.

High Precision Models

• Inclusive cross-section data taken from the ENDF/B-VI (Cross Section Evaluation Working Group, BNL) evaluated neutron data library.

• Supplemented with evaluated data on nuclear excitation levels, thus improving the energy spectra of de-excitation photons.

• Extensions based on the JENDL (Japanese Evaluated Nuclear Data Library), CENDL (Chinese Evaluated Nuclear Data Library for Neutron Reaction Data), and Brond (Russian Nuclear Data Libraries) data libraries.

• ”Full library” called G4NDL in Geant4, treated as point-wise cross-sections (explicitly includes also all neutron nuclear resonances); regularly updated and enhanced.

Elastic Scattering

• The final state of elastic scattering is described by sampling the differential scattering cross-sections.

• Two representations are supported. The first is a tabulation of the differential cross-section, as a function of the cosine of the scattering angle θ and the kinetic energy E of the incoming neutron (tabulations normalized by σ/(2π)). In the second representation, the normalized cross-section are represented as a series of Legendre polynomials Pl(cos θ), and the Legendre coefficients al are tabulated as a function of the incoming energy of the neutron.

Radiative Capture

• The final state of radiative capture is described by either photon multiplicities, or photon production cross-sections, and the discrete and continuous contributions to the photon energy spectra, along with the angular distributions of the emitted photons.

• Two descriptions of the photon multiplicity are supported. It can either be tabulated as a function of the energy of the incoming neutron for each discrete photon as well as the eventual continuum contribution, or the full transition probability array is known, and used to determine the photon yields. If photon production cross-sections are used, only a tabulated form is supported.

Fission

• For neutron induced fission, we take first chance, second chance, third chance and forth chance fission into account.

• Neutron yields are tabulated as a function of both the incoming and outgoing neutron energy. The neutron angular distributions are either tabulated, or represented in terms of an expansion in Legendre polynomials. In case no data are available on the angular distribution, isotropic emission in the centre of mass system of the collision is assumed.

• The mean kinetic energies for light and heavy fragments are assumed to be energy independent. The temperature is tabulated as a function of the kinetic energy of the incoming neutron.

• Fission photons are describes in analogy to capture photons, where evaluated data are available. The measured nuclear excitation levels and transition probabilities are used otherwise, if available.

Inelastic Scattering

• The currently supported final states are (nA→) nγs (discrete and continuum), np, nd, nt, n3He, nα, nd2α, nt2α, n2p, n2α, npα, n3α, 2n, 2np, 2nd, 2nα, 2n2α, nX, 3n, 3np, 3nα, 4n, p, pd, pα, 2p d, dα, d2α, dt, t, t2α, 3He, α, 2α, and 3α.

• The photon distributions are described as in the case of radiative capture.

• The representations for the distribution probability supported are: isotropic emission, discrete two-body kinematics, N-body phase-space distribution, continuum energy-angle distributions, and continuum angle-energy distributions in the laboratory system.

Conclusions

• Current Geant4 seems to be able to simulate low energy neutron interactions quite well.

• Should we care about the missing neutron-spin electron-spin interactions (i.e. magnetic moments’ interaction)?

• Should we care about neutrons with kinetic energies > 20 MeV (of the order of GeV and tens of GeV)? If yes, Geant4 contains appropriate classes, which need to be used in the ”physics list” (”G4LE[Anti]Neutron*” below 20 GeV, ”G4HE[Anti]Neutron*” above 45 GeV).

• Wishes?