Geant4 hadron elastic diffuse model

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Abstract

Differential elastic hadron–nucleus cross-sections are discussed in the framework of the optical approach. The model predictions implemented in the Geant4 toolkit are compared with the experimental data for protons and pions. The contribution of Coulomb scattering is discussed for charged hadrons.

Introduction

Elastic scattering of hadrons on nuclei corresponds to a significant (up to a half [1], [2]) part of the hadron–nucleus interactions. The process therefore is important for general simulation toolkits for the passage of particles through matter like Geant4 [3]. The Geant4 toolkit has a number of different models for hadron-nuclear elastic scattering:

  • (1)

    The GHEISHA/PITHA elastic model is implemented in the Geant4 G4LElastic class using a simplified parametrization [4] in terms of the invariant transfered momentum t<0. For atomic weight, A<62:dσeldΩ=A1.63exp(14.5A0.66t)+1.4A0.33exp(10t), and for A62:dσeldΩ=A1.33exp(60.0A0.33t)+0.4A0.4exp(10t).

  • (2)

    The CHIPS [5] approach (class G4QElastic) is based on a more dedicated parametrization of invariant differential cross-section, dσel/dt. The cross-section can be analytically integrated with respect to t to get the integral, σel,>t, and the total elastic σel,>0=σel cross-sections.

  • (3)

    The coherent elastic model (class G4ElasticHadrNucleusHE) utilizes the Glauber approach [6], [7], when a nucleus is considered as a set of ∼A nucleons.

Those models work satisfactory, showing however sometimes accuracy and numerical problems. The contribution of Coulomb scattering to the hadron elastic process is not completely clear for them.

It was therefore interesting to consider a model which could be simple (and with transparent correction for the Coulomb contribution), robust and universal enough for the description of hadronic calorimeters. In this paper we describe a simple hadron elastic scattering model based on the optical approach which provides a clear procedure for activation of the Coulomb scattering. The model is compared with the experimental data and with the predictions of the other Geant4 hadron elastic models.

Section snippets

The diffuse model description

Historically, the first model for hadron elastic scattering based on the optical approach was the nuclear black R-disk model for neutrons [8]. The differential elastic cross-section of neutrons on nuclei, dσel/dΩ for the black disk model reads:dσeldΩ=R2J12(kRθ)θ2,dΩ=2πsinθdθ, where Ω and θ are the solid and polar angles in the center of mass system, respectively, k is the neutron wave vector and R is the nucleus radius. The model was modified later on for the charged particles in [9]:dσeldΩ=R2{J

Implementation

The hadron diffuse elastic model was implemented within the Geant4 toolkit as the G4DiffuseElastic class. It provides access to the elastic generator according to the general interface defined in Geant4 hadronic processes. The interface is based on the methods GetCrossSection and GetElasticCrossSection which return the inelastic and the elastic cross-sections, respectively, using the hadron momentum and information on nucleus parameters. The method IsApplicable limits the hadron energy range

Validation

Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 8 show the elastic differential cross-section of protons with energies in the range 1–301 GeV on different targets: helium, carbon, silicon and lead. The solid, dash–dash, dot–dot and dash–dot histograms are the diffuse, Glauber, CHIPS and GHEISHA models, respectively. The solid circles are experimental data [13].

Fig. 9, Fig. 10, Fig. 11 show the elastic differential cross-section of pions with the momentum 9.92 GeV/c on carbon and lead. The solid,

Discussion and conclusions

In this paper we described the diffuse model for the hadron–nucleus elastic scattering. The model provides quite good description of the experimental data for protons and satisfactory describes the data for pions. One can see from the comparison with the other Geant4 models that the diffuse model provides a better description of the experimental data in the majority of use cases. The model parameters were taken from Ref. [11] where they were optimized for the proton–nucleus elastic scattering

Acknowledgements

This work was partly supported by the Commission of the European Communities under the 6th Framework Program “Structuring the European Research Area”, contract number RII3-026126. The author is thankful to J. Allison, J. Apostolakis, and members of Geant4 hadronic group for many stimulating discussions and help.

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