The results published in this web page are continuously evolving, and therefore not necessarily accurate, nor official, and might not even be true at a given point in time. These studies are only an excerpt of the hadronic benchmarks being performed inside the ALICE colaboration and a more precise and complete description of them might be found in some of the publications.

The picture on the left is a very simplified representation of the experimental setup we tried to simulate. A proton beam is directed towards a thin target of iron, aluminium or lead (see table 1). The proton energy goes from 113 MeV to 800 MeV. Neutrons are detected at several angles ranging from 7.5^o to 150^o depending on the incident energy. The angular width of the detectors is 10^o. Only one hadronic interaction is produced most of the times. For a more detailed description on the experiment look at:

• Nucl. Sci. Eng., 102, 310-321 (1989)
• Nucl. Sci. Eng., 110, 289-298 (1992)
• Nucl. Sci. Eng., 112, 76-86 (1992)
• Nucl. Sci. Eng., 115, 1-12 (1993)

Due to the hadronic interaction cross section, the probability of having a single interaction in a thin target is small. Most of the times, the protons traverse the target material without interacting. For this reason, to speed up computation, a setup different from the real one was simulated with GEANT4. A big box made of the target material was built to make sure that one hadronic interaction would take place. Only transportation and proton inelastic (class G4ProtonInelasticProcess) processes where activated. Immediately after the interaction, the kinematic properties of the secondaries produced were stored for further analysis, and the next primary interaction was generated. The direction of each neutron produced was compared with the position of the detectors in the experimental setup.

For this excersise two GEANT4 (version 3.2) hadronic models were used:

• The first model is the GEANT4 implementation of the GEISHA model (classes G4LEProtonInelastic and G4HEProtonInelastic). Some improvements with respect to the Geant3 implementation of the model are included. As it is a parameterised model, the nuclear fragments remaining from the inelastic collision are not calculated. To be able to verify the model we have deduced the fragment properties from the known conservation laws. The physics list used for this model can be found in Table 2.

Table 2: Physics list for the benchmark with GHEISHA.

theParticleIterator->reset(); while ((*theParticleIterator)()) { G4String particleName = theParticleIterator->value()->GetParticleName(); G4ProcessManager* pmanager = particle->GetProcessManager(); if (particleName == "proton") { G4ProtonInelasticProcess* theInelasticProcess = new G4ProtonInelasticProcess("Had_Inelastic_proton"); G4LEProtonInelastic* theLEInelasticModel = new G4LEProtonInelastic; G4HEProtonInelastic* theHEInelasticModel = new G4HEProtonInelastic; theInelasticProcess->RegisterMe(theLEInelasticModel); theInelasticProcess->RegisterMe(theHEInelasticModel); pmanager->AddDiscreteProcess(theInelasticProcess); } }

• The second model used is the GEANT4 implementation of the precompound model. It is a microscopic model which is supposed to complement the hadron kinetic model in the intermediate energy region for nucleon-nucleus inelastic collisions. The physics list used for this model can be found in Table 3.

Table 3: Physics list for the benchmark with the precompound model.

G4PreCompoundModel* thePreEquilib = new G4PreCompoundModel(new G4ExcitationHandler); theParticleIterator->reset(); while ((*theParticleIterator)()) { G4String particleName = theParticleIterator->value()->GetParticleName(); G4ProcessManager* pmanager = particle->GetProcessManager(); if (particleName == "proton") { G4ProtonInelasticProcess* theInelasticProcess = new G4ProtonInelasticProcess("Had_Inelastic_proton"); theInelasticProcess->RegisterMe(thePreEquilib); pmanager->AddDiscreteProcess(theInelasticProcess); } }

The interaction length follows a law of the form e^x/S (see the figures in table 2). Therefore, by fitting the histogram of the number of events versus the interaction length, one can estimate the value of S. This constant is related to the cross section, S, by the equation:

where, N_A is the Avogadro constant and A is the atomic mass for the target nuclei. 200K events were used for the fit, giving a relative error in the estimation of s well below 0.5%. The cross sections obtained for the two models under study with the fit are written in table 4. The cross sections obtained for both models under study with the fit are consistent with the one provided by the method G4ProtonInelasticProcess::GetMicroscopicCrossSection() for all nuclei.

The double differential

was calculated for the two materials being considered and for most of the energies. The plots in table 5 show the ratio between data and MC for both models: GEISHA and Precompound. 200K events where simulated in all cases.

There are several steps to be taken in the future:

• Extend the number of materials tested.
• Use the CHIPS and kinetic model whenever they become available.
• Repeat the test with newer versions of GEANT4.

• ALICE Internal Note: GEANT4: A Benchmark of Hadronic Processes