Geant4 simulation of neutron cross section of ²⁰⁸Pb, ⁹⁰Zr, ⁴⁰Ca

Xinjie Qiu

April 3, 2006

In the motivation of testing the physics list of Geant4 applicable to our simulation purpose, we compared the simulation result with the experimental cross section data of neutron interacting with ²⁰⁸Pb, ⁹⁰Zr, ⁴⁰Ca.

1. Geometry and Setup

A simple geometry of 24cm x 24cm x 24cm lead (and also Zirconium, Calcium) cube (see right figure, but ignore the blue dots inside the cube)is used in the simulation, with neutron beam at different energy shooting from the top to the center of the sample. It is the same geometry used in last notes, which compared the FLUKA simulation results with Geant4 results.

2. Cross Section Calculation from the Simulation Data

For each energy, five different runs with different random seeds are simulated. Each beam has 1000 incident neutron with the same energy. Beam energies are from 10 to 500 MeV, with 2 MeV spacing for energy lower than 100MeV, and 20 MeV for energy above 100 MeV. Neutron kinetic energy, momentum, position are recorded in files during simulations for later analysis, when they come out of the cube and hit on an imaginary sphere surface just a little bit bigger than the cube.

The number of non-interaction neutrons in each run is determined by counting the outgoing neutrons without losing any kinetic energy, and the trajectory is a straight line.

The cross sections can be calculated from the familiar relationship,

 1
σ = - ----- ln T
 n L

Where T is the transmission(number of non-interacting neutrons over total number of neutrons) of the sample , n is the number desity of atoms, L is the interaction length( L = 24cm in this case).

3. Physics List

Physics list LHEP_BIC_HP is chosen to be used in the simulation.

• LHEP, fastest, uses the LEP and HEP parametrized models for inelastic scattering. These models parametrize the final states of individual hadron-nuclear inelastic reactions, so you will not see resonances, and detailed angular distributions for O(100MeV) reactions will not be perfect, while the average quantities will be well described. You gain significantly in CPU in exchange.
• HP, point-wise evaluated cross-section data to model neutron scattering cross-sections and interactions from thermal energies to ~20MeV. This applies to capture, elastic scattering, fission and inelastic scattering.
• BIC, new, binary cascade code for modeling the inelastic interactions of pions and nucleons below 3 GeV. This list is expected to give the most precise results, but at the expense of CPU performance.

4. Results

The simulation results of the cross section agree satisfactory with the experiment data, except that,

1. there are "dips" at 20 MeV for ²⁰⁸Pb and ⁹⁰Zr, which might due to the swith of physics list model(HP and BIC)at that region, and that confused the program which model to choose.

2. Discontinuities between 32 MeV and 34 MeV for ⁹⁰Zr and ⁴⁰Ca, I don't know the reason yet.

3. Second peak at about ~80 MeV for ²⁰⁸Pb is higher than the experimental data, don't know reason either.

2 and 3 are at the BIC model effective region, which is expected to give more precise results, but turns out not true for our simulation.

I don't need worry too much about it as far as my simulation work is concerned, since my next step on the simulation is the neutron calibration, and ²⁵²Cf emited neutron peaks at ~1.5 MeV, which HP model describes pretty well for neutron-Pb cross section.

Geant4 Simulation result	Experiment Result(2)

5. Summary

Simulation result of the cross section of neutron with ²⁰⁸Pb, ⁹⁰Zr, ⁴⁰Ca are compared with experiment data, Agreements are found in most of the regions between 10 MeV to 500 MeV, except at some energy ranges. Other physics list will be tested.

6. Reference

1. A paper comparing physics simulations at the LHC between several geant4 physics models and fluka.

2. Neutron cross section on Pb from 10-500 MeV.

7. Future plan

As in the background meeting notes, my future working task will be,

• Simulate 252-Cf calibration runs with Geant4 and compare with Soudan data (provides check of low-energy neutrons). Benchmark Geant4 use spectrum for 252-Cf source.
• The effects of the stems and our shield against these low-energy neutrons. Simulate an assumed flux of low-energy neutrons from U/Th in the walls using the correct MC geometry).