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Question Questions on Thermal Neutron Scattering in Aluminium 

Forum: Hadronic Processes
Date: 22 Jun, 2011
From: Evan Askanazi <Evan Askanazi>

Now I have figured out how to get the right cross sections for liquid hydrogen, and therefore I have solved a previous problem, but now a new one has come up. I am trying to determine how the cross section, according to geant4, for neutrons of 2, 5 and 10 meV changes when the temperature of Aluminium is set to 300K and then changed to 20 K or 1 K so that the temperature dependence of cross sections at low energies can be seen.

So then what I did, using the Geant4 program, is simulate a group of 10000 neutrons of energies 2 meV, 5 meV and 10 meV and 100 meV launched against a block of Aluminium that is one meter cubed. I then compared the rates of elastic scattering for the neutrons when the Aluminium is set at 300 K and repeated the same experiment for when the Aluminium is set at 20 K.

What I found was that for incoming neutrons of 2 meV, there was a significant difference between the rate of scattering for Aluminium at 300 K and for Aluminium at 20 K. The rate of elastic neutron scattering, and therefore, the elastic cross section as a result, decreases somewhat as the temperature was lowered from 300 K to 20 K. But that for 5 and 10 meV, there was not a signficant difference for the rate of neutron scattering in Aluminium for 300 K vs the rate of scattering in Aluminium for 20 K. So the results showed that the change in thermal neutron scattering cross section , relative to the change in the temperature of Aluminium, was significant for incoming neutrons of energy 2 meV but not for neutrons of 5 meV or 10 meV or 100 meV. But the Debye-Weller factor increases as the energy of the scattered nuclei increases, and the energy of the scattered nuclei, I had thought , would increase as you increase the energy of the incoming neutrons. So this seems to suggest that the temperature dependence of the cross section would increase with increasing neutron energy, not decrease as my results showed. However, i feel I am missing an important point about the theory of scattering of neutrons in solids such as Aluminium.

When it comes to Geant4 , the questions are as follows. Is Geant4 calculating the cross section and rate of elastic scattering correctly when it shows that , for 2 meV and for higher energies like 5 and 10 meV, the elastic cross section and subsequent rate of elastic scattering decreases as the temperature drops from 300 K to 20 K ? And also, for a given material in general, where does Geant4 determine how the cross section and subsequent rate of elastic scattering depends on the temperature of the material and the energy of the incoming neutrons, i.e. what Geant4 class does the calculation ?

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