Neutron Time of Flight Jacobian

In summary, the forum user has been given a DT fusion spectrum and has converted it into dE/dE and then dE/dt. They are unsure if they need to consider a Jacobian when converting the spectrum and are seeking clarification.
  • #1
James_1978
37
3
Dear Forum,

I have been given a DT fusion spectrum where neutrons are produced in the following reactions,

DT = 14.1 MeV
DD = 2.45 MeV
TT = 0-9.8 MeV (three body spectrum)

The spectrum is given in the form dN/dE. I have converted this spectrum into the dE/dE by multipling the spectrum over the energy spectrum. I then convert the spectrum into time by just converting the Energy into time. This gives me a spectrum of dE/dt. However, I feel that this might be inaccurate.

My question is do I need a Jacobian when I convert this..such as

[tex] \frac{dE}{dt} = \frac{dE}{dn}\frac{dn}{dt} [/tex]

I am not very familiar with what a Jacobian will do to the spectrum. I appreaciate the help...Chad
 
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  • #2
The first two should be essentially mono-energetic, no need to consider a spectrum unless you are sensitive to the motion of the initial particles.

dE/dE=1?
$$\frac{dE}{dt} = \frac{dE}{dn}\frac{dn}{dt}$$
A similar approach should work to convert dN/dE to dN/dt.
 

1. What is the Neutron Time of Flight Jacobian and why is it important in neutron scattering experiments?

The Neutron Time of Flight Jacobian is a mathematical term used in neutron scattering experiments to describe the probability distribution of the flight times of neutrons. It takes into account the effects of the energy and time resolution of the detector, as well as the geometry of the experiment. This information is crucial for accurately interpreting the data collected in a neutron scattering experiment.

2. How is the Neutron Time of Flight Jacobian calculated?

The Neutron Time of Flight Jacobian is calculated using a mathematical formula that takes into account factors such as the energy and time resolution of the detector, the geometry of the experiment, and the energy of the neutrons. This formula can be quite complex, but it is essential for accurately interpreting the data collected in a neutron scattering experiment.

3. Why does the Neutron Time of Flight Jacobian change with experimental parameters?

The Neutron Time of Flight Jacobian is affected by various experimental parameters, such as the energy and time resolution of the detector, the geometry of the experiment, and the energy of the neutrons. Changes in these parameters can alter the shape of the probability distribution of the flight times of neutrons, which in turn affects the interpretation of the data collected in the experiment.

4. What is the significance of the Neutron Time of Flight Jacobian in neutron diffraction experiments?

In neutron diffraction experiments, the Neutron Time of Flight Jacobian is used to correct for the effects of the energy and time resolution of the detector, as well as the geometry of the experiment. This correction is necessary to accurately determine the structure and properties of materials being studied using neutron diffraction techniques.

5. Are there any limitations to the Neutron Time of Flight Jacobian?

Like any mathematical model, the Neutron Time of Flight Jacobian has its limitations. It assumes certain idealized conditions, such as perfect energy and time resolution of the detector, which may not always hold true in real experiments. Additionally, it may not be applicable to all types of neutron scattering experiments, and alternative methods may need to be used for accurate data interpretation.

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