Non-Relativistic Bethe-Bloch Calculation for Alpha Particle in Xenon"

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Discussion Overview

The discussion centers on the challenges of plotting the Bethe-Bloch function for alpha particles in Xenon, focusing on the parameters, units, and expected behavior of the resulting curve. Participants explore the theoretical and practical aspects of the calculation, including unit conversions and the shape of the energy loss curve.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in obtaining a sensible plot of the Bethe-Bloch function, noting that their calculated units are MeV/cm but the resulting curve appears incorrect.
  • Another participant suggests including the plot for better context and notes that alpha particles at low energies (e.g., 1 keV) experience significant energy loss even in gases.
  • Several participants question the choice of units, emphasizing the importance of using consistent and reasonable units throughout the calculations.
  • One participant mentions that the energy loss is typically plotted on a logarithmic scale, which could affect the interpretation of the results.
  • Another participant indicates that the expected curve should resemble a specific shape and mentions that the peak in stopping power should occur around 0.6 MeV, suggesting that something may be wrong with the current calculations.
  • Links to external resources are provided by some participants to illustrate expected results and comparisons with other materials, such as air and graphite.

Areas of Agreement / Disagreement

Participants generally agree that the plot does not match expectations and that unit consistency is crucial. However, there is no consensus on the specific cause of the discrepancies, and multiple views on the appropriate scaling and expected behavior of the curve remain unresolved.

Contextual Notes

Participants mention the ionization potential and the need for careful unit conversions, but specific assumptions or missing details in the calculations are not fully addressed.

CloudNine
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Hi all,

I got an exercise to plot Bethe-Bloch function (ignore the "Compare..." part, it belongs to an exercise above), for alpha particle in Xenon. See the question below:

Capture.PNG


I've been struggling to get a plot that makes sense. I checked my parameters and the units a million times already, but couldn't find where the problem is. On paper, the units I'm left with, after all the conversions, are MeV/cm, which is exactly what I want. But again, I get a weird curve...

Here is the Matlab code I wrote:

Code: 
E_dat=[ 0.001    0.002    0.003    0.003    0.004    0.005    0.006    0.007    0.008    0.009    0.010    0.013    0.015    0.018    0.020    0.023    0.025    0.028    0.030    0.035    0.040    0.045    0.050    0.055    0.060    0.065    0.070    0.075    0.080    0.085    0.090    0.095    0.100    0.125    0.150    0.175    0.200    0.225    0.250    0.275    0.300    0.350    0.400    0.450    0.500    0.550    0.600    0.650    0.700    0.750    0.800    0.850    0.900    0.950    1.000    1.250    1.500    1.750    2.000    2.250    2.500    2.750    3.000    3.500    4.000    4.500    5.000    5.500    5.544    6.000    6.500    7.000    7.500    8.000    8.500    9.000    9.500    10.000 ];%MeV

% Constants for Bethe-Bloch equation:
rho = 0.010592; % [g/cm^3] for Xenon in 2 bar and 25 C conditions
qe=1.602e-19; % C
me=9.109e-28; % g
NA=6.0226e23; % Avogadro constant, 1/mol
K=9e13; % K=1/4*pi*epsilon0 , units of N*cm^2/C^2
Z1=2;
malpha=6.646e-24; % g
v=sqrt(2*E_dat/malpha); % sqrt(MeV/g)
A=131.293; % g/mol
Z=54;
I=(16*Z^0.9)/1e6; % MeV
first=-rho*4*pi*NA;
second=((qe^4)*(K^2))/me;
third=((Z1^2)./(v.^2));
fourth=Z/A;
fifth=log((2*me*(v.^2))./I);
aaa=first*second*fourth;
bbb=third.*fifth;
dEdX_BB=aaa*bbb*3.9e21; % 3.9e21 is to convert from N^2*cm/MeV to MeV/cm

plot(E_dat,dEdX_BB)
xlabel('Alpha energy [MeV]')
ylabel('dE/dX [MeV/cm]')
title('Stopping power of non-relativistic analytical expression for alpha particle Xe')

I know that the peak shouldn't be that sharp, narrow, high (10^4!) and not that close to zero. Also, the dE/dx trend should be more moderate and to spread much more nicely, than this sharp drop to 0..
Would appreciate your thoughts!

Thanks.
 
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You could include your plot here.
Alpha particles at 1 keV will have an extreme energy loss even in a gas.
 
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Use a reasonable set of units! Newtons, cm, eV?
What value is the ionization potential?
 
mfb said:
You could include your plot here.
Alpha particles at 1 keV will have an extreme energy loss even in a gas.
Here's the plot:
Capture.PNG


I know it is not the right plot as the lecturer showed something similar in class and it looked differently...
 
hutchphd said:
Use a reasonable set of units! Newtons, cm, eV?
What value is the ionization potential?
There are a lot of variables in this formula. I changed all units so I can end up with MeV/cm. I suppose the problem is indeed relevant to the units, but, as I wrote, I can not find the mistake... hence this post.
The ionization potential is given in eV in the exercise so I turned it to MeV.
Would you mind going over the units and see if I messed up? I've reached to a dead-end...
 
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There is a good reason the energy loss is usually plotted on a logarithmic scale.
 
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mfb said:
There is a good reason the energy loss is usually plotted on a logarithmic scale.
You are right. However, in this case (as I know what to expect), it should look just fine even on a regular scale.
 
The curve should look something like - one would have to multiply by atomic density
https://www-nds.iaea.org/stopping/stopping_201410/index.html

Also, not quite as it's alpha particles in air and graphite.
https://www.nist.gov/system/files/documents/2017/04/26/newstar.pdf (see figures A.10 and A.11 respectively), which are somewhat consistent with the plot above.

It would help to plot energy in a log-scale as others suggested.

There should be a peak in S(E) about 0.6 MeV, so something appears to be amiss.

FYI - http://www.srim.org/Citations/Cit 02-54.pdf - but it's not complete.