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Numerical integration of Bethe formula in Excel: help!

by Moho
Tags: alpha, bethe, bloch, integration
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Feb21-13, 09:40 AM
P: 2

I am a PhD student in geology in need of help from a physicist! Can somebody spot the mistake in my spreadsheet?

I am using an Excel spreadsheet (attached .xls) to integrate the Bethe formula in order to estimate the range (in cm) of alpha particles in quartz. I am using the version of the formula given in Groom and Klein's "Passage of Particles through Matter": (but ignoring the density effect correction because I am not interested in high energies).

In Excel, I can plot the Bragg peak (dE/dX against x) or the energy of the alpha particle (E against x). Something is very wrong: the Bragg curve just goes up and up and never comes down again (don't be misled by Excel plotting #NUM! as 0). I would expect dE/dX to start out at something like 500 and then smoothly increase up to the peak (like the Bragg peaks in Google image search).

I must be doing something right, though, because it looks as if the stopping distance is going to be close to what I would expect (about 0.04 cm).

Can anybody find the problem in the attached spreadsheet? Reward: credit in my thesis acknowledgements!

Many thanks!

Attached Files
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Feb21-13, 02:57 PM
P: 12,065
For low energy (βγ<0.03), the Bethe-Bloch formula gives wrong results, as shown in figure 27.1 in the pdf.
Apart from that: After the energy is 0, the energy loss should be 0 as well, giving a nice Bragg peak.

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