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I have just written a simple simulation that models the tunnel-effect of alpha-particles for $^{212}$Po and $^{238}$Ur. In this simulation, I approximate the potential of the nucleus by a simple square well. Now I'm thinking about improving the simple model to a more complex one. My idea is to superimpose the Wood-Saxon potential with the Coulomb-potential. The result should look something like this picture:

enter image description here

My question is: how do I actually get there? Do I just add the Woods-Saxon and the Coulomb-potential?

FOLLOW UP @dmckee, thanks, it worked and only needed little tweaking. you were absolutely right!

enter image description here

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Why did you remove the image? –  Michael Brown Apr 6 '13 at 9:01
    
accident, i wanted to post a follow up. i'll put it back in. thanks for pointing it out! –  lomppi Apr 6 '13 at 10:25
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up vote 2 down vote accepted

"Do I just add the Woods-Saxon and the Coulomb-potential?"

Do you know any other way of combining potentials? You certainly do just add them up.

Two complications:

  1. You may need to tweak the parameters of your potentials if, for instance, they were set to get a certain $Q$

  2. You'll need some kind of charge distribution function for the nucleus (a uniform spherical distribution is not a terrible place to start).

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;-), thanks for pointing that out. the emphasis should be placed on the just. as you have written: there may be complications. thanks! –  lomppi Apr 5 '13 at 19:15
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