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Physics LibreTexts

4.4: Barrier Penetration

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In order to understand quantum mechanical tunnelling in fission it makes sense to look at the simplest fission process: the emission of a He nucleus, so called α radiation (Figure 4.4.1).

alpha_decay.png
Figure 4.4.1:The potential energy for alpha decay

Suppose there exists an α particle inside a nucleus at an (unbound) energy >0. Since it isn’t bound, why doesn’t it decay immediately? This must be tunnelling. In Figure 4.4.1) we have once again shown the nuclear binding potential as a square well (red curve), but we have included the Coulomb tail (blue curve),

VCoulomb(r)=(Z2)2e24πϵ0r.

The height of the barrier is exactly the coulomb potential at the boundary, which is the nuclear radius, RC=1.2A1.3 fm, and thus BC=2.4(Z2)A1/3. The decay probability across a barrier can be given by the simple integral expression P=e2γ, with

γ=(2μα)1/2bRC[V(r)Eα]1/2dr=(2μα)1/2bRC[2(Z2)e24πϵ0rEα]1/2dr=2(Z2)e22πϵ0v[arccos(Eα/BC)(Eα/BC)(1Eα/BC)],

where v is the velocity associated with Eα. In the limit that BCEα we find

P=exp[2(Z2)e22ϵ0v].

This shows how sensitive the probability is to Z and v!


This page titled 4.4: Barrier Penetration is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Niels Walet via source content that was edited to the style and standards of the LibreTexts platform.

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