As it is now known because of Gamow, how alpha decay occurs. We have taught this theory in our class in last week. There we have been introduced with a strange phenomenon happening because of which alpha particles decay and the phenomenon was named as Quantum Tunnelling. In the theory proposed by Gamow it was assumed that alpha particles as a complete entity reside in the nucleus and after certain amount of collisions and time, the alpha particle will tunnel through the potential barrier. The professor who taught us was reasonably satisfied that there is no analog of this phenomenon which comes from classical physics.
I do believe on his statement but later on thinking more on it, I came across certain explanation of this phenomenon which I am about to discuss.
The prior assumption in my explanation is that, the nuclear potential barrier satisfies La Place’s equation.
If the nuclear potential satisfies La Place’s equation, a very curious property of the equation is that, the potential at a given point is actually coming from the average of potential surrounding that point.
Now, suppose after many number of collisions of alpha particles with the potential barrier, the alpha particles tunnels through the barrier. When it tunnels through, it seems as if from the point it has tunnel, the barrier is defined at that point. Now, since the barrier has to satisfy under any circumstances, the average property of potential which mentioned above leads to shrinking of the overall size of potential barrier of nucleus after alpha decay as just happened.
This can be understood by an analogy with a cotton ball, in which if you made a whole, and now you want to fill it with same number of materials used for that ball, you sacrifice the size of ball and fill it.
For nucleus, as per my understanding the main property which must be driving this shrinking of size of barrier is because the collective potential of nucleus assumed is satisfying La Place’s equation. Now if $V$ satisfies La Place’s equation at a point say $x$ and in neighbourhood of $x$ there are $x_1$ and $x_2$ then,
$$V(x) = \frac{V(x_1) + V(x_2)}{2}$$
Now because the V has become undefined at a point momentarily because of the Tunnelling effect, but still the overall potential satisfies La Place’s equation, it tries to fill this point of indeterminacy by shrinking the size of potential barrier.
Now, the claim made here that it reduces the size of potential barrier is actually trivial, as the nuclear potential energy of daughter nuclide is less than that of parent nuclide.
I would be thankful if someone validate my understanding and explanation of alpha decay.
