Probability of $\alpha$-decay In standard Gamow model we assume that $\alpha$ particle is already in the nucleus, i.e. four nucleons are "glued" together and this particle is emitted. So, we assume that the probability of the existence $\alpha$ particle in the nucleus in equal to $1$. Is there any theoretical reason for this assumption? I know that the nuclear force can be described by Weinberg's chiral theory, but I cannot find explanation of this fact in articles of this theory.  
 A: If you want a more palatable assumption than a population of alpha particles dwelling inside each heavy nucleus waiting to escape, imagine this instead:  Inside the nucleus that you have many protons and neutrons rattling about, and that pairing interactions cause alpha particles to form and disintegrate with some frequency which doesn't depend (much) on the Coulomb barrier and is very fast compared to the alpha decay lifetime.  In this case you can recover Gamow's seminal results about relative lifetimes for alpha emitters depending on the Coulomb barrier; the difference is an overall constant in the tunneling probability that depends on how long the alphas survive within the nucleus, but that constant isn't known anyway.
Here is a 2002 Physics Today article by Merzbacher on the early history of tunneling.  You should dig up Gamow's original article, too: the citation is G. Gamow, 
Z. Phys.
51, 204 (1928).
A: It's actually not possible for alpha particles to exist inside a nucleus, because the wavefunction constructed in this way would violate the Pauli exclusion principle. Therefore there is no hope of adding rigor to the notion of a "probability of preformation" of the alpha. In any case, ab initio calculations of tunneling are never good enough to predict the over-all normalization of alpha decay half-lives, even to within several orders of magnitude. One is always going to need to fit parameters to data or work with quantities that are easier to predict, such as ratios of half-lives in different isotopes. So even if you could rigorously define and calculate a probability of preformation, it would just be absorbed into a normalization factor that would include lots of other effects.
