An Idea About Beta Decay

How can we possibly explain the continuous spectrum of electron energies in beta decay without having to invent another particle to properly arrive at conserved energy and momentum? There are two factors that give me hope that a solution is possible. One is the extreme difference in mass between the unstable nucleus and the escaping electron. For example, what was known as Radium E is, in fact, Bismuth - 210. This nucleus has a mass approximately 382,000 times bigger than the electron. Secondly, all atoms in solids undergo thermal oscillations. Thus, a decaying nucleus will have a unique velocity at the instant of ejection of the electron. The velocity distribution of the nuclei may be intimately related to the spectrum of the ejected electrons. This seems worth looking into.

If this is correct, then we would expect to see some much smaller variation in the energies of alpha particles ejected in alpha decay.