No, this is not possible. There are multiple reasons one could
give for this.
For example electric charge is not conserved; the neutron has no
charge, the beta particle has a charge of -1 (times the positive
elementary charge) and the alpha particle has a charge of +2.
Therefore you go from 0 charge to (-1 + 2 = 1) +1 charge. You could
fix this by making two beta particles (but it would still not work
for the reasons below).
Every such reaction must conserve baryon number. A baryon is an
object consisting of three quarks. The neutron is a baryon and
therefore has baryon number +1. The alpha particle consists of two
neutrons and two protons (the proton is also a baryon) so it has
baryon number +4. The beta particle has baryon number 0. So the
reaction n -> alpha + beta would increase the total baryon
number by (+4 - 1 = 3) 3 which is not allowed. To fix this one
would need, for example, to add three baryons to the initial
state.
The lepton number is also not conserved by this reaction.
Protons and neutrons both have lepton number 0, but the beta
particle has lepton number +1. Therefore this reaction would go
from lepton number 0 to +1, which is also not allowed. This could
be easily fixed by adding an antielectron-neutrino to the final
state.
A possible reaction that would fix everything would be something
like:
4n -> alpha + 2 beta + 2 antielectron-neutrinos
