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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

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Q: Can one neutron can split into an alpha particle and a beta particle?
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