Conundrum wrote ...

The idea is based on the observation that neutrinos seem to affect radioactive half life at least in certain isotopes used in nuclear medicine.
If this is indeed the case then a neutrino laser beam (if such a thing is possible) would affect very heavy atoms with large cross sectional areas much more than light ones causing an internal shift in nucleon structure leading to a multiple atomic number decrease in mass with the emission of alpha particles.

If there is enough gallium present (IIRC 3-5%) then there is a chance of a stable superheavy element forming with Z=122 as Ga (31)+Pu (94) with the previously mentioned induced alpha decay mode.
Here the reaction would be Z94+Z31 = Z125, single alpha emitted Z2 would yield Z=123 which would emit 1 neutron after about 300us to yield stable Z=122 with some minor nuclear shell reorganization.

A possible indirect reaction would be Z94+Z31 = Z125, double alpha emission would give Z=121 which would then convert a neutron into a proton to again yield stable Z122.
The latter might be more thermodynamically favorable and would be aneutronic with only high energy gammas given off.

Its possible at least theoretically, the catch is needing a neutrino laser.
This at the moment is the sticking point as we have no idea how to make one without something like a confined artificial singularity.
Perhaps if certain theories about quantum gravity are correct then there is a way to emit coherent neutrino beams from a specific nuclear transition within an existing metastable isotope ie 180Ta or 99Mo.
Or a wakefield accelerator could also do the trick, here the awkward part would be generating the terawatt class laser beam needed in something relatively compact and powering the laser and chirped pulse amplifiers.