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There are a few problems with your plan.
Large particles (alpha, beta, neutron) don't penetrate into the ground very far. You would need a very powerful gun to penetrate more than a few inches, or perhaps a few feet.
Would you get fusion?
You would likely get a mess of radioactive materials, not just selective for gold.
198Au --> 198Hg (stable) + β-One may not desire to contaminate one's gold with mercury, although presumably it would separate out easily enough.
The beta radiation given off would likely only be detectable to less than an inch from the source.
Cesium-137(Cs-137) and Americium-241/Beryllium (Am241Be) as used in portablemoisture/density gauges produce all four types of radiation. The alpha radiation will bestopped by the stainless steel capsule in which the sources are enclosed. We need only beconcerned with the external neutron and gamma type radiation.In the process of decaying to Barium-137 (Ba-137), the Cs-137 releases beta particleswhich will be stopped by the capsule wall. Most of the Ba-137 is in an active state; in goingto a stable state it releases gamma energy at 0.662Mev. This gamma energy will be usedto determine the density of the measured material.The Am-241 decays to Neptunium-237 (Np-237). In the process it releases 0.06Mevgamma energy and alpha particles. This additional source of low level gamma energy wouldconfuse our density measurement so it is shielded out by a 1/8 inch thick cup of carbide orlead. The alpha particles will not leave the capsule. However, by mixing the Am-241 withBeryllium-9 (Be-9), the alpha particles then bombard the Beryllium which results in theemission of free neutrons. These free neutrons, also known as fast neutrons will have anaverage energy of 4.5 Mev. When these fast neutrons collide with an average of 19Hydrogen atoms they become thermal neutrons with a reduced energy of around 0.025Ev. It is these thermal neutrons that the gauge counts to determine the moisture content ofa material.
It wouldn't work, but that's not the biggest problem.Dear Santa Claus.Please send me a powerful neutron source for Christmas.I promise to use it for searching for gold.I will not, for example, use it to irradiate people I don't like. And I have not even considered using it to produce radioisotopes that I can poison people with.Your FaithfullyA terrorist.P.S. I have been really good this year.