The commonly used radioisotopes have short half lives and so do not occur in nature in large amounts. They are produced by nuclear reactions. One of the most important processes is absorption of a  neutron by an atomic nucleus, in which the mass number of the element concerned increases by 1 for each neutron absorbed. For example,
:C + n → C
In this case the atomic mass increases, but the element is unchanged. In other cases the product nucleus is unstable and decays, typically emitting protons, electrons (beta particle) or alpha particles. When a nucleus loses a proton the atomic number decreases by 1. For example,
:S + n → P + p
Neutron irradiation is performed in a nuclear reactor. The other main method used to synthesize radioisotopes is proton bombardment. The proton are accelerated to high energy either in a cyclotron or a linear accelerator.