Aresearcher is using a particle accelerator in an expriment studying isotopes. how can the researcher change on isotope into a different isotope of the same element?

Neutron capture reactions.

Isotopes of the same element have the same number of protons in each nucleus. However, their nucleus differ in the number of neutrons. Adding one or more neutrons to a nucleus will converts it to a different isotope of the same element.

Neutrons can be produced with a particle accelerator. The researcher might aim fast moving alpha particles from the accelerator at a beryllium Be target.

Doing so will convert beryllium-9 to carbon-12 and release one neutron.

The neutron produced in this process moves very fast ("fast neutrons"). It might knock protons or alpha particles off the target nucleus. This is undesirable since the nucleus will have a change in its proton number. It will end up belonging to a different element.

The researcher should reduce the speed of those neutrons. Passing neutrons through moderators greatly reduces their speed. Moderators are materials that are rich in light nuclei. They remove the energy of neutrons as the two collide. Examples of moderators are heavy water (D₂O) and graphite (carbon). Slow neutrons are easier to capture than fast-moving ones. Combining those slow-moving neutrons to the source isotope will likely produce a different isotope of the same element.

Vitz, Ed. et. al, "19.5: Neutron Bombardment", ChemPRIME (Moore et al.), Libretexts Chemistry, 2017

the old alchemists made significant contributions to science even though there starting premises were off a bit. their conclusions after failure would steer them into better directions for investigation. science is no more than close observation and the initial mistakes result in rethinking and retrying experiments.