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

The researcher can change one isotope into a different isotope of the same element by ADDING OR REMOVING NEUTRONS.
Isotopes refers to two or more forms  of the same element, which have the same number of protons but different number of neutrons. The difference in the number of neutrons of a particular element is what brings about isotopes, thus, isotopes can be created by removing  or adding neutrons to a particular element.

the researcher has to obtain atoms with the same number of protons but different number of neutrons.

Explanation:

The isotopes are atoms of the same element (this is with the same number of protons) and different number of neutrons (which result in different atomic masses).

For example, all the atoms of hydrogen have 1 proton, all the atoms of sodium have 11 protons, all the atoms of uranium have 92 protons. But, while as said, all the atoms of hydrogen have the same number of protons, some atoms of hydrogen do not have neutrons, other may have 1 neutron (it is called deutirium) and others may have 2 neutrons (it is called tritium).

That means that, to change one isotope into a different isotope of the same element, the researcher has to obtain atoms with the same number of protons but different number of neutrons.