To determine which type of nuclear decay alters the atomic number but not the mass, we should understand the different types of nuclear decay processes mentioned in the options:

1. Alpha Decay: This type of decay involves the emission of an alpha particle, which consists of 2 protons and 2 neutrons. As a result, the atomic number decreases by 2, and the mass number decreases by 4. Therefore, alpha decay alters both the atomic number and the mass number.
2. Beta Decay: In this decay, a neutron in the nucleus is transformed into a proton with the emission of a beta particle (electron or positron) and an antineutrino or neutrino. The atomic number increases by 1 (if a beta-minus particle is emitted) or decreases by 1 (if a beta-plus particle is emitted), but the mass number remains unchanged. This type of decay alters only the atomic number and not the mass number.
3. Gamma Decay: This decay involves the release of gamma radiation, which is a form of electromagnetic energy. It does not alter the atomic number or the mass number; it simply relieves excess energy from the nucleus.
4. Fission: This is a type of nuclear reaction where a single nucleus splits into two or more smaller nuclei, along with the release of a significant amount of energy. This process involves a change in both the atomic number and the mass number of the original nucleus.

Based on the above explanations, it is clear that Beta Decay is the process that changes the atomic number of a nucleus while leaving the mass number unchanged.

Conclusion: The correct answer is Beta Decay, as it alters the atomic number but not the mass.