Mass Excess - Energy Scale of Nuclear Reactions

Energy Scale of Nuclear Reactions

The 12C standard makes it useful to think about nuclear mass in atomic mass units for the definition of the mass excess. However, its usefulness arises in the calculation of nuclear reaction kinematics or decay. From Einstein's work on mass-energy equivalence (E=mc2), it is well known that nuclear reactions transform energy into mass and vice versa. However, most of the energy remains in the mass of the nuclei involved, and only a small fraction of the total energy, on the order of 0.01 to 0.1% of the total mass, may be absorbed or liberated. Thus by working in terms of the mass excess, one has effectively removed much of the mass changes which arise from the mere transfer or release of nucleons, making more obvious the scale of the net energy difference.

Nuclear reaction kinematics are customarily performed in units involving the electron volt, a consequence of accelerator technology. The combination of this practical point with the theoretical relation E=mc2 makes units of mega electron volts over the speed of light squared (MeV/c2) a convenient form to express nuclear mass. However, the numerical values of nuclear masses in MeV/c2 are quite large (even the proton mass is ~938.27 MeV/c2), while mass excesses range in the tens of MeV/c2. This makes tabulated mass excess less cumbersome for use in calculations. One trivial point worth noting that the 1/c2 term is typically omitted when quoting mass excess values in MeV, since the interest is more often energy and not mass; if one wanted units of mass, one would simply change the units from MeV to MeV/c2 without altering the numerical value.