The nuclear reaction
conserves electric charge and total nucleon count: and . Its nuclear reaction Q-value is the initial minus final rest energy. It is additional to the incoming beam kinetic energy; the accelerator triggers a rearrangement whose products can carry much more kinetic energy than the incident proton.
Use one consistent set of neutral-atom isotope masses, in unified atomic mass units, from the National Institute of Standards and Technology:
These are isotope masses, not element-averaged atomic weights.[ref] With ,[ref]
The four electron rest masses cancel between sides. Differences of total electronic binding energies do not cancel exactly: this atomic-mass result approximates the bare-nucleus nuclear reaction Q-value at the displayed scale, not at arbitrary precision. No mixture of rounded nuclear binding energies is needed. At chosen incident kinetic energy on a stationary target, the two outgoing alpha particles together carry approximately before losses in the target and detector window.
Figure 1.
Reaction energy and the laboratory recoil of two alpha particles
. Original calculation using the stated neutral-atom isotope masses, electron-mass subtraction and neglected electronic binding corrections. Chosen incident proton energy 0.500 MeV and stationary lithium-7 target; no target or detector losses. Left: energy released by the mass difference plus incident kinetic energy. Right: exact two-body relativistic transformation within these mass assumptions; equal and opposite center-of-mass momenta need not give equal laboratory kinetic energies. Curves parameterize paired events and are not an angular probability distribution or historical data. Details.