text: When considering whether a specific nuclear transmutation, a reaction or a decay, is energetically allowed, one only needs to sum the masses of the initial nucleus/nuclei and subtract from that value the sum of the masses of the product particles.  If the result, or Q-value, is positive, then the transmutation is allowed, or exothermic because it releases energy, and if the Q-value is a negative quantity, then it is endothermic as at least that much energy must be added to the system before the transmutation may proceed. For example, to determine if C, the most common isotope of carbon, can undergo proton emission to B, one finds that about 16 MeV must be added to the system for this process to be allowed. While Q-values can be used to describe any nuclear transmutation, for particle decay, the particle separation energy quantity S, is also used, and it is equivalent to the negative of the Q-value. In other words, the proton separation energy S indicates how much energy must be added to a given nucleus to remove a single proton. Thus, the particle drip lines defined the boundaries where the particle separation energy is less than or equal to zero, for which the spontaneous emission of that particle is energetically allowed.
  Although the location of the drip lines is well defined as the boundary beyond which particle separation energy becomes negative, the definition of what constitutes a nucleus or an unbound resonance is unclear. Some known nuclei of light elements beyond the drip lines decay with lifetimes on the order of 10 seconds; this is sometimes defined to be a limit of nuclear existence because several fundamental nuclear processes (such as vibration and rotation) occur on this timescale. For more massive nuclei, particle emission half-lives may be significantly longer due to a stronger Coulomb barrier and enable other transitions such as alpha and beta decay to instead occur. This renders unambiguous determination of the drip lines difficult, as nuclei with lifetimes long enough to be observed exist far longer than the timescale of particle emission and are most probably bound. Consequently, particle-unbound nuclei are difficult to observe directly, and are instead identified through their decay energy.