Nuclear drip line

The nuclear drip line is the boundary delimiting the zone beyond which atomic nuclei decay by the emission of a proton or neutron. The nuclear drip line is the boundary delimiting the zone beyond which atomic nuclei decay by the emission of a proton or neutron. An arbitrary combination of protons and neutrons does not necessarily yield a stable nucleus. One can think of moving up and/or to the right across the table of nuclides by adding one type of nucleon to a given nucleus. However, adding nucleons one at a time to a given nucleus will eventually lead to a newly formed nucleus that immediately decays by emitting a proton (or neutron). Colloquially speaking, the nucleon has 'leaked' or 'dripped' out of the nucleus, hence giving rise to the term 'drip line'. Drip lines are defined for protons and neutrons at the extreme of the proton-to-neutron ratio; at p:n ratios at or beyond the drip lines, no bound nuclei can exist. While the location of the proton drip line is well known for many elements, the location of the neutron drip line is only known for elements up to neon. Nuclear stability is limited to those combinations of protons and neutrons described by the chart of the nuclides, also called the valley of stability. The boundaries of this valley are the neutron drip line on the neutron rich side, and the proton drip line on the proton-rich side. These limits exist because of particle decay, whereby an exothermic nuclear transition can occur by the emission of one or more nucleons (not to be confused with particle decay in particle physics). As such, the drip line may be defined as the boundary beyond which proton or neutron separation energy becomes negative, favoring the emission of a particle from a newly formed unbound system. 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 12C, the most common isotope of carbon, can undergo proton emission to 11B, 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 Sp 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 10−22 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. The energy of a nucleon in a nucleus is its rest mass energy minus a binding energy. In addition to this, there is an energy due to degeneracy: for instance, a nucleon with energy E1 will be forced to a higher energy E2 if all the lower energy states are filled. This is because nucleons are fermions and obey Fermi–Dirac statistics. The work done in putting this nucleon to a higher energy level results in a pressure, which is the degeneracy pressure. When the effective binding energy, or Fermi energy, reaches zero, adding a nucleon of the same isospin to the nucleus is not possible, as the new nucleon would have a negative effective binding energy — i.e. it is more energetically favourable (system will have lowest overall energy) for the nucleon to be created outside the nucleus. This defines the particle drip point for that species. In many cases, nuclides along the drip lines are not contiguous, but rather are separated by so-called one-particle and two-particle drip lines. This is a consequence of even and odd nucleon numbers affecting binding energy, as nuclides with even numbers of nucleons generally have a higher binding energy, and hence greater stability, than adjacent odd nuclei. These energy differences result in the one-particle drip line in an odd-Z or odd-N nuclide, for which prompt proton or neutron emission is energetically favorable in that nuclide and all other odd nuclides further outside the drip line. However, the next even nuclide outside the one-particle drip line may still be particle stable if its two-particle separation energy is non-negative. This is possible because the two-particle separation energy is always greater than the one-particle separation energy, and a transition to a less stable odd nuclide is energetically forbidden. The two-particle drip line is thus defined where the two-particle separation energy becomes negative, and denotes the outermost boundary for particle stability of a species. The one- and two-neutron drip lines have been experimentally determined up to neon, though unbound odd-N isotopes are known or deduced through non-observance for every element up to magnesium. For example, the last bound odd-N fluorine isotope is 26F, though the last bound even-N isotope is 31F.