Of the three types of naturally occurring
radioactivities (α, β, and γ), only
alpha decay is a type of decay resulting from the
nuclear strong force. The other proton and neutron decays occurred much earlier in the life of the atomic species and before the earth was formed. Thus, alpha decay can be considered either a form of particle decay or, less frequently, as a special case of
nuclear fission. The timescale for the
nuclear strong force is much faster than that of the
nuclear weak force or the
electromagnetic force, so the lifetime of nuclei past the drip lines are typically on the order of nanoseconds or less. For alpha decay, the timescale can be much longer than for proton or neutron emission owing to the high Coulomb barrier seen by an alpha-cluster in a nucleus (the alpha particle must
tunnel through the barrier). As a consequence, there are no naturally occurring nuclei on Earth that undergo proton or
neutron emission; however, such nuclei can be created, for example, in the laboratory with
accelerators or naturally in
stars. The
Facility for Rare Isotope Beams (FRIB) at
Michigan State University came online in mid-2022 and has created many novel radioisotopes, each of which is extracted in a beam and used for study. FRIB runs a beam of relatively stable isotopes through a medium, which disrupts the nuclei and creates numerous novel nuclei, which are then extracted.
Nucleosynthesis Explosive astrophysical environments often have very large
fluxes of high-energy nucleons that can be captured on
seed nuclei. In these environments, radiative proton or
neutron capture will occur much faster than beta decays, and as astrophysical environments with both large neutron fluxes and high-energy protons are unknown at present, the reaction flow will proceed away from beta-stability towards or up to either the neutron or proton drip lines, respectively. However, once a nucleus reaches a drip line, as we have seen, no more nucleons of that species can be added to the particular nucleus, and the nucleus must first undergo a beta decay before further nucleon captures can occur.
Photodisintegration While the drip lines impose the ultimate boundaries for nucleosynthesis, in high-energy environments the burning pathway may be limited before the drip lines are reached by
photodisintegration, where a high-energy gamma ray knocks a nucleon out of a nucleus. The same nucleus is subject both to a flux of nucleons and photons, so an equilibrium between neutron capture and photodisintegration is reached for nuclides with a sufficiently low neutron separation energy, particularly those near waiting points. As the photon bath will typically be described by a
Planckian distribution, higher energy photons will be less abundant, and so photodisintegration will not become significant until the nucleon separation energy begins to approach zero towards the drip lines, where photodisintegration may be induced by lower energy gamma rays. At kelvin, the photon distribution is energetic enough to knock nucleons out of any nuclei that have particle separation energies less than 3 MeV, but to know which nuclei exist in what abundances one must also consider the competing radiative captures. As
neutron captures can proceed in any energy regime, neutron photodisintegration is unimportant except at higher energies. However, as proton captures are inhibited by the Coulomb barrier, the cross sections for those charged-particle reactions at lower energies are greatly suppressed, and in the higher energy regimes where proton captures have a large probability to occur, there is often a competition between the proton capture and the photodisintegration that occurs in explosive hydrogen burning; but because the proton drip line is relatively much closer to the valley of beta-stability than is the neutron drip line, nucleosynthesis in some environments may proceed as far as either nucleon drip line.
Waiting points and time scales Once radiative capture can no longer proceed on a given nucleus, either from photodisintegration or the drip lines, further nuclear processing to higher mass must either bypass this nucleus by undergoing a reaction with a heavier nucleus such as 4He, or more often wait for the beta decay. Nuclear species where a significant fraction of the mass builds up during a particular nucleosynthesis episode are considered nuclear waiting points, since further processing by fast radiative captures is delayed. As has been emphasized, the beta decays are the slowest processes occurring in explosive nucleosynthesis. From the nuclear physics side, explosive nucleosynthesis time scales are set simply by summing the beta decay half-lives involved, since the time scale for other nuclear processes is negligible in comparison, although practically speaking this time scale is typically dominated by the sum of a handful of waiting point nuclear half lives.
The r-process The
rapid neutron capture process is believed to operate very close to the neutron drip line, though the astrophysical site of the r-process, while widely believed to take place in
core-collapse supernovae, is unknown. While the neutron drip line is very poorly determined experimentally, and the exact reaction flow is not precisely known, various models predict that nuclei along the r-process path have a two-neutron separation energy (
S2n) of approximately 2 MeV. Beyond this point, stability is thought to rapidly decrease in the vicinity of the drip line, with beta decay occurring before further neutron capture. In fact, the nuclear physics of extremely neutron-rich matter is a fairly new subject, and already has led to the discovery of the
island of inversion and
halo nuclei such as 11Li, which has a very diffuse neutron skin leading to a total radius comparable to that of 208Pb. Thus, although the neutron drip line and the r-process are linked very closely in research, it is an unknown frontier awaiting future research, both from theory and experiment.
The rp-process The
rapid proton capture process in
X-ray bursts runs at the proton drip line except near some photodisintegration waiting points. This includes the nuclei 21Mg, 30S, 34Ar, 38Ca, 56Ni, 60Zn, 64Ge, 68Se, 72Kr, 76Sr, and 80Zr. One clear nuclear structure pattern that emerges is the importance of
pairing, as one notices all the waiting points above are at nuclei with an even number of protons, and all but 21Mg also have an even number of neutrons. However, the waiting points will depend on the assumptions of the X-ray burst model, such as
metallicity, accretion rate, and the hydrodynamics, along with the nuclear uncertainties, and as mentioned above, the exact definition of the waiting point may not be consistent from one study to the next. Although there are nuclear uncertainties, compared to other explosive nucleosynthesis processes, the
rp-process is quite well experimentally constrained, as, for example, all the above waiting point nuclei have at the least been observed in the laboratory. Thus as the nuclear physics inputs can be found in the literature or data compilations, the Computational Infrastructure for Nuclear Astrophysics allows one to do post-processing calculations on various X-ray burst models, and define for oneself the criteria for the waiting point, as well as alter any nuclear parameters. While the rp-process in X-ray bursts may have difficulty bypassing the 64Ge waiting point, Photonuclear (γ,p) and (γ,α) reactions prevent any further progress beyond the so-called tin-antimony-tellurium (SnSbTe) cycles. Even before this limit is reached, the proton flux is thought to considerably decrease and thus slow down the
rp-process, and low capture rates mean that the terminating SnSbTe cycle should not usually be reached. However, it has been shown that if there are episodes of cooling or mixing of previous ashes into the burning zone, material as heavy as 126Xe can be created.
Neutron stars In
neutron stars, neutron heavy nuclei are found as relativistic electrons penetrate the nuclei and produce
inverse beta decay, wherein the electron combines with a proton in the nucleus to make a neutron and an electron-neutrino: n + ve -->: As more and more neutrons are created in nuclei the energy levels for neutrons get filled up to an energy level equal to the rest mass of a neutron. At this point any electron penetrating a nucleus will create a neutron, which will "drip" out of the nucleus. At this point we have: : E_\text{F}^n = m_n c^2 \, And from this point onwards the equation : E_\text{F}^n = \sqrt{\left(p_\text{F}^n\right)^2 c^2 + m_n^2 c^4} \, applies, where
pF
n is the
Fermi momentum of the neutron. As we go deeper into the neutron star the free neutron density increases, and as the Fermi momentum increases with increasing density, the
Fermi energy increases, so that energy levels lower than the top level reach neutron drip and more and more neutrons drip out of nuclei so that we get nuclei in a neutron fluid. Eventually all the neutrons drip out of nuclei and we have reached the neutron fluid interior of the neutron star. ==Known values==