Proton drip line

For very neutron-deficient (i.e., proton-rich) nuclei, the Q value for proton emission, Qp, becomes positive. One estimate, based on the semiempirical mass equation, of the line that describes the locus of the nuclei where Qp becomes positive for ground-state decay is shown in Figure 7.11. This line is known as the proton-drip line. Our ability to know the position of this line is a measure of our ability to describe the forces holding nuclei together. Nuclei to the left of the proton dripline in Figure 7.11 can decay by proton emission. 

As the temperature and density continue to increase, the 0(a,y) Ne and 0(a,p) F reactions lead to break out from the CNO cycle to a process of rapid proton capture (rp-process) which involves sequential proton captures out to the proton drip line or until the Coulomb barrier becomes too large. Each of these transitions to higher-temperature reactions lead to orders-of-magnitude increases in the rates of energy production. Thus, in addition to effects on nucleosynthesis, the dynamics of the various high temperature environments are intimately coupled to the cross sections for proton and alpha-particle capture reactions on unstable nuclei. In a few cases [WAL81] even the question of whether the next proton or aphha capture leads to a bound nuclear state can have a dramatic effect on the evolution of the environment. 

The details of the nuclear physics for the p-process have been discussed by [32], and are not reviewed here. Static properties have to be known for a large variety of neutron-deficient nuclei from about iron to lead located between the valley of nuclear stability and the vicinity of the proton-drip line, As made clear in Fig. 32, nucleon and a-par tide capture rates by these nuclei are needed as well. Free electron captures may also be requested. 

A thermonuclear runaway develops near the base of the He envelope. The associated outward-moving detonation wave heats the matter to temperatures around 3 x 10 K, and leads to the ejection of about 0.2 M0 into the interstellar medium. The associated nucleosynthesis is especially complex, and is reviewed in detail by [32]. The situation may be summarized by saying that a quite high neutron density builds up at the beginning of the detonation, and leads to a weak r-process. Subsequently, the nuclear flow is pushed back to the valley of nuclear stability, and eventually into the neutron-deficient region, by photodisintegrations that become more and more efficient as temperature rises. A process coined pn-process by [87] then develops. The associated flow is displayed in Fig. 36. Its main path lies much further away from the proton-drip line than in the classical rp-process, which eases somewhat the nuclear physics problems. This results from the lower proton concentration... 

Brown, B.A. 1991. Diproton decay of nnclei on the proton drip line. Physical Review, C43 R1513-R1517. 

Ormand, W.E. 1996. Properties of proton drip-line nuclei at the sd-fp-shell interface. Physical Review, C53 214. 

The study of proton emission may offer very important information on the nuclear structure near the proton drip line. Spectroscopic factors can be derived, providing information on the configurations of the initial and final states. In contrast to a-decay, the formation probability of a proton need not be calculated. The decay constant (A,) is determined mainly by the penetration probability through the potential barrier and the structure of states. 

Decay properties of transuranium nuclides lead to the understanding of proton excess heavy nuclei verification of the proton drip line, nuclear structure of large deformed nuclei such as octupole and hexadecapole deformation, and fission barrier heights. There are several textbooks and review articles on nuclear decay properties of transuranium nuclei (e.g., Hyde et al. 1964 Seaborg and Loveland 1985 Poenaru 1996). Theoretical nuclear models of heavy nuclei are presented by Rasmussen (1975) and the nuclear structure with a deformed single-particle model is discussed by Chasman et al. (1977). Radioactive decay properties of transuranium nuclei are tabulated in the Table of Isotopes (Firestone and Shirley 1996). Recent nuclear and decay properties of nuclei in their ground and isomeric states are compiled and evaluated by Audi et al. (1997), while the calculated atomic mass excess and nuclear ground-state deformations are tabulated by MoUer et al. (1995). 

One of the most basic questions in nuclear astrophysics is How do the nuclei heavier than iron get produced This question was first answered by Burbidge, Burbidge, Fowler and Hoyle in 1957 [35]. They proposed that these elements are produced through the slow (s) and rapid (r) neutron-capture processes. The words rapid/slow refer to the rate of neutron capture compared to the rate of /3-decay in the astrophysical conditions. Figure 13 shows the nuclei involved in the r- and s-processes. The s-process path stays close to the valley of stability whereas the r-process path moves staying close to the drip line. The figure also shows the nuclei involved in the rp-process these are proton rich nuclei where capture of protons are involved and that the rate is compared to the / + rates. 

Fig. 33. Location in the (N, Z)-plane of the stable isotopes of the elements between Fe and Bi. The p-isotopes are represented by black squares, while both the s-, r-, sr- or sp-isotopes are identified with open squares (see Figs. 13 - 15 for details). The p-nuclides are the progeny of unstable neutron-deficient isobars located on the down-streaming p-process flow (thick black line for more details on the p-process flow, see [32]). Some possible r-process flows derived from a high-temperature parametric model (Sect. 7) are also shown, as well as the up-streaming s-process flow (thin black line) confined at the bottom of the valley of nuclear stability. The proton and neutron drip lines correspond to the locations of zero proton and neutron separation energies...

Fig. 36. Snapshots in the nuclidic chart of flow patterns in a ID model of a detonating He layer accreted onto a 0.8M WD. The selected times and corresponding temperatures or densities are given in different panels. The stable nuclides are indicated with open squares. The magic neutron and proton numbers are identified by vertical and horizontal double lines. The drip lines predicted by a microscopic mass model are also shown. The abundances are coded following the grey scales shown in each panel. At early times (bottom left panel), an r-process type of flow appears on the neutron-rich side of the valley of nuclear stability. At somewhat later times (top left panel), the material is pushed back to the neutron-deficient side rather close to the valley of /3-stability. As time passes (two right panels), a pn-process [87] develops...

Moller et al. (1995) calculated the atomic mass excess and nuclear ground-state deformation for 8,979 nuclei from to A = 339 between the proton and neutron drip lines (see O Fig. 2.7). The calculations with the finite-range droplet model (FRDM) contain 16 mass-like and 22 other parameters. In the framework of FRDM it is possible to calculate a large number of nuclear structure properties in addition to the ground-state masses, such as even multipole ground-state deformations (s2, 4, 65), 3-decay properties, pairing quantities, odd-particle spins, Qt-decay properties, octupole properties ( 3), etc. 

Chart of the nuclides. Black squares show stable nuclides as a function of atomic number Z and neutron number N. Sp zero and Sn zero curves indicate proton and neutron drip lines, respectively, which can be predicted, e.g., from different mass formulae. The 6/rcurves show limits, where the potential barrier disappears for fission. Grey regions indicate the domain of known nuclides. Magic numbers are shown by horizontal and vertical lines... 

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