Neutron-drip line

From time to time, a -decay occurs, increasing Z by 1 unit this leads to an increase in Q (corresponding to the increased distance above the neutron drip line) and consequently to further neutron captures until Q is again reduced to the appropriate value and a further fi-decay occurs. At the magic numbers, this leads to a vertical zig-zag track, paralleling the rise in the neutron drip line. Along this track,... 

Fowler Clayton 1965). The dotted curve shows a possible location of the neutron drip line after Uno, Tachibana and Yamada (1992). Adapted from Rolfs and Rodney (1988). 

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...

The nuclear physics for the r-process. This has been reviewed in some detail by [24], and is not dealt with in these lectures. Let us just say that much effort has been put recently in the development of microscopic nuclear models aiming at reliable predictions of nuclear ground-state properties of thousands of nuclides located between the valley of nuclear stability and the neutron-drip line that may be involved in the r-process. Besides some remarkable achievements in the field, clearly much remains to be done. 

At extreme NIZ ratios beyond the so called neutron drip-line, or for highly excited nuclei, neutron emission is an alternative to decay. 

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... 

Fig. 1 The calculated microscopic corrections to liquid-drop masses [24, 56-59] for the heavy elements, showing a prediction of the location of the Island of Stability, centered at Contours are labeled in MeV. The neutron-drip line is indicated, as are the pathways to the heavy elements followed by the stellar and thermonuclear r-ptoeesses. The compound nuclei produced in representative heavy-ion reactions are also shown, eonneeted to the target nuclide by a dotted line...

When not constrained to the stable nuclei, beams of particles with neutron numbers out to the neutron-drip line can be considered as possible reactants. Though the lack of suitable accelerator facilities makes this a hypothetical exercise, there are practical concerns governing production of the radioactive species for acceleration as the secondary beam. Continuous production of large quantities of these nuclides is required for the generation of a radioactive beam that is sufficiently intense for a superheavy element synthesis experiment. This limits our discussions to radioactive species close to the line of stability, because of both primary production rate and half-life. To confine the following discussion, only radioactive ions within four mass numbers of the heaviest stable isotope of each element will be considered as projectiles unless there is a stable isotope of a nearby element at higher neutron number (e.g., " Ar, at the same neutron number as Ca). 

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. 

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. 

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. 

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...

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... 

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