Neutron excess

Structures of this sort, with a mantle of helions and a core of neutrons, have minimum Coulomb energy. We may expect these structures to have the minimum neutron excess compatible with stability any more protons would be forced from the mantle into the core. In fact, 44RuB2 has the largest atomic number for which N — Z equals 8 for a stable isotope. 

Atoms which are deficient in neutrons tend to decay via positron-emission, whereas those which have a neutron excess decay via -emission. 

Hainebach KL, Clayton DD, Arnett WD, Woosley SE (1974) On the e-process. Its components and their neutron excesses. Astrophys J 193 157-168... 

The most tightly bound nuclei, i.e. the most stable and robust, in the iron peak are not symmetric arrangements bringing together equal numbers of protons and neutrons (N = Z). Rather, they possess a neutron excess (N — Z) between 2 and 4. Close to iron, the most stable nucleus Fe has a number of neutrons which exceeds the number of protons by 4 units N — Z = 4). 

Neutron excess is the difference between the number of neutrons and the number of protons in an atomic nucleus. This is found by subtracting the atomic number of that nuclide from the neutron number or by subtracting twice the atomic number from the mass number. 

It was relatively recently that heavy cluster emission was observed at a level enormously lower than these estimates. Even so, an additional twist in the process was discovered when the radiation from a 223Ra source was measured directly in a silicon surface barrier telescope. The emission of 14C was observed at the rate of 10-9 times the a-emission rate, and 12C was not observed. Thus, the very large neutron excess of the heavy elements favors the emission of neutron-rich light products. The fact that the emission probability is so much smaller than the simple barrier penetration estimate can be attributed to the very small probability... 

As a final point in the introduction, it is interesting to note that the analogous process of positron capture by neutron excessive nuclei should be possible in principle. However, such captures are hindered by two important facts First, the number of positrons available for capture is vanishingly small in nature, and second, both the nucleus and the positron are positively charged and will repel one another. Compare this to the situation for electron capture in which the nucleus is surrounded by (negative) electrons that are attracted to the nucleus, of course, and the most probable position to find any s electrons is at the nucleus (r = 0). 

The equivalence between Sk, the infinite Farey tree structure and the nuclide mapping is shown graphically in Figure 8.4. The stability of a nuclide depends on its neutron imbalance which is defined, either by the ratio Z/N or the relative neutron excess, (N — Z) jZ. When these factors are in balance, Z2 + NZ — N2 = 0, with the solution Z = N(—1 /5)/2 = tN. The minimum (Z/N) = r and hence all stable nuclides are mapped by fractions larger than the golden mean. 

Because the range of nuclidic stability is bounded by fractions that derive from Fibonacci numbers, it probably means that nuclear stability relates directly to the golden mean. To demonstrate this relationship it is noted that the plot of A vs Z, shown in figure 13 for the A(mod4) = 0 series of nuclides, separates into linear sections of constant neutron excess (A — 2Z) and slope 2. Each section terminates at both ends in a radioactive nuclide. The range of stability for each section follows directly from... 

Figure 2.14 Nuclides have a limited range of stability for each value of neutron excess, A-2Z. The maximum Z of these ranges plotted against A-2Z define the right arm of the parabola shown in the diagram. The left arm of the parabola is obtained by plotting minimum Z as negative integers. The curve is described by the equation x2 — 2rx — 4r2n = 0, i.e. x = r(l vT+4n)...

By comparison of the number of protons P and the number of neutrons N in stable nuclei, it is found that for light elements (small Z)N x P. With increasing atomic number Z, however, an increasing excess of neutrons is necessary in order to give stable nuclei. Z - 2Z is a measure of the neutron excess. For He the neutron excess is zero. It is 3 for " Sc, 11 for 25 for La, and 43 for ° Bi. Thus, if in the chart of the nuclides the stable nuclides are connected by a mean line, which starts from the origin with a slope of 1 and is bent smoothly towards the abscissa. This mean line is called the line of f stability (Fig. 2.3). 

Figure 5.15. Neutron excess of the fission products due to the neutron excess of heavy nuclei.

Fission of heavy nuclei always results in a high neutron excess of the hssion products, because the neutron-to-proton ratio in heavy nuclides is much larger than in stable nuclides of about half the atomic number, as already explained for spontaneous hssion (Fig. 5.15). The primary fission products formed in about 10 " s by fission and emission of prompt neutrons and y rays decay by a series of successive / transmutations into isobars of increasing atomic number Z. The final products of these decay chains are stable nuclides. 

The aforementioned requirements on neutron concentration and temperature suffice to fix qualitatively several of the main features of the nuclear flow associated with the r-process and to identify the involved nuclear physics. Figure 22 depicts the situation very schematically. In the course of the transformation of a given seed into more neutron-rich isotopes by a series of (n,y) reactions, (y,n) photodisintegrations have a rate increasing with the neutron excess or, equivalently, with the associated decrease of the neutron separation energy Sn. For low enough Sn, the (y,n) reactions counteract efficiently the radiative neutron captures. At this point, the nuclear flow may proceed to... 

The close-packed-spheron theory of nuclear structure and the neutron excess for stable nuclei. Revue Roumain de Physique 11(9,10) (1966) 825—833. 

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