Odd-even nuclei

Harkins s rule of the dissymmetry between even-odd nuclei is sometimes referred to as the Oddo-Harkins rule. In 1914 the Italian chemist Guiseppe Oddo suggested that elements with atomic weights a multiple of... 

Note that there is a pattern Nuclei with an even number of protons and neutrons (even-even) have spin zero odd-even and even-odd nuclei tend to be spin-Vi and odd-odd nuclei tend to have a spin greater than 1/2. This is just a rule of thumb (e.g., 170 violates the rule ). Nuclei with spin greater than 1/2 are more difficult to observe than spin-Vi nuclei because they have a nuclear quadrupole moment that makes their NMR peaks very broad. For this reason, most NMR work is focused on the spin-Vi nuclei. Because NMR is usually done in deuterated solvents (D2O, CD3OD, etc.), we will have to occasionally consider the effects of a spin-1 (three quantum states) nucleus. 

P even, N even (even-even nuclei) P even, N odd (even-odd nuclei) P odd, N even (odd-even nuclei) P odd, N odd (odd-odd nuclei)... 

There are approximately 275 different nuclei which have shown no evid ce of radioactive decay and, hence, are said to be stable with respect to radioactive decay. When these nuclei are compared for their constiturat nucleons, we find that approximately 60% of them have both an even number of protons and an evra number of neutrons (even-even nuclei). The remaining 40% are about equally divided between those that have an ev i number of protons and an odd number of neutrons (even-odd nuclei) and those with an odd number of protons and an even number of neutrons (odd-even nuclei). There are only 5 stable nuclei known which have both an odd number of protons and odd number of neutrons (odd-odd nuclei), jH, Li, and 2 - It is significant that the first stable odd-odd nuclei are... 

Fig. 52. Level spacings (Do) as a function of atomic weight, after Levin and Hughes. The full curve corresponds to Bethe s formula (for 7 Mev) the dashed curve is that of Lang and Le Couteur. Full circles odd-odd nuclei open circles, even-odd nuclei open squares, even-even nuclei.

The regular behaviour shown in Fig. 60 is in marked contrast to the energies of the excited states in even-odd nuclei which can take much lower values. In even-even nuclei, as we have seen, low values obtain in the heaviest elements but they vary continuously and systematically from one nucleus to another. Preiswerk and Stahelin noting this difference have pointed out that the levels of even-even nuclei do not show the continuous displacement with mass number... 

A feature of the N2 spectrum is an intensity alternation of 1 3 for the J value of the initial level of the transition even odd. This is an effect due to the nuclear spin of the nuclei, which will now be discussed in some detail. 

Another difference between nucleons and electrons is that nucleons pair whenever possible. Thus, even if a particular energy level can hold more than two particles, two particles will pair when they are present. Thus, for two particles in degenerate levels, we show two particles as II rather than II. As a result of this preference for pairing, nuclei with even numbers of protons and neutrons have all paired particles. This results in nuclei that are more stable than those which have unpaired particles. The least stable nuclei are those in which both the number of neutrons and the number of protons is odd. This difference in stability manifests itself in the number of stable nuclei of each type. Table 1.3 shows the numbers of stable nuclei that occur. The data show that there does not seem to be any appreciable difference in stability when the number of protons or neutrons is even while the other is odd (the even-odd and odd-even cases). The number of nuclides that have odd Z and odd N (so-called odd-odd nuclides) is very small, which indicates that there is an inherent instability in such an arrangement. The most common stable nucleus which is of the odd-odd type is 147N. 

Dr. Hafemeister Most isotopes really can be studied just as well or better by beta decay. I can think of only one that can t—Le, potassium-40. This is a strange case because it is an odd-odd nucleus, and there are only about four odd-odd nuclei that are stable. An odd-odd nucleus means that it decays to the neighboring even-even nuclei, and in this case one cannot populate it by beta decay. However, in most cases one does just as well with beta decay, particularly since using a nuclear reaction for direct population is so expensive. It can be done, so there should be a good reason to spend the money. Radiation damage studies by these techniques are feasible and may well be useful. 

What then of the clouds of nuclei billowing out from the stellar furnace One notable feature is that nature seems to prefer even numbers to odd. Apart from light hydrogen (A = 1), which is indeed a very special case, nature clearly favours the even. Abundances thus feature a marked even-odd imbalance. For those nuclei with fewer than 20 protons, the most abundant isotopes contain the... 

Likewise, even nuclei (with even numbers of protons) have lower probability (cross-section) for neutron capture than odd nuclei, and this results in a greater abundance of the former. The even-odd imbalance is manifested once again. 

Any of the foregoing conditions may be achieved when the nucleus contains an even number of both protons and neutrons, or an even number of one and ail odd number of the oilier. Since Ihere is an excess of neutrons over protons for all but the lowest atomic number elements, in the odd-odd situation there is a deficiency of protons necessary to complete the two-proton-two-neutron quartets. It might be expected that these could be provided by the production of protons via beta decay. However, there exist only four stable nuclei of odd-odd composition, whereas there are 108 such nuclei in the even-odd form and 162 in the even-even series. It will be seen that the order of stability, and presumably the binding energy per nucleon, from greatest to smallest, seems to be even-even, even-odd, odd-odd. 

Figure 2.3 Positions of the stable odd A and even A nuclei in a Segre chart from W. E. Meyerhof, Elements of Nuclear Physics. Copyright 1967 by McGraw-Hill Book Company, Inc. Reprinted by permission of McGraw-Hill Book Company, Inc.

In Figure 2.3, we compare the positions of the known stable nuclides of odd A with those of even A in the chart of the nuclides. Note that as Z increases, the line of stability moves from N = Z to N/Z 1.5 due to the influence of the Coulomb force. For odd A nuclei, only one stable isobar is found while for even A nuclei there are, in general, no stable odd-odd nuclei. This is further demonstrated by the data of Table 2.1 showing the distribution of stable isotopes. 

As another illustrative application of supersymmetry extension to odd-odd nuclei we consider the spectrum of odd-odd 29 33 if one assumes -that the evenreven nucleus odd-even nucleus 29Cu34 ax 3i odd ... 

So far, we have concentrated only on the even-even nucleus. Of course, our model encompass the even-odd as well as odd-odd nuclei as well (by the study of other seniority states). 

Recently Heyde et al. have reviewed the experimental evidence for shape coexistence in odd A nuclei and the theoretical approaches which are made to describe the experimental data [HEY83]. Also in several even mass nuclei there is evidence for shape coexistence. A nice example are the rotational bands on JTT=0+ intruder states in the even mass Sn isotopes [BR079]. 

Figure 1. The systematics of excitation energies for the CT " intruder states in the even Pb nuclei and of the intruder states in the odd-mass T1 and Bi nuclei. For more details, see IC0E85, DUP85a].

In 1917 Harkins found that on the average elements of even atomic number (Z) are about 70 times as abundant in meteorites as those of odd Z he further noted that the first seven elements in the order of their abundance are all even-numbered and make up almost 99% of the material in meteorites. [28] Four years later he elaborated his assumption that the relative abundances of the atomic species of low atomic weight may be used as an index... of their relative stability. He now suggested several more rules, including that atoms with even A (mass number) and an odd number of electrons are extremely rare. [29] These rules were claimed to be valid for isotopes, and not merely elements. In 1931, after more data on the distribution of isotopes had been collected, he reported that even-A nuclei were much more frequent than odd-A nuclei. [30]... 

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