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Innuclear physics, properties of anucleus depend onevenness or oddness of itsatomic number (proton number)Z,neutron numberN and, consequently, of their sum, themass numberA. Most importantly, oddness of bothZ andN tends to lower thenuclear binding energy, making odd nuclei generally less stable. This effect is not only experimentally observed, but is included in thesemi-empirical mass formula and explained by some othernuclear models, such as thenuclear shell model. This difference of nuclear binding energy between neighbouring nuclei, especially of odd-Aisobars, has important consequences forbeta decay.

Thenuclear spin is zero for even-Z, even-N nuclei, integer for all even-A nuclei, and odd half-integer for all odd-A nuclei.

Theneutron–proton ratio is not the only factor affecting nuclear stability. Adding neutrons to isotopes can vary their nuclear spins and nuclear shapes, causing differences inneutron capturecross sections andgamma spectroscopy andnuclear magnetic resonance properties. If too many or too few neutrons are present with regard to thenuclear binding energy optimum, the nucleus becomes unstable and subject to certain types ofnuclear decay. Unstable nuclides with a nonoptimal number of neutrons or protons decay bybeta decay (including positron decay),electron capture, or other means, such asspontaneous fission andcluster decay.

Even-mass-number nuclides, which comprise 150/251 = ~60% of all stable nuclides, arebosons, i.e., they have integerspin. 145 of the 150 are even-proton, even-neutron (EE) nuclides, which necessarily have spin 0 because of pairing. The remainder of the stable bosonic nuclides are five odd-proton, odd-neutron stable nuclides (²
₁H,⁶
₃Li,¹⁰
₅B,¹⁴
₇N and^180m
₇₃Ta), all having a non-zero integer spin.

Beta decay of aneven–even nucleus produces an odd–odd nucleus, and vice versa. An even number of protons or of neutrons are more stable (higherbinding energy) because ofpairing effects, so even–even nuclei are much more stable than odd–odd. One effect is that there are few stable odd–odd nuclides, but another effect is to prevent beta decay of many even–even nuclei into another even–even nucleus of the same mass number but lower energy, because decay proceeding one step at a time would have to pass through an odd–odd nucleus of higher energy.Double beta decay directly from even–even to even–even skipping over an odd–odd nuclide is only occasionally possible, and even then with ahalf-life more than a billion times theage of the universe. For example, the double beta emitter¹¹⁶
Cd has a half-life of2.9×10¹⁹ years. This makes for a larger number of stable even–even nuclides, withsome mass numbers having two stable nuclides, and some elements (atomic numbers) having as many asseven.

For example, the extreme stability of helium-4 due to a double pairing of two protons and two neutrons prevents any nuclides containing five or eight nucleons from existing for long enough to serve as platforms for the buildup of heavier elements vianuclear fusion inBig Bang nucleosynthesis; only in stars is there enough time for this (seetriple-alpha process). This is also the reason why⁸
₄Be decays so quickly into twoalpha particles, makingberyllium the only even-numbered element that ismonoisotopic.

There are 145 stable even–even nuclides, forming ~58% of the 251 stable nuclides. There are also 22 primordial long-lived even–even nuclides. As a result, many of the 41 even-numbered elements from 2 to 82 havemany primordial isotopes. Half of these even-numbered elements have six or more stable isotopes. The lightest stable even-even isotope is⁴
₂He and the heaviest is²⁰⁸
₈₂Pb. These are also the lightest and heaviest knowndoubly magic nuclides.^[1]208
₈₂Pb is the final decay product of²³²
₉₀Th,^[2] a primordial radionuclide with an even proton and neutron number.²³⁸
₉₂U is another notable primordial radionuclide with a half-life of 4.468 billion years,^[3] and produces almost half of all radioactive heat within the Earth.^[4]

All even–even nuclides havespin 0 in their ground state, due to thePauli exclusion principle (SeePairing Effects for more details).

Only five stable nuclides contain both an odd number of protons and an odd number of neutrons. The first four "odd–odd" nuclides occur in low mass nuclides, for which changing a proton to a neutron or vice versa would lead to a very lopsided proton–neutron ratio (²
₁H,⁶
₃Li,¹⁰
₅B, and¹⁴
₇N; spins 1, 1, 3, 1). All four of these isotopes have the same number of protons and neutrons, and they all have an odd number for theirnuclear spin. The only other observationally stable odd–odd nuclide is^180m
₇₃Ta (spin 9), the only primordialnuclear isomer, which has not yet been observed to decay despite experimental attempts.^[5] Also, four long-lived radioactive odd–odd nuclides (⁴⁰
₁₉K – the most common radioisotope in the human body,^[6][7]50
₂₃V,¹³⁸
₅₇La,¹⁷⁶
₇₁Lu with spins 4, 6, 5, 7, respectively) occur naturally. As in the case of^180m
₇₃Ta decay of high spin nuclides bybeta decay (includingelectron capture),gamma decay, orinternal conversion is greatly inhibited if the only decay possible betweenisobar nuclides (or in the case of^180m
₇₃Ta between nuclear isomers of the same nuclide) involves high multiples of a change in spin of 1 unit, the "preferred" change of spin that is associated with rapid decay. This high-spin inhibition of decay is the cause of the five heavy stable or long-lived odd-proton, odd-neutron nuclides discussed above. For an example of this effect where the spin effect is subtracted, tantalum-180, the odd–odd low-spin (theoretical) decay product of primordial tantalum-180m, itself has a half life of only about eleven hours.^[8]

Many odd–odd radionuclides (like tantalum-180) with comparatively short half-lives are known. These almost always decay by positive or negative beta decay, in order to produce stable even–even isotopes which have paired protons and paired neutrons. In some odd–odd radionuclides where the ratio of protons to neutrons is neither too large nor too small (i.e., falling too far from the ratio of maximal stability), this decay can proceed in either direction, turning a proton into a neutron, or vice versa. An example is⁶⁴
₂₉Cu, which can decay either by positron emission to⁶⁴
₂₈Ni, or by electron emission to⁶⁴
₃₀Zn.

Of the nine primordial odd–odd nuclides (five stable and four radioactive with long half-lives), only¹⁴
₇N is the most common isotope of a common element. This is because proton capture on¹⁴
₇N is the rate-limiting step of theCNO-I cycle.⁶
₃Li and¹⁰
₅B are minority isotopes of elements that are themselves rare compared to other light elements, while the other six isotopes make up only a tiny percentage of the natural abundance of their elements. For example,^180m
₇₃Ta is thought to be the rarest of the 251stable nuclides.

No primordial (i.e., stable or nearly stable) odd–odd nuclide has spin 0 in the ground state. This is because the single unpaired neutron and unpaired proton have a largernuclear force attraction to each other if their spins are aligned (producing a total spin of at least 1 unit), instead of anti-aligned. Seedeuterium for the simplest case of this nuclear behavior.

For a given odd mass number, there is exactly onebeta-stable nuclide. There is not a difference in binding energy between even–odd and odd–even comparable to that between even–even and odd–odd, leaving other nuclides of the same mass number (isobars) free tobeta decay toward the lowest-mass nuclide. For mass numbers of 147, 151, and 209+, the beta-stable isobar of that mass number has been observed to undergoalpha decay. (In theory, mass number 143 to 155, 160 to 162, and 165+ can also alpha decay.) This gives a total of 101 stable nuclides with odd mass numbers. There are another nine radioactive primordial nuclides (which by definition all have relatively long half lives, greater than 80 million years) with odd mass numbers.

Odd-mass-number nuclides arefermions, i.e., havehalf-integerspin. Generally speaking, since odd-mass-number nuclides always have an even number of either neutrons or protons, the even-numbered particles usually form part of a "core" in the nucleus with a spin of zero. The unpaired nucleon with the odd number (whether proton or neutron) is then responsible for the nuclear spin, which is the sum of the orbital angular momentum and spin angular momentum of the remaining nucleon.

The odd-mass number stable nuclides are divided (roughly evenly) into odd-proton–even-neutron, and odd-neutron–even-proton nuclides, which are more thoroughly discussed below.

These 48 stable nuclides, stabilized by their even numbers of paired neutrons, form most of the stable isotopes of the odd-numbered elements; the very few odd–odd nuclides comprise the others. There are 41 odd-numbered elements withZ = 1 through 81, of which 30 (including hydrogen, sincezero is an even number) have one stable odd-even isotope, the elementstechnetium (
₄₃Tc) andpromethium (
₆₁Pm) have no stable isotopes, and nine elements:chlorine (
₁₇Cl),potassium (
₁₉K),copper (
₂₉Cu),gallium (
₃₁Ga),bromine (
₃₅Br),silver (
₄₇Ag),antimony (
₅₁Sb),iridium (
₇₇Ir), andthallium (
₈₁Tl), have two odd–even stable isotopes each. This makes a total of 30×1 + 9×2 = 48 stable odd–even isotopes. The lightest example of this type of nuclide is¹
₁H (protium) while the heaviest example is²⁰⁵
₈₁Tl. There are also five primordial long-lived radioactive odd–even isotopes,⁸⁷
₃₇Rb,^[9]115
₄₉In,^[10][11]187
₇₅Re,^[12]151
₆₃Eu,^[13][14] and²⁰⁹
₈₃Bi.^[15][16] The last two were only recently found to undergo alpha decay, with half-lives greater than 10¹⁸ years.

These 53 stable nuclides have an even number of protons and an odd number of neutrons. By definition, they are all isotopes of even-Z elements, where they are a minority in comparison to the even–even isotopes which are about 3 times as numerous. Among the 41 even-Z elements that have a stable nuclide, only two elements (argon and cerium) have no even–odd stable nuclides. One element (tin) has three. There are 24 elements that have one even–odd nuclide and 13 that have two even–odd nuclides. The lightest example of this type of nuclide is³
₂He and the heaviest is²⁰⁷
₈₂Pb.

Of 34 primordial radionuclides there exist three even–odd nuclides (see table at right), including thefissile²³⁵
₉₂U. Because of their odd neutron numbers, the even–odd nuclides tend to have largeneutron capture cross sections, due to the energy that results from neutron-pairing effects.

These stable even-proton odd-neutron nuclides tend to be uncommon by abundance in nature, generally because in order to form and contribute to the primordial abundance, they must have escaped capturing neutrons to form yet other stable even–even isotopes, during both thes-process andr-process of neutron capture, during nucleosynthesis in stars. For this reason, only¹⁹⁵
₇₈Pt and⁹
₄Be are the most naturally abundant isotopes of their element, the former only by a small margin, and the latter only because the expectedberyllium-8 has lowerbinding energy than twoalpha particles and therefore immediatelyalpha decays.

Actinides with odd neutron numbers are generallyfissile (withthermal neutrons), while those with even neutron numbers are generally not, though they arefissionable withfast neutrons.Only⁹
₄Be,¹⁴
₇N, and¹⁹⁵
₇₈Pt have an odd neutron number and are the most naturally abundant isotopes of their element.

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