Even and odd atomic nuclei

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

The neutron–proton ratio is not the only factor affecting nuclear stability. Adding neutrons to isotopes can vary their nuclear spins and nuclear shapes, causing differences in neutron capture cross sections and gamma spectroscopy and nuclear magnetic resonance properties. If too many or too few neutrons are present with regard to the nuclear binding energy optimum, the nucleus becomes unstable and subject to certain types of nuclear decay. Unstable nuclides with a nonoptimal number of neutrons or protons decay by beta decay (including positron decay), electron capture, or other means, such as spontaneous fission and cluster decay.

Data on specific nuclides below is from NUBASE2020 unless otherwise stated. See also List of nuclides for a complete enumeration.

Even mass number

Even-mass-number nuclides, which comprise 150/251 = ~60% of all stable nuclides, are bosons, i.e., they have integer spins. 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.

Pairing effects

Beta decay of an even–even nucleus produces an odd–odd nucleus, and vice versa. An even number of protons or of neutrons are more stable (higher binding energy) because of pairing 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 a half-life more than a billion times the age of the universe. For example, the double beta emitter ¹¹⁶
Cd has a half-life of 2.69×10¹⁹ years. This makes for a larger number of stable even–even nuclides, with some mass numbers having two stable nuclides, and one element (atomic number), tin, having as many as seven.

For example, the extreme stability of helium-4 due to the double pairing (two protons, two neutrons, filling the lowest shell) prevents any nuclides containing five or eight nucleons from existing for long enough to serve as platforms for the buildup of heavier elements via nuclear fusion in Big Bang nucleosynthesis; only in stars is there enough time for this (see triple-alpha process). This is also the reason why ⁸
₄Be decays so quickly into two alpha particles, making beryllium the only even-numbered element that is monoisotopic.

Even–even (even proton, even neutron)

There are 145 stable even–even nuclides, forming ~58% of the 251 stable nuclides. There are also 23 primordial even–even nuclides currently known to be radioactive. As a result, many of the 41 even-numbered elements from 2 to 82 have many primordial isotopes. With 145 isotopes, they average 145/41 ~ 3.54 stable isotopes each. The lightest stable even–even isotope is ⁴
₂He and the heaviest is ²⁰⁸
₈₂Pb. These are also the lightest and heaviest known doubly magic nuclides. ²⁰⁸
₈₂Pb is the final decay product of ²³²
₉₀Th, a primordial radionuclide with an even proton and neutron number. ²³⁸
₉₂U is another such primordial radionuclide with a half-life of 4.463 billion years; these two, with their decay products, each produce nearly half the radioactive heat within the Earth.

All even–even nuclides have spin 0 in their ground state, due to the Pauli exclusion principle. (See the pairing effect for more details.)

Odd–odd (odd proton, odd neutron)

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 light elements, 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, and ¹⁴
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 their nuclear spin. The only other observationally stable odd–odd nuclide is ^180m
₇₃Ta (spin 9), the only primordial nuclear isomer, which has not yet been observed to decay despite experimental attempts. Also, four long-lived radioactive odd–odd nuclides – ⁴⁰
₁₉K (the most common radioisotope in the human body), ⁵⁰
₂₃V, ¹³⁸
₅₇La, and ¹⁷⁶
₇₁Lu with spins 4, 6, 5, 7, respectively – occur naturally. As in the case of ^180m
₇₃Ta decay of high spin nuclides by beta decay (including electron capture), gamma decay, or (to a lesser extent) internal conversion is greatly inhibited if the only decay possible between isobar nuclides (or in the case of ^180m
₇₃Ta between nuclear isomers) involves a large change in spin, the "preferred" change of spin that is associated with rapid decay being 0 or 1 for beta decay and also 2 for gamma 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 8.15 hours.

Many odd–odd radionuclides (like the ground state of 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 near the line of stability, this decay can proceed in either direction, turning a proton into a neutron, or vice versa. An example is ⁶⁴
₂₉Cu, which can decay by positron emission or electron capture to ⁶⁴
₂₈Ni or by electron emission to ⁶⁴
₃₀Zn.

Of the nine primordial odd–odd nuclides (five stable and four radioactive), only ¹⁴
₇N is the most common isotope of a common element. This is because proton capture on ¹⁴
₇N is the rate-limiting step of the CNO-I cycle. ⁶
₃Li and ¹⁰
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 all the stable nuclides.

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