Even and odd atomic nuclei

Last updated March 23, 2024

In nuclear physics, properties of a nucleus depend on evenness or oddness of its atomic number (proton number) Z, neutron number N and, consequently, of their sum, the mass number A. Most importantly, oddness of both Z and N tends to lower the nuclear binding energy, making odd nuclei generally less stable. This effect is not only experimentally observed, but is included in the semi-empirical mass formula and explained by some other nuclear models, such as the nuclear shell model. This difference of nuclear binding energy between neighbouring nuclei, especially of odd-A isobars, has important consequences for beta decay.

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.

Even mass number

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

Even/odd Z, N (Hydrogen-1 included as OE)
p,n	EE	OO	EO	OE	Total
Stable	145	5	53	48	251
Long-lived	22	4	4	5	35
All primordial	167	9	57	53	286

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 greater than a billion times the age of the universe. For example, the double beta emitter ¹¹⁶
Cd has a half-life of 2.9×10¹⁹ years. This makes for a larger number of stable even–even nuclides, with some mass numbers having two stable nuclides, and some elements (atomic numbers) having as many as seven.

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 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 proton, even neutron

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 have many primordial isotopes. Half of these even-numbered elements have six or more stable isotopes. 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.^[1] ²⁰⁸
₈₂Pb is the final decay product of ²³²
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 have spin 0 in their ground state, due to the Pauli exclusion principle (See Pairing Effects for more details).

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 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 , 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.^[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 by beta decay (including electron capture), gamma decay, or internal conversion is greatly inhibited if the only decay possible between isobar 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. Almost invariably, these 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 excessively large nor excessively 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 is ⁶⁴
₂₉Cu , which can decay either by positron emission to ⁶⁴
₂₈Ni , or by electron emission to ⁶⁴
₃₀Zn .

Of the nine primordial odd–odd nuclides (five stable and four radioactive with long half lives), only ¹⁴
₇N is the most common isotope of a common element. This is the case because proton capture on ¹⁴
₇N is the rate-limiting step of the CNO-I cycle. The nuclides 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 the 251 stable nuclides.

None of the primordial (i.e., stable or nearly stable) odd–odd nuclides have 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.

Odd mass number

For a given odd mass number, there is exactly one beta-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 to beta 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 undergo alpha 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 are fermions, i.e., have half-integer spin. 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. In all, 29 of the 110 primordial odd-mass nuclides have spin 1/2, 30 have spin 3/2, 24 have spin 5/2, 17 have spin 7/2, and nine have spin 9/2.^{[ citation needed ]}

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.

Odd proton, even neutron

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 with Z = 1 through 81, of which 30 (including hydrogen, since zero is an even number) have one stable odd-even isotope, the elements technetium (^₄₃Tc) and promethium (^₆₁Pm) have no stable isotopes, and nine elements: chlorine (^₁₇Cl), potassium (^₁₉K), copper (^₂₉Cu), gallium (^₃₁Ga), bromine (^₃₅Br), silver (^₄₇Ag), antimony (^₅₁Sb), iridium (^₇₇Ir), and thallium (^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 is ¹
₁H (protium) as zero is an even number while the heaviest example is ²⁰⁵
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] and ²⁰⁹
₈₃Bi .^[15]^[16] The last two were only recently found to undergo alpha decay, with half-lives greater than 10¹⁸ years.

Even proton, odd neutron

Even–odd long-lived
	Decay	Half-life
¹¹³ ₄₈Cd	beta	7.7×10¹⁵ a
¹⁴⁷ ₆₂Sm	alpha	1.06×10¹¹ a
²³⁵ ₉₂U	alpha	7.04×10⁸ a

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 is ³
₂He and the heaviest is ²⁰⁷
₈₂Pb .

Of 34 primordial radionuclides there exist three even–odd nuclides (see table at right), including the fissile ²³⁵
₉₂U . Because of their odd neutron numbers, the even–odd nuclides tend to have large neutron 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 the s-process and r-process of neutron capture, during nucleosynthesis in stars. For this reason, only ¹⁹⁵
₇₈Pt and ⁹
₄Be are the most naturally abundant isotopes of their element, the former only by a small margin, and the latter only because the expected beryllium-8 has lower binding energy than two alpha particles and therefore immediately alpha decays.

Odd neutron number

Neutron number parity
N	Even	Odd
Stable	193	58
Long-lived	27	8
All primordial	220	66

Actinides with odd neutron numbers are generally fissile (with thermal neutrons), while those with even neutron numbers are generally not, though they are fissionable with fast neutrons. Only ⁹
₄Be , ¹⁴
₇N , and ¹⁹⁵
₇₈Pt have an odd neutron number and are the most naturally abundant isotope of their element.

Related Research Articles

Atoms are the basic particles of the chemical elements. An atom consists of a nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished from each other by the number of protons that are in their atoms. For example, any atom that contains 11 protons is sodium, and any atom that contains 29 protons is copper. Atoms with the same number of protons but a different number of neutrons are called isotopes of the same element.

In nuclear physics, beta decay (β-decay) is a type of radioactive decay in which an atomic nucleus emits a beta particle, transforming into an isobar of that nuclide. For example, beta decay of a neutron transforms it into a proton by the emission of an electron accompanied by an antineutrino; or, conversely a proton is converted into a neutron by the emission of a positron with a neutrino in so-called positron emission. Neither the beta particle nor its associated (anti-)neutrino exist within the nucleus prior to beta decay, but are created in the decay process. By this process, unstable atoms obtain a more stable ratio of protons to neutrons. The probability of a nuclide decaying due to beta and other forms of decay is determined by its nuclear binding energy. The binding energies of all existing nuclides form what is called the nuclear band or valley of stability. For either electron or positron emission to be energetically possible, the energy release or Q value must be positive.

A radionuclide (radioactive nuclide, radioisotope or radioactive isotope) is a nuclide that has excess numbers of either neutrons or protons, giving it excess nuclear energy, and making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transferred to one of its electrons to release it as a conversion electron; or used to create and emit a new particle (alpha particle or beta particle) from the nucleus. During those processes, the radionuclide is said to undergo radioactive decay. These emissions are considered ionizing radiation because they are energetic enough to liberate an electron from another atom. The radioactive decay can produce a stable nuclide or will sometimes produce a new unstable radionuclide which may undergo further decay. Radioactive decay is a random process at the level of single atoms: it is impossible to predict when one particular atom will decay. However, for a collection of atoms of a single nuclide the decay rate, and thus the half-life (t_1/2) for that collection, can be calculated from their measured decay constants. The range of the half-lives of radioactive atoms has no known limits and spans a time range of over 55 orders of magnitude.

Stable nuclides are nuclides that are not radioactive and so do not spontaneously undergo radioactive decay. When such nuclides are referred to in relation to specific elements, they are usually termed stable isotopes.

<span class="mw-page-title-main">Nuclide</span> Atomic species

A nuclide is a class of atoms characterized by their number of protons, Z, their number of neutrons, N, and their nuclear energy state.

<span class="mw-page-title-main">Decay chain</span> Series of radioactive decays

In nuclear science, the decay chain refers to a series of radioactive decays of different radioactive decay products as a sequential series of transformations. It is also known as a "radioactive cascade". The typical radioisotope does not decay directly to a stable state, but rather it decays to another radioisotope. Thus there is usually a series of decays until the atom has become a stable isotope, meaning that the nucleus of the atom has reached a stable state.

<span class="mw-page-title-main">Neutron emission</span> Type of radioactive decay

Neutron emission is a mode of radioactive decay in which one or more neutrons are ejected from a nucleus. It occurs in the most neutron-rich/proton-deficient nuclides, and also from excited states of other nuclides as in photoneutron emission and beta-delayed neutron emission. As only a neutron is lost by this process the number of protons remains unchanged, and an atom does not become an atom of a different element, but a different isotope of the same element.

<span class="mw-page-title-main">Isotone</span> Different nuclides with the same neutron number

Two nuclides are isotones if they have the same neutron number N, but different proton number Z. For example, boron-12 and carbon-13 nuclei both contain 7 neutrons, and so are isotones. Similarly, ³⁶S, ³⁷Cl, ³⁸Ar, ³⁹K, and ⁴⁰Ca nuclei are all isotones of 20 because they all contain 20 neutrons. Despite its similarity to the Greek for "same stretching", the term was formed by the German physicist K. Guggenheimer by changing the "p" in "isotope" from "p" for "proton" to "n" for "neutron".

Natural tantalum (₇₃Ta) consists of two stable isotopes: ¹⁸¹Ta (99.988%) and ^180m
Ta (0.012%).

Technetium (₄₃Tc) is one of the two elements with Z < 83 that have no stable isotopes; the other such element is promethium. It is primarily artificial, with only trace quantities existing in nature produced by spontaneous fission or neutron capture by molybdenum. The first isotopes to be synthesized were ⁹⁷Tc and ⁹⁹Tc in 1936, the first artificial element to be produced. The most stable radioisotopes are ⁹⁷Tc, ⁹⁸Tc, and ⁹⁹Tc.

Natural nitrogen (₇N) consists of two stable isotopes: the vast majority (99.6%) of naturally occurring nitrogen is nitrogen-14, with the remainder being nitrogen-15. Thirteen radioisotopes are also known, with atomic masses ranging from 9 to 23, along with three nuclear isomers. All of these radioisotopes are short-lived, the longest-lived being nitrogen-13 with a half-life of 9.965(4) min. All of the others have half-lives below 7.15 seconds, with most of these being below 620 milliseconds. Most of the isotopes with atomic mass numbers below 14 decay to isotopes of carbon, while most of the isotopes with masses above 15 decay to isotopes of oxygen. The shortest-lived known isotope is nitrogen-10, with a half-life of 143(36) yoctoseconds, though the half-life of nitrogen-9 has not been measured exactly.

A table or chart of nuclides is a two-dimensional graph of isotopes of the elements, in which one axis represents the number of neutrons and the other represents the number of protons in the atomic nucleus. Each point plotted on the graph thus represents a nuclide of a known or hypothetical chemical element. This system of ordering nuclides can offer a greater insight into the characteristics of isotopes than the better-known periodic table, which shows only elements and not their isotopes. The chart of the nuclides is also known as the Segrè chart, after the Italian physicist Emilio Segrè.

<span class="mw-page-title-main">Valley of stability</span> Characterization of nuclide stability

In nuclear physics, the valley of stability is a characterization of the stability of nuclides to radioactivity based on their binding energy. Nuclides are composed of protons and neutrons. The shape of the valley refers to the profile of binding energy as a function of the numbers of neutrons and protons, with the lowest part of the valley corresponding to the region of most stable nuclei. The line of stable nuclides down the center of the valley of stability is known as the line of beta stability. The sides of the valley correspond to increasing instability to beta decay. The decay of a nuclide becomes more energetically favorable the further it is from the line of beta stability. The boundaries of the valley correspond to the nuclear drip lines, where nuclides become so unstable they emit single protons or single neutrons. Regions of instability within the valley at high atomic number also include radioactive decay by alpha radiation or spontaneous fission. The shape of the valley is roughly an elongated paraboloid corresponding to the nuclide binding energies as a function of neutron and atomic numbers.

The neutron number is the number of neutrons in a nuclide.

<span class="mw-page-title-main">Isotope</span> Different atoms of the same element

Isotopes are distinct nuclear species of the same chemical element. They have the same atomic number and position in the periodic table, but differ in nucleon numbers due to different numbers of neutrons in their nuclei. While all isotopes of a given element have almost the same chemical properties, they have different atomic masses and physical properties.

Beta-decay stable isobars are the set of nuclides which cannot undergo beta decay, that is, the transformation of a neutron to a proton or a proton to a neutron within the nucleus. A subset of these nuclides are also stable with regards to double beta decay or theoretically higher simultaneous beta decay, as they have the lowest energy of all isobars with the same mass number.

<span class="mw-page-title-main">Isobar (nuclide)</span> Atoms with the same number of nucleons

Isobars are atoms (nuclides) of different chemical elements that have the same number of nucleons. Correspondingly, isobars differ in atomic number but have the same mass number. An example of a series of isobars is ⁴⁰S, ⁴⁰Cl, ⁴⁰Ar, ⁴⁰K, and ⁴⁰Ca. While the nuclei of these nuclides all contain 40 nucleons, they contain varying numbers of protons and neutrons.

A monoisotopic element is an element which has only a single stable isotope (nuclide). There are 26 such elements, as listed.

<span class="mw-page-title-main">Neutron–proton ratio</span> Ratio of neutrons to protons in an atomic nucleus

The neutron–proton ratio of an atomic nucleus is the ratio of its number of neutrons to its number of protons. Among stable nuclei and naturally occurring nuclei, this ratio generally increases with increasing atomic number. This is because electrical repulsive forces between protons scale with distance differently than strong nuclear force attractions. In particular, most pairs of protons in large nuclei are not far enough apart, such that electrical repulsion dominates over the strong nuclear force, and thus proton density in stable larger nuclei must be lower than in stable smaller nuclei where more pairs of protons have appreciable short-range nuclear force attractions.

References

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↑ Mcclain, D. E.; Miller, A. C.; Kalinich, J. F. (December 20, 2007). "Status of Health Concerns about Military Use of Depleted Uranium and Surrogate Metals in Armor-Penetrating Munitions" (PDF). NATO. Archived from the original (PDF) on April 19, 2011. Retrieved November 14, 2010.
↑ Arevalo, Ricardo; McDonough, William F.; Luong, Mario (2009). "The K-U ratio of the silicate Earth: Insights into mantle composition, structure and thermal evolution". Earth and Planetary Science Letters. 278 (3–4): 361–369. Bibcode:2009E&PSL.278..361A. doi:10.1016/j.epsl.2008.12.023.
↑ Hult, Mikael; Elisabeth Wieslander, J.S.; Marissens, Gerd; Gasparro, Joël; Wätjen, Uwe; Misiaszek, Marcin (2009). "Search for the radioactivity of 180mTa using an underground HPGe sandwich spectrometer". Applied Radiation and Isotopes. 67 (5): 918–21. doi:10.1016/j.apradiso.2009.01.057. PMID 19246206.
↑ "Radiation and Radioactive Decay. Radioactive Human Body". Harvard Natural Sciences Lecture Demonstrations. Retrieved July 2, 2016.
↑ Winteringham, F. P. W; Effects, F.A.O. Standing Committee on Radiation, Land And Water Development Division, Food and Agriculture Organization of the United Nations (1989). Radioactive fallout in soils, crops and food: a background review. Food & Agriculture Org. p. 32. ISBN 978-92-5-102877-3.{{cite book}}: CS1 maint: multiple names: authors list (link)
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↑ Planck Collaboration (2016). "Planck 2015 results. XIII. Cosmological parameters (See Table 4 on page 31 of pfd)". Astronomy & Astrophysics. 594: A13. arXiv: 1502.01589 . Bibcode:2016A&A...594A..13P. doi:10.1051/0004-6361/201525830. S2CID 119262962.
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↑ Dvornický, R.; Šimkovic, F. (13–16 June 2011). "Second unique forbidden β decay of ¹¹⁵In and neutrino mass". AIP Conf. Proc. AIP Conference Proceedings. 1417 (33): 33. Bibcode:2011AIPC.1417...33D. doi:10.1063/1.3671032.
↑ Bosch, F.; Faestermann, T.; Friese, J.; et al. (1996). "Observation of bound-state β⁻ decay of fully ionized ¹⁸⁷Re: ¹⁸⁷Re-¹⁸⁷Os Cosmochronometry". Physical Review Letters . 77 (26): 5190–5193. Bibcode:1996PhRvL..77.5190B. doi:10.1103/PhysRevLett.77.5190. PMID 10062738.
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[magic-1] Blank, B.; Regan, P.H. (2000). "Magic and doubly-magic nuclei". Nuclear Physics News. 10 (4): 20–27. doi:10.1080/10506890109411553. S2CID 121966707.

[2] A. Yu. Smirnov; V. D. Borisevich; A. Sulaberidze (July 2012). "Evaluation of specific cost of obtainment of lead-208 isotope by gas centrifuges using various raw materials". Theoretical Foundations of Chemical Engineering. 46 (4): 373–378. doi:10.1134/S0040579512040161. S2CID 98821122.

[3] Mcclain, D. E.; Miller, A. C.; Kalinich, J. F. (December 20, 2007). "Status of Health Concerns about Military Use of Depleted Uranium and Surrogate Metals in Armor-Penetrating Munitions" (PDF). NATO. Archived from the original (PDF) on April 19, 2011. Retrieved November 14, 2010.

[4] Arevalo, Ricardo; McDonough, William F.; Luong, Mario (2009). "The K-U ratio of the silicate Earth: Insights into mantle composition, structure and thermal evolution". Earth and Planetary Science Letters. 278 (3–4): 361–369. Bibcode:2009E&PSL.278..361A. doi:10.1016/j.epsl.2008.12.023.

[5] Hult, Mikael; Elisabeth Wieslander, J.S.; Marissens, Gerd; Gasparro, Joël; Wätjen, Uwe; Misiaszek, Marcin (2009). "Search for the radioactivity of 180mTa using an underground HPGe sandwich spectrometer". Applied Radiation and Isotopes. 67 (5): 918–21. doi:10.1016/j.apradiso.2009.01.057. PMID 19246206.

[6] "Radiation and Radioactive Decay. Radioactive Human Body". Harvard Natural Sciences Lecture Demonstrations. Retrieved July 2, 2016.

[7] Winteringham, F. P. W; Effects, F.A.O. Standing Committee on Radiation, Land And Water Development Division, Food and Agriculture Organization of the United Nations (1989). Radioactive fallout in soils, crops and food: a background review. Food & Agriculture Org. p. 32. ISBN 978-92-5-102877-3.{{cite book}}: CS1 maint: multiple names: authors list (link)

[8] P. Mohr, F. Kaeppeler, and R. Gallino (2007). "Survival of Nature's Rarest Isotope 180Ta under Stellar Conditions". Phys. Rev. C. 75: 012802. arXiv: astro-ph/0612427 . doi:10.1103/PhysRevC.75.012802. S2CID 44724195.{{cite journal}}: CS1 maint: multiple names: authors list (link)

[9] Planck Collaboration (2016). "Planck 2015 results. XIII. Cosmological parameters (See Table 4 on page 31 of pfd)". Astronomy & Astrophysics. 594: A13. arXiv: 1502.01589 . Bibcode:2016A&A...594A..13P. doi:10.1051/0004-6361/201525830. S2CID 119262962.

[10] Audi, Georges; Bersillon, Olivier; Blachot, Jean; Wapstra, Aaldert Hendrik (2003), "The NUBASE evaluation of nuclear and decay properties", Nuclear Physics A, 729: 3–128, Bibcode:2003NuPhA.729....3A, doi:10.1016/j.nuclphysa.2003.11.001

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