Beta-decay stable isobars

{{Short description|Set of nuclides that cannot undergo beta decay}} thumb|right|upright=1 '''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 regard to double beta decay or theoretically higher simultaneous beta decay, as they have the lowest energy of all isobars with the same mass number.

This set of nuclides is also known as the '''line of beta stability''', a term already in common use in 1965.<ref>Proc. Int. Symposium on Why and How should we investigate Nuclides Far Off the Stability Line", Lysekil, Sweden, August 1966, eds. W. Forsling, C.J. Herrlander and H. Ryde, Stockholm, Almqvist & Wiksell, 1967</ref><ref>{{cite journal|doi=10.1146/annurev.ns.29.120179.000441|doi-access=free|title=Nuclei Far Away from the Line of Beta Stability: Studies by On-Line Mass Separation|year=1979|last1=Hansen|first1=P. G.|journal=Annual Review of Nuclear and Particle Science|volume=29|pages=69–119|bibcode=1979ARNPS..29...69H}}</ref> This line lies along the bottom of the nuclear valley of stability.

== Introduction == The line of beta stability can be defined mathematically by finding the nuclide with the greatest binding energy for a given mass number, by a model such as the classical semi-empirical mass formula developed by C. F. Weizsäcker. These nuclides are local maxima in terms of binding energy for a given mass number.

{| class="wikitable" align="right" style="text-align: right" |+β decay stable / even ''A'' |- !βDS!!One!!Two!!Three |- |2–34||17|||| |- |36–58||6||6|| |- |60–72||5||2|| |- |74–116||2||20|| |- |118–154||2||12||5 |- |156–192||5||14|| |- |194–210||6||3|| |- |212–262||7||19|| |- !Total||50||76||5 |}

All odd mass numbers have only one beta decay stable nuclide.

Among even mass number, five (124, 130, 136, 150, 154) have three beta-stable nuclides. None have more than three; all others have either one or two. * From 2 to 34, all have only one. * From 36 to 72, only eight (36, 40, 46, 50, 54, 58, 64, 70) have two, and the remaining 11 have one. * From 74 to 122, three (88, 90, 118) have one, and the remaining 22 have two. * From 124 to 154, only one (140) has one, five have three, and the remaining 10 have two. * From 156 to 262, only eighteen have one, and the remaining 36 have two, though there may also exist some undiscovered ones.

All primordial nuclides are beta decay stable, with the exception of ⁴⁰K, ⁵⁰V, ⁸⁷Rb, ¹¹³Cd, ¹¹⁵In, ¹³⁸La, ¹⁷⁶Lu, and ¹⁸⁷Re. In addition, ¹²³Te and ^180mTa have not been observed to decay, but are believed to undergo beta decay with extremely long half-lives (over 10¹⁵ years). Theoretically, ¹²³Te can only undergo electron capture to ¹²³Sb, whereas ^180mTa can decay in both directions, to ¹⁸⁰Hf or ¹⁸⁰W. Among non-primordial nuclides, there are some other cases of theoretically possible but never-observed beta decay, notably including ²²²Rn<ref name=222Rn01>{{cite journal |last1=Belli |first1=P. |last2=Bernabei |first2=R. |last3=Cappella |first3=C. |last4=Caracciolo |first4=V. |last5=Cerulli |first5=R. |last6=Danevich |first6=F.A. |last7=Di Marco |first7=A. |last8=Incicchitti |first8=A. |last9=Poda |first9=D.V. |last10=Polischuk |first10=O.G. |last11=Tretyak |first11=V.I. |title=Investigation of rare nuclear decays with BaF₂ crystal scintillator contaminated by radium |date=2014 |journal=European Physical Journal A |volume=50 |issue=9 |pages=134–143 |doi=10.1140/epja/i2014-14134-6 |arxiv=1407.5844|bibcode=2014EPJA...50..134B |s2cid=118513731 }}</ref> and ²⁴⁷Cm (the most stable isotopes of their elements considering all decay modes). Finally, ⁴⁸Ca has not been observed to undergo beta decay (theoretically possible) which is extremely suppressed, but double beta decay has been observed. Similar suppression of single beta decay occurs also for ¹⁴⁸Gd, a rather short-lived alpha emitter; and also for ⁹⁶Zr, where single beta decay is again possible, but suppressed to the point that it has a half-life an order of magnitude longer than the double beta decay.<ref name=Barabash>{{cite arXiv |first1=A. S. |last1=Barabash |first2=S. |last2=Evseev |first3=D. |last3=Filosofov |first4=Yu. M. |last4=Gavrilyuk |first5=A. M. |last5=Gangapshev |first6=N. |last6=Gorshkov |first7=V. V. |last7=Kazalov |first8=S. |last8=Kazartsev |first9=T. |last9=Khussainov |first10=V. V. |last10=Kuzminov |first11=A. |last11=Lubashevskiy |first12=D. V. |last12=Ponomarev |first13=S. |last13=Rozov |first14=N. |last14=Temerbulatova |first15=S. |last15=Vasilyev |first16=E. A. |last16=Yakushev |first17=V. I. |last17=Yumatov |date=19 May 2026 |title=First observation of single beta decay of ⁹⁶Zr |arxiv=2605.18344 |class=nucl-ex}}</ref>

All elements up to and including nobelium, except technetium, promethium, and mendelevium, are known to have at least one beta-stable isotope. It is known that technetium and promethium have no beta-stable isotopes; current measurement uncertainties are not enough to say whether mendelevium has them or not. {{clear}}

== List of known beta-decay stable isobars == {{see also|List of stable isotopes}}

346 nuclides (including {{sup|260}}Fm whose discovery is unconfirmed) have been definitively identified as beta-stable.<ref>{{Cite web |url=http://www.nndc.bnl.gov/chart |title=Interactive Chart of Nuclides (Brookhaven National Laboratory) |access-date=2009-06-19 |archive-date=2020-07-25 |archive-url=https://web.archive.org/web/20200725182342/https://www.nndc.bnl.gov/nudat2/ }}</ref>{{AME2020 II|ref}} Theoretically predicted or experimentally observed double beta decay is shown by arrows, i.e. arrows point toward the lightest-mass isobar. This is sometimes dominated by alpha decay or spontaneous fission, especially for the heavy elements. Observed decay modes are listed as α for alpha decay, SF for spontaneous fission, and n for neutron emission in the special case of {{sup|5}}He. For mass 5 there are no bound isobars at all; mass 8 has bound isobars, but the beta-stable {{sup|8}}Be is unbound.<ref name="Tretyak2002"> {{cite journal |last1=Tretyak |first1=V.I. |last2=Zdesenko |first2=Yu.G. |year=2002 |title=Tables of Double Beta Decay Data — An Update |journal=At. Data Nucl. Data Tables |volume=80 |issue=1 |pages=83–116 |doi=10.1006/adnd.2001.0873 |bibcode=2002ADNDT..80...83T }}</ref>

Two beta-decay stable nuclides exist for odd neutron numbers 1 (²H and ³He), 3 (⁵He and ⁶Li – the former has an extremely short half-life), 5 (⁹Be and ¹⁰B), 7 (¹³C and ¹⁴N), 55 (⁹⁷Mo and ⁹⁹Ru), and 85 (¹⁴⁵Nd and ¹⁴⁷Sm); the first four cases involve very light nuclides where odd-odd nuclides are more stable than their surrounding even-even isobars, and the last two surround the proton numbers 43 and 61 which have no beta-stable isotopes. Also, two beta-decay stable nuclides exist for odd proton numbers 1, 3, 5, 7, 17, 19, 29, 31, 35, 47, 51, 63, 77, 81, and 95; the first four cases involve very light nuclides where odd-odd nuclides are more stable than their surrounding even-even isobars, and the other numbers surround the neutron numbers 19, 21, 35, 39, 45, 61, 71, 89, 115, 123, 147 which have no beta-stable isotopes. (For ''N'' = 21 the long-lived primordial ⁴⁰K exists, and for ''N'' = 71 there is ¹²³Te whose electron capture has not yet been observed, but neither are beta-stable.)

All even proton numbers 2 ≤ ''Z'' ≤ 102 have at least two beta-decay stable nuclides, with exactly two for ''Z'' = 4 (⁸Be and ⁹Be – the former having an extremely short half-life) and 6 (¹²C and ¹³C). Also, the only even neutron numbers with only one beta-decay stable nuclide are 0 (¹H) and 2 (⁴He); at least two beta-decay stable nuclides exist for even neutron numbers in the range 4 ≤ ''N'' ≤ 160, with exactly two for ''N'' = 4 (⁷Li and ⁸Be), 6 (¹¹B and ¹²C), 8 (¹⁵N and ¹⁶O), 66 (¹¹⁴Cd and ¹¹⁶Sn, noting also primordial but not beta-stable ¹¹⁵In), 120 (¹⁹⁸Pt and ²⁰⁰Hg), and 128 (²¹²Po and ²¹⁴Rn – both very unstable to alpha decay). Seven beta-decay stable nuclides exist for the magic ''N'' = 82{{efn-lr|¹³⁶Xe, ¹³⁸Ba, ¹³⁹La, ¹⁴⁰Ce, ¹⁴¹Pr, ¹⁴²Nd, and ¹⁴⁴Sm}} and five for ''N'' = 20{{efn-lr|³⁶S, ³⁷Cl, ³⁸Ar, ³⁹K, and ⁴⁰Ca}}, 50{{efn-lr|⁸⁶Kr, ⁸⁸Sr, ⁸⁹Y, ⁹⁰Zr, and ⁹²Mo, noting also primordial but not beta-stable ⁸⁷Rb}}, 58{{efn-lr|¹⁰⁰Mo, ¹⁰²Ru, ¹⁰³Rh, ¹⁰⁴Pd, and ¹⁰⁶Cd}}, 74{{efn-lr|¹²⁴Sn, ¹²⁶Te, ¹²⁷I, ¹²⁸Xe, and ¹³⁰Ba}}, 78{{efn-lr|¹³⁰Te, ¹³²Xe, ¹³³Cs, ¹³⁴Ba, and ¹³⁶Ce}}, 88{{efn-lr|¹⁴⁸Nd, ¹⁵⁰Sm, ¹⁵¹Eu, ¹⁵²Gd, and ¹⁵⁴Dy – the last not primordial}}, and 90{{efn-lr|¹⁵⁰Nd, ¹⁵²Sm, ¹⁵³Eu, ¹⁵⁴Gd, and ¹⁵⁶Dy}}.

For ''A'' ≤ 209, the only beta-decay stable nuclides that are not primordial nuclides are ⁵He, ⁸Be, ¹⁴⁶Sm, ¹⁵⁰Gd, and ¹⁵⁴Dy. (¹⁴⁶Sm has a half-life long enough that it should barely survive as a primordial nuclide, but it has never been experimentally confirmed as such.) All beta-decay stable nuclides with ''A'' ≥ 209 are known to undergo alpha decay, though for some, spontaneous fission is the dominant decay mode. Cluster decay is sometimes also possible, but in all known cases it is a minor branch compared to alpha decay or spontaneous fission. Alpha decay is energetically possible for all beta-stable nuclides with ''A'' ≥ 165 with the single exception of ²⁰⁴Hg, but in most cases the ''Q''-value is small enough that such decay has never been seen.<ref name="bellidecay">{{cite journal |last1=Belli |first1=P. |last2=Bernabei |first2=R. |last3=Danevich |first3=F. A. |last4=Incicchitti |first4=A. |last5=Tretyak |first5=V. I. |display-authors=3 |title=Experimental searches for rare alpha and beta decays |journal=European Physical Journal A |date=2019 |volume=55 |issue=8 |pages=140–1–140–7 |doi=10.1140/epja/i2019-12823-2 |issn=1434-601X |arxiv=1908.11458|bibcode=2019EPJA...55..140B |s2cid=201664098 }}</ref>

With the exception of ²⁶²No, no nuclides with ''A'' > 260 are currently known to be beta-stable. Moreover, the known beta-stable nuclei for individual masses ''A'' = 222, ''A'' = 256, and ''A'' ≥ 258 (corresponding to proton numbers ''Z'' = 86 and ''Z'' ≥ 98, or to neutron numbers ''N'' = 136 and ''N'' ≥ 158) may not represent the complete set.<ref name=SHlimit/><ref name=CN14>{{cite web|url=https://wwwndc.jaea.go.jp/CN14/ |title=Chart of the Nuclides |last=Koura|first=H. |last2=Katakura|first2=J|last3=Tachibana|first3=T |last4=Minato|first4=F |date=2015 |publisher=Japan Atomic Energy Agency |access-date=30 October 2018}}</ref>

{|align="right" class="wikitable" ! !!Even ''N''!!Odd ''N'' |- !Even ''Z'' |Even ''A''||bgcolor="pink"|Odd ''A'' |- !Odd ''Z'' |bgcolor="yellow"|Odd ''A''||bgcolor="cyan"|Even ''A'' |}

{| class="wikitable" style="text-align:center" |+ All known beta-decay stable isobars sorted by mass number |- !Odd ''A''!!Even ''A''!!Odd ''A''!!Even ''A''!!Odd ''A''!!Even ''A''!!Odd ''A''!!Even ''A'' |- |bgcolor="yellow"|¹H |bgcolor="cyan"|²H |bgcolor="pink"|³He ||⁴He |bgcolor="pink"|⁵He (n) |bgcolor="cyan"|⁶Li |bgcolor="yellow"|⁷Li ||⁸Be (α) |- |bgcolor="pink"|⁹Be |bgcolor="cyan"|¹⁰B |bgcolor="yellow"|¹¹B ||¹²C |bgcolor="pink"|¹³C |bgcolor="cyan"|¹⁴N |bgcolor="yellow"|¹⁵N ||¹⁶O |- |bgcolor="pink"|¹⁷O ||¹⁸O |bgcolor="yellow"|¹⁹F ||²⁰Ne |bgcolor="pink"|²¹Ne ||²²Ne |bgcolor="yellow"|²³Na ||²⁴Mg |- |bgcolor="pink"|²⁵Mg ||²⁶Mg |bgcolor="yellow"|²⁷Al ||²⁸Si |bgcolor="pink"|²⁹Si ||³⁰Si |bgcolor="yellow"|³¹P ||³²S |- |bgcolor="pink"|³³S ||³⁴S |bgcolor="yellow"|³⁵Cl ||³⁶S ← ³⁶Ar |bgcolor="yellow"|³⁷Cl ||³⁸Ar |bgcolor="yellow"|³⁹K ||⁴⁰Ar ← ⁴⁰Ca |- |bgcolor="yellow"|⁴¹K ||⁴²Ca |bgcolor="pink"|⁴³Ca ||⁴⁴Ca |bgcolor="yellow"|⁴⁵Sc ||⁴⁶Ca → ⁴⁶Ti |bgcolor="pink"|⁴⁷Ti ||⁴⁸Ti{{efn|⁴⁸Ca is theoretically capable of beta decay to ⁴⁸Sc, thus making it not a beta-stable nuclide. However, such a process has never been observed, having a partial half-life greater than 1.1{{su|p=+0.8|b=−0.6}}×10²¹&nbsp;years, longer than its double beta decay half-life, meaning that double beta decay would usually occur first.<ref>{{cite journal |last1=Aunola |first1=M. |last2=Suhonen |first2=J. |last3=Siiskonen |first3=T. |title=Shell-model study of the highly forbidden beta decay ⁴⁸Ca → ⁴⁸Sc |date=1999 |journal=EPL |volume=46 |issue=5 |page=577 |doi=10.1209/epl/i1999-00301-2|bibcode=1999EL.....46..577A }}</ref>}} |- |bgcolor="pink"|⁴⁹Ti ||⁵⁰Ti ← ⁵⁰Cr |bgcolor="yellow"|⁵¹V ||⁵²Cr |bgcolor="pink"|⁵³Cr ||⁵⁴Cr ← ⁵⁴Fe |bgcolor="yellow"|⁵⁵Mn ||⁵⁶Fe |- |bgcolor="pink"|⁵⁷Fe ||⁵⁸Fe ← ⁵⁸Ni |bgcolor="yellow"|⁵⁹Co ||⁶⁰Ni |bgcolor="pink"|⁶¹Ni ||⁶²Ni |bgcolor="yellow"|⁶³Cu ||⁶⁴Ni ← ⁶⁴Zn |- |bgcolor="yellow"|⁶⁵Cu ||⁶⁶Zn |bgcolor="pink"|⁶⁷Zn ||⁶⁸Zn |bgcolor="yellow"|⁶⁹Ga ||⁷⁰Zn → ⁷⁰Ge |bgcolor="yellow"|⁷¹Ga ||⁷²Ge |- |bgcolor="pink"|⁷³Ge ||⁷⁴Ge ← ⁷⁴Se |bgcolor="yellow"|⁷⁵As ||⁷⁶Ge → ⁷⁶Se |bgcolor="pink"|⁷⁷Se ||⁷⁸Se ← ⁷⁸Kr |bgcolor="yellow"|⁷⁹Br ||⁸⁰Se → ⁸⁰Kr |- |bgcolor="yellow"|⁸¹Br ||⁸²Se → ⁸²Kr |bgcolor="pink"|⁸³Kr ||⁸⁴Kr ← ⁸⁴Sr |bgcolor="yellow"|⁸⁵Rb ||⁸⁶Kr → ⁸⁶Sr |bgcolor="pink"|⁸⁷Sr ||⁸⁸Sr |- |bgcolor="yellow"|⁸⁹Y ||⁹⁰Zr |bgcolor="pink"|⁹¹Zr ||⁹²Zr ← ⁹²Mo |bgcolor="yellow"|⁹³Nb ||⁹⁴Zr → ⁹⁴Mo |bgcolor="pink"|⁹⁵Mo ||⁹⁶Mo ← ⁹⁶Ru{{efn|⁹⁶Zr is capable of beta decay to ⁹⁶Nb, thus making it not a beta-stable nuclide. However, the process has a partial half-life greater than the double beta decay, so double beta decay usually occurs first.<ref name=Barabash/>}} |- |bgcolor="pink"|⁹⁷Mo ||⁹⁸Mo → ⁹⁸Ru |bgcolor="pink"|⁹⁹Ru ||¹⁰⁰Mo → ¹⁰⁰Ru |bgcolor="pink"|¹⁰¹Ru ||¹⁰²Ru ← ¹⁰²Pd |bgcolor="yellow"|¹⁰³Rh ||¹⁰⁴Ru → ¹⁰⁴Pd |- |bgcolor="pink"|¹⁰⁵Pd ||¹⁰⁶Pd ← ¹⁰⁶Cd |bgcolor="yellow"|¹⁰⁷Ag ||¹⁰⁸Pd ← ¹⁰⁸Cd |bgcolor="yellow"|¹⁰⁹Ag ||¹¹⁰Pd → ¹¹⁰Cd |bgcolor="pink"|¹¹¹Cd ||¹¹²Cd ← ¹¹²Sn |- |bgcolor="yellow"|¹¹³In ||¹¹⁴Cd → ¹¹⁴Sn |bgcolor="pink"|¹¹⁵Sn ||¹¹⁶Cd → ¹¹⁶Sn |bgcolor="pink"|¹¹⁷Sn ||¹¹⁸Sn |bgcolor="pink"|¹¹⁹Sn ||¹²⁰Sn ← ¹²⁰Te |- |bgcolor="yellow"|¹²¹Sb ||¹²²Sn → ¹²²Te |bgcolor="yellow"|¹²³Sb ||¹²⁴Sn → ¹²⁴Te ← ¹²⁴Xe |bgcolor="pink"|¹²⁵Te ||¹²⁶Te ← ¹²⁶Xe |bgcolor="yellow"|¹²⁷I ||¹²⁸Te → ¹²⁸Xe |- |bgcolor="pink"|¹²⁹Xe ||¹³⁰Te → ¹³⁰Xe ← ¹³⁰Ba |bgcolor="pink"|¹³¹Xe ||¹³²Xe ← ¹³²Ba |bgcolor="yellow"|¹³³Cs ||¹³⁴Xe → ¹³⁴Ba |bgcolor="pink"|¹³⁵Ba ||¹³⁶Xe → ¹³⁶Ba ← ¹³⁶Ce |- |bgcolor="pink"|¹³⁷Ba ||¹³⁸Ba ← ¹³⁸Ce |bgcolor="yellow"|¹³⁹La ||¹⁴⁰Ce |bgcolor="yellow"|¹⁴¹Pr ||¹⁴²Ce → ¹⁴²Nd |bgcolor="pink"|¹⁴³Nd ||¹⁴⁴Nd (α) ← ¹⁴⁴Sm |- |bgcolor="pink"|¹⁴⁵Nd ||¹⁴⁶Nd → ¹⁴⁶Sm (α) |bgcolor="pink"|¹⁴⁷Sm (α) ||¹⁴⁸Nd → ¹⁴⁸Sm (α){{efn|¹⁴⁸Gd was previously thought to be a third beta-stable isobar for mass 148,<ref name=Tretyak2002/> but according to current mass determinations it has a higher mass than ¹⁴⁸Eu and can undergo electron capture. Nevertheless, the mass difference is very small (27.0&nbsp;keV, even lower than likewise unseen electron capture of ¹²³Te), and only alpha decay has been observed experimentally for ¹⁴⁸Gd.}} |bgcolor="pink"|¹⁴⁹Sm ||¹⁵⁰Nd → ¹⁵⁰Sm ← ¹⁵⁰Gd (α) |bgcolor="yellow"|¹⁵¹Eu (α) ||¹⁵²Sm ← ¹⁵²Gd (α) |- |bgcolor="yellow"|¹⁵³Eu ||¹⁵⁴Sm → ¹⁵⁴Gd ← ¹⁵⁴Dy (α) |bgcolor="pink"|¹⁵⁵Gd ||¹⁵⁶Gd ← ¹⁵⁶Dy |bgcolor="pink"|¹⁵⁷Gd ||¹⁵⁸Gd ← ¹⁵⁸Dy |bgcolor="yellow"|¹⁵⁹Tb ||¹⁶⁰Gd → ¹⁶⁰Dy |- |bgcolor="pink"|¹⁶¹Dy ||¹⁶²Dy ← ¹⁶²Er |bgcolor="pink"|¹⁶³Dy ||¹⁶⁴Dy ← ¹⁶⁴Er |bgcolor="yellow"|¹⁶⁵Ho ||¹⁶⁶Er |bgcolor="pink"|¹⁶⁷Er ||¹⁶⁸Er ← ¹⁶⁸Yb |- |bgcolor="yellow"|¹⁶⁹Tm ||¹⁷⁰Er → ¹⁷⁰Yb |bgcolor="pink"|¹⁷¹Yb ||¹⁷²Yb |bgcolor="pink"|¹⁷³Yb ||¹⁷⁴Yb ← ¹⁷⁴Hf (α) |bgcolor="yellow"|¹⁷⁵Lu ||¹⁷⁶Yb → ¹⁷⁶Hf |- |bgcolor="pink"|¹⁷⁷Hf ||¹⁷⁸Hf |bgcolor="pink"|¹⁷⁹Hf ||¹⁸⁰Hf ← ¹⁸⁰W (α) |bgcolor="yellow"|¹⁸¹Ta ||¹⁸²W |bgcolor="pink"|¹⁸³W ||¹⁸⁴W ← ¹⁸⁴Os (α) |- |bgcolor="yellow"|¹⁸⁵Re ||¹⁸⁶W → ¹⁸⁶Os (α) |bgcolor="pink"|¹⁸⁷Os ||¹⁸⁸Os |bgcolor="pink"|¹⁸⁹Os ||¹⁹⁰Os ← ¹⁹⁰Pt (α) |bgcolor="yellow"|¹⁹¹Ir ||¹⁹²Os → ¹⁹²Pt |- |bgcolor="yellow"|¹⁹³Ir ||¹⁹⁴Pt |bgcolor="pink"|¹⁹⁵Pt ||¹⁹⁶Pt ← ¹⁹⁶Hg |bgcolor="yellow"|¹⁹⁷Au ||¹⁹⁸Pt → ¹⁹⁸Hg |bgcolor="pink"|¹⁹⁹Hg ||²⁰⁰Hg |- |bgcolor="pink"|²⁰¹Hg ||²⁰²Hg |bgcolor="yellow"|²⁰³Tl ||²⁰⁴Hg → ²⁰⁴Pb |bgcolor="yellow"|²⁰⁵Tl ||²⁰⁶Pb |bgcolor="pink"|²⁰⁷Pb ||²⁰⁸Pb |- |bgcolor="yellow"|²⁰⁹Bi (α) ||²¹⁰Po (α) |bgcolor="pink"|²¹¹Po (α) ||²¹²Po (α) ← ²¹²Rn (α) |bgcolor="pink"|²¹³Po (α) ||²¹⁴Po (α) ← ²¹⁴Rn (α) |bgcolor="yellow"|²¹⁵At (α) ||²¹⁶Po (α) → ²¹⁶Rn (α) |- |bgcolor="pink"|²¹⁷Rn (α) ||²¹⁸Rn (α) ← ²¹⁸Ra (α) |bgcolor="yellow"|²¹⁹Fr (α) ||²²⁰Rn (α) → ²²⁰Ra (α) |bgcolor="pink"|²²¹Ra (α) ||²²²Ra{{efn|While the AME2020 atomic mass evaluation gives ²²²Rn a lower mass than ²²²Fr (the β⁻-decay energy is given as (−6 ± 8) keV),{{AME2020 II|ref}} implying beta-stability, it is predicted that single beta decay of ²²²Rn is energetically possible (albeit with very low decay energy),<ref name=222Rn01></ref> and it falls within the error margin given in AME2020. Hence, current mass determinations cannot decisively determine whether ²²²Rn is beta-stable or not, though only the alpha decay mode is experimentally known for that nuclide, and the search for beta decay yielded a lower partial half-life limit of 8 years.<ref name=222Rn01 />}} (α) |bgcolor="pink"|²²³Ra (α) ||²²⁴Ra (α) ← ²²⁴Th (α) |- |bgcolor="yellow"|²²⁵Ac (α) ||²²⁶Ra (α) → ²²⁶Th (α) |bgcolor="pink"|²²⁷Th (α) ||²²⁸Th (α) |bgcolor="pink"|²²⁹Th (α) ||²³⁰Th (α) ← ²³⁰U (α) |bgcolor="yellow"|²³¹Pa (α) ||²³²Th (α) → ²³²U (α) |- |bgcolor="pink"|²³³U (α) ||²³⁴U (α) |bgcolor="pink"|²³⁵U (α) ||²³⁶U (α) ← ²³⁶Pu (α) |bgcolor="yellow"|²³⁷Np (α) ||²³⁸U (α) → ²³⁸Pu (α) |bgcolor="pink"|²³⁹Pu (α) ||²⁴⁰Pu (α) |- |bgcolor="yellow"|²⁴¹Am (α) ||²⁴²Pu (α) ← ²⁴²Cm (α) |bgcolor="yellow"|²⁴³Am (α) ||²⁴⁴Pu (α) → ²⁴⁴Cm (α) |bgcolor="pink"|²⁴⁵Cm (α) ||²⁴⁶Cm (α) |bgcolor="yellow"|²⁴⁷Bk (α) ||²⁴⁸Cm (α) → ²⁴⁸Cf (α) |- |bgcolor="pink"|²⁴⁹Cf (α) ||²⁵⁰Cf (α) |bgcolor="pink"|²⁵¹Cf (α) ||²⁵²Cf (α) ← ²⁵²Fm (α) |bgcolor="yellow"|²⁵³Es (α) ||²⁵⁴Cf (SF) → ²⁵⁴Fm (α) |bgcolor="pink"|²⁵⁵Fm (α) ||²⁵⁶Fm{{efn|While the AME2020 atomic mass evaluation gives ²⁵⁶Cf a lower mass than ²⁵⁶Es (the β⁻-decay energy is given as (−140# ± 330#) keV),{{AME2020 II|ref}} implying beta-stability, the error margin between them is larger than the mass difference. Hence, current mass determinations cannot decisively determine whether ²⁵⁶Cf is beta-stable or not.}} (SF) |- |bgcolor="pink"|²⁵⁷Fm (α) ||²⁵⁸Fm (SF) ← ²⁵⁸No (SF) ||{{efn|While the AME2020 atomic mass evaluation gives ²⁵⁹Md a lower mass than ²⁵⁹Fm (the β⁺-decay energy is given as (−140# ± 300#) keV),{{AME2020 II|ref}} implying beta-stability, the error margin between them is larger than the mass difference. Hence, current mass determinations cannot decisively determine which one of ²⁵⁹Fm and ²⁵⁹Md is beta-stable.}} ||²⁶⁰Fm{{efn|Discovery of this nuclide is unconfirmed}} (SF) → ²⁶⁰No (SF) ||{{efn|There is no known beta-stable isobar for mass 261, although they are known for the surrounding masses 260 and 262. Various models suggest that one of the undiscovered ²⁶¹Md and ²⁶¹No should be beta-stable.{{NUBASE2020|ref}}<ref name=SHlimit />}} ||²⁶²No (SF){{efn|While the AME2020 atomic mass evaluation gives ²⁶²Rf a higher mass than ²⁶²Lr (the β⁺-decay energy is given as (290# ± 300#) keV),{{AME2020 II|ref}} implying non-beta-stability, the error margin between them is larger than the mass difference. Hence, current mass determinations cannot decisively determine whether ²⁶²Rf is beta-stable or not.}} || || |}

thumb|right|480px|One chart of known and predicted nuclides up to ''Z'' = 149, ''N'' = 256. Black denotes the predicted beta-stability line, which is in good agreement with experimental data, though it fails to predict that Tc and Pm have no beta-stable isotope (the mass differences causing these anomalies are small). Islands of stability are predicted to center near ²⁹⁴Ds and ³⁵⁴126, beyond which the model appears to deviate from several rules of the semi-empirical mass formula.<ref name=SHlimit />

The general patterns of beta-stability are expected to continue into the region of superheavy elements, though the exact location of the center of the valley of stability is model dependent. It is widely believed that an island of stability exists along the beta-stability line for isotopes of elements around copernicium that are stabilized by shell closures in the region; such isotopes would decay primarily through alpha decay or spontaneous fission.<ref name=Zagrebaev>{{cite journal|title=Future of superheavy element research: Which nuclei could be synthesized within the next few years?|url=http://nrv.jinr.ru/pdf_file/J_phys_2013.pdf|first1=Valeriy|last1=Zagrebaev|first2=Alexander|last2=Karpov|first3=Walter|last3=Greiner|date=2013|journal=Journal of Physics|volume=420|issue=1|article-number=012001|doi=10.1088/1742-6596/420/1/012001|arxiv=1207.5700|bibcode=2013JPhCS.420a2001Z|s2cid=55434734|archive-date=2015-10-03|access-date=2019-01-24|archive-url=https://web.archive.org/web/20151003154020/http://nrv.jinr.ru/pdf_file/J_phys_2013.pdf|url-status=dead}}</ref> Beyond the island of stability, various models that correctly predict many known beta-stable isotopes also predict anomalies in the beta-stability line that are unobserved in any known nuclides, such as the existence of two beta-stable nuclides with the same odd mass number.<ref name=SHlimit>{{cite conference|last=Koura|first=H.|date=2011|title=Decay modes and a limit of existence of nuclei in the superheavy mass region|url=http://tan11.jinr.ru/pdf/10_Sep/S_2/05_Koura.pdf|conference=4th International Conference on the Chemistry and Physics of the Transactinide Elements|access-date=18 November 2018}}</ref><ref name=frdm2012>{{cite journal |last1=Möller |first1=P. |last2=Sierk |first2=A.J. |last3=Ichikawa |first3=T. |last4=Sagawa |first4=H. |title=Nuclear ground-state masses and deformations: FRDM(2012) |journal= Atomic Data and Nuclear Data Tables|date=2016 |volume=109–110 |pages=1–204 |doi=10.1016/j.adt.2015.10.002 |arxiv=1508.06294|bibcode=2016ADNDT.109....1M |s2cid=118707897 }}</ref> This is a consequence of the fact that a semi-empirical mass formula must consider shell correction and nuclear deformation, which become far more pronounced for heavy nuclides.<ref name=frdm2012 /><ref name=liquiddrop>{{cite journal|last=Möller|first=P.|date=2016|title=The limits of the nuclear chart set by fission and alpha decay|journal=EPJ Web of Conferences|volume=131|pages=03002:1–8|url=http://inspirehep.net/record/1502715/files/epjconf-NS160-03002.pdf|doi=10.1051/epjconf/201613103002|bibcode=2016EPJWC.13103002M|doi-access=free}}</ref>

The beta-stable ''fully ionized'' nuclei (with all electrons stripped) are somewhat different. Firstly, if a proton-rich nuclide can only decay by electron capture (because the energy difference between the parent and daughter is less than 1.022&nbsp;MeV, the amount of decay energy needed for positron emission), then full ionization makes decay impossible. This happens for example for ⁷Be.<ref> {{cite journal |author-first=Fritz |author-last=Bosch |year=1995 |title=Manipulation of Nuclear Lifetimes in Storage Rings |journal=Physica Scripta |volume=T59 |pages=221–229 |doi=10.1088/0031-8949/1995/t59/030 |bibcode=1995PhST...59..221B |s2cid=250860726 |url=http://www.ca.infn.it/~oldeman/resneu/physscr5_T59_030.pdf |archive-url=https://web.archive.org/web/20131226210737/http://www.ca.infn.it/~oldeman/resneu/physscr5_T59_030.pdf |archive-date=2013-12-26 }}</ref> Moreover, sometimes the energy difference is such that while β⁻ decay violates conservation of energy for a neutral atom, bound-state β⁻ decay (in which the decay electron remains bound to the daughter in an atomic orbital) is possible for the corresponding bare nucleus. Within the range {{nowrap|2 ≤ ''A'' ≤ 270}}, this means that ¹⁶³Dy, ¹⁹³Ir, ²⁰⁵Tl, ²¹⁵At, and ²⁴³Am among beta-stable neutral nuclides cease to be beta-stable as bare nuclides, and are replaced by their daughters ¹⁶³Ho, ¹⁹³Pt, ²⁰⁵Pb, ²¹⁵Rn, and ²⁴³Cm (bound-state β⁻ decay has been observed for ¹⁶³Dy, ²⁰⁵Tl and is predicted for ¹⁹³Ir, ²¹⁵At, ²⁴³Am).<ref>{{cite journal |last1=Liu |first1=Shuo |last2=Gao |first2=Chao |last3=Xu |first3=Chang |date=2021 |title=Investigation of bound state β⁻ decay half-lives of bare atoms |url= |journal=Physical Review C |volume=104 |issue=2 |article-number=024304 |doi=10.1103/PhysRevC.104.024304 }}</ref> {{clear}}

== Beta decay toward minimum mass == [[File:Valley of Stability Parabola 2.jpg|thumb|right|upright=1.5|The negative of binding energy per nucleon for nuclides with atomic mass number 125 plotted as a function of atomic number. The profile of binding energy across the valley of stability is roughly a parabola. Tellurium-125 (₅₂Te) is stable, while antimony-125 (₅₁Sb) is unstable to β− decay. Nuclei up the walls decay toward the middle.]] Beta decay generally causes nuclides to decay toward the isobar with the lowest mass (which is often, but not always, the one with highest binding energy) with the same mass number. Those with lower atomic number and higher neutron number than the minimum-mass isobar undergo beta-minus decay, while those with higher atomic number and lower neutron number undergo beta-plus decay or electron capture.

However, there are a few odd-odd nuclides between two beta-stable even-even isobars, that predominantly decay to the ''higher''-mass of the two beta-stable isobars. For example, ⁴⁰K could either undergo electron capture or positron emission to ⁴⁰Ar, or undergo beta minus decay to ⁴⁰Ca: both possible products are beta-stable. The former process would produce the lighter of the two beta-stable isobars, yet the latter is more common.

{| class="wikitable" ! !! rowspan=12| !! Nuclide !! Mass !! rowspan=12| !! Nuclide !! Mass !! rowspan=12| !! Nuclide !! Mass |- ! Parent | Cl-36 || 35.96830698 || K-40 || 39.96399848 || Ag-108 || 107.905956 |- ! Minority decay (β+/EC) | 2% to S-36 || 35.96708076 || 10.72% to Ar-40 || 39.9623831225 || 3% to Pd-108 || 107.903892 |- ! Majority decay (β−) | 98% to Ar-36 || 35.967545106 || 89.28% to Ca-40 || 39.96259098 || 97% to Cd-108 || 107.904184 |- ! !! Nuclide !! Mass !! Nuclide !! Mass !! Nuclide !! Mass |- ! Parent | Eu-150m || 149.919747 || Eu-152m1 || 151.9217935 || Am-242 || 242.0595474 |- ! Minority decay (β+/EC) | 11% to Sm-150 || 149.9172755 || 28% to Sm-152 || 151.9197324 || 17.3% to Pu-242 || 242.0587426 |- ! Majority decay (β−) | 89% to Gd-150 || 149.918659 || 72% to Gd-152 || 151.9197910 || 82.7% to Cm-242 || 242.0588358 |- ! !! Nuclide !! Mass !! Nuclide !! Mass !! Nuclide !! Mass |- ! Parent | Pm-146 || 145.914696 |- ! Minority decay (β−) | 37% to Sm-146 || 145.913041 |- ! Majority decay (β+/EC) | 63% to Nd-146 || 145.9131169 |} * Isotope masses from: ** {{NUBASE 2020}}

== Notes == === Explanatory notes === {{notelist}} === Lists of beta-decay stable nuclides === {{notelist-lr}}

== References == {{reflist}}

== External links == * Decay-Chains https://www-nds.iaea.org/relnsd/NdsEnsdf/masschain.html * (Russian) [https://web.archive.org/web/20131217155419/http://wsyachina.narod.ru/physics/all_matter/sist-1a.jpg Beta-decay stable nuclides up to ''Z'' = 118] (data for ''Z'' ≥ 102 are predictions)

{{DEFAULTSORT:Beta-Decay Stable Isobars}} Category:Nuclear physics