Beta-decay stable isobars

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. 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.

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 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 have two, and the remaining 11 have one.
From 74 to 122, three have one, and the remaining 22 have two.
From 124 to 154, only one 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. 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 and ²⁴⁷Cm. Finally, ⁴⁸Ca and ⁹⁶Zr have not been observed to undergo beta decay which is extremely suppressed, but double beta decay is known for both. Similar suppression of single beta decay occurs also for ¹⁴⁸Gd, a rather short-lived alpha emitter.
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.

List of known beta-decay stable isobars

346 nuclides have been definitively identified as beta-stable. 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 He. For mass 5 there are no bound isobars at all; mass 8 has bound isobars, but the beta-stable Be is unbound.
Two beta-decay stable nuclides exist for odd neutron numbers 1, 3, 5, 7, 55, and 85 ; 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.
All even proton numbers 2 ≤ Z ≤ 102 have at least two beta-decay stable nuclides, with exactly two for Z = 4 and 6. Also, the only even neutron numbers with only one beta-decay stable nuclide are 0 and 2 ; at least two beta-decay stable nuclides exist for even neutron numbers in the range 4 ≤ N ≤ 160, with exactly two for N = 4, 6, 8, 66, 120, and 128. Seven beta-decay stable nuclides exist for the magic N = 82 and five for N = 20, 50, 58, 74, 78, 88, and 90.
For A ≤ 209, the only beta-decay stable nuclides that are not primordial nuclides are ⁵He, ⁸Be, ¹⁴⁶Sm, ¹⁵⁰Gd, and ¹⁵⁴Dy. 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.
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 may not represent the complete set.

	Even N	Odd N
Even Z	Even A	Odd A
Odd Z	Odd A	Even A

Odd A	Even A	Odd A	Even A	Odd A	Even A	Odd A	Even A
¹H	²H	³He	⁴He	⁵He	⁶Li	⁷Li	⁸Be
⁹Be	¹⁰B	¹¹B	¹²C	¹³C	¹⁴N	¹⁵N	¹⁶O
¹⁷O	¹⁸O	¹⁹F	²⁰Ne	²¹Ne	²²Ne	²³Na	²⁴Mg
²⁵Mg	²⁶Mg	²⁷Al	²⁸Si	²⁹Si	³⁰Si	³¹P	³²S
³³S	³⁴S	³⁵Cl	³⁶S ← ³⁶Ar	³⁷Cl	³⁸Ar	³⁹K	⁴⁰Ar ← ⁴⁰Ca
⁴¹K	⁴²Ca	⁴³Ca	⁴⁴Ca	⁴⁵Sc	⁴⁶Ca → ⁴⁶Ti	⁴⁷Ti	⁴⁸Ti
⁴⁹Ti	⁵⁰Ti ← ⁵⁰Cr	⁵¹V	⁵²Cr	⁵³Cr	⁵⁴Cr ← ⁵⁴Fe	⁵⁵Mn	⁵⁶Fe
⁵⁷Fe	⁵⁸Fe ← ⁵⁸Ni	⁵⁹Co	⁶⁰Ni	⁶¹Ni	⁶²Ni	⁶³Cu	⁶⁴Ni ← ⁶⁴Zn
⁶⁵Cu	⁶⁶Zn	⁶⁷Zn	⁶⁸Zn	⁶⁹Ga	⁷⁰Zn → ⁷⁰Ge	⁷¹Ga	⁷²Ge
⁷³Ge	⁷⁴Ge ← ⁷⁴Se	⁷⁵As	⁷⁶Ge → ⁷⁶Se	⁷⁷Se	⁷⁸Se ← ⁷⁸Kr	⁷⁹Br	⁸⁰Se → ⁸⁰Kr
⁸¹Br	⁸²Se → ⁸²Kr	⁸³Kr	⁸⁴Kr ← ⁸⁴Sr	⁸⁵Rb	⁸⁶Kr → ⁸⁶Sr	⁸⁷Sr	⁸⁸Sr
⁸⁹Y	⁹⁰Zr	⁹¹Zr	⁹²Zr ← ⁹²Mo	⁹³Nb	⁹⁴Zr → ⁹⁴Mo	⁹⁵Mo	⁹⁶Mo ← ⁹⁶Ru
⁹⁷Mo	⁹⁸Mo → ⁹⁸Ru	⁹⁹Ru	¹⁰⁰Mo → ¹⁰⁰Ru	¹⁰¹Ru	¹⁰²Ru ← ¹⁰²Pd	¹⁰³Rh	¹⁰⁴Ru → ¹⁰⁴Pd
¹⁰⁵Pd	¹⁰⁶Pd ← ¹⁰⁶Cd	¹⁰⁷Ag	¹⁰⁸Pd ← ¹⁰⁸Cd	¹⁰⁹Ag	¹¹⁰Pd → ¹¹⁰Cd	¹¹¹Cd	¹¹²Cd ← ¹¹²Sn
¹¹³In	¹¹⁴Cd → ¹¹⁴Sn	¹¹⁵Sn	¹¹⁶Cd → ¹¹⁶Sn	¹¹⁷Sn	¹¹⁸Sn	¹¹⁹Sn	¹²⁰Sn ← ¹²⁰Te
¹²¹Sb	¹²²Sn → ¹²²Te	¹²³Sb	¹²⁴Sn → ¹²⁴Te ← ¹²⁴Xe	¹²⁵Te	¹²⁶Te ← ¹²⁶Xe	¹²⁷I	¹²⁸Te → ¹²⁸Xe
¹²⁹Xe	¹³⁰Te → ¹³⁰Xe ← ¹³⁰Ba	¹³¹Xe	¹³²Xe ← ¹³²Ba	¹³³Cs	¹³⁴Xe → ¹³⁴Ba	¹³⁵Ba	¹³⁶Xe → ¹³⁶Ba ← ¹³⁶Ce
¹³⁷Ba	¹³⁸Ba ← ¹³⁸Ce	¹³⁹La	¹⁴⁰Ce	¹⁴¹Pr	¹⁴²Ce → ¹⁴²Nd	¹⁴³Nd	¹⁴⁴Nd ← ¹⁴⁴Sm
¹⁴⁵Nd	¹⁴⁶Nd → ¹⁴⁶Sm	¹⁴⁷Sm	¹⁴⁸Nd → ¹⁴⁸Sm	¹⁴⁹Sm	¹⁵⁰Nd → ¹⁵⁰Sm ← ¹⁵⁰Gd	¹⁵¹Eu	¹⁵²Sm ← ¹⁵²Gd
¹⁵³Eu	¹⁵⁴Sm → ¹⁵⁴Gd ← ¹⁵⁴Dy	¹⁵⁵Gd	¹⁵⁶Gd ← ¹⁵⁶Dy	¹⁵⁷Gd	¹⁵⁸Gd ← ¹⁵⁸Dy	¹⁵⁹Tb	¹⁶⁰Gd → ¹⁶⁰Dy
¹⁶¹Dy	¹⁶²Dy ← ¹⁶²Er	¹⁶³Dy	¹⁶⁴Dy ← ¹⁶⁴Er	¹⁶⁵Ho	¹⁶⁶Er	¹⁶⁷Er	¹⁶⁸Er ← ¹⁶⁸Yb
¹⁶⁹Tm	¹⁷⁰Er → ¹⁷⁰Yb	¹⁷¹Yb	¹⁷²Yb	¹⁷³Yb	¹⁷⁴Yb ← ¹⁷⁴Hf	¹⁷⁵Lu	¹⁷⁶Yb → ¹⁷⁶Hf
¹⁷⁷Hf	¹⁷⁸Hf	¹⁷⁹Hf	¹⁸⁰Hf ← ¹⁸⁰W	¹⁸¹Ta	¹⁸²W	¹⁸³W	¹⁸⁴W ← ¹⁸⁴Os
¹⁸⁵Re	¹⁸⁶W → ¹⁸⁶Os	¹⁸⁷Os	¹⁸⁸Os	¹⁸⁹Os	¹⁹⁰Os ← ¹⁹⁰Pt	¹⁹¹Ir	¹⁹²Os → ¹⁹²Pt
¹⁹³Ir	¹⁹⁴Pt	¹⁹⁵Pt	¹⁹⁶Pt ← ¹⁹⁶Hg	¹⁹⁷Au	¹⁹⁸Pt → ¹⁹⁸Hg	¹⁹⁹Hg	²⁰⁰Hg
²⁰¹Hg	²⁰²Hg	²⁰³Tl	²⁰⁴Hg → ²⁰⁴Pb	²⁰⁵Tl	²⁰⁶Pb	²⁰⁷Pb	²⁰⁸Pb
²⁰⁹Bi	²¹⁰Po	²¹¹Po	²¹²Po ← ²¹²Rn	²¹³Po	²¹⁴Po ← ²¹⁴Rn	²¹⁵At	²¹⁶Po → ²¹⁶Rn
²¹⁷Rn	²¹⁸Rn ← ²¹⁸Ra	²¹⁹Fr	²²⁰Rn → ²²⁰Ra	²²¹Ra	²²²Ra	²²³Ra	²²⁴Ra ← ²²⁴Th
²²⁵Ac	²²⁶Ra → ²²⁶Th	²²⁷Th	²²⁸Th	²²⁹Th	²³⁰Th ← ²³⁰U	²³¹Pa	²³²Th → ²³²U
²³³U	²³⁴U	²³⁵U	²³⁶U ← ²³⁶Pu	²³⁷Np	²³⁸U → ²³⁸Pu	²³⁹Pu	²⁴⁰Pu
²⁴¹Am	²⁴²Pu ← ²⁴²Cm	²⁴³Am	²⁴⁴Pu → ²⁴⁴Cm	²⁴⁵Cm	²⁴⁶Cm	²⁴⁷Bk	²⁴⁸Cm → ²⁴⁸Cf
²⁴⁹Cf	²⁵⁰Cf	²⁵¹Cf	²⁵²Cf ← ²⁵²Fm	²⁵³Es	²⁵⁴Cf → ²⁵⁴Fm	²⁵⁵Fm	²⁵⁶Fm
²⁵⁷Fm	²⁵⁸Fm ← ²⁵⁸No		²⁶⁰Fm → ²⁶⁰No		²⁶²No

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. 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. 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.
The beta-stable fully ionized nuclei are somewhat different. Firstly, if a proton-rich nuclide can only decay by electron capture, then full ionization makes decay impossible. This happens for example for ⁷Be. Moreover, sometimes the energy difference is such that while β⁻ decay violates conservation of energy for a neutral atom, bound-state β⁻ decay is possible for the corresponding bare nucleus. Within the range, 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.