Beta-decay Stable Isobars
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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 regards to double beta decay or theoretically higher simultaneous beta decay, as they have the lowest energy of all nuclides 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.[1][2] 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.

? decay stable / even A
?DS One Two Three
2-34 17
36-58 5 7
60-72 5 2
74-116 2 19 1
118-154 2 11 6
156-192 5 14
194-210 6 3
212-262 7 19
Total 49 75 7

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

Among even mass number, seven (96, 124, 130, 136, 148, 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 nine (36, 40, 46, 48, 50, 54, 58, 64, 70) have two, and the remaining 11 have one.
• From 74 to 122, only three (88, 90, 118) have one, and the remaining 22 have two.
• From 124 to 154, only one (140) has one, six have three, and the remaining 9 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 an extremely long half-life (over 1015 years). All elements up to and including nobelium, except technetium and promethium, are known to have at least one beta-stable isotope.

## List of known beta-decay stable isobars

350 beta-decay stable nuclides are currently known.[3][4] Theoretically predicted or experimentally observed double beta-decay (if not dominated by alpha decay or spontaneous fission) is shown by arrows, i.e. arrows point towards the lightest-mass isobar.

No beta-decay stable nuclide has proton number 43 or 61 and no beta-decay stable nuclide has neutron number 19, 21, 35, 39, 45, 61, 71, 89, 115, 123, or 147.

Even N Odd N
Even Z Even A Odd A
Odd Z Odd A Even A
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
1H 2H 3He 4He 5He (n) 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 48Ca[a] -> 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 96Zr[b] -> 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 (?) 148Gd (?) 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[c] (?) 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 (SF) -> 254Fm (?) 255Fm (?) 256Cf (SF) -> 256Fm (SF)
257Fm (?) 258Fm (SF) 258No (SF) 259Md (SF) 260Fm (SF) -> 260No (SF) 262No (SF)
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. 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.[8]

All beta-decay stable nuclides with A >= 209 were observed to decay by alpha decay except some where spontaneous fission dominates. With the exception of 262No, no nuclides with A >= 260 have been definitively identified as beta-stable, although 260Fm and 262No are unconfirmed.[4]

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.[9] Beyond the island of stability, various models that correctly predict the known beta-stable isotopes 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.[8][10] 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.[10][11]

## Beta decay toward minimum mass

Beta decay generally causes isotopes to decay toward the isobar with the lowest mass (highest binding energy) with the same mass number, those not in italics in the table above. Thus, 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 four nuclides that are exceptions, in that the majority of their decays are in the opposite direction:

 Chlorine-36 35.9683 Potassium-40 39.964 Silver-108 107.906 Promethium-146 145.915 2% to Sulfur-36 35.9671 11.2% to Argon-40 39.9624 3% to Palladium-108 107.904 37% to Samarium-146 145.913 98% to Argon-36 35.9675 89% to Calcium-40 39.9626 97% to Cadmium-108 107.904 63% to Neodymium-146 145.913

## Notes

1. ^ This isotope 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+0.8
-0.6
×1021 years, longer than its double beta decay half-life, meaning that double beta decay would usually occur first.[5]
2. ^ This isotope is theoretically capable of beta decay to 96Nb, thus making it not a beta-stable nuclide. However, such a process has never been observed, having a partial half-life greater than 2.4×1019 years, longer than its double beta decay half-life, meaning that double beta decay would usually occur first.[6]
3. ^ While the AME2016 atomic mass evaluation gives 222Rn a lower mass than 222Fr,[4] implying beta stability, it is predicted that single beta decay of 222Rn is energetically possible (albeit with very low decay energy),[7] and it falls within the error margin given in AME2016.[4] Hence, 222Rn is probably not beta-stable, 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.[7]

## References

1. ^ 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
2. ^ Annual Review of Nuclear and Particle Science Vol. 29: 69-119 (Volume publication date December 1979) P G Hansen, "Nuclei Far Away from the Line of Beta Stability: Studies by On-Line Mass Separation" doi:10.1146/annurev.ns.29.120179.000441
3. ^ Interactive Chart of Nuclides (Brookhaven National Laboratory)
4. ^ a b c d Audi, G.; Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S. (2017). "The NUBASE2016 evaluation of nuclear properties" (PDF). Chinese Physics C. 41 (3): 030001. Bibcode:2017ChPhC..41c0001A. doi:10.1088/1674-1137/41/3/030001.
5. ^ Aunola, M.; Suhonen, J.; Siiskonen, T. (1999). "Shell-model study of the highly forbidden beta decay 48Ca -> 48Sc". EPL. 46 (5): 577. doi:10.1209/epl/i1999-00301-2.
6. ^ Finch, S.W.; Tornow, W. (2016). "Search for the ? decay of 96Zr". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 806: 70-74. doi:10.1016/j.nima.2015.09.098.
7. ^ a b Belli, P.; Bernabei, R.; Cappella, C.; Caracciolo, V.; Cerulli, R.; Danevich, F.A.; Di Marco, A.; Incicchitti, A.; Poda, D.V.; Polischuk, O.G.; Tretyak, V.I. (2014). "Investigation of rare nuclear decays with BaF2 crystal scintillator contaminated by radium". European Physical Journal A. 50: 134-143. arXiv:1407.5844. doi:10.1140/epja/i2014-14134-6.
8. ^ a b Koura, H. (2011). Decay modes and a limit of existence of nuclei in the superheavy mass region (PDF). 4th International Conference on the Chemistry and Physics of the Transactinide Elements. Retrieved 2018.
9. ^ Zagrebaev, Valeriy; Karpov, Alexander; Greiner, Walter (2013). "Future of superheavy element research: Which nuclei could be synthesized within the next few years?" (PDF). Journal of Physics. 420: 012001. arXiv:1207.5700. doi:10.1088/1742-6596/420/1/012001.
10. ^ a b Möller, P.; Sierk, A.J.; Ichikawa, T.; Sagawa, H. (2016). "Nuclear ground-state masses and deformations: FRDM(2012)". Atomic Data and Nuclear Data Tables. 109-110: 1-204. arXiv:1508.06294. doi:10.1016/j.adt.2015.10.002.
11. ^ Möller, P. (2016). "The limits of the nuclear chart set by fission and alpha decay" (PDF). EPJ Web of Conferences. 131: 03002:1-8. doi:10.1051/epjconf/201613103002.