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Beta-decay stable isobars

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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.

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

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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.

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 an extremely long half-life (over 1015 years). (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[3] and 247Cm (the most stable isotopes of their elements considering all decay modes). Finally, 48Ca and 96Zr have not been observed to undergo beta decay (theoretically possible for both) 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

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See also: List of stable isotopes

346 beta-decay stable nuclides (including 260Fm whose discovery is unconfirmed) have been definitively identified as beta-stable.[4][5] Theoretically predicted or experimentally observed double beta-decay is shown by arrows, i.e. arrows point towards the lightest-mass isobar. This is sometimes dominated by alpha decay or spontaneous fission, especially for the heavy elements. Possible decay modes are listed as α for alpha decay, SF for spontaneous fission, and n for neutron emission in the special case of 5He. For mass 5 there are no bound isobars at all; there are bound isobars for mass 8, but the beta-stable one 8Be is unbound.[6]

Two beta-decay stable nuclides exist for odd neutron numbers 1 (2H and 3He), 3 (5He and 6Li – the former having 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 (136Xe, 138Ba, 139La, 140Ce, 141Pr, 142Nd, and 144Sm) and five for N = 20 (36S, 37Cl, 38Ar, 39K, and 40Ca), 50 (86Kr, 88Sr, 89Y, 90Zr, and 92Mo, noting also primordial but not beta-stable 87Rb), 58 (100Mo, 102Ru, 103Rh, 104Pd, and 106Cd), 74 (124Sn, 126Te, 127I, 128Xe, and 130Ba), 78 (130Te, 132Xe, 133Cs, 134Ba, and 136Ce), 88 (148Nd, 150Sm, 151Eu, 152Gd, and 154Dy – the last not primordial), and 90 (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.[7]

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.[8][9]

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 (α)
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[a]
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[b]
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 (α) ← 144Sm
145Nd 146Nd → 146Sm (α) 147Sm (α) 148Nd → 148Sm (α)[c] 149Sm 150Nd → 150Sm ← 150Gd (α) 151Eu (α) 152Sm ← 152Gd (α)
153Eu 154Sm → 154Gd ← 154Dy (α) 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 (α) 175Lu 176Yb → 176Hf
177Hf 178Hf 179Hf 180Hf ← 180W (α) 181Ta 182W 183W 184W ← 184Os (α)
185Re 186W → 186Os (α) 187Os 188Os 189Os 190Os ← 190Pt (α) 191Ir 192Os → 192Pt
193Ir 194Pt 195Pt 196Pt ← 196Hg 197Au 198Pt → 198Hg 199Hg 200Hg
201Hg 202Hg 203Tl 204Hg → 204Pb 205Tl 206Pb 207Pb 208Pb
209Bi (α) 210Po (α) 211Po (α) 212Po (α) ← 212Rn (α) 213Po (α) 214Po (α) ← 214Rn (α) 215At (α) 216Po (α) → 216Rn (α)
217Rn (α) 218Rn (α) ← 218Ra (α) 219Fr (α) 220Rn (α) → 220Ra (α) 221Ra (α) 222Ra[d] (α) 223Ra (α) 224Ra (α) ← 224Th (α)
225Ac (α) 226Ra (α) → 226Th (α) 227Th (α) 228Th (α) 229Th (α) 230Th (α) ← 230U (α) 231Pa (α) 232Th (α) → 232U (α)
233U (α) 234U (α) 235U (α) 236U (α) ← 236Pu (α) 237Np (α) 238U (α) → 238Pu (α) 239Pu (α) 240Pu (α)
241Am (α) 242Pu (α) ← 242Cm (α) 243Am (α) 244Pu (α) → 244Cm (α) 245Cm (α) 246Cm (α) 247Bk (α) 248Cm (α) → 248Cf (α)
249Cf (α) 250Cf (α) 251Cf (α) 252Cf (α) ← 252Fm (α) 253Es (α) 254Cf (SF) → 254Fm (α) 255Fm (α) 256Fm[e] (SF)
257Fm (α) 258Fm (SF) ← 258No (SF) [f] 260Fm[g] (SF) → 260No (SF) [h] 262No (SF)[i]
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.[8]

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.[13] 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.[8][14] 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.[14][15]

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 MeV, the amount of decay energy needed for positron emission), then full ionization makes decay impossible. This happens for example for 7Be.[16] 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 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.[17]

Beta decay toward minimum mass

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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.

Nuclide Mass Nuclide Mass 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:
    • Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S.; Audi, G. (2021). "The NUBASE2020 evaluation of nuclear properties" (PDF). Chinese Physics C. 45 (3): 030001. doi:10.1088/1674-1137/abddae.

Notes

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  1. ^ 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+0.8
    −0.6    ×1021 years, longer than its double beta decay half-life, meaning that double beta decay would usually occur first.[10]
  2. ^ 96Zr 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.[11]
  3. ^ 148Gd was previously thought to be a third beta-stable isobar for mass 148,[6] 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 keV, even lower than likewise unseen electron capture of 123Te), and only alpha decay has been observed experimentally for 148Gd.
  4. ^ While the AME2020 atomic mass evaluation gives 222Rn a lower mass than 222Fr (the β−-decay energy is given as (−6 ± 8) keV),[5] implying beta-stability, it is predicted that single beta decay of 222Rn is energetically possible (albeit with very low decay energy),[3] 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.[3]
  5. ^ While the AME2020 atomic mass evaluation gives 256Cf a lower mass than 256Es (the β−-decay energy is given as (−140# ± 330#) keV),[5] 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.
  6. ^ While the AME2020 atomic mass evaluation gives 259Md a lower mass than 259Fm (the β+-decay energy is given as (−140# ± 300#) keV),[5] 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.
  7. ^ Discovery of this nuclide is unconfirmed
  8. ^ 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.[12][8]
  9. ^ While the AME2020 atomic mass evaluation gives 262Rf a higher mass than 262Lr (the β+-decay energy is given as (290# ± 300#) keV),[5] 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.

References

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  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. ^ Hansen, P. G. (1979). "Nuclei Far Away from the Line of Beta Stability: Studies by On-Line Mass Separation". Annual Review of Nuclear and Particle Science. 29: 69–119. Bibcode:1979ARNPS..29...69H. doi:10.1146/annurev.ns.29.120179.000441.
  3. ^ a b c 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 (9): 134–143. arXiv:1407.5844. Bibcode:2014EPJA...50..134B. doi:10.1140/epja/i2014-14134-6. S2CID 118513731.
  4. ^ "Interactive Chart of Nuclides (Brookhaven National Laboratory)". Archived from the original on 2020-07-25. Retrieved 2009-06-19.
  5. ^ a b c d e Wang, Meng; Huang, W.J.; Kondev, F.G.; Audi, G.; Naimi, S. (2021). "The AME 2020 atomic mass evaluation (II). Tables, graphs and references". Chinese Physics C. 45 (3): 030003. doi:10.1088/1674-1137/abddaf.
  6. ^ a b Tretyak, V.I.; Zdesenko, Yu.G. (2002). "Tables of Double Beta Decay Data — An Update". At. Data Nucl. Data Tables. 80 (1): 83–116. Bibcode:2002ADNDT..80...83T. doi:10.1006/adnd.2001.0873.
  7. ^ Belli, P.; Bernabei, R.; Danevich, F. A.; et al. (2019). "Experimental searches for rare alpha and beta decays". European Physical Journal A. 55 (8): 140–1–140–7. arXiv:1908.11458. Bibcode:2019EPJA...55..140B. doi:10.1140/epja/i2019-12823-2. ISSN 1434-601X. S2CID 201664098.
  8. ^ a b c d 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 18 November 2018.
  9. ^ Koura, H.; Katakura, J; Tachibana, T; Minato, F (2015). "Chart of the Nuclides". Japan Atomic Energy Agency. Retrieved 30 October 2018.
  10. ^ Aunola, M.; Suhonen, J.; Siiskonen, T. (1999). "Shell-model study of the highly forbidden beta decay 48Ca → 48Sc". EPL. 46 (5): 577. Bibcode:1999EL.....46..577A. doi:10.1209/epl/i1999-00301-2.
  11. ^ Finch, S.W.; Tornow, W. (2016). "Search for the β decay of 96Zr". Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment. 806: 70–74. Bibcode:2016NIMPA.806...70F. doi:10.1016/j.nima.2015.09.098.
  12. ^ Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S.; Audi, G. (2021). "The NUBASE2020 evaluation of nuclear properties" (PDF). Chinese Physics C. 45 (3): 030001. doi:10.1088/1674-1137/abddae.
  13. ^ 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 (1): 012001. arXiv:1207.5700. Bibcode:2013JPhCS.420a2001Z. doi:10.1088/1742-6596/420/1/012001. S2CID 55434734.
  14. ^ 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. Bibcode:2016ADNDT.109....1M. doi:10.1016/j.adt.2015.10.002. S2CID 118707897.
  15. ^ Möller, P. (2016). "The limits of the nuclear chart set by fission and alpha decay" (PDF). EPJ Web of Conferences. 131: 03002:1–8. Bibcode:2016EPJWC.13103002M. doi:10.1051/epjconf/201613103002.
  16. ^ Bosch, Fritz (1995). "Manipulation of Nuclear Lifetimes in Storage Rings" (PDF). Physica Scripta. T59: 221–229. Bibcode:1995PhST...59..221B. doi:10.1088/0031-8949/1995/t59/030. S2CID 250860726. Archived from the original (PDF) on 2013-12-26.
  17. ^ Liu, Shuo; Gao, Chao; Xu, Chang (2021). "Investigation of bound state β− decay half-lives of bare atoms". Physical Review C. 104 (2): 024304. doi:10.1103/PhysRevC.104.024304.
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