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%I #31 Feb 22 2024 20:09:53
%S 1,2,1,2,2,2,2,2,2,1,3,1,3,1,3,1,3,1,3,0,5,0,3,1,3,1,3,1,4,1,4,1,3,1,
%T 3,0,3,1,3,0,4,1,4,1,4,0,4,1,4,1,5,1,4,1,3,2,3,1,5,1,4,0,4,1,4,1,2,1,
%U 3,1,4,0,4,1,5,1,3,1,5,1,3,1,7,1,3,2,3,1,5,0,5
%N Number of beta-stable isotones of neutron number n.
%C A beta-stable nuclide is a nuclide whose beta decay (beta-minus and beta-plus decay) is energetically disallowed; that is to say, a nuclide that has lower energy than its isobars with one more or one less proton. Note that double beta decay is allowed. A nuclide whose beta decay is energetially allowed, even if not observed (in the case of 48Ca, 96Zr, 123Te, 148Gd, 180mTa, 222Rn and 247Cm), is not classified as being beta-stable.
%C We know 2 beta-stable isotopes with 160 neutrons (260Fm and 262No), but the unobserved nuclides 258Cf, 261No and 264Rf could be beta-stable as well.
%C Different from A318998: for N <= 126, 5He, 8Be, 146Sm, 150Gd, 154Dy, 210Po and 212Rn are beta-stable but not primordial. 40K, 48Ca, 50V, 96Zr, 113Cd, 115In, 123Te, 138La, 176Lu, 187Re and 180mTa are primordial but not beta-stable.
%C a(n) >= 2 for even 4 <= n <= 160, with a(n) = 2 for n = 4 (7Li and 8Be - the latter having an extremely short half-life), 6 (11B and 12C), 8 (15N and 16O), 66 (114Cd and 116Sn), 120 (198Pt and 200Hg) and 128 (212Po and 214Rn - both very unstable to alpha decay). a(82) = 7, and a(n) = 5 for n = 20, 50, 58, 74, 78, 88 and 90.
%C a(n) = 2 for odd n = 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). Page 12 of the Zagrebaev et al. link predicts that a(181) = 2 (corresponding to 293Cn and 295Fl).
%C Prediction of a(159)-a(187) from a Russian source: 1, 3, 1, 3, 1, 3, 1, 3, (0, 3 or 1, 2), 1, 4, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1.
%C Prediction of a(159)-a(209) from pages 14-15 of the Hiroyuki Koura link: 0, 5, 1, 3, 1, 4, 1, 4, 1, 4, 1, 3, 1, 5, 1, 4, 1, 5, 1, 4, 1, 5, 1, 4, 0, 6, 1, 4, 1, 3, 1, 4, 0, 4, 1, 4, 1, 3, 1, 5, 1, 3, 1, 4, 1, 3, 1, 4, 1, 2, 1.
%H Jianing Song, <a href="/A368860/b368860.txt">Table of n, a(n) for n = 0..158</a>
%H Hiroyuki Koura, <a href="http://tan11.jinr.ru/pdf/10_Sep/S_2/05_Koura.pdf">Decay Modes and a limit of existence of nuclei</a>, 4th International Conference on the Chemistry and Physics of the Transactinide Elements. (See <a href="https://en.wikipedia.org/wiki/User:ComplexRational/Isotopes#Beta-stable_isotopes_of_superheavy_elements">here</a> for an excerpted table.)
%H Web Archive, <a href="https://web.archive.org/web/20131217155419/http://wsyachina.narod.ru/physics/all_matter/sist-1a.jpg">The Russian prediction for the continuation of the line of beta stability to the superheavy region</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Beta-decay_stable_isobars">Beta-decay stable isobars</a>.
%H Valeriy Zagrebaev et al., <a href="https://iopscience.iop.org/article/10.1088/1742-6596/420/1/012001">Future of superheavy element research: Which nuclei could be synthesized within the next few years?</a>, Journal of Physics: Conference Series, 420 (March 2013).
%e a(56) = 3 because the beta-stable nuclides with 56 neutrons are 98Mo, 100Ru and 102Pd. Note that 96Zr is not beta-stable even if its beta decay has never been observed.
%e a(88) = 5 because the beta-stable nuclides with 88 neutrons are 148Nd, 150Sm, 151Eu, 152Gd and 154Dy, with the last one being not primordial.
%e a(126) = 4 because the beta-stable nuclides with 126 neutrons are 208Pb, 209Bi, 210Po and 212Rn, with the last two being not primordial.
%e a(158) = 4 because the beta-stable nuclides with 158 neutrons are 256Cf, 258Fm, 259Md and 260No.
%Y Cf. A368859 (beta-stable isotopes), A367461 (isodiaphers), A318998.
%Y Cf. A370457.
%K nonn,fini,hard
%O 0,2
%A _Jianing Song_, Jan 08 2024