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August 24

The magic number N = 126

This question is mostly theoretical, because there's no feasible way to create such heavy neutron-rich isotopes at present. But: what predictions are there on the N = 126 shell closure at low proton numbers? In particular, is ¹⁷⁶Sn (Z = 50, N = 126) expected to be doubly magic, or will this shell closure disappear that far from the valley of stability (like N = 20 does)?

(I got some links about this at User talk:ComplexRational#fluorine-30: thanks, Nucleus hydro elemon! But I thought it'd be worth asking for more answers.) Double sharp (talk) 17:41, 24 August 2024 (UTC)[reply]

Even if it exists it will be extremally unstable relative beta decay. Ruslik_Zero 19:57, 24 August 2024 (UTC)[reply]

Yes of course, since ⁷⁸Ni is also quite unstable to beta decay. What I'm curious about is (1) whether ¹⁷⁶Sn should exist and (2) whether it does close the neutron shell, or if the energy gaps are expected to change in this extremely neutron-rich region. Double sharp (talk) 04:33, 25 August 2024 (UTC)[reply]

The heaviest isotope of tin known is ¹⁴⁰
₅₀Sn
, which lives less 50 ms and already drips neutrons. The existence of an isotope as heavy as ¹⁷⁶
₅₀Sn
seems unlikely. Magic number itself does not mean that the nucleus exists in any meaningful way. You can look at ¹⁰
₂He
. Ruslik_Zero 20:48, 26 August 2024 (UTC)[reply]

That's beta-delayed neutron emission, so the drip line hasn't been reached yet, as expected.

It seems then that the best we could find at the moment are the papers Nucleus hydro elemon found at first, which suggest that ¹⁷⁶Sn should be more or less on the border between being bound and being unbound. Those two papers suggest N = 126 is still magic (because the two-neutron separation energy has a big jump going from ¹⁷⁶Sn to ¹⁷⁸Sn), but this one makes it less clear. Since this is so far from what's currently known, it's probably not possible to do better at the moment. I'd guess, therefore, that the best possible answer to my question at the moment would have to be "no one really knows; could be either way". Double sharp (talk) 06:27, 27 August 2024 (UTC)[reply]

I found a reference by Fang et al. about beta decay of ¹⁷⁶Sn. Its β⁻ decay energy is around 22 MeV (comparable with ²⁹F 21.7 MeV) and has a half-life of <1 ms. ¹⁷⁶Sn should undergo β⁻n instead of only β⁻.

The calculated mass excess of ¹⁷⁶Sn is 217.59 MeV, as predicted by KTUY. Mass excess of ¹⁷⁶Sb is predicted to be 195.49 MeV, thus the β⁻ decay energy will be 22.10 MeV, not far away from Fang et al. Somehow the decay process β⁻,23n to ¹⁵³Sb+23n is actually possible with decay energy 2.47 MeV.

KTUY predicts S_2n of ^174,176,178Sn are −0.42,−0.52,−2.69 MeV, implies all of them can possibly undergo 2n emission. The big jump from ¹⁷⁶Sn to ¹⁷⁸Sn suggest N = 126 is still magic.

I think ¹⁷⁶Sn wouldn't get seriously affected by 2n emission, due to some trends related to atomic number. There is no heavy 2n emitters (the heaviest is ^26,28O with Z = 8), so I just show it with 2p emitters. Despite ¹²O (S_2p = −1.737 MeV, Z = 8) has a lower decay energy than ⁶⁷Kr (S_2p = −2.89 MeV, Z = 36), it decays much faster (8.9×10⁻²¹ s vs 7.4 ms). If the trend follows, then 2n emission of ¹⁷⁶Sn is just not important compared to beta decay.

So, I think there is nothing that forbids the existence of ¹⁷⁶Sn. Nucleus hydro elemon (talk) 14:50, 27 August 2024 (UTC)[reply]

@Nucleus hydro elemon: Thanks, very cool!

I think I'll upgrade my personal hunch to bet on ¹⁷⁶Sn being doubly magic, but I'll be interested as new predictions come. :) Double sharp (talk) 04:47, 28 August 2024 (UTC)[reply]