Talk:Even and odd atomic nuclei

Pairing effects

The primordial nuclide total listed here (289) does not match that given elsewhere in wikipedia i.e. at Primordial Nuclide (288). The EE value there is 169. I think that U-234 was accidently included here. The next long lived nuclide after Pu-244 (82My) is Nb-92 (37My). This should be the 289th primordial nuclide. U-235 has only a 245ky half life. The tables at the start and end of the article also need fixed to show 288 total primordial nuclides. 99.32.172.114 (talk) 05:23, 14 April 2013 (UTC)

Fissile nuclides

Fissile nuclides tend to have even Z and odd N. This is very important and should perhaps be more prominently stated in the article.

• https://www.researchgate.net/publication/253845692_Statistical_Approaches_to_the_Even-odd_Effect_in_Fission
• https://www.sciencedirect.com/topics/earth-and-planetary-sciences/nuclear-binding-energy
• https://link.springer.com/article/10.1134/S1063778823010222

Looking for better sources. Andrewa (talk) 04:07, 6 February 2024 (UTC)

I believe that they can also have odd Z, but those tend to have shorter half-life. But yes, odd N, and the article should explain that. It is the extra binding energy of paired neutrons that does it. Gah4 (talk) 06:42, 6 February 2024 (UTC)

Interesting... what would be an example of a fissile nuclide with odd Z? Andrewa (talk) 07:15, 6 February 2024 (UTC)

It appears that the odd-odd neptunium-236 is fissile, and not only fissionable. See page 13 of [1]. ^Complex/_Rational 18:35, 6 February 2024 (UTC)

Interesting... that's the source given here too. That document doesn't seem to cite the source of its information, and the document as a whole is a very deliberately conservative evaluation. Can we do better, I wonder? Andrewa (talk) 19:46, 12 February 2024 (UTC)

@Andrewa: I found some more about it (and fissile nuclides in general) in doi:10.1119/1.4966630 – the key takeaway is that ²³⁶Np is fissile, but so difficult to produce that its critical mass has not been experimentally measured. It also clearly states that even-N nuclides such as ²³⁷Np and ²⁴¹Am are not fissile, despite other sources categorizing them as such. I can email you a pdf of the article if you can't access it online. ^Complex/_Rational 23:44, 12 February 2024 (UTC)

Odd-odd nuclides that are very stable to beta decay and/or IT

For some odd-odd nuclides, beta decay and/or IT requires high spin change. For the following nuclides, a such decay process is at least 3 forbidden non-unique or 4 forbidden unique. The states are taken from:

https://www.nndc.bnl.gov/nudat3/getdataset.jsp?nucleus=X&unc=NDS, where X is a nuclide symbol (for example https://www.nndc.bnl.gov/nudat3/getdataset.jsp?nucleus=50V&unc=NDS);

If the link does not work, an alternative is

https://www.nndc.bnl.gov/ensnds/M/X/adopted.pdf, where X is an element name and M is a mass number (for example https://www.nndc.bnl.gov/ensnds/50/V/adopted.pdf).

Nuclide	QITmax (keV)	QECmax (keV)	Qβ−max (keV)	Possible IT processes	Possible EC processes	Possible β− processes
50V	-	2204.9	1037.9	-	6+→0+ (ΔJΔπ = 6+), 2204.9 6+→2+ (ΔJΔπ = 4+), 651.1	6+→0+ (ΔJΔπ = 6+), 1037.9 6+→2+ (ΔJΔπ = 4+), 254.6
180mTa	77.2	929.4	785.5	9−→1+ (ΔJΔπ = 8−), 77.2 9−→2+ (ΔJΔπ = 7−), 37.7	9−→0+ (ΔJΔπ = 9−), 929.4 9−→2+ (ΔJΔπ = 7−), 837.0 9−→4+ (ΔJΔπ = 5−), 620.8 9−→6+ (ΔJΔπ = 3−), 288.6	9−→0+ (ΔJΔπ = 9−), 785.5 9−→2+ (ΔJΔπ = 7−), 681.9 9−→4+ (ΔJΔπ = 5−), 447.9 9−→6+ (ΔJΔπ = 3−), 97.0
210mBi	271.3	207.8	1432.6	9−→1− (ΔJΔπ = 8+), 271.3 9−→0− (ΔJΔπ = 9+), 224.8	9−→0+ (ΔJΔπ = 9−), 207.8	9−→0+ (ΔJΔπ = 9−), 1432.6 9−→2+ (ΔJΔπ = 7−), 251.2 9−→4+ (ΔJΔπ = 5−), 5.9
214mAt	231.0	1321.4	1170.9	9−→1− (ΔJΔπ = 8+), 231.0 9−→0− (ΔJΔπ = 9+), 153.0 9−→2− (ΔJΔπ = 7+), 85.9 9−→3− (ΔJΔπ = 6+), 44.0 9−→4− (ΔJΔπ = 5+), 2.9	9−→0+ (ΔJΔπ = 9−), 1321.4 9−→2+ (ΔJΔπ = 7−), 712.1 9−→4+ (ΔJΔπ = 5−), 306.3 9−→3− (ΔJΔπ = 6+), 46.6	9−→0+ (ΔJΔπ = 9−), 1170.9 9−→2+ (ΔJΔπ = 7−), 476.1 9−→4+ (ΔJΔπ = 5−), 29.7

103.166.228.86 (talk) 15:29, 15 April 2024 (UTC)

Note that the spins of ¹⁸⁰Hf and ¹⁸⁰W are also due to collective nuclear rotation. 14.52.231.91 (talk) 00:56, 20 August 2024 (UTC)

Beta decays of odd-odd nuclides with low spin change that take a long time to happen

Look at the level diagram (in keV) of some decay products:

Nuclide	0+ → 2+	2+ → 4+	4+ → 6+	6+ → 8+	8+ → 10+	10+ → 12+	12+ → 14+
176Hf	88.35	201.83	306.64	400.91	483.33	553.60	611.94
236U	45.24	104.24	160.31	212.47	260.14	303.00	341.00
236Pu	44.6	102.8	158.4	209.9	257.8	300.8	339.3
248Cm	43.4	100.4	155.1	207.5	256.4	301.3	342.1
248Cf	41.5	96.3	149.6	200.6	249.5

These levels are separated by $2\hbar$ units of spin, and their energies get further apart as the spin increases. That's a classic sign of collective nuclear rotation, with a rigid rotor having kinetic energy $E\propto J^{2}$. On the other hand, the high spins of ¹⁷⁶Lu, ²³⁶Np, and ²⁴⁸Bk are intrinsic, so the decay processes must overcome a terrible match even if the spin change is low. Their β decay information:

Decay process	Qβ (keV)	Spin change	Half-life (a)	Intensities taken from
176Lu → 176Hf	593.33	7− → 6+ (ΔJΔπ = 1−, 1 forbidden non-unique)	3.72×1010	[2]
	192.49	7− → 8+ (ΔJΔπ = 1−, 1 forbidden non-unique)	9.49×1012
236Np → 236U	783.52	6− → 4+ (ΔJΔπ = 2−, 1 forbidden unique)	unknown (at the order of 108?)	[3]
	623.21	6− → 6+ (ΔJΔπ = 0−, 1 forbidden non-unique)	1.78×105
	85.40	6− → 5− (ΔJΔπ = 1+, allowed)	1.55×108
236Np → 236Pu	329.15	6− → 4+ (ΔJΔπ = 2−, 1 forbidden unique)	unknown (at the order of 109?)	[4]
	170.80	6− → 6+ (ΔJΔπ = 0−, 1 forbidden non-unique)	1.29×106
248Bk → 248Cm	388.07	6+ → 6+ (ΔJΔπ = 0+, allowed)	unknown (at the order of 107?)
248Bk → 248Cf	552.01	6+ → 6+ (ΔJΔπ = 0+, allowed)	unknown (at the order of 106?)

On the other hand, the longevity is probably not applicable to the unknown decay processes ^212mAt → ²¹²Po (9⁻ → 8⁺, Q_EC = 271.84 keV) and ^216mAt → ²¹⁶Rn (9⁻ → 8⁺, Q_β− = 517.68 keV), because the high spin of ²¹²Po and ²¹⁶Rn does not seem to be a result of collective nuclear rotation, as their level diagrams are irregular:

Nuclide	0+ → 2+	2+ → 4+	4+ → 6+	6+ → 8+	8+ → 10+	10+ → 12+	12+ → 14+
212Po	727.33	405.18	222.98	120.90	357.50	868.34	183.17
216Rn	461.4	379.1	385.4	419.1	294.7	465.9	420.5

It should be pointed out that, although not specified, it seems that ^212mBi → ²¹²Po (9⁻ → 8⁺, Q_β− = 775.11 keV) is known, as shown in the last diagram of here. 129.104.241.193 (talk) 15:10, 7 May 2024 (UTC)

According to here, collective nuclear rotation of even-even nuclides is being charateristic of having transition energies $E={\dfrac {C}{A^{5/3}}}j(j+1)$, where $A$ is the mass number, $j$ is the spin and $C$ is a constant about $70\,{\rm {MeV}}$. This matches the first table above in this section extremely well. We can also see that the spins of states of ²¹²Po or ²¹⁶Rn are by no means due to collective nuclear rotation.

According to the same link above, collective nuclear rotation is typical for nuclides with $150<A<190$ or $A>220$. 14.52.231.91 (talk) 07:20, 15 August 2024 (UTC)

Other than ¹⁷⁶Lu, ²³⁶Np, ²⁴⁸Bk, lack of beta decay of ^186mRe and ^242mAm (but their IT decays are known in contrast to the former three nuclides) is also due to collective nuclear rotation of beta daughters (¹⁸⁶Os, ²⁴²Pu/²⁴²Cm). 14.52.231.91 (talk) 00:22, 16 August 2024 (UTC)

Well I'm not quite sure about ^186mRe. In theory the only available beta process should be ^186mRe (8⁺) → ¹⁸⁶Os (6⁺), Q = 149.93 keV. This is itself a 2 forbidden non-unique process with a relative small decay energy. And considering that the similar process ⁹⁸Tc (6⁺) → ⁹⁸Mo (4⁺) (where the 4⁺ spin of ⁹⁸Mo is not due to collective nuclear rotation), Q = 173.95 keV is not even known... 14.52.231.91 (talk) 02:04, 16 August 2024 (UTC)

Also, it is worthy noting that the transition energies of ¹⁸⁶W and 186Os still satisfy $E={\dfrac {C}{A^{5/3}}}j(j+1)$, but here $C$ is about $119\,{\rm {MeV}}$, about 1.7 times compared to other even-even nuclides considered above. Are there any explanations? 14.52.231.91 (talk) 02:14, 16 August 2024 (UTC)

Odd-odd isomers

Many odd-odd nuclides have a low-spin state and a high-spin state whose energies are close to each other. For these nuclides, IT of the state with higher energy is pratically impossible, so the two states behave somehow like "two ground states". Here are some examples.

Nuclide	Low-spin state	High-spin state
92Nb	2+ (135.5 keV, β+=10.15 d, β-=?)	7+ (0 keV, EC=3.47×107 y, β-=6.94×1010 y)
166Ho	0- (0 keV, β-=26.824 h)	7- (5.985 keV, β-=1.20×103 y)
176Lu	1- (122.845 keV, β-=3.667 h, EC=160.7 d)	7- (0 keV, β-=3.701×1010 y, EC=8.22×1012 y)
180Ta	1+ (0 keV, EC=9.593 h, β-=2.265 d)	9- (77.1 keV, EC=very long, β-=very long)
248Bk	1- (order uncertain, β-=1.41 d, EC=3.29 d)	6+ (order uncertain, β-=?, EC=?)

Note that this list does not include ¹⁸⁶Re or ²⁴²Am, because the ITs of their isomers are well known. — Preceding unsigned comment added by 103.166.228.86 (talk) 00:59, 12 September 2024 (UTC)