Talk:Cluster decay

How is cluster decay different from spontaneous fission? --Smack (talk) 02:47, 25 Jun 2005 (UTC)

SF happens as fission, where the daughter products are fairly random. You will never know if any single atom will decay into Tc-100 and Sb-124 or something else. In cluster decay there is always the same particle emitted. --metta, The Sunborn 18:28, 25 Jun 2005 (UTC)

Could someone add a definition for "decay percentage"?

Barium-114

Although I found some references suggesting that 114Ba might cluster-decay, subsequent studies seem to rule it out. See, for example, [1] or [2]. I've commented it out of the table. -- Xerxes (talk) 22:03, 21 April 2008 (UTC)

OE91Pa231?

A cluster emission decay mode is not shown in my 15th edition isotopes chart. And other than that, the rest of the emitted nuclides are noted to be of even numbered element nuclei with possibly an odd number of neutrons. This brings up the possibility that the emitted particle is that of a structure that is an accumulation of a (2Z)times an integer nuclide which might be sheared off from the top of the original nucleus. This would be an indication of the existence of a shear strength fault in the structure due to the nature of their physical construction properties. This possibility is not apparent under the assumption of a spherical shape for the parent nucleus. However if the shape of the parent nucleus were 4 sided the possibility of a stressed nuclear corner condition becomes apparent.WFPM (talk) 18:28, 1 December 2012 (UTC)

"24Ne" CD as decay mode - full set

In current text:

Penetrability theory predicted eight decay modes: ¹⁴C, ²⁴Ne, ²⁸Mg, ^32,34Si, ⁴⁶Ar, and ^48,50Ca from the following parent nuclei: ^222,224Ra, ^230,232Th, ^236,238U, ^244,246Pu, ^248,250Cm, ^250,252Cf, ^252,254Fm, and ^252,254No.

However, {{NUBASE2020}} has a different set (defined as "24Ne = heavy cluster decay"). Below is a table to gather & hunt the complete set. Technically, I am working in {{Isotopes/decay-mode/overview}} (content documentation), and this tech set. -DePiep (talk) 06:48, 11 February 2023 (UTC)

CD

developing table as of 06:48, 11 February 2023 (UTC)

to improve: source by examplary isotope from NUMBASE, enwiki?

decay	source	example	note
14C	NUBASE
20Ne	NUBASE
24Ne	NUBASE
25Ne	NUBASE
26Ne	NUBASE		only as part of 24Ne 26Ne
24Ne 26Ne	NUBASE	234U
28Mg	NUBASE
30Mg	NUBASE
32Si	NUBASE
34Si	242Cm	NUBASE
46Ar	? (enwiki)
48Ca	? (enwiki)
50Ca	? (enwiki)

DePiep (talk) 06:48, 11 February 2023 (UTC)

The explanation re ³⁴Si, ⁴⁶Ar, ⁴⁸Ca, and ⁵⁰Ca is that those decay modes were predicted here, but have never been seen yet. Double sharp (talk) 15:21, 11 February 2023 (UTC)

Theoretical calculation of cluster decay half-lives

If the formula given here is also true for cluster decays, then to find the lowest stable cluster decay mode is to find the emission nuclide $X$ with the smallest ${\sqrt {\dfrac {A_{X}}{Q_{X}}}}(Z-Z_{X})Z_{X}$, where $A_{X}$ is the mass number of $X$, $Q_{X}$ is the Q value of the decay mode, and $Z,Z_{X}$ is respectively the charge number of the parent nuclide and $X$.

Although the nuclide ejected in cluster decays seems to be arbitrary, fortunately, the formula shows that it is enough to consider the following 10 cluster decay modes in addition to alpha decay: ¹²C, ¹⁴C, ¹⁶O, ²⁴Ne, ²⁶Mg, ³⁰Si, ³²Si, ³⁶S, ⁴⁶Ca and ⁴⁸Ca.

Suppose that one wants to find the most stable nuclide that is energetically allowed to decay, and fission into at least three parts is ignored. That nuclide must have the lowest energy among its isobars, because cluster decays are neglegible compared to beta decays and double beta decays. Now suppose that the formula given in the above link also applies to cluster decays. For nuclides having the lowest energy among their isobars, there are several regions:

For mass numbers ≤ 92 (other than 5 and 8), no cluster decay can occur.

For mass numbers 93-142 (starting from 3 neucleons above ⁹⁰Zr with semi-magic Z and magic N), ³⁶S emission kicks in, but these nuclides are among the most stable ones, so only emission of relatively heavier nuclides can occur. The lowest stable cluster decay modes are among emission of ¹⁶O, ²⁶Mg, ³⁰Si, ³²Si, ³⁶S, ⁴⁶Ca and ⁴⁸Ca. But of course, such processes take long time beyond imagination.

Note that all isotopes of zirconium with N ≥ 50 (this includes all (almost) beta-stable ones), plus ¹⁰⁰Mo, are still stable to ³⁶S emission; this is somewhat like that all N = 82 isotones with Z ≤ 62 (includes all beta-stable ones) are stable to alpha decay. Still, none of ⁹⁴Zr, ⁹⁶Zr and ¹⁰⁰Mo is stable to ⁴⁸Ca emission (with a half-life greater than 10²⁰⁰⁰ years, perhaps).

For mass numbers ≥ 143 (starting from 3 neucleons above ¹⁴⁰Ce with semi-magic Z and magic N), alpha decay kicks in. Alpha half-lives for nuclides in this region are usually short enough (≤ T_α1/2(¹⁶¹Dy) ~ 10^132.24 y), so cluster decays can be ignored. But still, ¹⁵²Sm, ¹⁵³Eu, ^{155,156,157,158}Gd, ¹⁵⁹Tb, ^162,163,164Dy, ¹⁶⁵Ho, ^201,202Hg, and ²⁰⁵Tl have long enough alpha half-lives (≥ T_α1/2(¹⁵³Eu) ~ 10^144.69 y), so their main decay modes will be cluster decay. The least stable cluster decay modes are among emission of ¹²C, ¹⁴C or ²⁴Ne.

In a nutshell, there's no need to consider cluster decay in general, unless the nuclide has the lowest anergy among its isobars, has mass number ≥ 93 and either is stable to alpha decay or has alpha decay half-life > T_α1/2(¹⁶¹Dy), or ≥ T_α1/2(¹⁵³Eu).

In order not to make this comment too long, the theoretical calculations are posted in the following comments. 14.52.231.91 (talk) 03:25, 29 August 2024 (UTC)

By the way, the nuclides with the longest half-life of following mass numbers are not the ones having the lowest energy among their isobars: 144 (¹⁴⁴Sm > ¹⁴⁴Nd), 146 (¹⁴⁶Nd > ¹⁴⁶Sm), 148 (¹⁴⁸Nd > ¹⁴⁸Sm), 176 (¹⁷⁶Yb > ¹⁷⁶Hf: 3.889×10²¹ years predicted here and (2.0-6.6)×10²⁰ years here), and 186 (¹⁸⁶W > ¹⁸⁶Os). 129.104.241.89 (talk) 15:33, 12 November 2024 (UTC)

Theoretical calculation of cluster decays for mass numbers 93-142

Warning: I should have used nuclear masses to substitute $E_{\alpha }$ in the formula here, but actually I used atomic masses for all decay modes including alpha decay. I think it is OK because all are theoretical, so there's nothing serious.

The table lists common logarithm values of theoretical half-lives in years. Red means that the corresponding value is within 10000 times the minimal value.

Nuclide	16O	26Mg	30Si	32Si	36S	46Ca	48Ca	Minimum	Note
93Nb	-	-	-	-	1013.38	2334.79	-	1013.38
94Mo	-	-	473.29	564.63	461.86	666.06	-	461.86
95Mo	-	-	629.59	646.02	514.86	592.97	1040.10	514.86
96Mo	-	-	670.21	568.18	542.92	484.55	612.53	484.55
97Mo	-	-	1111.73	690.54	701.44	506.58	523.06	506.58
98Ru	-	1058.78	346.68	418.49	331.29	385.35	521.24	331.29
99Ru	-	-	382.25	440.17	344.97	375.67	453.56	344.97
100Ru	-	1251.32	402.36	413.00	345.32	374.78	392.77	345.32
101Ru	-	2360.51	456.44	429.00	362.67	386.08	370.45	362.67
102Ru	-	-	480.00	429.08	369.91	408.29	361.65	361.65
103Rh	395.64	548.70	363.40	374.04	329.06	360.43	349.00	329.06
104Pd	238.64	405.10	311.92	353.30	317.97	329.50	343.45	238.64
105Pd	277.91	413.08	325.20	362.22	328.38	335.80	336.59	277.91
106Pd	542.66	392.56	-	344.60	334.62	345.44	330.87	330.87
107Ag	277.17	331.83	294.04	329.82	312.38	323.96	327.59	277.17
108Pd	-	381.43	354.72	-	355.62	377.83	335.16	335.16
109Ag	1042.77	309.93	304.80	317.95	323.93	339.43	323.90	304.80
110Cd	377.02	277.43	274.45	301.75	305.05	314.81	315.99	274.45
111Cd	464.70	274.76	278.30	301.96	311.30	323.16	317.22	274.76
112Cd	-	266.19	280.00	293.73	-	327.60	314.87	266.19
113In	520.08	236.16	255.91	282.95	297.55	316.57	315.63	236.16
114Sn	329.65	219.40	241.90	274.35	287.05	316.08	324.19	219.40
115Sn	652.09	232.08	245.88	-	292.96	325.06	328.36	232.08
116Sn	-	254.67	243.17	264.62	289.38	328.12	323.01	243.17
117Sn	-	273.03	257.11	262.85	291.85	338.46	326.88	257.11
118Sn	-	314.78	284.08	257.49	292.37	342.79	327.80	257.49
119Sn	-	348.37	307.41	267.49	299.47	352.85	333.48	267.49
120Sn	-	450.41	360.03	292.36	304.26	362.61	335.43	292.36
121Sb	-	314.42	291.54	260.75	273.60	333.00	322.03	260.75
122Te	648.32	259.82	251.33	238.86	253.11	-	311.92	238.86
123Sb	-	516.79	383.61	302.59	316.56	352.77	328.88	302.59
124Te	-	345.70	298.18	266.65	280.99	324.48	-	266.65
125Te	-	419.70	333.40	279.88	295.82	331.06	-	279.88
126Te	-	580.98	410.67	308.21	323.98	339.73	320.98	308.21
127I	-	381.04	322.73	275.91	293.46	319.46	312.78	275.91
128Xe	521.12	297.57	277.80	253.86	269.03	303.48	303.99	253.86
129Xe	-	326.27	305.49	264.83	280.65	309.95	305.15	264.83
130Xe	-	374.21	341.40	292.79	300.69	313.52	305.03	292.79
131Xe	-	434.39	374.98	318.27	322.98	327.22	309.53	309.53
132Xe	-	577.85	448.68	349.93	361.01	348.30	311.04	311.04
133Cs	-	366.52	341.73	307.38	317.03	325.55	300.10	300.10
134Ba	364.09	295.96	294.02	276.81	290.21	306.63	291.42	276.81
135Ba	686.30	327.24	317.17	291.00	309.86	318.09	298.13	291.00
136Ba	-	374.20	351.18	308.80	330.99	334.36	308.30	308.30
137Ba	-	455.69	401.00	332.50	353.58	354.57	319.05	319.05
138Ba	-	570.63	472.18	359.72	384.84	377.61	331.59	331.59
139La	643.77	370.85	359.32	312.25	336.36	349.58	319.57	312.25
140Ce	256.65	300.21	304.28	283.12	307.33	325.89	307.72	256.65
141Pr	210.85	262.41	270.94	264.10	286.95	312.32	301.63	210.85
142Nd	185.32	234.57	249.11	249.10	270.65	301.90	297.73	185.32	12C = 188.35

14.52.231.91 (talk) 03:40, 29 August 2024 (UTC)

Theoretical calculation of cluster decays for mass numbers 152-165, 201-205

Nuclide	α	12C	14C	24Ne	Decay mode(s)	Minimum	Note
152Sm	164.24	115.84	111.23	187.96	14C to 138Ba	111.23
153Eu	144.69	108.55	110.99	186.92	12C to 141La or 14C to 139La	108.55
154Gd	54.37	101.00	109.65	185.24	α	54.37
155Gd	304.37	111.31	117.55	184.32	12C to 143Ce	111.31
156Gd	-	127.89	130.31	182.19	12C to 144Ce or 14C to 142Ce	127.89
157Gd	-	150.39	144.38	181.80	14C to 143Ce	144.38
158Gd	-	175.63	159.36	178.65	14C to 144Ce	159.36
159Tb	-	159.93	157.32	179.61	12C to 147Pr, 14C to 145Pr or 16O to 143La	157.32	16O = 157.48
160Dy	110.29	135.61	144.68	177.93	α	110.29
161Dy	132.24	156.10	160.63	175.85	α	132.24
162Dy	336.47	171.38	175.29	173.99	12C to 150Nd, 14C to 148Nd, 16O to 146Ce or 24Ne to 138Ba	171.00	16O = 171.00
163Dy	-	193.71	202.49	181.18	24Ne to 139Ba	181.18
164Dy	-	204.89	210.06	187.41	24Ne to 140Ba	187.41
165Ho	242.65	169.21	194.22	187.58	12C to 153Pm	169.21
201Hg	171.10	174.61	173.33	210.54	α, 12C to 189W or 14C to 187W	171.10
202Hg	305.64	188.90	186.02	215.28	12C to 190W or 14C to 188W	186.02
203Tl	80.46	166.47	176.50	214.19	α	80.46
204Pb	35.56	144.36	163.00	211.38	α	35.56
205Tl	283.07	201.02	201.97	226.19	12C to 193Re or 14C to 191Re	201.02

14.52.231.91 (talk) 03:55, 29 August 2024 (UTC)

The CD half-lives are actually highly overestimated with that formula. For example, ²²³Ra partial CD half-life according to the formula is on the order of 10⁷⁵ years, but it is only 10⁷ years by experiment. Nucleus hydro elemon (talk) 04:28, 27 September 2024 (UTC)

Interesting observation, thanks! :) 129.104.241.231 (talk) 17:46, 1 October 2024 (UTC)

After some regressions I came out with this. By the formula, some decay processes like ¹⁵⁴Gd(¹²C) have half-lives short enough to be observed. :) Nucleus hydro elemon (talk) 13:56, 4 October 2024 (UTC)

A rather less optimistic prediction for ¹⁵⁴Gd cluster decay (most probable cluster emitted ¹⁶O to get to the N = 82 closure in one step, but with predicted half-life 8.04×10⁵⁰ s). Double sharp (talk) 07:39, 10 October 2024 (UTC)

The problem is that in the table above, while having the shortest cluster decay half-lives, ¹⁵⁴Gd has way "too short" alpha half-life. In comparison, ¹⁵²Sm, ¹⁵³Eu, and ¹⁵⁵Gd would be more ideal to study cluster decay (well, theoretically). 129.104.241.83 (talk) 00:14, 12 November 2024 (UTC)

Regardless of the actual half-life values, perhaps ²⁰⁵Tl would be the most stable nuclide with mass number at least 142, being nearly as stable as ¹⁴¹Pr. This is extremely counter-intuitive! 129.104.241.211 (talk) 02:46, 16 November 2024 (UTC)

¹⁴C emission is the only known cluster decay mode to have short enough half-lives

By "short enough half-lives", I mean that the ¹⁴C emission decay mode can be seen as a common decay mode like α, β , β^-, SF, IT, since some isotopes of Ra and Ac (perhaps also Fr, but its isotopes have far too short α/β half-lives) are known to have short ¹⁴C emission half-life.

In comparison, while there are other decay modes known, they are often seen as exotic and are often ignored. For example, the nuclide with shortest known ²²Ne emission half-life is ²³⁰U with a half-life of 1.15×10¹² years; the nuclide with shortest known ²⁴Ne emission half-life is ²³²U with a half-life of 7.74×10¹² years; the shortest known double beta decay half-life is 7.07×10¹⁸ years for ¹⁰⁰Mo. 129.104.241.231 (talk) 17:46, 1 October 2024 (UTC)