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January 2

proton numbers and neutron numbers from unstable to stable

We assume:

All currently unknown nuclides are more unstable (i.e. have shorter half-life) then all currently known nuclides.

And theoretically, the proton numbers having stable nuclides are 0~66 except 43, 61, 62, 63, and the neutron numbers having stable nuclides are 0~98 except 19, 21, 35, 39, 45, 61, 71, 83~91, 95, 96. We do not consider these two unconfirmed kinds of nuclear decay:

proton decay (may be possible, if so, then there are no theoretically stable nuclides)
spontaneous fission for the nuclears with mass number < 232 (may be possible for the nuclear with mass number >= 93, if so, then the proton numbers having theoretically stable nuclides are 0~40, and the neutron numbers having theoretically stable nuclides are 0~52 except 19, 21, 35, 39, 45)

For consistency, we regard (proton number, neutron number) = (0, 0) as a theoretically stable nuclide, thus the proton number 0 also has only one stable nuclide, just like the proton numbers 4, 9, 11, 13, 15, 21, 23, … and the neutron numbers 2, 3, 4, 9, 11, 13, 15, …, and the neutron number 0 has two stable nuclides (corresponding to the proton numbers 0 and 1), and every mass number 0~164 except 5, 8, 143~155, 160~162 has exactly one theoretically stable nuclide (which is the only one nuclide with these mass numbers which are stable to both beta decay and double beta decay, see Beta-decay stable isobars).

By the Mattauch isobar rule, all nuclides with proton number 43, 61, … are unstable to beta decay, and all nuclides with neutron numbers 19, 21, 35, 39, 45, 61, 71, 89, 115, 123, 147, … are unstable to beta decay, see Beta-decay stable isobars.

For other proton numbers <= 118 and other neutron numbers <= 178 (which are the proton numbers and the neutron numbers having currently known nuclides) from unstable to stable: (use the data in the "isotopes of elements" articles in Wikipedia, for observationally stable but theoretically unstable (alpha decay, beta decay, double beta decay, electron capture, double electron capture, or isomeric transition) nuclides (i.e. the proton numbers table from "75" and so on, and the neutron numbers table from "111" and so on, respectively), we use the data in [1])

Proton numbers: (listed up to 98) (not include the proton numbers with theoretically stable nuclides)

proton number	the most stable neutron number	half-life
87	136	22 mins
85	125	8.1 hours
86	136	3.82 days
61	84	17.7 years
89	138	21.8 years
84	125	125 years
98	153	900 years
97	150	1380 years
88	138	1600 years
95	148	7370 years
91	140	32760 years
93	144	2.14*10^6 years
43	54	4.21*10^6 years
96	151	1.56*10^7 years
94	150	8.08*10^7 years
92	146	4.468*10^9 years
90	142	1.405*10^10 years
83	126	2.01*10^19 years
75	110 (112 neutrons will make beta decay)	3.4*10^24 years
71	104 (105 neutrons will make beta decay)	2.5*10^34 years
74	109 (112 neutrons will make double-beta decay and the half-life may be shorter)	4.9*10^36 years
73	108	4.2*10^38 years
72	108	6.4*10^45 years
69	100	1.5*10^46 years
76	114 (116 neutrons will make double-beta decay and the half-life may be shorter)	2.0*10^47 years
77	116	2.6*10^66 years
79	118	1.3*10^72 years
70	104 (106 neutrons will make double-beta decay and the half-life may be shorter)	4.4*10^75 years
78	118 (120 neutrons will make double-beta decay and the half-life may be shorter)	6.6*10^82 years
68	100 (102 neutrons will make double-beta decay and the half-life may be shorter)	4.0*10^92 years
63	90	4.0*10^141 years
82	125	1.2*10^156 years
62	90	7.3*10^159 years
67	98	8.8*10^239 years
81	124	2.5*10^280 years
80	122	5.1*10^301 years

Neutron numbers: (listed up to 128) (not include the neutron numbers with theoretically stable nuclides)

neutron number	the most stable proton number	half-life
39	32	11.3 days
128	82	22.2 years
115	78	50 years
89	62	94.6 years
35	28	100 years
19	17	3.01*10^5 years
45	34	3.27*10^5 years
127	83 (nuclear isomer)	3.04*10^6 years
61	46	6.5*10^6 years
123	82	1.73*10^7 years
21	19	1.248*10^9 years
111	76	4.1*10^16 years
87	62	8.3*10^17 years
71	52	5.710^19 years (the article says 4.2~7.2 10^19 years, we use the median value)
105	72 (71 protons will make beta decay)	4.5*10^20 years
85	60	1.9*10^22 years
106	72	3.4*10^23 years
112	76	1.4*10^26 years
84	58	3.4*10^27 years for the alpha decay, but no information for the double-beta decay
88	62 (60 protons will make double-beta decay and the half-life may be shorter)	8.7*10^27 years
107	72	4.5*10^29 years
113	76	4.8*10^29 years
86	60	2.0*10^34 years
101	70	4.0*10^34 years
110	74	7.4*10^35 years
109	74	4.9*10^36 years
102	70 (68 protons will make double-beta decay and the half-life may be shorter)	2.1*10^42 years
108	72	6.4*10^45 years
114	76	2.0*10^47 years
117	78	4.5*10^59 years
103	70	2.3*10^60 years
116	77 (76 protons will make double-beta decay and the half-life may be shorter)	2.6*10^66 years
104	70	4.4*10^75 years
99	68	1.9*10^79 years
83	60	3.8*10^80 years
118	78	6.6*10^82 years
119	80	1.8*10^85 years
100	68	4.0*10^92 years
120	80 (78 protons will make double-beta decay and the half-life may be shorter)	5.6*10^95 years
95	66	6.6*10^127 years
126	82	7.8*10^127 years
125	82	1.2*10^156 years
90	62	7.3*10^159 years
121	80	2.4*10^169 years
124	81	2.5*10^280 years
122	80	5.1*10^301 years
91	64	2.6*10^311 years
96	66	6.2*10^318 years

Are my two tables right? Also fill these two tables to proton numbers up to 118 and neutron numbers up to 178, respectively. —— 61.223.151.50 (talk) 06:08, 2 January 2024 (UTC)[reply]

Are you asking people to check that you have correctly looked up numbers and put them in a table, and then look up more numbers and put them in a table for you? It's unclear what your question is. PianoDan (talk) 20:28, 2 January 2024 (UTC)[reply]

I just mean: The proton numbers 0~98 from unstable to stable are 87, 85, 86, 61, 89, 84, 98, 97, 88, 95, 91, 93, 43, 96, 94, 92, 90, 83, (from here in theory) 75, 71, 74, 73, 72, 69, 76, 77, 79, 70, 78, 68, 63, 82, 62, 67, 81, 80, (0~42 and 44~60 and 64~66, which theoretically have stable nuclides), but what is the proton numbers 0~118 from unstable to stable? Also, the neutron numbers 0~128 from unstable to stable are 39, 128, 115, 89, 35, 19, 45, 127, 61, 123, 21, (from here in theory) 111, 87, 71, 105, 85, 106, 112, 84 (I do not know the theoretically place of 84, since I cannot find the theoretically half-life of the double-beta decay of Ce142), 88, 107, 113, 86, 101, 110, 109, 102, 108, 114, 117, 103, 116, 104, 99, 83, 118, 119, 100, 120, 95, 126, 125, 90, 121, 124, 122, 91, 96, (0~18 and 20 and 22~34 and 36~38 and 40~44 and 46~60 and 62~70 and 72~82 and 92~94 and 97~98, which theoretically have stable nuclides), but what is the proton numbers 0~178 from unstable to stable? 118.170.28.204 (talk) 06:39, 3 January 2024 (UTC)[reply]

You're esssentially asking us to theoretically extrapolate the lifetimes of many heavy neutron-rich nuclides. I doubt the results at the level of precision you'll need to determine the stability order will be that meaningful right now, since we don't have many experimental results to refine our models in this region. Double sharp (talk) 07:25, 3 January 2024 (UTC)[reply]

OK, if we only consider the proton numbers or the neutron numbers with no observationally stable nuclides, what is the answer (for these numbers from unstable to stable)? The answer for proton numbers <= 118 is in List of elements by stability of isotopes#Elements with no primordial isotopes, but what is the answer for the neutron numbers <= 178? 211.20.197.240 (talk) 07:31, 3 January 2024 (UTC)[reply]

As that article says (footnote f): "For elements with a higher atomic number than californium (with Z>98), there might exist undiscovered isotopes that are more stable than the known ones." The same problem will affect the higher neutron numbers. If you're happy with predictions (and the fact that these predictions may not actually be correct), then the online JAEA chart of the nuclides might interest you. Double sharp (talk) 08:44, 3 January 2024 (UTC)[reply]

Well, List of elements by stability of isotopes#Elements with no primordial isotopes has the proton numbers <= 118 (with no observationally stable nuclides) from stable to unstable, I just want the neutron numbers <= 178 (with no observationally stable nuclides) from stable to unstable. 211.20.197.240 (talk) 09:17, 3 January 2024 (UTC)[reply]

You're asking for a lot of work extracting the data from the "isotopes of X" pages (which are organised by Z rather than by N). Not to mention that error bars overlap near the top end (it's not clear whether ²⁹²Lv or ²⁹³Ts is longer-lived for N = 176, for example). Double sharp (talk) 11:36, 3 January 2024 (UTC)[reply]

What is the most stable (i.e. longest-lived) nuclide with N neutrons for 129<=N<=134? I just use the Table of nuclides to make my data, but for 129<=N<=134, all nuclides are white, i.e. with half-life < 1 day (this also holds for N>=160, but all 135<=N<=159 have a nuclide with half-life > 1 day). 61.224.143.214 (talk) 05:13, 4 January 2024 (UTC)[reply]

Okay, this is actually a reasonably-scaled request. They seem to be ²¹²Bi, ²¹²Pb, ²¹⁴Bi, ²¹⁴Pb, ²¹⁶Bi, ²²¹Fr respectively. :) Double sharp (talk) 17:04, 4 January 2024 (UTC)[reply]

How about N>=160? 223.141.52.225 (talk) 12:18, 5 January 2024 (UTC)[reply]

Now you're asking about 19 columns on the table of isotopes, and I think we're back to an unreasonable ask. PianoDan (talk) 21:44, 5 January 2024 (UTC)[reply]

Finding a particular academic paper

There is a document - probably an academic paper - that has an attached Excel file listing various academic publications discussing palaeoclimate studies that concern North Africa during the Holocene. I think one of these studies listed is about the Fezzan. Does anyone have a link to this paper? I have searched myself on several databases, so far without success. Jo-Jo Eumerus (talk) 09:14, 2 January 2024 (UTC)[reply]

Perform your search at scholar.google.com instead of a basic search engine to find research papers. 12.116.29.106 (talk) 12:23, 2 January 2024 (UTC)[reply]

Nope. Tried that, didn't work. There is just no way to usefully narrow things down so that they can catch a supplementary file. Jo-Jo Eumerus (talk) 17:02, 2 January 2024 (UTC)[reply]

Cambridge University Press publish "Holocene climatic changes in an archaeological landscape: The case study of Wadi Tanezzuft and its drainage basin (SW Fezzan, Libyan Sahara)" [2] Philvoids (talk) 18:55, 2 January 2024 (UTC)[reply]

Closer, but sans an excel file it's not what I am looking for, I'm afraid. I think it was a ScienceDirect imprint. Jo-Jo Eumerus (talk) 08:19, 3 January 2024 (UTC)[reply]

This might be teaching grandmother to suck eggs, but I would then use Google Scholar to examine what articles cite that paper, and if any sound relevant I would then examine what articles cite those, etc. For instance, it seems also worth examining who cites "Reconstructing palaeoclimate and hydrological fluctuations in the Fezzan Basin (southern Libya) since 130 ka: A catchment-based approach". If any of the titles that come up in such searches ring any bells with you, you can investigate further whether they have an Excel table as supplementary data; failing that, check all of them. JMCHutchinson (talk) 10:11, 3 January 2024 (UTC)[reply]

Thanks for the suggestion. It doesn't seem like the paper I am looking for cites these articles, though. I suspect that the Fezzan studies listed were from before 2000. Jo-Jo Eumerus (talk) 13:18, 3 January 2024 (UTC)[reply]

These articles cite some pre-2000 studies about Fezzan climate (e.g. "Late Quaternary geological evidence for environmental changes in south-western Fezzan (Libyan Sahara)", published 1998), so all I can suggest is that you repeat the "who-cites" operation with some of these. JMCHutchinson (talk) 14:15, 3 January 2024 (UTC)[reply]