Talk:Magic number (physics)

Image incorrect

Table isotopes en.svg

The image needs to be corrected, there are a number of places where there is beta minus decay diagonally opposite beta plus decay. This is inaccurate as it implies the atoms here would just oscillate between these states emitting (anti)electrons - which isn't possible. —Preceding unsigned comment added by Billy Huang (talk • contribs) 22:23, 24 June 2010 (UTC)

Possible if you keep feeding it with energy. JIMp _talk·cont 07:06, 25 January 2011 (UTC)

I noticed there was a hole in the diagram for Xenon-119, which appears to decay via beta capture (like all of the isotopes around it) to Iodine-119. For example http://www.periodictable.com/Isotopes/054.119/index.p.full.html Casu Marzu (talk) 00:07, 31 January 2018 (UTC)

I also believe the image is wrong. For example, the image implies that there is no stable isotope of Tungsten (look at the strange break in the stable isotope line near the top).There are 2 stable isotopes of tungsten though. A nearly equivalent interactive chart exists here: https://www.nndc.bnl.gov/nudat3/. There are about a dozen cases where the NNDC and wikipedia image disagree. For example: 149Sm is stable according to nndc, but decays via alpha particle according to the image. This image needs to be fixed. — Preceding unsigned comment added by 100.36.67.95 (talk) 16:30, 1 January 2022 (UTC)

Not Magic

I removed 6 and 14, they're not magic numbers, even according to the link provided.

I doubt that 2 is a magic number, because I know for certain that Helium has a far lower nucleus energy state than Deuterium. (Source: My Physics school book)

Interesting. My source is http://www.research.att.com/projects/OEIS?Anum=A018226. I'll check my physics textbooks to confirm, too. Giftlite 23:54, 24 Mar 2004 (UTC)~

Yes, ⁴
He, two protons & two neutrons, is in a very low energy state. This is because two is magic. JIMp _talk·cont 07:02, 25 January 2011 (UTC)

The article doesn't make it so obvious, but magic numbers apply to protons and neutrons separately, not their sum. That is why it is helium. Gah4 (talk) 23:46, 11 November 2016 (UTC)

Belief

I believe the magic numbers refer to number of protons OR number of neutrons, not the sum. So Helium 4 is especially stable because it has both 2 protons and 2 neutrons.

A reference - http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html. Giftlite 01:12, 8 May 2004 (UTC)

"If the count of protons is one of those magic numbers, then a neutral atom has the same number of electrons , arranged into complete shells around the atomic nucleus."

Regardless of the magic in the nucleus , ANY neutral atom has the same number of electrons (as protons); and they are NOT necessary complete ELECTRONIC shells(ie noble gases). I have excized the previous DOUBLELY STUPID sentence. The electron, absent or not, have NOTHING to do with the stability of the nucleus (to any measurable extent).67.124.102.77 06:05, 4 Jan 2005 (UTC)

Furthermore, the magic numbers for electrons are different than those of protons and nuetrons. That statement leads to the idea that a magically numbered atom is particularly stable electronically also, which is not the case.

Nuclear magic numbers are similar to electron shell numbers, but because of additional interaction, the numbers aren't the same. As with electrons, they are related to a shell structure in the nucleus. Gah4 (talk) 05:34, 4 September 2017 (UTC)

What of three?

Friends, I have it on good authority that three is a magic number, yet it is missing from the list. Should the list be marked incomplete? 86.20.180.82 20:04, 7 May 2007 (UTC)

No, 3 is not a magic number. What good authority? I have citable one. Say lecture notes : Nuclear and Particle Physics, University of Edinburgh - Dr Daniel Watts; or book : Introduction to Nuclear and Particle Physics 2nd Edition, A. Das and T. Ferbel. -- KTC 00:01, 15 May 2007 (UTC)

The authority referred to above is probably Jack Johnson. He has written about this here. --TraceyR (talk) 19:05, 28 September 2009 (UTC)

Magic numbers have to be even. Because of Fermi-Dirac pairing, each level holds to protons or two neutrons. Such pairing is also why even-even nuclides are more stable, and odd-odd are rare. Also, the extra stability of an even number of neutrons is what allows for slow neutron fission. Gah4 (talk) 05:37, 4 September 2017 (UTC)

Original Research

Dear Wiki editors, over the past months some of you have made reference to the non empirical derivation by Xavier Borg, namely our paper 'Magic numbers derived from variable phase nuclear model' on-line at http://www.blazelabs.com/magicnumbers.pdf There seems to be some disagreement upon whether or not such work should be cited on Wikipedia, which pretty messed up this talk page as shown in its history, so I'm cleaning this up and clearing the point in question. The above referenced paper IS original research, and is strictly NOT peer-reviewed, even though some university students collaborated with us to generate peer- reviewed scientific papers based on the core of its content. Keep in mind, Wiki, is used mainly by mainstream education, and is used by many scholars, and does not permit original research to be published. So, please, even though the contents of this paper read like common sense to some of you, I hereby ask you to refrain from copying any of its contents on the magic numbers page, since this would go against Wiki's policies, and would also breach copyright laws. If anybody sees the necessity of referencing this work, I would suggest to add it as an external link, and clearly label it as 'non mainstream'. Thanks.

(Blaze Labs Research (talk) 06:54, 3 July 2008 (UTC))

Copyright protects the expression of ideas, not the ideas themselves. All wikipedia editors, and journal authors in general, should know how to express an idea in their own words, and avoid copyright problems. I don't know of a rule against non-peer reviewed articles, though a single source is not, in general, good enough. Gah4 (talk) 05:42, 4 September 2017 (UTC)

Not Magic

I removed 6 and 14, they're not magic numbers, even according to the link provided.

I doubt that 2 is a magic number, because I know for certain that Helium has a far lower nucleus energy state than Deuterium. (Source: My Physics school book)

Interesting. My source is http://www.research.att.com/projects/OEIS?Anum=A018226. I'll check my physics textbooks to confirm, too. Giftlite 23:54, 24 Mar 2004 (UTC)~

2 is exactly the magic number. Energy wells for neutrons and protons are separate, so helium-4 is doubly-magic nucleus. You'd have 2 protons and 2 neutrons in it's shells. — Preceding unsigned comment added by 78.90.43.45 (talk) 07:16, 14 July 2011 (UTC)

Belief

I believe the magic numbers refer to number of protons OR number of neutrons, not the sum. So Helium 4 is especially stable because it has both 2 protons and 2 neutrons.

A reference - http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html. Giftlite 01:12, 8 May 2004 (UTC)

"If the count of protons is one of those magic numbers, then a neutral atom has the same number of electrons , arranged into complete shells around the atomic nucleus."

Regardless of the magic in the nucleus , ANY neutral atom has the same number of electrons (as protons); and they are NOT necessary complete ELECTRONIC shells(ie noble gases). I have excized the previous DOUBLELY STUPID sentence. The electron, absent or not, have NOTHING to do with the stability of the nucleus (to any measurable extent).67.124.102.77 06:05, 4 Jan 2005 (UTC)

Furthermore, the magic numbers for electrons are different than those of protons and nuetrons. That statement leads to the idea that a magically numbered atom is particularly stable electronically also, which is not the case.

Hassium

Sorry if this is a stupid question, but, based on what is in this article, how can Hassium-270 be doubly magic when neither 108 nor 162 are magic numbers? A good answer could be used to improve this article, so the next person doesn't have to ask :) Skittle 16:21, 9 November 2007 (UTC)

Xavier Borg references are unpublished, non-mainstream articles of no original work. Magic numbers derive directly and completely from shell model. Xavier model is, on contrary, a rough simplistic classical (since Greeks) interpretation. This references are a clear attempt of self-promotion of a crackpot working in "free-energy". —Preceding unsigned comment added by 85.52.164.135 (talk) 13:22, 17 February 2008 (UTC)

Why don't you read the ref., which is anpunished (not depublished). Other magic numera may be ±12-off or ±6-off. How do you think 114 came up when it's not even in the series? -lysdexia 11:04, 17 March 2008 (UTC)

Dear Anon IP 85.52.164.135, please stop vandalizing this page, and your offensive comments. There are several mainstream papers which regard the nucleus as a face-center cube (FCC) structure, and Xavier's model takes this a step further into a 4D simplex pair. The references in his papers are all mainstream. Also, you seem to be irritated by 'free energy' technologies. You may be surprised to know that free energy is not a crackpot science, but a very important research topic. Perhaps you are mistaking it with over unity which has got nothing to do with our research. (Blaze Labs Research (talk) 15:39, 20 May 2008 (UTC))

Proposed merger

Fisdof9 proposed to merge article Magic number (chemistry) into this one. Actually, I don't think this is appropriate because the cause for the existence of magic numbers for atomic nuclei and the chemical clusters is quite different. In the first case it is due to the strong and electromagnetic interaction, in the latter case due to chemical forces.

This difference will become more obvious if someone expands the "Magic number (chemistry)" article. The only common thing is that the same concept can be used to understand the existence of magic numbers.

--Cyfal (talk) 09:55, 21 June 2008 (UTC)

Although the Magic number (physics) definition is the one which most older chemistry textbooks refer to, the present Magic number (chemistry) definition refers to a completely different (and probably less known) concept. Merging these 2 articles will result in confusion and is therefore not recommended.

--(Blaze Labs Research (talk) 10:48, 1 July 2008 (UTC))

Well, because there have been no further contributions to this discussion, I remove the merger proposal now. --Cyfal (talk) 15:20, 10 August 2008 (UTC)

Both are side effects of Pauli exclusion, but the interactions are different, and so the numbers are different. It seems to me that they deserve separate articles, but maybe not so obvious. Gah4 (talk) 01:01, 12 November 2016 (UTC)

"Lasts"? Which isotopes? Citations?

Today the text includes: "as of 2007, the longest-lived, known isotope among all of the elements between 110 and 120 lasts only 12 min., next 22 sec"

Surely "lasts" should be replaced by "have half lives of", actual isotopes should be given, and citations quoted.

NickSharp (talk) 05:28, 12 October 2008 (UTC)

I would remove that sentence, for example Uub-285 has half-life 40±30 min. —Quilbert (talk) 18:21, 26 November 2008 (UTC)

Ni-28 not most proton rich isotope

Ni-28 is not the most proton rich isotope, regardless of what the cited source says.

Ni-28 has a 7/5 Proton/Neutron ratio. He-3 has a 2/1 Proton/Neutron ratio. H-1 has a 1/0 Proton/Neutron ratio.

Ni-28 is the most proton rich isotope beyond helium-3 —Preceding unsigned comment added by 70.130.130.193 (talk) 19:03, 7 April 2009 (UTC)

First Ni-28 is poorly named. Ni has 28 protons, so having Ni-28 would mean zero neutrons. Not physically possible. The article as mentioned Ni-48 as being doubly magic, with 20 neutrons and 28 protons. This is not a "real" isotope. Here, I use real to mean having a measurable half-life (or stable). Ni-49 has a half-life of ~300 ns (). Ni-48, with less neutrons stabilizing this nucleus would not be able to hold together. Ni-56 is doubly magic (28 of each, protons and neutrons). It is not stable, but its half-life (5.9 days) is orders longer than either Ni-55 (212 ms) or Ni-57 (35.60 hrs).18.189.8.62 (talk) 08:40, 3 December 2012 (UTC)

Actually Ni-48 can hold together (half-life >500 ns, theorized to be 10 ms), though I suspect this is only because it is doubly magic. Double sharp (talk) 02:14, 20 July 2014 (UTC)

References

Definition of 'magic'?

Is there a generally-accepted definition of what 'magic' means, apart from the vague idea "more stable than the rest" or "with complete shells" (although the shell model is not universally accepted either)? In an article in the current issue (7) of Physik Journal (for members of the German Physics Society/Deutsche Physikalische Gesellschaft), Jan Jolie and Peter Reiter from Darmstadt state that the only criterion for a shell closure (presumably w.r.t magicity) is the energy gap between completed levels. This is backed up with data relating to 30Si and 24O (both with 16 neutrons), whereby 24O is deemed to be magic due to the larger energy gap and 30Si, with a smaller gap, is not. On this basis, 24O is doubly magic (Z=8 and N=16). It certainly seems odd that the term "magic" seems to have mean different things to different people: Everyone 'knows' what it means but there doesn't seems to be a universal definition. --TraceyR (talk) 13:07, 8 July 2009 (UTC)

Magic are such numbers of protons/neutrons which fills the corresponding shell in the corresponding energy well. Now there are corrections to the numbers in heavy nuclei, because of collective and other correlations, some energy levels from the upper shell are moved down to the previous. This is where the confusion lies. So levels from the upper shell would be filled before closing the lower shell, which means, for stable nucleus to occur the numbers should be modified to reflect that. For reference one could go to atomic physics, where some electron orbitals of higher level are filled before the last level, which is consequence of energy levels/sublevels ordering. I think it's acceptable to use the shell gap as criterion. — Preceding unsigned comment added by 78.90.43.45 (talk) 07:14, 14 July 2011 (UTC)

Pascal Magic

Several people have found connections between the nuclear (semi)magic numbers and the Pascal Triangle's values.

Because of the way spin-orbit coupling splits orbitals and the way the energy levels of these parts interact, there are two different types of (semi)magic number. They can be rationalized in pairs 2 2 : 6 8 : 14 20 : 28 40 : 50 70 : 82 112 : 126 168 : 184 240 and so on. The right member of each pair is a doubled Pascal Triangle tetrahedral number- in fact each in sequence as- 2=2x1, 8=2x4, 20=2x10, 40=2x20, 70=2x35, 112=2x56, 168=2x84, 240=2x120, etc.

The left member of each pair can be represented two ways, either as a doubled tetrahedral value with the doubled triangular value directly above it in the Triangle subtracted from it (for example 112-30=82, 168-42=126, where 30 and 42 are doubled triangular numbers), or as doubled tetrahedral numbers plus an even integer increment that comes from the doubled natural number line, where the particular number falls along the same shallow diagonal as the doubled tetrahedral numbers it adds to, such shallow diagonals also used to sum Fibonacci numbers (here doubled).

There are several more such Pascal-related mathematical behaviors in the nuclear system. Interestingly there are also Pascal mathematical behaviors in the electronic system, though these are based not on doubled, but normal single values. 69.121.117.192 (talk) 23:56, 28 September 2012 (UTC)

The double tetrahedral numbers shown above are generated by the harmonic oscillator number in spherical nuclei. It turns out that one can extend the Pascal Triangle effect over ellipsoidally deformed nuclei as well. Double tetrahedral numbers show up on the surface only for spheres, which can be thought of as default ellipsoids. In the sphere the oscillator magics have double triangular number intervals, each adding the next increment leading to the next magic double tetrahedral number.

Thus each double triangular increment appears only once. Also, every magic number has a double triangular number interval. However, if the nucleus is deformed, the manner in which double triangular numbers contribute to each new sum changes. The wave ratio, related to the ellipsoid's axial ratio but not identical to it, is one way to define the deformation. The wave ratio for the sphere is 1:1, where normally the polar semimajor axis is defined as the numerator, and the equatorial semimajor axis as the denominator in Nilsson depictions.

It is found that the numerator determines how many copies of a double triangular number are needed in sequence. For the sphere we have one copy, and the ratio is 1:1. In the case of ratio 2:1, a prolate nucleus, we need TWO copies in sequence so 2,2,6,6,12,12,20,20,30,30... and so on, summing to 2,4,10,16,28,40,60,80,110,140... which is the correct system of magic numbers for this ratio. For 3:1 we need THREE copies. For the simple harmonic oscillator model there are no exceptions.

With oblate nuclei of wave ratio 1:2 we find instead that there is still only one copy of each double triangular number increment, but that the the double triangular number distance occurs not for EVERY magic number, but now EVERY OTHER. For 1:3 that distance is EVERY THIRD. This rule breaks down only early in the count when one has not yet cumulated enough magic numbers for the double triangular number interval to be seen. These early sequences can still be easily generated with a different rule.

When neither the numerator nor denominator of the wave ratio is 1, then we have both rules come into play. Thus for the simple harmonic oscillator the wave ratio's numerator, related to the polar semimajor axis, determines how many copies of any double triangular number interval must be utilized (multiplication), while the denominator, related to the equatorial semimajor axis, tells you how many magic numbers you need to jump to find double triangular distances (division).

When other effects such as spin-orbit coupling are added in this pattern breaks down. Even so there is still Pascal-based order remaining, but it is distributed very differently. 69.121.117.192 (talk) 13:04, 28 March 2013 (UTC)

Nuclear isomerism occurs when there is competition for relative position between low spin final orbital partials near the end of nuclear period analogues and the highest spin orbital partial belonging to the next higher period analogue. Pascal behavior is found in that the positioning itself, at least for neutrons in spheres, can be calculated simply by subtracting successive double triangular numbers from the classical spin-orbit magic numbers thusly: 28-0=28, 50-2=48, 82-6=76, 126-12=114, 184-20=164. These differences represent the count number where the intruding high spin orbital partial ENDS. One can determine where it begins by subtracting the size of the partial (so for example 1g9/2 is ten neutrons, so subtracting 10 from 48 gives 38, which is correct, while subtracting 12 from 76 gives 64, also correct, and 14 from 114 gives 100, also correct. 96.234.78.23 (talk) 18:42, 30 November 2014 (UTC)

Is 6 a nuclear magic number? Mathematically it *should* be, based on the above. But in terms of energy gap and reaction stability of carbon, it doesn't actually seem to be. Yet there is the fact that the magics are reflected in the cosmic abundances of the elements. Magic nuclei are much more commonly attested in these abundances than others. Carbon is one of the most abundant 'metals' in the universe. 69.114.46.208 (talk) 19:30, 24 January 2017 (UTC)

Unsourced?

http://en.wiki.x.io/wiki/Electron_shell <-- Seems to be the source

"This is equivalent to saying that the outer electron shell is 'full'."

That article has tons of sources for this claim. 75.70.89.124 (talk) 07:02, 31 July 2013 (UTC)

Separately

This article does not make it obvious enough that magic numbers are computed separately for protons and neutrons. Note that the usual pictures that people draw of nuclei have a ball of separate protons and neutrons. But there is no Pauli exclusion between them, so there is no need for them to be separate. Also, ones of opposite spin don't have exclusion. Gah4 (talk) 00:55, 12 November 2016 (UTC)

Chemical elements with magic numbers of neutrons.

It would be helpful to simply LIST the stable or nearly-stable isotopes with just magic numbers of neutrons. 2, 8, 20, 28, 50, 82, and 126. Easy to do, too, but it's not so easy to make it complete.
These start the list: He-3, N-15, S-38, Cl-37, Ar-38, K-39, all stable.
Ti-50, V-51 (its only stable isotope), Cr-52, Fe-54.
Rb-87 with a very long half-life, Sr-88, Y-89 (its only stable isotope), Zr-90, and Mo-92.
These are the elements helium (two stable isotopes), nitrogen (two stable isotopes), sulfur (four stable isotopes), chlorine (just two), argon (just three), potassium (just two), titanium (five stable isotopes), vanadium (just one), chromium (four stable isotopes), iron (four stable isotopes), rubidium (one stable isotope Rb-85), strontium (four stable isotopes), yttrium (just one), zirconium (four stable isotopes), and molybdenum (six stable isotopes, but Mo-92 being the lightest one).
I will let you other weenies figure out the ones with 82 and 126 neutrons. I would have thought that there was a magic number of neutrons associated with thorium-232, uranium-238, and plutonium-242, but this is not so.
The number 20 + 20 = 40 is an interesting one, but it is not a magic one.
Ca-40, with 20p and 20n, is very, very stable for its atomic mass number.
K-40, with 19p and 21n, decays three ways, into Ar-40 (18p + 22n) or Ca-40 (20p + 20n), by electron capture or positron emission.
Also, the two nearby isotopes, K-39 and K-41, are both stable, but Ca-39 and Ca-41 is radioactive, despite having 20 protons. Ar-39, Ar-41, and Sc-41 are all radioactive. The most common isotope of argon on the Earth is Ar-40, but in the Universe it is Ar-36 (18p + 18n).

47.215.183.159 (talk) 02:02, 4 September 2017 (UTC)

I believe that the large amount of Ar-40 in the earth's atmosphere is due to decay of K-40. Also, elements with nice oxides tend to be more abundant in the earth's crust than ones that don't. (Oxides float.) I am not, then, suprised that it is different from the rest of the universe. Gah4 (talk) 05

51, 4 September 2017 (UTC)

I listed the elements to cover the proton magic numbers. Feel free to add a list of isotopes with magic neutron numbers. --mfb (talk) 14:52, 4 September 2017 (UTC)

Th and U have semi-closed shells, at least theoretically, though since actinide nuclei are not spherical the applicability of the unaltered shell model is a little suspect. Double sharp (talk) 15:06, 3 December 2017 (UTC)

double magic

Recently more nuclides were added to a paragraph on double magic nuclides. I believe that is fine, but also that we should separate stable (or almost stable) from unstable ones. Ca-40 and Ca-48 have a 1e28s or so half life, close enough to stable for most of us. The extreme nickel and tin nuclides, while more stable than many, are not very stable. Gah4 (talk) 23:16, 8 April 2019 (UTC)

Nomenclature and mistakes

Looking over this article, a number of rather minor mistaken terminology uses, omissions, and inconsistencies are noticeable throughout. I just added 56Ni to the list of doubly magic nuclei (see discussions above as to whether this list may really be useful), but it was strange to see the exotic species 48Ni and 78Ni without the long-known 56Ni in such a list. "Double magic" seems less preferred than "doubly magic" in the literature (a quick internet search for nuclear physics shows more than five times the results for the latter than the former). 4He is called "most abundant (and stable)" lending a superlative to a binary fact of beta-stability ("tightly-bound" would be correct, but "most stable" is not sensible). Another misleading term is "proton-rich isotope" which is a misnomer; an isotope is defined (in part) by its proton number; therefore, while "neutron-rich isotope" and "neutron-deficient isotope" are sensible terms, "proton-rich isotope" is not meaningful (e.g., all isotopes of nickel have 28 protons by definition). 48Ca is (as noted above) not in fact stable, but very long lived (in contrast to what is here). Contrast this with 208Pb, which is stated as "the heaviest stable nuclide"; while in fact true, 209Bi is very long lived which leads to an inconsistency for the treatment of long-lived isotopes. The lone (and incomplete paragraph) on hassium feels rather biased (considering other omissions) and hence out of place over a decade after its discovery; note that the article does not delve into the concept of shifting magic numbers far from stability, and as it stands the article does not support Z=108 nor N=162 as magic numbers. I would like to clean up these points in a few weeks' time, if there is no extended discussion to oppose these wide-ranging but relatively simple updates. DAID (talk) 20:04, 14 May 2019 (UTC)

I like to use nuclide over isotope, but the latter is commonly used, where you note that it should not be. Isotope might be the WP:COMMONNAME, though I am not sure about that. Gah4 (talk) 21:57, 25 September 2024 (UTC)

Etymology

This is a Compound (linguistics) and has an etymology. Catchpoke (talk) 15:33, 12 July 2021 (UTC)

Effect of magic number on alpha decay is present for each of them

In normal cases alpha decay energies decreases as neutron number increases, and we know that there are huge increases when passing N = 82 and N = 126. Actually, the energy increase is present around every magic number. Data copied from NNDC.

Magic number	Nuclide with that many neutrons	Qα (keV)	Nuclide with that 2 more neutrons	Qα (keV)	Difference of the two Qα's (keV)
8	16O	-7162	18O	-6228	934
20	38Ar	-7208.05	40Ar	-6800.69	407.36
	39K	-7218.58	41K	-6222.94	995.64
	40Ca	-7162	42Ca	-6257.34	905
28	52Cr	-9351.3	54Cr	-7927.9	1423.4
	54Fe	-8417.1	56Fe	-7613.3	803.8
50	90Zr	-6674.3	92Zr	-2963.2	3711.1
	92Mo	-5604	94Mo	-2064.2	3540
82	140Ce	-1614.1	142Ce	1304	2918
	142Nd	-806	144Nd	1906.4	2712
	144Sm	-140	146Sm	2528.8	2669
126	210Po	5407.45	212Po	8954.20	3546.75
	212Rn	6385.1	214Rn	9208	2823

129.104.241.231 (talk) 18:10, 25 September 2024 (UTC)