Talk:Nuclear shell model

Copyright?
I noticed that the image used on this page is the same as is used on the hyperphysics page. http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/shell.html

Is this image legit? I do not know how to check for myself. &#91;Tycho?] 03:04, 12 December 2005 (UTC)

For the phrase, "Z=40", Z should be defined. I presume it is referring to the number of charged nucleons (protons) = 40 ... implying specifically that 40 is a semi-magic number for protons and not neutrons?

Title
Is there a reason this article is at Shell model instead of Nuclear shell model? The latter seems more descriptive, and more analogous to Atomic shell model. Would anyone object to a move? --Doradus 19:39, 28 December 2006 (UTC)


 * Oops... Ironically, atomic shell model is actually at electron configuration. --Doradus 19:58, 28 December 2006 (UTC)


 * I see your point. Nuclear physicists generally just call it 'the shell model', Krane refers to it as such [].  I think in an encyclopedia it might be best if it were under 'Nuclear Shell Model', but a move is nowhere near as urgent as the need for the contents of the article to receive a great deal of attention!  At the minute it is not a great article, no matter what the title is.Mumby 16:08, 29 December 2006 (UTC)

There is no n=0 !!!
You count n wrong, there is no n=0 n starts from 1 —Preceding unsigned comment added by 62.1.248.249 (talk • contribs)
 * Actually there are different conventions about that, but the most popular one is to start with n=0. Dan Gluck 06:46, 16 September 2007 (UTC)
 * No, n>=0 is not a commonly used convention. It is wrong. The value of n should match spectrographic notation. Look around the web. The Quantum Numbers article referenced from here uses n>=1. Hyperphysics uses that notation. Wolfram's Scienceworld  uses that notation. My Krane text here uses that notation. This article should be changed. Ehinson56 (talk) 04:47, 5 August 2008 (UTC)

I agree with the fact that there is no n=0 !!!!! and, l should be between 0 and n-1 !! This article is completely wrong!, I started correcting it yesterday, but i dont know who, or for what reason edited it back!! —Preceding unsigned comment added by 193.147.171.167 (talk) 11:09, 16 December 2008 (UTC)


 * Sorry that I confused you – that was me who changed your modifications back, you can see both the reason and my name in the history. I you want to modify the article again, you may start from your version in the history, but in this case please take care the all formulae and text are consistently starting will zero before you save your new version. Nevertheless, I don't think it is necessary to modify the numbering because a renumbering doesn't change the physical results, therefore it's not "wrong". --Cyfal (talk) 16:35, 17 December 2008 (UTC)

The commonly used connotation of the Z number is that it is the number of protons contained in the nucleus, and that that is the most important factor as to to the nuclide's properties. But if you consisder the property of nucleon pairing within the nucleus, and then consider the Z number as the number of paired protons/neutrons, then you can get away with the idea that the Z number zero is apopropriate for the neutron, because it doesn't yet have a proton/neutron pair. And of course the next question is which came first, the proton or the neutron?. And maybe the neutron came first.WFPM (talk) 16:55, 17 April 2010 (UTC)See Talk:Nuclear model.WFPM (talk) 17:00, 17 April 2010 (UTC)


 * Hmm - the (I assume) humorous question "which came first the proton or the neutron" makes me wonder - is there some similar "shell theory" concerning the binding of quarks into nucleons? If so, maybe the question is: which comes first, the u quark (in which case the nucleon "fill up" udu giving a proton), or the d (where it's dud giving a neutron)?
 * Googling "quark shell model nucleon" does come up with quite a lot - one promising article might be Petry et al. 1985, but I really have no idea. Jimw338 (talk) 01:31, 27 November 2016 (UTC)

I think I understand the confusion here. The spherically symmetric harmonic oscillator frequently does start at n=0. The Coulomb potential solution (ie the model for a hydrogen atom) conventionally labels electron states starting at n=1. Both are spherically symmetric and thus have angular and magnetic quantum numbers l and m. However, we are not talking about the electron states of a hydrogen atom here, so starting at n=0 is perfectly valid. Drkarat (talk) 18:11, 24 June 2019 (UTC)

Neutrons are indistinguishable ...
... (comment from recent edit) ... so this needs to be taken into account in the article in other places too. Not being a nuclear physicist, I leave this to the experts. --TraceyR (talk) 09:58, 2 May 2008 (UTC)

Upper magic number for protons
Can someone explain why the article says that the upper magic number for protons is 114 when 114 is not a magic number? --Ben Best (talk) 15:16, 6 September 2008 (UTC)

114 is the termination point for the intruder level 1i13/2. Starting with 1g9/2 (according to Goeppert-Mayer and Jensen), with 10 nucleons, the insertion comes after total count of 38, and ends at 48. 2s1/2 rounds the shell out yielding the total magic of 50 here.

1h11/2 (12 nucleons) gets inserted after 64, and ends at 76. 1i13/2 (14 nucleons) gets inserted after 100, and ends at 114.

Note that the 'period analogues' in nuclear shells, ignoring intruder levels, are all lengths that are doubled triangular numbers: s=2 p=6 ds=12 fp=20 gds=30 hfp=42 igds=56 jhfp=72

In keeping with the overall Pascal Triangle mathematical motivation of the system, the depths of insertion of intruders are also all doubled triangular numbers: 1g9/2=2, 1h11/2=6, 1i13/2=12, 1j15/2=20 and so on (though supposedly there are alternative depths possible especially for protons (giving 106 rather than 114 for 1i13/2). The double triangular depths come directly out of the organization of the period analogues and ordering of the component partial orbitals (partial because spin-orbit coupling breaks them up into a larger and smaller part, the larger getting reduced in energy and the smaller getting raised).

While this doesn't actually explain why 114 would be considered 'magic' (why not count the entire intruder-augmented period analogue, with magic number 126 for spheres?), it might help motivate other aspects of the system. For example, each intruder adds precisely the number of nucleons needed by the simpler double-triangular number sized period analogue to make its length the very next doubled triangular number.

1f2p  (20 nucleons) adds 1g9/2 (10) to yield 30; 1g2d3s (30) adds 1h11/2 (12) to yield 42; 1h2f3p (42) adds 1i13/2 (14) to yield 56; and so on. Similarly the size of the intruder's donor period analogue correspondingly gets lowered in size to the next lower doubled triangular number. All of a piece.

69.114.46.208 (talk) 20:01, 12 December 2016 (UTC)

Image Error
The 2d shell splits to two 1d shells in the image. That doesn't seem right. Therealmaddox (talk) 02:49, 4 February 2010 (UTC)


 * You are right -- it's a misprint. Bakken (talk) 09:10, 4 February 2010 (UTC)

The 2d shell is now out of order. The 1g 7/2 shell should come before the 2d 5/2 shell, as well as the next two 3s and 2d shells should be switched also. I have corrected the image if I can upload it? — Preceding unsigned comment added by 24.215.117.5 (talk) 01:52, 7 March 2012 (UTC)

What is n?
In the following text, n is clearly not the shell number, but neither is it the quantum number of the harmonic potential (which should be be n=1 for the =7/2 4th shell, as in the figure). So what is it? I would propose to keep that same n everywhere.


 * 1st Shell: 2 states (n = 0, j = 1/2).
 * ''2nd Shell: 6 states (n = 1, j = 1/2 or 3/2).
 * ''3rd shell: 12 states (n = 2, j = 1/2, 3/2 or 5/2).
 * ''4th shell: 8 states (n = 3, j = 7/2).
 * ''5th shell: 22 states (n = 3, j = 1/2, 3/2 or 5/2; n = 4, j = 9/2)...

Jor63 (talk) 13:39, 27 August 2010 (UTC)

Binding energy of the nuclei
I see nothing about the binding energy of the nuclei. Does it mean that the shell model is unable to calculate it? It seems that there exists no other model able to do it except mine, as shown in my Glasgow presentation(http://storage.canalblog.com/59/81/292736/64343067.pdf) and in my paper http://www.springerlink.com/content/h673n477n243vu46/. Bernard Schaeffer (talk) 07:58, 3 December 2011 (UTC)

Alpha Particle Model
Is anyone able to expand on the Alpha Particle Model section? I feel that it ought to either give more information than it does, or alternatively link to a relevant explanation on another page. I know too little to be sure of linking it to the right place, I'm afraid. EdwardRussell (talk) 14:52, 29 June 2013 (UTC)

Magic numbers and the harmonic oscillator
For the simple harmonic oscillator model of energy levels, the magic numbers predicted are all doubled tetrahedral numbers, thus: 2,8,20,40,70,112,168,240... Presumably doubled since pairs of nucleons are bound by opposing spin.

It turns out that for biaxially deformed nuclei under the harmonic oscillator the magic numbers are all variations on this theme, through Pascal Triangle combinatorics. If deformation is defined by the oscillator ratio, with numerator related to the polar radius and the the denominator the equatorial, then the numerator defines how many copies of a doubled triangular number interval are added to the growing total to make magics. The denominator, on the other hand, defines how many magic numbers have to be passed to give a doubled triangular number interval between the target magics. Issues only occur where the total number of magics hasn't yet reached the minimum needed. Then doubled natural numbers can be used to fill in this region. Within this limited domain there are no exceptions and the results match theory exactly. 71.127.246.169 (talk) 17:51, 10 January 2014 (UTC)

Section "Predicted magic numbers": Explanation vor l > n
Before the subsection "Predicted magic numbers", the harmonic oscillator and its quantum numbers are discussed. For the three-dimensional harmonic oscillator, n ≤ l. However, in the subsection "Predicted magic numbers" and the corresponding image, l can suddenly assume values much larger than n (e.g. 1d, 1f, 1g...). There is no clear explanation for this. Maybe it can be added? Socob (talk) 19:20, 21 February 2015 (UTC)

Spin-orbit intruders
Spin-orbit coupling causes highest spin spin-split orbital partials to fall in energy, eventually enough to start being incorporated into the preceding period analogue.

The effect starts to become pronounced with the inclusion of 1g9/2, with 10 nucleons. In terms of total neutron or proton count, this fall is 2 nucleons. The pure harmonic oscillator magic number would be 40 (double tetrahedral number), but with the addition of these 10 nucleons into the previous shell, total count now becomes 50, which is the observed spin-orbit magic number. The DEPTH of insertion is 2 nucleons- that is 1g9/2 starts after 38 (40-2) and ends at 48 (50-2).

The next intruder is 1h11/2, with 12 nucleons. This orbital partial starts after 64 and ends at 76, with 'depth' 6- that is harmonic oscillator magic (double tetrahedral) 70-6=64 and spin-orbit magic 82-6=76.

After this comes 1i13/2, with 14 nucleons. Depth is 12. That is, harmonic oscillator magic 112 (double tetrahedral)-12=100, and the intruder starts after this point. It ends at spin-orbit magic 126-12=114.

Finally, within known nuclei, 1j15/2, with 16 nucleons. Harmonic oscillator magic 168-20=148... while spin-orbit magic 184-20=164

For neutrons these sequences are without exception as regards intruder positioning according to Nobelists such as Maria Goeppert-Mayer. For protons they work up to 1i13/2, and this failure is only one option, since there is an energy level close enough to compete with the prevailing pattern as found with the neutrons.

Interestingly, the depth sequence 2,6,12,20... is that of doubled triangular numbers, from a value doubled Pascal Triangle.

Below magic number 50 depth of intrusion is zero, which means that the highest spin-split orbital partial simply rides on top of the previous shell.

108.5.120.133 (talk) 23:47, 26 June 2015 (UTC)

Because of parity sorting (either all positive or all negative parity) of orbital components within the simpler harmonic oscillator shell, total proton or neutron counts within nuclear period analogues are all doubled triangular numbers:

s=2 p=6 ds=12 fp=20 gds=30 hfp=42 igds=56 jhfp=72

When one adds intruder levels to these to give the spin-orbit shells, the period analogue size increases to the very next doubled triangular number for the acceptor shell, and is reduced to the previous doubled triangular number for the donor shell.

Thus: 1f2p=20, plus 10 (1g9/2) yields 30, while 1g2d3s=30 loses 1g9/2, yielding 20. 1g2d3s=30, plus 12 (1h11/2) yields 42, while 1h2f3p=42 loses 1h11/2, yielding 30 1h2f3p=42, plus 14 (1i13/2) yields 56, while 1i2g3d4s=56 loses 1i13/2, yielding 42

And because each intruder level in turn is 2 nucleons larger than the one that came before, then when loss and gain of intruders both occur it produces the net differences between spin-orbit magic numbers, which is doubled triangular PLUS TWO.

108.35.168.107 (talk) 23:01, 24 July 2016 (UTC)

Section References
In the early 1900s, scientists discovered that atoms were not indivisible after all. In fact, they found that atoms were made up of smaller particles called protons and neutrons. This discovery led to a revolution in our understanding of the atom. Shaaam1 (talk) 04:13, 24 November 2022 (UTC)

Empirical shell gap?
Hey hi howdy all; I've added a basic empirical shell gap graph, and can't help but notice there are no references to this formula. Considering how abundantly clear this makes nuclear shells from what is effectively just AME data, this should be included; are there other articles which reference this, or should I throw it in somewhere in the article? Mia Dobson (talk) 15:30, 12 March 2020 (UTC)

Modified harmonic oscillator model
As I understand the spherically-symmetric three-dimensional harmonic oscillator is modified by adding spin-orbit interaction and changing the profile of the (spherical-symmetric) potential to a more realistic one. And therewith the shells matching the magic-numbers are found.

I see similarity with the orbits of electrons (clouds). In that model the electrons are attracted to the protons in the kernel via the electric field. This electric field causes the spherical-symmetric potential V(r).

What is the source of the potential in the nuclear shell model? And how does this attracts protons and neutrons? And also, why is the changed profile more realistic? — Preceding unsigned comment added by Raetox (talk • contribs) 23:04, 8 October 2020 (UTC)

Nuclear Diagonal Rule (analogue to electronic Madelung or Aufbau Rule): The electronic version, taught to children in middle-school discussions of chemistry, is based on n+l (the sum of the principle quantum number n and the angular momentum quantum number l). This was based on a Left-Step periodic table depiction (from Charles Janet in the late 1920's), where the order of introduction of orbitals is paramount, and the s-block elements are on the RIGHT edge of the depiction.

A similar depiction can be easily generated for spherical nuclear shell structures under the simple quantum harmonic model.

This leads to: 1s 1p 1d2s 1f2p 1g2d3s 1h2f3p 1i2g3d4s 1j2h3f4p

It turns out that the analogue to the electronic diagonal rule, for spherical nuclei here, is 2n+l rather than n+l

1s> 2(1)+0=2 1p> 2(1)+1=3 1d> 2(1)+2=4, 2s=2(2)+0=4 1f> 2(1)+3=5, 2p=2(2)+1=5 1g> 2(1)+4=6, 2d=2(2)+2=6, 3s=2(3)+0=6 1h> 2(1)+5=7, 2f=2(2)+3=7, 3p=2(3)+1=7 1i> 2(1)+6-8, 2g=2(2)+4=8, 3d=2(3)+2=8, 4s=2(4)+0=8 1j> 2(1)+7=9, 2h=2(2)+5=9, 3f=2(3)+3=9, 4p=2(4)+1=9

Ellipsoidally deformed harmonic oscillator nuclei are underlyingly based on this same pattern, but additionally have 'correction' factors that shift the resultant shell structures, and each different simple oscillator ratio has a different formula associated with it, And the correction term is based ON the oscillator ratio.

2601:89:C601:C3B0:4D70:9AF6:620E:94F6 (talk) 15:45, 24 May 2021 (UTC)

YouTube video mention
Just wanted to let y'all know that this article was mentioned in this YouTube vid, at timestamp 27:30. It gives a correction (which has been actioned) and jokingly suggests that the video should be cited as a source (and then tells the audience not to). Just in case any mischief is afoot. Sojup (talk) 14:52, 27 August 2023 (UTC)

Oxygen-28 fails under these theories
Please add information from this experiement.

https://physicsworld.com/a/newly-observed-oxygen-28-nucleus-fails-double-magic-test/ — Preceding unsigned comment added by 2603:7080:2E00:4067:3DF8:2F8A:F61E:8AD3 (talk) 16:47, 12 September 2023 (UTC)


 * The spherical shell model often fails for nuclei far from stability (with extreme neutron to proton ratios). Oxygen-28, with 8 protons and 20 neutrons, has quite the extreme ratio for nuclei in this region of the chart of nuclides. It's good to remember that all models are wrong, but some are useful. In any case, it doesn't seem beneficial to add information specific to one of many cases where the model fails.
 * However, it might be nice to add this information to the article "Isotopes of oxygen" Maicany (talk) 05:57, 15 November 2023 (UTC)