Main Page: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
No edit summary
No edit summary
 
(333 intermediate revisions by more than 100 users not shown)
Line 1: Line 1:
{{Unreferenced|date=February 2009}}
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


The '''nuclear magnetic moment''' is the [[magnetic moment]] of an [[atomic nucleus]] and arises from the [[Spin_(physics)|spin]] of the [[proton]]s and [[neutron]]s. It is mainly a magnetic dipole moment; the [[quadrupole moment]] does cause some small shifts in the [[hyperfine structure]] as well.  
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


The nuclear magnetic moment varies from [[isotope]] to isotope of an [[Chemical element|element]]. It can only be zero if the numbers of protons and of neutrons are ''both'' even.
Registered users will be able to choose between the following three rendering modes:


==Shell model==
'''MathML'''
According to the [[shell model]], [[proton]]s or [[neutron]]s tend to form pairs of opposite [[total angular momentum]]. Therefore the magnetic moment of a nucleus with even numbers of both protons and neutrons is zero, while that of a nucleus with an odd number of protons and even number of neutrons (or vice versa) will have to be that of the "last", unpaired proton (or neutron). For a nucleus with odd numbers of both protons and neutrons, the total magnetic moment will be some combination of the magnetic moments of both of the "last", unpaired proton and neutron.
:<math forcemathmode="mathml">E=mc^2</math>


Nuclear magnetic moment is only partly predicted by simple versions of the [[shell model]]. The magnetic moment is calculated through ''j'', ''l'' and ''s'' of the "last" nucleon, but nuclei are not in states of well defined ''l'' and ''s''. Furthermore, for [[odd-odd nuclei]], one has to consider the two "last" [[nucleon]]s, as in [[Deuterium#Magnetic_and_electric_multipoles|deuterium]]. Therefore there are several possible answers for the nuclear magnetic moment, one for each possible combined ''l'' and ''s'' state, and the real state of the nucleus is a [[Superposition principle|superposition]] of them. Thus the real (measured) nuclear magnetic moment is somewhere in between the possible answers.
<!--'''PNG''' (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


==g-factors==
'''source'''
The values of g<sup>(l)</sup> and g<sup>(s)</sup> are known as the [[g-factor (physics)|g-factor]]s of the [[nucleon]]s.
:<math forcemathmode="source">E=mc^2</math> -->


The measured values of g<sup>(l)</sup> for the [[neutron]] and the [[proton]] are according to their [[electric charge]]. Thus, in units of [[nuclear magneton]], g<sup>(l)</sup> = 0 for the [[neutron]] and g<sup>(l)</sup> = 1 for the [[proton]].
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


The measured values of g<sup>(s)</sup> for the [[neutron]] and the [[proton]] are twice their magnetic moment (either the [[neutron magnetic moment]] or the [[proton magnetic moment]]). In [[nuclear magneton]] units, g<sup>(s)</sup> = -3.8263 for the [[neutron]] and g<sup>(s)</sup> = 5.5858 for the [[proton]].
==Demos==


==Calculating the magnetic moment==
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:
In the [[shell model]], the magnetic moment of a nucleon of [[total angular momentum]] ''j'', [[orbital angular momentum]] ''l'' and [[Spin (physics)|spin]] ''s'', is given by
:<math>\mu=\langle(l,s),j,m_j=j|\mu_z|(l,s),j,m_j=j\rangle</math>


By projecting with the [[total angular momentum]] '''j''' we get
<math>\mu=\langle(l,s),j,m_j=j|\overrightarrow{\mu}\cdot \overrightarrow{j}|(l,s),j,m_j=j\rangle \frac{\langle (l,s)j,m_j=j|j_z|(l,s)j,m_j=j\rangle}{\langle (l,s)j,m_j=j|\overrightarrow{j}\cdot \overrightarrow{j}|(l,s)j,m_j=j\rangle}</math>
<math>= {1\over (j+1)}\langle(l,s),j,m_j=j|\overrightarrow{\mu}\cdot \overrightarrow{j}|(l,s),j,m_j=j\rangle</math>


<math>\overrightarrow{\mu}</math> has contributions both from the [[orbital angular momentum]] and the [[Spin (physics)|spin]], with different coefficients g<sup>(l)</sup> and g<sup>(s)</sup>:
* accessibility:
:<math>\overrightarrow{\mu} = g^{(l)}\overrightarrow{l} + g^{(s)}\overrightarrow{s} </math>
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
by substituting this back to the formula above and rewriting
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
:<math>\overrightarrow{l}\cdot\overrightarrow{j} = {1\over 2} \left(\overrightarrow{j}\cdot \overrightarrow{j} + \overrightarrow{l}\cdot \overrightarrow{l} - \overrightarrow{s}\cdot \overrightarrow{s}\right)</math>
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
:<math>\overrightarrow{s}\cdot\overrightarrow{j} = {1\over 2} \left(\overrightarrow{j}\cdot \overrightarrow{j} - \overrightarrow{l}\cdot \overrightarrow{l} + \overrightarrow{s}\cdot \overrightarrow{s}\right)</math>
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


<math>\mu = {1\over (j+1)}\langle(l,s),j,m_j=j|(g^{(l)}{1\over 2} \left(\overrightarrow{j}\cdot \overrightarrow{j} + \overrightarrow{l}\cdot \overrightarrow{l} - \overrightarrow{s}\cdot \overrightarrow{s}\right) + g^{(s)}{1\over 2} \left(\overrightarrow{j}\cdot \overrightarrow{j} - \overrightarrow{l}\cdot \overrightarrow{l} + \overrightarrow{s}\cdot \overrightarrow{s}\right)|(l,s),j,m_j=j\rangle </math>
==Test pages ==
<math>=  
{1\over (j+1)}\left(g^{(l)}{1\over 2} \left(j(j+1) + l(l+1) - s(s+1)\right) + g^{(s)}{1\over 2} \left(j(j+1) - l(l+1) + s(s+1)\right)\right)</math>


For a single [[nucleon]] ''s'' =1/2. For <math>j = l+1/2</math> we get
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
:<math>\mu_j = g^{(l)} l + {1\over 2}g^{(s)}</math>
*[[Displaystyle]]
*[[MathAxisAlignment]]
*[[Styling]]
*[[Linebreaking]]
*[[Unique Ids]]
*[[Help:Formula]]


and for <math>j = l-1/2</math>
*[[Inputtypes|Inputtypes (private Wikis only)]]
:<math>\mu_j = {j \over j+1} \left( g^{(l)} (l+1) - {1\over 2}g^{(s)} \right)</math>
*[[Url2Image|Url2Image (private Wikis only)]]
 
==Bug reporting==
== See also ==
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
* [[Gyromagnetic ratio]]
* [[Nuclear magneton]]
* [[Magnetic moment]]
* [[Neutron magnetic moment]]
* [[Electron magnetic dipole moment]]
* [[Deuterium#Magnetic_and_electric_multipoles|Deuterium magnetic moment]]
 
== External links ==
* [[Image:Queryensdf.jpg]] '''[http://www-nds.iaea.org/queryensdf Nuclear Structure and Decay Data - IAEA ]''' with query on Magnetic Moments
* '''[http://magneticmoments.info/wp magneticmoments.info/wp]''' A blog with all recent publications on electromagnetic moments in nuclei
 
[[Category:Magnetism]]
[[Category:Nuclear physics]]
 
[[es:Momento magnético nuclear]]
[[eu:Momentu magnetiko nuklear]]
[[ml:അണുകേന്ദ്ര-അഘൂർണം]]
[[sr:Нуклеарни магнетни момент]]

Latest revision as of 23:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

Retrieved from "https://en.formulasearchengine.com/index.php?title=Main_Page&oldid=329754"