Talk:Einstein coefficients

Untitled

A new spectral line intensity formula for optical emission spectroscopy was presented by Dr:s Bo Thelin (experimental physicist) and Sten Yngström (theoretical physicist) at the beginning of the 1980:s. This formula has shown very good agreement between experiments (Ref 1) and the new theory (Ref 2). These references are summaries of earlier papers.

I = K \ left (frac { v^2 }{ c^2 }\ right ) \ e^left (\ frac { -J}{ k \ T \ right )} \ \ left (\ e^left ( \ frac { h \ v }{ k \ T \right - \ 1)^-1

K includes transition rates and element concentrations I= spectral line intensity, V= frequency , J=ionization energy and T=temperature

Many independent experimental methods strongly support the new formula, while the standard intensity formula with the Boltzmann term (upper energy level), deviates very much from experiments. Ref 1 Yngström,S. and Thelin,B. Applied Spectroscopy, 44, 1566, (1990) Ref 2 Yngström,S. International Journal of Theoretical Physics,Vol.33, No 7,(1994)--79.138.179.27 (talk) 21:34, 10 March 2008 (UTC)

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1. In section oscillator strength: $~a_{12}~$ is undefined.

2. Comparing the formular connecting $~A_{21}~$ and $~f_{12}~$ with the expression in the book of Bransden&Joachain "Physics of atoms and molecules", one get's the impression that CGS-units are used here, where the permeability of vacuum, $~\epsilon _{0}~$, is $~1/(4\pi )~$. Maybe SI units are more appropriate here on wikipedia.

3. Comparing the expressions for $~B_{21}~$ and $~B_{12}~$ to Bransden&Joachain, $~\epsilon _{0}~$ would be $~c/(4\pi )~$, inconsistent with point(2.). It seems like the "$c$" in the denominators should not appear there.

Question

These questions were moved from the article. PAR 14:59, 22 June 2006 (UTC)

Question: The Wikipedia article on Einstein refers to his publishing the concept of spontaneous emission in Physikalische Zeitschrift in 1917, not 1916. Is there documentary evidence for the 1916 date?

Also, Bertolotti's book on the history of masers and lasers says that Einstein did not actually use the term "stimulated emission", which was only introduced later by Van Vleck. Comments on this?

stimulated emission image

I believe that the created photon in the stimulated emission image should be moving in the same direction as the catalyst photon.

Good idea - I have changed it. PAR 02:21, 5 October 2006 (UTC)

$B_{12}$, is it function of $\nu$ ?

$~B_{12}~$ and $~B_{21}~$: shouldn't they be replaced to $~B_{12}(\nu )~$, $~B_{21}(\nu )~$?

No, they are frequency-independent. JDMcKellar (talk) 14:32, 3 February 2016 (UTC)

rewritten introduction

A few points

• Yes, the distinction between emission and absorption lines should be noted in the beginning.
• absorption is not the same as the photoelectric effect. In the photoelectric effect the electron is ejected from the material, not pushed to a higher energy level.
• Continuum radiation is well defined. Continuum radiation comes about when the distribution of photon energies is continuous over a relatively large interval. The spectrum itself may not be continuous in the usual sense, but the probability distribution for photon energies is.
• Spectral lines only occur in bound-bound transitions. Bound-bound transitions are crucial to the understanding of atomic lines and should not be stuck at the end of the article under a "terminology" section. Bound-free transitions form a continuum, not a spectral line.

PAR 14:24, 27 October 2006 (UTC)

What is A12?

"When this relation is inserted into the original equation, one can also find a relation between A12 and B12, involving Planck's law."

In terms of oscillator strengths

At the bottom of the article, the coefficients are expressed in terms of the oscillator strength $f_{12}$. The formulas there cannot all be correct: when one makes the divisions, not the same expressions (e.g. for ${\frac {A_{12}}{B_{21}}}$) are found as those stated above. E.g., both have a factor $\pi ^{2}$ which disappears when the division is done, and also the speed of light $c$ is present as $c$ in one and as $c^{3}$ in the other; the division would lead to $c^{2}$, not $c^{3}$. —Preceding unsigned comment added by 131.155.108.140 (talk) 10:25, 8 January 2008 (UTC)

--- What is $~A_{12}~$? dima 13:01, 21 December 2006 (UTC)

error in article

The section on Detailed Balancing has an error: the equation for A21/B21 should only have F(nu) on the right-hand-side, not any g's.

Here's a site that has it right:

http://scienceworld.wolfram.com/physics/EinsteinCoefficients.html

For a more conventional reference, see Mihalas, D, "Stellar Atmospheres". Also, I'm sure the Chandrasekhar reference in your article is correct. (Don't have these handy right here to give chapter & verse, but you can look it up in the index.)

Apologies for using this page to point this out, I didn't see any other way to do it other than creating an account, which I have no interest in doing. —Preceding unsigned comment added by 68.124.160.242 (talk) 19:43, 28 June 2008 (UTC)

Are you sure that continuum radiation is produced when an electron is (b-f) emitted ? What´s about (f-f) transitions ? HH 08.09.08 15:10 (CEST) —Preceding unsigned comment added by 212.144.109.190 (talk) 13:10, 16 September 2008 (UTC)

article title

Why is this article called "Atomic" when nothing in the contents is specific to atoms? — Preceding unsigned comment added by 192.249.47.174 (talk) 20:46, 12 March 2012 (UTC)

"fix" by Evgeny

Evgeny notes his restoration of his "fix" as follows: "Chjoaygame - you are confusing energy released per steradian with the Einstein coefficient."

Evgeny's "fix" has a trivial error that I did not mention. In spontaneous emission the final state is here labeled as state 1, not state 2 as in Evgeny's "fix". It also has a substantial error in introducing the degeneracy in his added equation. The degeneracy comes in with the B coefficients, not with the A coefficient as per Evgeny.

Evgeny is concerned about a factor 4π in relation to the Einstein coefficient A₂₁ .

As far as I can see, different texts give slightly different definitions of the Einstein coefficients, along the lines indicated by Evgeny's note. Evgeny's note says, in effect, that I am confused about this.

As the article stood before Evgeny's "fix", it was logically and physically rational and consistent with its cited sources. After Evgeny's "fix", the artticle's derivation following the "fix", and the article's definition of the Einstein coefficient preceding his "fix", are faulty, and need correction to be in line with Evgeny's "fix". Evgeny offers no source for his "fix".

I do not intend to engage in an edit war with Evgeny. I think his "fix" is wrong.Chjoaygame (talk) 22:01, 7 August 2012 (UTC)

The previously standing version gave the number densities per steradian of emission and absorption. I have corrected this to total number densities, and I have made some other minor changes.Chjoaygame (talk) 07:27, 9 August 2012 (UTC)

Proposed move

I propose this article be moved to Einstein coefficients, a title that currently redirects here. The bulk of the article relates to that topic and not to atomic spectral lines. The introductory material is already covered in the spectral line article and could be removed in favor of an introduction to the Einst.ein coefficients. ronningt (talk) 01:54, 5 December 2012 (UTC)

I agree. IMHO, the whole set of subjects including Absorption coefficient, Attenuation coefficient, Absorption Coefficient, Opacity (optics), Beer-Lambert Law, Einstein coefficients etc is now a complete mess as a result of mergers. I would like to see each of those topics having its own entry with links to the other topics as appropriate. Reinstating Einstein coefficients would be a good first step in sorting that mess out. A B McDonald (talk)

Unit of B_21

"Einstein coefficient B_{21} (J−1 m3 s−1), which gives the probability per unit time per unit spectral energy density of the radiation field"

Shouldn't the unit of B_{21} then be (J−1 m3 s−2)? [probability per unit time]/[spectral energy density] = (s-1)/(J s m-3) = J-1 m3 s-2 — Preceding unsigned comment added by 153.96.32.62 (talk) 15:30, 22 January 2014 (UTC)

Question

Where can I find actual values for A12 for specific molecules,e.g. H20 and C02? — Preceding unsigned comment added by BuzzBloom (talk • contribs) 14:15, 18 February 2015 (UTC)

Try http://home.strw.leidenuniv.nl/~moldata/ JDMcKellar (talk) 14:31, 3 February 2016 (UTC)

Absorption coefficient

Hi, I'm a bit concerned about the expression for the absorption coefficient $\kappa ^{\prime }.$

(1) Firstly, it is a bit misleading, because it is, as it stands, correct only for Einstein B coefficients defined in terms of the incoming radiant flux rather than the energy density, which is what is used lower on this page to define the Bs. The page should either use radiant flux or energy density, not mix them up like this. In terms of the former, the correct expression for $F(\nu )$ becomes (see for example the Wikipedia page Planck's law)

$F(\nu )={\frac {2h\nu ^{3}}{c^{2}}},$

under which definition $B_{21}$ becomes

$B_{21}={\frac {c^{2}}{2h\nu ^{3}}}A_{21}.$

With these changes, the expression for $\kappa ^{\prime }$ becomes correct (or nearly, see next point). Otherwise, if we want to keep the energy-density Bs, the `correct' expression for $\kappa ^{\prime }$ in this case is

$\kappa ^{\prime }={\frac {h\nu }{c}}(n_{1}B_{12}-n_{2}B_{21}).$

(2) $\kappa ^{\prime }$ as a quantity only really makes physical sense for a range of frequencies much narrower than the line shape. This point is not conveyed clearly in the section. The fully correct definition for $\kappa ^{\prime }$, which has dimensions L^{-1}, or MKS unit m^{-1}, is to make its frequency dependence explicit by writing it as follows:

$\kappa ^{\prime }(\nu )={\frac {h\nu }{c}}(n_{1}B_{12}-n_{2}B_{21})\phi (\nu )$

where the lineshape function $\phi (\nu )$ is normalized such that its integral over all $\nu$ is unity. The units now check out. Units of $h\nu /c$ are Js/m. Units of n_1, n_2 are m^{-3}. Units of the Bs are m^3/J/s^2. Units of $\phi$ are s (i.e., Hz^{-1}). This all cancels to m^{-1} as desired. The multiplication by the lineshape function is not some sort of add-on for extra mileage, as is implied, but something which should be there from the start as an essential in the definition of $\kappa ^{\prime }$. Note also that the effect of multiplication by $\phi$ is not, as claimed, to change the units of $\kappa ^{\prime }$ to m^{-1} Hz^{-1}. If you wanted to integrate $\kappa ^{\prime }(\nu )$ over frequency to get some sort of average coefficient for the line, the units of that would become Hz/m.

(3) Would not this whole section on the relation between the emission and absorption coefficients and the Einstein ones be better placed after the derivation of the Einstein coeffs, instead of before it? This is the arrangement used in most texts I have seen. JDMcKellar (talk) 14:23, 3 February 2016 (UTC)

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Assessment comment

The comment(s) below were originally left at Talk:Einstein coefficients/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

The idea of an atomic spectral line is of "top" importance for physics. The explanation of these was THE big prediction of early quantum mechanics and motivated developments in all other areas of physics. I think this article is just a "start" though. It has some discussion of Einstein coefficients and such, but perhaps material that is more related to atomic physics would be useful too -- eg, explain the Balmer or Lyman series, mention the idea of jumping between energy levels defined by the Schrodinger equation, etc, to get a wider viewpoint. Also some introduction for the non-scientifically-literate user in the beginning would be nice too. Wesino 00:51, 29 November 2006 (UTC)

Substituted at 21:41, 26 June 2016 (UTC)

Error in the section Oscillator strength

The formula for the Einstein coefficient for spontaneous emission in the section oscillator strength is missing a $4\pi$. The correct formula should be:

$A_{21}={\frac {8\pi ^{2}\nu ^{2}e^{2}}{4\pi \varepsilon _{0}m_{e}c^{3}}}~{\frac {g_{1}}{g_{2}}}~f_{12}$

instead of:

$A_{21}={\frac {8\pi ^{2}\nu ^{2}e^{2}}{\varepsilon _{0}m_{e}c^{3}}}~{\frac {g_{1}}{g_{2}}}~f_{12}$

See for example "Quantum mechanics of One- and Two-Electron Atoms" by Hans A. Bethe and Edwin E. Salpeter.

I did not check the other equations in this section for similar errors. DieMuzi (talk) 06:53, 9 October 2016 (UTC)

The entire section on Oscillator Strength was poorly presented and not self consistent. I've revised that section to be fully consistent with Hilborn's 2002 article, and I've added that citation. Please review that article and see if the distinctions he draws between different presentations addresses your question. — Preceding unsigned comment added by Ronningt (talk • contribs) 14:53, 9 October 2016 (UTC)

Thanks for editing! I still find the unit issue a bit confusing. The equations are presented in SI units, but in the last sentence the units of the coefficients are given in cgs units. Maybe it can be useful to write the equations explicitly in both systems, or to omit the last sentence.DieMuzi (talk) 06:20, 10 October 2016 (UTC)

You're right. The sentence about units was misplaced, because Hilborn is specifically presenting in SI units, and not particularly relevant. I removed that sentence from the article.ronningt (talk) 23:51, 10 October 2016 (UTC)

Several Errors

There are several errors in this page. I correct here only the most obvious ones that immediately jump into the eye. (1) In the equation $\left({\frac {dn_{1}}{dt}}\right)_{\text{pos. absorb.}}=-B_{12}n_{1}\rho (\nu )$, $n_{1}$ drops out, the remaining left-hand side has obviously the unit [s^-1] and the spectral energy density $\rho (\nu )$ has obviously the unit [J m^-3 Hz^-1]. Therefore, the Einstein B coefficient has the unit [m^3 J^-1 s^-2]. This is correct. (2) In the equation ${\frac {A_{21}}{B_{21}}}=F(\nu )$, with the equation $F(\nu )={\frac {2h\nu ^{3}}{c^{2}}}$ inserted, the Einstein B coefficient would have the unit [m^2 J^-1 s^-1]. This is incorrect, because the equation $F(\nu )={\frac {2h\nu ^{3}}{c^{2}}}$ is incorrect. The equation must read $F(\nu )={\frac {2h\nu ^{3}}{c^{3}}}$. Then also the unit of B is correct. (3) In the text it is claimed that the unit of B is [m^2 J^-1], which, again, is incorrect. I have corrected the mistakes in (2) and (3). (User Pollnau) 09:03, 24 April 2020 (UTC) — Preceding unsigned comment added by Pollnau (talk • contribs)