Talk:Einstein coefficients

message: 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)
thread_title: Untitled

message: 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)
thread_title:  stimulated emission image 

message: ~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)
thread_title:  <math>B_{12}</math>, is it function of <math>\nu</math> ? 

message: 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)
thread_title:  rewritten introduction 

message: 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)
thread_title:  In terms of oscillator strengths 

message: 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)
thread_title:  error in article 

message: 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)
thread_title:  article title 

message: 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  coefficients, not with the  coefficient as per Evgeny.
Evgeny is concerned about a factor  in relation to the Einstein coefficient  .
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)
thread_title:  "fix" by Evgeny 

message: 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)
thread_title:  Proposed move 

message: "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)
thread_title:  Unit of  B_21 

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

message: 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{2 h \nu^3}{c^2},
under which definition B_{21} becomes
:B_{21} = \frac{c^2}{2 h \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)
thread_title:  Absorption coefficient 

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thread_title:  External links modified 

message: Substituted at 21:41, 26 June 2016 (UTC)
thread_title: Assessment comment

message: 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)
replies: text: 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)

text: 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)

text: 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)
thread_title:  Error in the section Oscillator strength 

message: 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{2 h\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{2 h\nu^3}{c^2} is incorrect. The equation must read F(\nu) = \frac{2 h\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)
thread_title:  Several Errors