Talk:Hyperfine structure

Improve opening sentence

The opening sentence ("In atomic physics, hyperfine structure refers to small shifts and splittings in the energy levels of atoms, molecules and ions, due to interaction between the state of the nucleus and the state of the electron clouds.") is unclear and misleading. The interaction between the magnetic moments of the nucleus and electron, i.e. the "hyperfine interaction", determines the allowed states in the hyperfine structure. I don't think "interaction between the state of the nucleus and the state of the electron clouds" makes sense. The second sentence (first sentence of second paragraph) is clear, well-worded and says essentially what the first sentence means to say. I suggest combining and/or rewording the two. A well-worded description can be found here. — Preceding unsigned comment added by Ethanque (talk • contribs) 06:41, 27 April 2018 (UTC)

Wrong units

ΔE ≈ ħ ? How can this be? ħ doesn't have units of energy. —The preceding unsigned comment was added by 69.137.135.226 (talk) 02:40, 15 March 2007 (UTC).

Yes, of course. I correct that expression to $~\Delta E_{\rm {hfs}}/\hbar ~\sim ~1~{\rm {[[GHz]]}}$.

Also, I add definition of $~{\vec {B}}_{J}~$. Is it correct? Could LAk loho check this? dima 03:51, 4 April 2007 (UTC).

Vector Multiplication?

Under the Theory section, the equation:

$a={\frac {g_{I}{\vec {\mu }}_{\rm {N}}{\vec {B}}_{J}}{\sqrt {J(J+1)}}}$

appears to contain a product of two vectors. If this is the case, in order to result in a scalar value (the fine structure constant), shouldn't this product be written as a vector dot product? Or is the product really of the magnitudes of the two vectors? CosineKitty (talk) 14:23, 21 November 2007 (UTC)

I have gone back and resolved this ambiguity in two places. Based on this discussion, it becomes clear that ${\vec {\mu }}\times {\vec {B}}$ is a torque expression, and $-({\vec {\mu }}\cdot {\vec {B}})$ is a potential energy expression. Since the equation in question has to do with an energy value, it made more sense to use a dot product. It also seems to be required, since the result (energy) is a scalar value. Finally, even though energy and torque both have nominally the same units (force times distance), energy is usually expressed as a dot product in the direction of the force, while torque is expressed as a cross product perpendicular to both the force and the radius vector. Can somebody who knows more about subatomic physics verify that my changes to these equations are correct? CosineKitty (talk) 17:07, 14 June 2008 (UTC)

It is common in math and physics textbooks that the dots are simply omitted in dot products. In my opinion there's no ambiguity in this article; it is simply using this very common way of writing dot products… AdamSiska (talk) 00:55, 24 January 2009 (UTC)

Undefined variable

As mentioned above, I have changed one of the formulas in the Theory section to

$a={\frac {g_{I}({\vec {\mu }}_{\rm {N}}\cdot {\vec {B}}_{J})}{\sqrt {J(J+1)}}}$

But nowhere that I can find in this article is the variable $g_{I}$ defined. Can somebody explain what this is? CosineKitty (talk) 17:14, 14 June 2008 (UTC)

I guess it's the atom's G-factor... not really clear anyway DracoRPG (talk) 00:38, 27 September 2008 (UTC)

The g-factor is introduced so that the magnetic dipole moment, μ, can be given in terms of the nuclear magneton, μ_N,

${\boldsymbol {\mu }}_{I}=g_{I}\mu _{\text{N}}\mathbf {I}$.

The product g_Iμ_N (units JT^-1) determines the energy for a particular nucleus associated with a given nuclear angular momentum (vector), placed in a given magnetic field (vector). The energy is given by:

$E_{B}=-{\boldsymbol {\mu }}\cdot \mathbf {B}$.

The orbital (g_L=1) and spin (g_S≈2) electronic g-factors equivalently allow their respective magnetic dipole moments to be given in terms of the Bohr magneton, μ_B.

--DJIndica (talk) 19:57, 15 February 2009 (UTC)

Image description page

The image description page for File:Fine hyperfine levels.png doesn't define I, J, F, S, n, or P, so it's virtually impossible for a layperson to understand. -- Beland (talk) 15:41, 1 July 2009 (UTC)

I have added additional explanation, defining all the symbols with wikilinks to articles with further explanation. Do you feel it is now sufficient? --DJIndica (talk) 02:38, 5 July 2009 (UTC)

Relatively simple experiment to demonstrate hyperfine splitting.

This was the most interesting Physics experiment in my entire brief stay at university. This was in 1975, so maybe my memory of it is a little rusty :)

We had a rubidium lamp with a deep red filter to select the appropriate emission line.

The light passed through a circularly polarising filter, which meant that the line was fine split - that is, the filter selected photons emitted from energy levels where the upper and lower energy levels had J-numbers that differed by one. From memory, either J=1/2 to J = 3/2, or the reverse, depending on the sense of rotation of the polarising filter wrt the magnetic field (described below)

The light then proceeded to a cell containing rubidium vapour which would selectively absorb the light.

Around the cell was an electromagnet, powered by a very slow (from memory, about 1/5 Hertz; that is with a period of about 5 seconds) sawtooth voltage.

Perpendicular to the light beam entering cell was an RF oscillator at 50MHz. What is interesting about this is that at 50MHz, RF energy would normally be considered as a wave; but in the context of this experiment, it clearly demonstrated photon behaviour.

On the other side of the cell was a simple RF detector; I think nothing more than a piece of wire to an LC circuit with a diode and a resistor.

A feed from the sawtooth voltage and the output of the diode/resistor and were fed, respectively, to the X-Y plates of an oscilloscope.

As the light passed through the varying magnetic field it was hyperfine split. The varying magnetic field varied the hyperfine split energy levels. When the energy levels were integral multiples of the energy of the 50MHz photons, those photons were absorbed, creating a "dip" in the oscilloscope trace.

Finally, if the amplitude of the RF oscillator was varied, an interesting effect was observed. If it was set reasonably "high", then transitions requiring absorptions of two RF photons "simultaneously" (that is, the F value of the transition went from F=0 to F=2) had a sufficiently high probability of occurring and thus being detected. If the amplitude was set to "low", then only transitions corresponding to a of a single change in hyperfine energy levels (that is from F=0 to F=1 or F=1 to F=2, but not the F=0 to F=2) would occur and be measured. Thus, at the high level, more dips in the oscilloscope trace could be seen.

A fabulous experiment !!!! Old_Wombat (talk) 12:38, 14 December 2011 (UTC)

"No emitter available"?

It's unclear to me what the second paragraph under "Qubit in ion-trap quantum computing" is refering to. It says "possible to drive hyperfine transitions using microwave radiation ... at present no emitter available". This makes it sound like we don't know how to build microwave emitters at the relevant frequencies. But in fact such emitters appear to be standard technology driving e.g., the passive Hydrogen maser clock, or a Rubidium clock. I'm guessing that the "no emitter available" is meant to refer to a particular hyperfine transition with a relative high frequency, but neglected to mention which? — Preceding unsigned comment added by 118.93.139.195 (talk) 05:24, 10 August 2013 (UTC)

Hyperfine structure, Applications, Astrophysics

The community needs to get to work on this paragraph, because the information it wishes to convey seems worthwhile, but the originators doubtless fail to realize that it is unintelligible . . . even to knowledgeable readers.

In radio astronomy, heterodyne receivers are widely used in detection of the electromagnetic signals from celestial objects. The separations among various components of a hyperfine structure are usually small enough to fit into the receiver's IF band. Because optical depth varies with frequency, strength ratios among the hyperfine components differ from that of their intrinsic intensities. From this we can derive the object's physical parameters.

FIRST CUT AT A REVISION: The dominant design among radio receivers today, heterodyne receivers, are also widely used in radio astronomy, where hyperfine splitting is present in the radio waves emitted by celestial objects. Unfortunately, the separations (frequency differences) among various components of a hyperfine structure are usually small enough to fit into the receiver's IF band so they cannot be separated -- the radio cannot be tuned to individual hyperfine lines to separately measure their intensity.

For some purposes such as [give example] it is sufficient to measure the aggregate (overall) strength of all the hyperfine emissions. Otherwise, additional processing [does it have a name, anything we can cross-reference to articles here in the Wikipedia?] is used to resolve the hyperfine components, whose starting relative strengths we can know -- under normal circumstances -- from physics, but which, because of their differing frequencies, differ in their absorption characteristics as they traverse interstellar space. This enables one to infer something of the properties of the intervening gas and dust clouds, such as whether [what?] Also, the resolved structure of the hyperfine ensemble reflects the nuclear and magnetic environment at the object of origin, which can shed some light on [what? ]
END FIRST CUT AT A REVISION.

These are some doubts and contradictions raised by the original paragraph above. It is time for a good Samaritan to rescue this paragraph and the frustrated readers it leaves in its wake. Thank you in advance.
Jerry-VA (talk) 17:31, 29 September 2013 (UTC)

SI second and meter

I removed, "Since 1983, the meter is defined by declaring the speed of light in a vacuum to be exactly 299,792,458 metres per second. Dividing the number of cycles with the speed of light yields: The metre is the length of the path travelled by light in vacuum during a time interval of 30.6633189884984 caesium-133 hyperfine transition cycles."

because, first, it is incorrect, the meter is not defined by the speed of light, and, second, it seems to include original research, as I can find nowhere any definition of the meter as given here in italics (italics in original).

I placed into the article the correct definition of the meter.

I realize I might be incorrect on both points. But before you revert, or rewrite, you need to find references to the definitions I removed. Nick Beeson (talk) 03:51, 14 August 2014 (UTC)

Tough to understand

Yeah, it's true Uddhav9 (talk) 17:31, 18 May 2020 (UTC)

It would be helpful is the lead were more clearly written for lay people.

We might need to create a split for the quantum mechanical math description and an simple version for people interested in everyday technology that don't have a background in quantum mechanics but are interested in applications such as atomic clocks, the SI definition of the system , and the world of accurately measuring the time for diverse fields, including electronic business stock transactions, satellite mapping, and geodesy. ScientistBuilder (talk) 21:16, 13 February 2022 (UTC)

Talk:Atomic clock/Archive 1#Hyperfine Transition Frequency — Preceding unsigned comment added by ScientistBuilder (talk • contribs) 01:52, 15 February 2022 (UTC)

Undefined symbols

In the equation after The magnetic field of a point dipole moment, μs, is given by:, the lowercase delta symbol appears, but the article doesn't state what it is, or why it's there. Both of the refs on that statement are books, so checking their text just to define a symbol is a pretty high hurdle.

Also, the second term in that equation is unexplained; online descriptions of the magnetic field of a point dipole moment that I can find have just the first term.

So this article needs some more stuff in it. 2600:8800:1180:25:1C8F:40F1:22F2:FE40 (talk) 20:15, 14 January 2024 (UTC)