Magnetic resonance

[dl914282]

I'd like some help in understanding how Rabi's resonance method works.
The figure bellow is the apparatus used.

 

Molecules (or other particles) originate from source and travel through magnetic field of magnet A, then through collimator, and then are deflected by B magnet to detector. In the region of C magnet, a static field H_o exists and an additional rotating field H₁, which precesses around H₀.

From what I understand, in a static magnetic field, nuclear magnetic moment vector will precess around the field vector with Larmor frequency.

The angle between the magnetic moment and field vector remains constant, right?
But what happens when the rotating field H₁ is added?

"If energy is absorbed by the nucleus, then the angle of precession will change. For a nucleus of spin 1/2, absorption of radiation "flips" the magnetic moment so that it opposes the applied field (the higher energy state)."

http://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/nmr1.htm

Radiation is absorbed by nucleus if radiation's frequency matches nuclei's Larmor frequency?

So, if the energy of an atom is changed, it gets deflected differently at magnet B and the detection signal changes.
So, you can measure these states of nuclei if you tune the frequency of rotating field to Larmor frequency?

 

 

 

Please correct any mistakes you may find. I'm sure there are many. Any help is appreciated.

 

EDIT:
After further investigation, I believe this animation shows what happens to the angular momentum (and thus magnetic moment) in the region C:
http://en.wikipedia.org/wiki/Rotating_reference_frame#mediaviewer/File:Animated_Rotating_Frame.gif

Edited November 18, 2014 by dl914282

[dl914282]

Updated version (understanding):

 

- Atoms originate from the source and pass through inhomogeneous field of magnet A (which selects those in lower energy state), then through region C in which a weak static field H₀ exists, with field H₁ rotating around it with frequency f, and then pass through another inhomogeneous field (magnet B, which selects those in HIGHER energy state) before reaching the detector.

 

- In the static field H_o, nuclear magnetic moment vector rotates around static field vector H_o with Larmor frequency f₀.

 

- If f = f₀ , in the static + rotating field, as viewed from H₁'s frame of reference, magnetic moment vector will rotate around H₁ (animation), and this will cause the angle of magnetic moment with respect to H₀ to continuously change. (pic)

 

- If an atom flips its moment, it gets deflected differently, and corresponding decrease in intensity at detector is observed.

 

- Frequency of radiation (of rotating field H₁ ; f) is tuned so that there is maximum change in intensity at detector.

 

animation of precession in rotating frame of reference: http://upload.wikimedia.org/wikipedia/commons/d/d8/Animated_Rotating_Frame.gif

pic: http://www.quantiki.org/mediawiki/images/0/05/Precession.jpg

 

 

Is this correct?

Edited November 18, 2014 by dl914282

[swansont]

The rotating wave approximation is often used so you can worry only about static fields, which give static energy shifts. The field changes the energy level of the atom, so you can tune it into or out of resonance. On resonance will cause more atoms to change state and thus make it to the detector or be deflected, depending on how it's set up.

[dl914282]

@swansont:
Thanks for the answer.

So, the stuff I wrote about Larmor precession and motion of magnetic moment vector is correct (at least as an approximation)?
That's what I figured out from this paper: http://www.colorado.edu/physics/phys7550/phys7550_sp07/extras/Ramsey90_RMP.pdf

It's for an assignment on Nobel prize in 1989. and atomic clocks. I needed to figure out Rabi's method in order to understand Ramsey's method, in order to understand cesium beam standard clock...

I'm in 3rd semester of physics so it's kinda above my current knowledge of physics

Edited November 18, 2014 by dl914282

[swansont]

The explanation about Larmor precession looks OK, but that class was a long while ago for me. I'm more up to speed on Ramsey interrogation, since that's what I do for a living.

[Enthalpy]

The angular and magnetic momenta can only have discrete values in any direction, so the image of a magnetic vector with a definite direction is approximate. QM doesn't use this vocabulary - at least in courses and textbooks - and I fear (unsure!) such a description would be inaccurate.

 

Sorry I can't make a definite statement about this: I've no clear mental image of the intrinsic angular and magnetic momenta in QM.

 

Anyway, the descriptions I've seen up to now don't tell about an orientation of the momenta (which must be impossible to measure), they tell only about the probabilities of every value along one direction. Though, the final result resembles a set of probabilities computed from a vector orientation.