Magnetic Precession and Photon Absorption

[fargoth]

In my understanding, when a nuclei absorbes a photon with the right freq it changes its spin...
now, if this atom is in a magnetic field B on the Z direction, its magnetization vector is precessing around the Z direction, and after absorbing a photon it changes its angle relative to the Z axis.
with enough photons we can make the magnetization vectore exist only on the X-Y plane, and with even more photons it is possible to make the magnetization vector point to the -Z direction.

am i right?
if my view of the process is right, i have trouble seeing why would there be frequency involved... it seems pretty contineus to me.
and I've seen the use of rotating axis in some explanations... why would we need these? do the photons have circular polarization?
im a bit confused...

 

[ZapperZ]

In my understanding, when a nuclei absorbes a photon with the right freq it changes its spin...
now, if this atom is in a magnetic field B on the Z direction, its magnetization vector is precessing around the Z direction, and after absorbing a photon it changes its angle relative to the Z axis.
with enough photons we can make the magnetization vectore exist only on the X-Y plane, and with even more photons it is possible to make the magnetization vector point to the -Z direction.
am i right?
if my view of the process is right, i have trouble seeing why would there be frequency involved... it seems pretty contineus to me.
and I've seen the use of rotating axis in some explanations... why would we need these? do the photons have circular polarization?
im a bit confused...

The problem here is that you are trying to match two different picture - the quantum picture of energy states and the classical picture of a precessing BULK magnetization. While they are not different things, they have different "world view".

You need to explain a bit more of what "frequency" you're talking about here. The "frequency" of the RF, for example, is to match the Larmour frequency of the precessing magnetization. The external magnetic field doesn't have a "frequency" (usually). It is static. Once you have this, then the bulk magnetization has a precession frequency about the external magnetic field. Think of it as precessing in the form of an inverted cone.

An external RF field to change the magnetization will need to be applied at the same frequency as this or else the energy transfer is not efficient (i.e. a typical resonance phenomenon). This is the same as giving photons of the wrong energy and won't cause a transition - it must be the same as the gap between the energy levels or else nothing will occur.

Zz.

 

[fargoth]

thanks for the quick reply.
i was talking about the larmor freq...
the part about the bulk magnetization which has a precession frequency about the external magnetic field i can imagine.
and if i understand the part about the rf, circular polarized rf would be even more efficient.
if i use the classical view you described here, rf at the precession freq which we project along the Z axis would have the same direction as the bulk magnetization vector but its stregnth would increase and decrease like abs(sin(wt)), while if circular polarized it would have the same strength at all times.
am i right?
the rf would increase the X-Y component of the bulk magnetization that way, but it will never make the Z component go away...
i guess we need to project along some line on the XY plane inorder to make 90 or 180 degree change...
now i need some feedback here, I am getting myself lost.

 

[ZapperZ]

thanks for the quick reply.
i was talking about the larmor freq...
the part about the bulk magnetization which has a precession frequency about the external magnetic field i can imagine.
and if i understand the part about the rf, circular polarized rf would be even more efficient.
if i use the classical view you described here, rf at the precession freq which we project along the Z axis would have the same direction as the bulk magnetization vector but its stregnth would increase and decrease like abs(sin(wt)), while if circular polarized it would have the same strength at all times.
am i right?
the rf would increase the X-Y component of the bulk magnetization that way, but it will never make the Z component go away...
i guess we need to project along some line on the XY plane inorder to make 90 or 180 degree change...
now i need some feedback here, I am getting myself lost.

Er.. no. Circular polarization will have E and B-field vectors rotating in the x-y plane in the simplest case (you can have other modes in an NMR and MRI application). This is how you would flip the spins and cause the z-component of the bulk magnetization to completely disappear in the 90 degree pulse in a Pulse NMR.

I also remember that even plane polarized RF field would work because you are applying the field at the same rate. Remember that the bulk magnetization is simply the sum of many smaller magnetization. Each one of these vectors, while having a particular z-component, have randomly oriented x-and y component. Applying an RF field at the same frequency as the lamour freq. would affect these miniature magnetization.

We really need a professional NMR person in here. :)

Zz.

 

[fargoth]

ok, i didnt understand about what part you said "err.. no."...

and i can't see how a field in the right freq on the X-Y plane would shift the bulk magnetization vector in 90 degrees or even 180...

 

[ZapperZ]

You may want to refer to Fukushima "Pulse NMR- A Nuts and Bolts Approach".

Zz.

 

[noamholz]

a basic question

Hi,
if I could measure the magnetization of a single spin,
I'd expect the value to be constant (+1/2, -1/2) with time, cause the state/wavefunction has collapsed.
what happens in the NMR measurement?
if all the spins were measured *together* (magnetization measurement) in a continues matter, shouldn't each one of them have a constant defined value (+1/2, -1/2 ) so that the magnetization would stay constant with time?

I know that in fact, there are oscillations of the Magnetization all time,
how does it cope the qtn above?

thanks a lot

 

[marcusl]

thanks for the quick reply.
i was talking about the larmor freq...
the part about the bulk magnetization which has a precession frequency about the external magnetic field i can imagine.
and if i understand the part about the rf, circular polarized rf would be even more efficient.
if i use the classical view you described here, rf at the precession freq which we project along the Z axis would have the same direction as the bulk magnetization vector but its stregnth would increase and decrease like abs(sin(wt)), while if circular polarized it would have the same strength at all times.
am i right?
the rf would increase the X-Y component of the bulk magnetization that way, but it will never make the Z component go away...
i guess we need to project along some line on the XY plane inorder to make 90 or 180 degree change...
now i need some feedback here, I am getting myself lost.

This might help:
In the classical model, the RF magnetic field lies in the plane normal to the z-directed static magnetic field. The main field is called B0, the RF magnetic field B1. The RF field causes the nuclear magnetic moment to precess about the z axis in a spiral. After a time, the moment is located in the x-y or transverse plane, and B1 is typically turned off (this is a 90 degree pulse). The moment continues rotating at the Larmor frequency in the transverse plane until losses "relax" it back to +z. If B1 is still applied, however, precession continues until the moment is pointing along -z, then back up to the transverse plane, +z, and then repeating for as long as B1 is applied. Think of a vector on a sphere that rotates azimuthally (phi) at the Larmor frequency and moves in polar angle (theta) at a speed determined by the strength of B1.

Circ pol (CP) applies twice the effective B1 field as linear pol. Remember that LP can be decomposed into right and left CP components of equal strength. One couples to the spin system, the other effectively rotates far from the Larmor frequency and has no effect.

 

[Ygggdrasil]

Hi,
if I could measure the magnetization of a single spin,
I'd expect the value to be constant (+1/2, -1/2) with time, cause the state/wavefunction has collapsed.

Not quite. The spin is still interacting with its environment. Often, the thermal energy in the environment can excite a -1/2 spin into the +1/2 spin state and similarly, interactions with the environment can induce a +1/2 spin to return to the -1/2 state (via stimulated emission, spontaneous emission is negligible at NMR frequencies). At equilibrium, the rate of spins moving from -1/2 to +1/2 is equal to the rate of spins moving from +1/2 to -1/2, so the populations of each state remain constant in time even though the individual spins are moving between the two states.

what happens in the NMR measurement?
if all the spins were measured *together* (magnetization measurement) in a continues matter, shouldn't each one of them have a constant defined value (+1/2, -1/2 ) so that the magnetization would stay constant with time?

In an NMR experiment, you first pump the system with an RF field that puts the system in a non-equilibrium state (too many +1/2 spins, not enough -1/2 spins). You then examine the relaxation of the system back to equilibrium. The frequencies of RF released by the system during relaxation and the time taken for the system to relax to equilibrium give you information about the sample.

 

[noamholz]

in other words:

thanks for the reply!
I'm not sure if my question was written clear enough.

looking at the signal of NMR, AFTER the RF pulse was given, we see modulation of a "hi-freq" wave & a relatively slow decaying signal (exponent i guess). The "hi freq" wave, which should represent the precession of the magnetization (if I'm not wrong), is the one I ask about.
here is what puzzles me:
while a static z-axis Mag field is applied, and the "measuring coil" is along the x-axis:
I expect a measurement to FIX the state of the spin being measured (on +1/2, -1/2 with respect to x-axis): once a spin was measured, it should "line up" with the x-axis field, and stop precessing relative to the x-axis. being fixed on a Sx defined state, and being in an undefined z-axis state.
so instead of <Sx>~sin(wt), I expect to get a fixed static picture, and a "sin" fashion change of energy of the spin (cause Mag field's aligned on z-axis, and now <Sz> precess)! it all gets crazy&wrong!

HELP ! (thanks)

 

[Ygggdrasil]

thanks for the reply!
I'm not sure if my question was written clear enough.

looking at the signal of NMR, AFTER the RF pulse was given, we see modulation of a "hi-freq" wave & a relatively slow decaying signal (exponent i guess). The "hi freq" wave, which should represent the precession of the magnetization (if I'm not wrong), is the one I ask about.
here is what puzzles me:
while a static z-axis Mag field is applied, and the "measuring coil" is along the x-axis:
I expect a measurement to FIX the state of the spin being measured (on +1/2, -1/2 with respect to x-axis): once a spin was measured, it should "line up" with the x-axis field, and stop precessing relative to the x-axis. being fixed on a Sx defined state, and being in an undefined z-axis state.
so instead of <Sx>~sin(wt), I expect to get a fixed static picture, and a "sin" fashion change of energy of the spin (cause Mag field's aligned on z-axis, and now <Sz> precess)! it all gets crazy&wrong!

HELP ! (thanks)

You're getting the two pictures of NMR confused. The precession of a spin around a static B-field in z is the classical picture of NMR. The ideas with +1/2 and -1/2 are involved in the quantum picture of NMR.

There is, however, a way to unite these pictures, by invoking the concept of a the Bloch sphere. In this picture, you can think of the bulk magnetization on the positive z-axis as the |1/2> state, the bulk magnetization in the negative z-axis as the |-1/2> state, and all vectors in between as superpositions of the |+1/2> and |-1/2> states. If you are familiar with density matrices, the z-axis is related to the on-diagonal terms of the density matrix (the populations) whereas the x- and y-axes are related to the off-diagonal terms of the DM (the coherences). Since states with components in the transverse plane are not eigenvectors of the Hamiltonian, they are not stationary states and therefore evolve in time.

Also, the "precession" in the classical picture corresponds to the quantum mechanical concept of Rabi oscillations.

 

[noamholz]

thanks for the answer (it took some time for me to return to that..),
I'm not familiar enough with density matrices, but I get the impression I should be already.
The stuff you wrote concerning that makes sense, so the mystery's partly resolved for me.
thanks again!