NMR nuclear spin absorption/emission question

NMR textbooks often state that an ensemble of nuclei cannot absorb the excitation radiowaves if the spin population is "saturated" (wherein "saturated" is often described as equal spin population in all energy states, or a population inversion). But these same NMR textbooks show that a 180 degree "flip" of nuclei population can be executed by a pulse of radiowaves, thus causing a population inversion.

My question is: How can a population inversion be created by incoming radiowaves when "saturation" should prohibit the radiowaves from being absorbed by the nuclei once the spin population is equalized?

HAYAO
Gold Member
180 degree "flip" of nuclei population can be executed by a pulse of radiowaves, thus causing a population inversion
nuclei cannot absorb the excitation radiowaves if the spin population is "saturated"
"saturated" is often described as [...] population inversion

I don't see any contradiction. How did you end up from these three non-contradicting facts to the question you are asking?

Ok let me explain more clearly for the case of an ensemble of spin 1/2 nuclei: If "flipping" a spin requires absorption of radiowave energy, and the net rate of absorption of radiowave energy goes to zero when the ensemble spin population is equal between "up" and "down" states, then the radiowaves should never be able to force spin populations to be inverted, because absorption of radiowaves goes to zero once the spin population is equalized.

Let's say we have the ensemble of spin 1/2 nuclei in a ~1 T time-constant magnetic field called B0. As a crude approxmition, at equilibrium, let's say approximately 51.00% of the nuclei are pointing in the same direction as B0 and 49.00% are pointing anti-directional to B0. The excitation radiowaves should only be able to cause the spin populations to become 50.00% up and 50.00% down (which would cause the spin flip angle to be 90 degrees). If the Einstein stimulated-emission principle holds true then no net radiowave energy can be absorbed by the ensemble of nuclei after they have become 50.00% up and 50.00% down.

DrDu
If the population is 50 - 50, then the system can in deed not absorb radio energy. However this does not mean that 51-49 cannot be inverted into 49-51. But on the long run, 49-51 will relax to 50-50 and then there will be no absorption of radiowaves any more.

If B0 points up, please explain how 51% up and 49% down can become "inverted" (where the definition of "inversion" is 49% up and 51% down) when the populations are incapable of absorbing net energy at the 50% up and 50% down state. The populations have to pass through the 50% up 50% down state in order to create the inversion! How can the populations move beyond the 50% up 50% down state when they can't absorb any net energy!

DrDu
The populations have to pass through the 50% up 50% down state in order to create the inversion!

The point is that during inversion, the electronic states are coherent, while in the 50-50 equilibrium state which forms after a long time, the electronic states are incoherent. I.e. during inversion, you don't pass the 50-50 statistical mixture.

During the 180 pulse there surely is a point-in-time in which the overall spins have a population of 50-50. I assume the the Einstein stimulated emission phenomena applies to coherent ensembles equally as well as incoherent ensembles. And, either way, I assume the incoming B1 radiation exchanges energy predominantly with spins that are coherent (or approximately coherent) with the incoming radiation.

Do you know of a hard core physics textbook that explains the probability and rate of energy exchange between the incoming radiation and spins (coherent vs incoherent spins)?

It seems like all the popular NMR textbooks gloss over physical explanations of these phenomena.

DrDu
During the 180 pulse there surely is a point-in-time in which the overall spins have a population of 50-50. I assume the the Einstein stimulated emission phenomena applies to coherent ensembles equally as well as incoherent ensembles.
Only in the sense that upon measuring spin up/ down you will get a 50% chance of finding one of the two. However, it will not be an incoherent 50-50 ensemble.
As you already speculated, the coherent state has interacts more strongly with the field than an incoherent superposition. On the other hand, the incoherent superposition can be thought of equivalently as a 50-50 mixture of two coherent states, the first one being in phase with the electric field and the other one being 180 degrees of phase out with respect to the field. While the coherent with the field one is due to originally spin down being inverted into spin up, the anti-coherent one is due to spin ups being converted into spin down. The first one taking energy from the field while the other one depositing energy into the field. So the net interaction with the field is zero.

Well I had pre-stated that B0 points up, so the directions you mentioned in your final two sentences should be switch vice versa, right?

And, to be fully explicit with your explanation, the "saturated" state should have nuclei spins that are: i) anti-coherent and pointing up, ii) coherent and pointing up, iii) anti-coherent and pointing down, iv) coherent and pointing down. I have always assumed that when a nuclei spin absorbs energy from the B1 radiation (B0 pointing up), it causes a coherent up spin to become a coherent down spin. This is contrary to what you said happens in the last two sentences of your last post). Am I wrong here?

DrDu