[Petra988]

Hi! do i understand it correctly?:
if you put sample in a magnetic field, the protons spins allign pararell or antipararell to the applied external magnetic field, the energy is splitted into two spin levels - with lower and higher energy. when we apply 90 pulse at x axis direction, this from lower energy levels flip into high energy levels, spin axes are dephased and they are precessing along z axis with different angles, after we turn off the rf energy pulse, after some time they go back to equlibrium (lower energy state) and it is relaxation t1 (they give back absorbed energy to the lattice). then e.g. we apply another pulse, 180 pulse, they move about 180 degrees, and the fastest spins become slower, the slowest become faster what result in refocusing and we obtain one vector again. when the pulse2 is off, again relaxation, t2, it turnes back to equilibrium (along z axis) and gives back energy to the other spins...
Thanks!

[Enthalpy]

Hi, just some elements, until someone knowing NMR better passes by...

"Parallel or antiparallel" is correct. That's a fundamental behaviour of electron or proton spin, which can't be stronger or weaker - it has two values only. What may be faster or slower is the frequency at which it precesses; this frequency depends on the magnetic field it feels.

At room temperature, man-made magnetic fields orient about 1ppm of all protons. That is, from 1,000,000 protons, you would have 500,000 up and as many down without a field (plus the statistical fluctuation of about 1,000 particles), and the man-made field changes this to mean 499,999 and 500,001. It's because the energy difference between up and down in the man-made field strength is much smaller than kT.

At relaxation, 1,000 particles still fluctuate, while 500,001 and 499,999 become again 500,000 and 500,000 - so 1,000,000 particles aren't enough to observe anything. It takes (much) more than 10¹² particles to observe more signal than noise.

In NRM imagery (not analysis as far as I know), a field gradient changes the resonant frequency according to the position along one direction, and this gives resolution in one dimension, while a temporary gradient in an other direction can change the phase, and many different gradients permit a discrimination of the position by Fourier transformation. Is that what you mean?

Medical NMR uses dozens of varied pulse scenarios having different benefits, so one explanation won't cover them all. Beginning with NMR for chemical analysis is wise.

[Irlanur]

"Parallel or antiparallel" is correct. That's a fundamental behaviour of electron or proton spin, which can't be stronger or weaker - it has two values only.

I think this is not very precise. You can never know the exact direction of a single spin angular momentum (this is due to the Heisenberg uncertainty principle). What you can know are expectation values. But if you just look at the z-component, it turns out that it is quantized (+1/2 or -1/2 in units of hbar for a spin-1/2).

The Magnetization, which is proportional to the expectation value of spin angular Momentum, does align with the z-axis at equilibrium.

when we apply 90 pulse at x axis direction, this from lower energy levels flip into high energy levels

That's only partially true. a 90deg pulse at x turn the total magnetization to the -y axis. In terms of the individual spins, this is a superposition of up and down states (even more concrete: a coherence).

spin axes are dephased

I am not sure what you mean by that in this context

after some time they go back to equlibrium (lower energy state) and it is relaxation t1 (they give back absorbed energy to the lattice).

I think you mean the right thing. the T1 is the time constant for the z-component of the magnetization.

then e.g. we apply another pulse, 180 pulse, they move about 180 degrees, and the fastest spins become slower, the slowest become faster what result in refocusing and we obtain one vector again.

this is not true. the precession frequency doesn't change after a refocusing pulse. look at the spin echo animation: https://en.wikipedia.org/wiki/Spin_echo

when the pulse2 is off, again relaxation, t2, it turnes back to equilibrium (along z axis) and gives back energy to the other spins...

The T2 is just the characteristic time for the decay of x and y components of the Magnetization, doesn't matter if you have a pulse or not.

The dephasing which you can refocus is usually due to an inhomogeneous magnetic field (and couplings etc...). A detailed treatment of relaxation processes needs much more time.

In general, I think you understood quite a lot, for a detailed view you should probably look at the Bloch equations, they include T1 and T2 as well.
 





 

[Enthalpy]

I have no clear mental image of the spin (nor the resulting magnetic momentum, hence) and imagine it only by analogy with the orbital momentum.

I've been tempted for long to imagine a definite vector representing the spin, but whose direction can't be measured since we get only quantized and incompatible projections over XYZ. Though, books avoid this representation - in line with general QM practice not to introduce data (here the vector) that can't be measured, that would be called a "hidden variable".

The quantum texts I've seen up to now (I didn't go deep!) only tell about probabilities over each axis, with matrices (resulting from the external induction) that tell how these probabilities evolve over time. Though, this is uneasy, and it's pretty clear that most people jump to a vector mental image.

So, how accurate is the representation as a definite vector? Does it provide correct predictions often? Always?

And: can this vector be "measured" nevertheless, maybe through weak measures over many particles and a statistics?

[Irlanur]

And: can this vector be "measured" nevertheless, maybe through weak measures over many particles and a statistics?

I would answer with a clear yes, but the "vector" is not a single spin, it is an ensemble, that's why the Quantum Description uses Density Operators and not wavefunctions.

nevertheless as long as it's possible, it is much easier to just think in the vector model. But this can't even describe a coupled spin System or a Spin > 1 ...

[Enthalpy]

Silly me, as soon as the probabilities look like sin² and cos² one can write them as the consequence of an angle (or two angles in 3D).

Spin=1 is a P orbital: one direction and one momentum suffice to describe a few ones - the peacock and the doughnut ones - but in general they're elliptic and these need more information.

It must be like the wavefunction of a photon: for one beam, the electric field can abusively serve as the wavefunction (like a vector comfortably describes the spin=1/2), but the proper representation is a scalar ψ(orientation, position, time), and as soon as two photons are entangled, the electric field fails and forces to revert to ψ.

If some day one finds a theory beyond QM and Relativity I hope it'll be simpler...