SpinSpinA fundamental property of nature like electrical charge or mass.A fundamental property of nature like electrical charge or mass.Comes in multiples of 1/2 and can be + or Comes in multiples of 1/2 and can be + or --. . Protons, electrons, and neutrons possess spin. Protons, electrons, and neutrons possess spin. Individual unpaired electrons, protons, and neutrons each possesIndividual unpaired electrons, protons, and neutrons each possesses a spin of 1/2.ses a spin of 1/2.
SpinSpinTwo or more particles with spins having opposite signs can pair Two or more particles with spins having opposite signs can pair up to eliminateup to eliminatethe observable manifestations of spin. the observable manifestations of spin.
Helium Atom ( Helium Atom ( 44He ) He ) -- No SpinNo Spin
When placed in a magnetic field, particles with a net spin absorWhen placed in a magnetic field, particles with a net spin absorb photons.b photons.
νννννννν = = γγγγγγγγ BBoo
BBoo = magnetic field strength= magnetic field strengthνννννννν = frequency of the absorbed photon= frequency of the absorbed photonγγγγγγγγ = = gyromagneticgyromagnetic ratio (for hydrogen, ratio (for hydrogen, γγγγγγγγ = 42.58 MHz/Tesla)= 42.58 MHz/Tesla)
NMR can only be performed on isotopes whose natural abundance isNMR can only be performed on isotopes whose natural abundance is high high enough to be detected.enough to be detected.
NucleiNuclei UnpairedUnpaired Unpaired Unpaired Net Net γγγγγγγγ NaturalNatural BiologicalBiologicalProtonsProtons Neutrons Neutrons Spin Spin (MHz/T)(MHz/T) AbundanceAbundance AbundanceAbundance
How many spins areHow many spins arealigned with the field and aligned with the field and how many are opposed?how many are opposed?
(((( ))))KTE
o
j eNN ∆∆∆∆−−−−
∝∝∝∝
NNjj = Spins in high energy configuration= Spins in high energy configurationNNoo = Spins in low energy configuration= Spins in low energy configuration∆∆∆∆∆∆∆∆E = Energy difference between E = Energy difference between
configurationsconfigurationsK = K = BoltzmannBoltzmann Constant Constant
(1.3805x10(1.3805x10--23 J/Kelvin)23 J/Kelvin)T = Temperature (T = Temperature (KelvenKelven))
Groups of spins experiencing exactly the sameGroups of spins experiencing exactly the sameBBoo magnetic field.magnetic field.
It is convenient to talk of the It is convenient to talk of the magnetization in a spin packet magnetization in a spin packet and represent it as a vector. and represent it as a vector.
At equilibrium, this vector is At equilibrium, this vector is pointing in the direction of Bpointing in the direction of Boo..
The sum of all the spin magnetization vectors from allThe sum of all the spin magnetization vectors from allthe spin packets in a sample region.the spin packets in a sample region.
At equilibrium, this vector is At equilibrium, this vector is pointing in the direction of Bpointing in the direction of Boo..
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
Longitudinal magnetization not at equilibrium wants toLongitudinal magnetization not at equilibrium wants toreturn to its equilibrium value.return to its equilibrium value.
SpinSpin--Lattice Relaxation Time (TLattice Relaxation Time (T11))
The time constant that describes how MThe time constant that describes how MZZ returns to returns to its equilibrium value Mits equilibrium value Moo..
The time (t) required to change the Z component ofThe time (t) required to change the Z component ofmagnetization by a factor of e.magnetization by a factor of e.
Net magnetization placed in the XY plane will rotate about the Net magnetization placed in the XY plane will rotate about the Z axis at the frequency of the photon that causes a transition Z axis at the frequency of the photon that causes a transition between the two energy levels of the spin. between the two energy levels of the spin.
This frequency is called the This frequency is called the LarmorLarmor frequency.frequency.
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
Transverse magnetization (MTransverse magnetization (MXYXY) wants to return to its ) wants to return to its equilibrium value, Mequilibrium value, MXYXY=0.=0.
SpinSpin--Spin Relaxation Time (TSpin Relaxation Time (T22))
The time constant that describes how MThe time constant that describes how MXYXY returns to returns to its equilibrium value Mits equilibrium value MXYXY=0.=0.
The time (t) required to reduce the XY component ofThe time (t) required to reduce the XY component ofmagnetization by a factor of e.magnetization by a factor of e.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
TranvserseTranvserse magnetization always decays to zero magnetization always decays to zero before relaxing to equilibrium along +Z. before relaxing to equilibrium along +Z.
Rotating Frame of ReferenceRotating Frame of Reference
It is convenient to define a rotating frame of reference It is convenient to define a rotating frame of reference that rotates about the Z axis at the that rotates about the Z axis at the LarmorLarmor frequency. frequency.
Rotating Frame of ReferenceRotating Frame of Reference
Vector precession compared to the rotating frame.Vector precession compared to the rotating frame.faster than faster than equal toequal to slower thanslower than
Rotating Frame of ReferenceRotating Frame of Reference
Longitudinal relaxation is looks the same in theLongitudinal relaxation is looks the same in therotating frame and laboratory frame of reference.rotating frame and laboratory frame of reference.
Spin RelaxationSpin RelaxationSpin relaxation is caused by time varying magnetic fields.Spin relaxation is caused by time varying magnetic fields.Source:Source: Translational motion of moleculesTranslational motion of molecules
Rotational motion of moleculesRotational motion of moleculesParamagnetic atoms or moleculesParamagnetic atoms or molecules
Paramagnetic atoms have unpaired electrons and hence a net Paramagnetic atoms have unpaired electrons and hence a net electron spin (magnetic field). Gadolinium is an example of a electron spin (magnetic field). Gadolinium is an example of a paramagnetic atom, and oxygen is an example of a paramagnetic paramagnetic atom, and oxygen is an example of a paramagnetic molecule.molecule.
SpinSpin--Lattice Relaxation {TLattice Relaxation {T11} requires time varying magnetic fields at } requires time varying magnetic fields at the the LarmorLarmor frequency.frequency.
SpinSpin--Spin Relaxation {TSpin Relaxation {T22} requires time varying magnetic fields with } requires time varying magnetic fields with frequencies frequencies << to the to the LarmorLarmor frequency.frequency.
![ν e ν ν ν arXiv:1709.07711v1 [hep-ph] 22 Sep 2017 · e ν ν Z0 e −p2 p4 p1 p3 (a) ν ν ν Z0 ν −p2 p4 p1 p3 (b) FIG. 1. The incoming and outgoing momenta, for lepton pair](https://static.documents.pub/doc/80x56/605b3edc8714c4658f50824b/-e-arxiv170907711v1-hep-ph-22-sep-2017-e-z0-e-ap2-p4-p1-p3.jpg)
