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The spin-echo effect was discovered by Erwin Hahn when he applied two successive 90° pulses separated by short time period, but detected a signal, the echo, when no pulse was applied. This phenomenon of spin echo was explained by Erwin Hahn in his 1950 paper, [ 5 ] and further developed by Carr and Purcell who pointed out the advantages of ...
When the spins are rephased, they become coherent, and thus signal (or "echo") is generated to form images. Unlike spin echo, gradient echo does not need to wait for transverse magnetisation to decay completely before initiating another sequence, thus it requires very short repetition times (TR), and therefore to acquire images in a short time.
Each of the spin-echo signal is a sinc function of time, which can be described by = Where = + ¯ Here ¯ is the gyromagnetic ratio constant, and is the basic resonance frequency of the spin. Due to the presence of the gradient G , the spatial information r is encoded onto the frequency ω {\displaystyle \omega } .
The spin echo is a 90° pulse followed by a 180° pulse after a time period τ and is applied on the proton, the sensitive nucleus (designated, perhaps counter-intuitively, as the I spin, while the insensitive nucleus is the S spin; note, however, that the original paper on INEPT used the opposite designations). [1] Spin Echo
INEPT is a common building block of NMR experiments to improve 15 N signal. [ 1 ] In Fourier transform NMR spectroscopy and imaging , a pulse sequence describes a series of radio frequency pulses applied to the sample, such that the free induction decay is related to the characteristic frequencies of the desired signals.
An extra spin echo step can then optionally be used to decouple the signal, simplifying the spectrum by collapsing multiplets to a single peak. The undesired uncoupled signals are removed by running the experiment twice with the phase of one specific pulse reversed; this reverses the signs of the desired but not the undesired peaks, so ...
Throughout this section, the reduced Planck constant = for convenience.. The product operator formalism is usually applied to sets of spin-1/2 particles, since the fact that the individual operators satisfy = =, where is the identity operator, makes the commutation relations of product operators particularly simple.
Neutron spin echo is a time-of-flight technique. Concerning the neutron spins it has a strong analogy to the so-called Hahn echo, [13] well known in the field of NMR.In both cases the loss of polarization (magnetization) due to dephasing of the spins in time is restored by an effective time reversal operation, that leads to a restitution of polarization (rephasing).