Memory decay

We see than that three of the problems likely to be encountered when using echo envelope spectroscopy in place of ENDOR can either be discounted or disposed of. Failure to observe modulation is, assuming adequacy of the electron spin echo equipment, a possible source of information in itself. Lifetime broadening due to phase memory decay, and unwanted complexity of the modulation pattern due to sum and difference terms can both be avoided by performing experiments in the stimulated echo mode. The remaining problem is less tractable and has not yet been solved in a wholly satisfactory manner. This is the problem of transforming the echo envelope to yield a frequency spectrum. 

From the form of the theoretical expressions (Equations 2 and 5) it would seem that the shfs frequencies might be obtained quite straightforwardly by making a Fourier cosine transform. Some minor problems could arise at the very low frequency end on account of phase memory decay or in cases where the modulation is shallow, but... 

Hi and H2 are called hereditary functions. Instead of an exponential decay of memory, we could have a sinusoidal or some other ftmctional form of memory decay, depending on the physical situation. 

A two-pulse spin echo experiment consists of a 90°-r-180°-r-echo pulse sequence (see Chapter 2.3, Section 2.3.2). The amplitude of the echo is monitored as a function of the time r between the echoes, and the decay time constant is denoted as Jin, the phase memory decay time. J is strongly dependent upon dynamic processes that result in echo dephasing on the time scale of the experiment. In Cu(dtc)2 the coupling of the unpaired electron to the spins of the protons of the ethyl groups is too small to be resolved in the CW spectra. However, when the rate of rotation of the... 

As the spins precess in the equatorial plane, they also undergo random relaxation processes that disturb their movement and prevent them from coming together fiilly realigned. The longer the time i between the pulses the more spins lose coherence and consequently the weaker the echo. The decay rate of the two-pulse echo amplitude is described by the phase memory time, which is the time span during which a spin can remember its position in the dephased pattern after the first MW pulse. Tyy is related to the homogeneous linewidth of the individual spin packets and is usually only a few microseconds, even at low temperatures. 

The characteristic time of the tliree-pulse echo decay as a fimction of the waiting time T is much longer than the phase memory time T- (which governs the decay of a two-pulse echo as a function of x), since tlie phase infomiation is stored along the z-axis where it can only decay via spin-lattice relaxation processes or via spin diffusion. 

In electron spin echo relaxation studies, the two-pulse echo amplitude, as a fiinction of tire pulse separation time T, gives a measure of the phase memory relaxation time from which can be extracted if Jj-effects are taken into consideration. Problems may arise from spectral diflfrision due to incomplete excitation of the EPR spectrum. In this case some of the transverse magnetization may leak into adjacent parts of the spectrum that have not been excited by the MW pulses. Spectral diflfrision effects can be suppressed by using the Carr-Purcell-Meiboom-Gill pulse sequence, which is also well known in NMR. The experiment involves using a sequence of n-pulses separated by 2r and can be denoted as [7i/2-(x-7i-T-echo) J. A series of echoes separated by lx is generated and the decay in their amplitudes is characterized by Ty. ... 

The main advantage of tlie tln-ee-pulse ESEEM experiment as compared to the two-pulse approach lies m the slow decay of the stimulated echo intensity detemiined by T, which is usually much longer than the phase memory time Ty that limits the observation of the two-pulse ESE. 

The "add-to-memory" signal averaging method currently available to us distorts fluorescence intensity versus time plots when the fluorescence intensity is a non-linear function of incident laser energy and the laser energy varies from shot to shot. For this reason we have not attempted detailed kinetic modelling of the observed fluorescence intensity decay curves recorded at high 532 nm laser fluence. 

In the impact approximation (tc = 0) this equation is identical to Eq. (1.21), angular momentum relaxation is exponential at any times and t = tj. In the non-Markovian approach there is always a difference between asymptotic decay time t and angular momentum correlation time tj defined in Eq. (1.74). In integral (memory function) theory Rotc is equal to 1/t j whereas in differential theory it is 1/t. We shall see that the difference between non-Markovian theories is not only in times but also in long-time relaxation kinetics, especially in dense media. 

After each pulse, the digitizer (ADC) converts the FID into digital form and stores it in the computer memory. Ideally, we should keep sampling i.e., acquiring data till each FID has decayed to zero. This would require about 57) seconds, where 7) is the spin-lattice relaxation time of the slowest-relaxing protons. Since this may often take minutes, it is more convenient... 

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