General treatment of paramagnetic relaxation enhancement associated with translational diffusion.
A theory of nuclear spin relaxation in isotropic liquids for nuclear spins interacting with electron spins, residing in other molecules (the outer-sphere relaxation), is presented. The approach, valid outside of the Redfield limit for electron spin relaxation, is an extension of the Swedish slow motion theory [Benetis et al., Mol. Phys. 48, 329 (1983); Nilsson and Kowalewski, J. Magn. Reson. 146, 345 (2000)] for inner-sphere relaxation. It is demonstrated that the outer-sphere relaxation rate can be expressed as an integral of a product of a translational diffusion correlation function and a function analogous to the inner-sphere spectral density. A numerical implementation of the theory is described and applied to a large number of realistic parameter sets for S = 7/2 and S = 1, which may correspond to Gd(III) and Ni(II) systems. It is shown that the outer-sphere contribution is relevant and should be included into the analysis of nuclear magnetic relaxation dispersion relaxation profiles, especially for slow relative translational diffusion and fast molecular tumbling.
Relaxation theory of the electronic spin of a complexed paramagnetic metal ion in solution beyond the Redfield limit.
The relaxation of the electronic spin S of a paramagnetic metal ion with fully quenched orbital angular momentum in its ground state is investigated in an external magnetic field through a systematic study of the time correlation functions governing the evolution of the statistical operator (density matrix). Let omega0 be the Larmor angular frequency of S. When the relaxation is induced by a time-fluctuating perturbing Hamiltonian hH1(t) of time correlation tauc, it is demonstrated that after a transient period the standard Redfield approximation is relevant to calculate the evolution of the populations of the spin states if parallelH1 parallel2tauc2/(1+omega0(2)tauc2)<<1 and that this transient period becomes shorter than tauc at sufficiently high field for a zero-field splitting perturbing Hamiltonian. This property, proven analytically and confirmed by numerical simulation, explains the surprising success of several simple expressions of the longitudinal electronic relaxation rate 1/T1e derived from the Redfield approximation well beyond its expected validity range parallelH1 paralleltauc<<1. It has favorable practical consequences on the interpretation of the paramagnetic relaxation enhancement of nuclei used for structural and dynamic studies.
rPET detectors design and data processing
Small animal PET systems based on rotating planar detectors posses some interesting advantages for high sensitivity, high resolution imaging. We have designed the rPET detectors based on MLS crystals assembled on a 30times30 matrix optically coupled to a flat-panel PS-PMT. Weighted position readout circuits pre-process the 64 signals from the 8times8 anodes matrix, which are digitized using a charge-integrating converter. The amplification electronics, including the trigger output for coincidence detection, and the high voltage supply are integrated in a three PCBs stack that forms the base attached to the back of the PMT. The whole assembly is enclosed in a light tight, lead (Pb) shielded aluminum box. The detectors are mounted on a rotating gantry with more than 180 degrees rotation span. The digitized events are screened and histogramed, and a modified center of gravity algorithm removes from the position calculation those signals with poor signal to noise ratio. Apparent mean crystal size on the 511 keV field-flood images is 0.6 mm, mean peak-to-valley ratio is better than 8, and intrinsic resolution is 1.5 mm at the central row, with the energy window wide open. Sensitivity (CPS) for a pair of these detectors set in coincidence at 160 mm distance is 1%