On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

Linewidth-resolved 15N HSQC, a simple 3D method to measure 15N relaxation times from T1 and T2 linewidths

A three-dimensional approach for measuring 15N relaxation times is described. Instead of selecting particular values for the relaxation period, in the proposed method the relaxation period is incremented periodically in order to create a 3D spectrum. This additional frequency domain of the transformed spectrum contains the relaxation time information in the T1 and T2 linewidths, and thus the longitudinal and transverse 15N relaxation times can be measured without determination of 2D cross peak volumes/intensities and subsequent curve fitting procedures.     

A formulation of the saturation of absorption lines,which are partially homogeneous broadened by collision processes

With considering the influence of velocity changing collisions a is given. The result including also effects of the frequency detuning from the line center is between the known limiting cases of homogeneous and inhomogeneous broadening.     

Applications of DNP-NMR for the measurement of heteronuclear T1 relaxation times

Measurement of heteronuclear spin-lattice relaxation times is hampered by both low natural abundance and low detection sensitivity. Combined with typically long relaxation times, this results in extended acquisition times which often renders the experiment impractical. Recently a variant of dynamic nuclear polarisation has been demonstrated in which enhanced nuclear spin polarisation, generated in the cryo-solid state, is transferred to the liquid state for detection. Combining this approach with small flip angle pulse trains, similar to the FLASH-T(1) imaging sequence, allows the rapid determination of spin-lattice relaxation times. In this paper we explore this method and its application to the measurement of T(1) for both carbon-13 and nitrogen-15 at natural abundance. The effects of RF inhomogeneity and the influence of proton decoupling in the context of this experiment are also investigated.     

Changes of relaxation times T1 and T2 in rat tissues after biopsy and fixation

NMR spectroscopical measurements of relaxation times were conducted on muscle, intestine, fatty tissue and cerebral cortex and white matter of the rat at various time intervals following removal of the tissue. It appeared that most tissues can be stored at 4 degrees C up to 24 hours without noticeable effects on NMR relaxation parameters. Exceptions are the T2 of muscle and the T1 and T2 of intestine, which tended to change in the first hour after biopsy. Relaxation parameters change considerably after fixation of the tissues. Therefore the effects of fixation have to be taken into account when carrying out NMR measurements on fixed tissues.     

Measurements of the rotational relaxation times for absorption lines with Voigt profiles

A new method for determining the relaxation parameters T ₁ and T ₂ for the Voigt profile of an absorption line is presented. The method was tested on gaseous OCS with the use of a phase-switching spectrometer. The method is equally applicable for both pure gases and gas mixtures.     

14N Pulsed nuclear quadrupole resonance. 4. Two-pulse sequences for the determination of T1 and T2 relaxation times

A general theory, based on density matrix calculations, has been developed for the special case of a two-pulse sequence applied to spin 1 (¹⁴N) nuclear quadrupole resonance (NQR) of a powder sample. It is shown that the homolog of the NMR inversion-recovery experiment leads easily to the spin-lattice relaxation time T ₁ (associated with the diagonal elements of the density matrix) provided that an appropriate phase cycling is used. Conversely, in spite of two-step phase cycling schemes adapted to spin-spin relaxation measurements, the homolog of the NMR Hahn spin-echo sequence may pose some problems if the results are displayed in the magnitude mode. First, at short decay times, the echo may be corrupted by unwanted signals. Secondly, in that case, the amplitude of the resulting signal can evolve unexpectedly and differently as a function of the phase of the second pulse. Thirdly, at long decay times, the echo maximum occurs earlier than expected. All these problems in principle disappear with a complete four-step phase cycling scheme and the echo decay curve yields reliably the spin-spin relaxation time T ₂ (associated with off-diagonal elements). This theory allowed the exploitation of many test experiments performed at different frequencies on hexamethylenetetramine (HMT) and sodium nitrite.     

A new method for determination of the electron number density in the e region of the ionosphere from relaxation times of artificial periodic inhomogeneities

We propose a new method for determination of the electron number density in the E region of the ionosphere on the basis of scattering of radio waves from artificial periodic inhomogeneities formed by the high-power radio emission at two frequencies and having different spatial periods. The ratio of relaxation times of the artificial periodic inhomogeneities at a given altitude is determined only by the ratio of their spatial periods, which makes it possible to determine electron number density. The paper presents the corresponding calculations and the estimates of possible measurement errors. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 9, pp. 744–750, September 2006.     

A method for estimating the error in determining the position of XPS sectral lines from experimental data

A method is proposed for estimating the errors in determining the position of spectral lines, which takes into account possible errors of the measuring instrument and methods of mathematical treatment of spectra, as well as their dependence on the half-width of spectral lines, spacing between them, and the background noise height.     

Collision induced transitions of ammonia calculation of relaxation timesT 1 andT 2, line widths,line shifts,and the double resonance effect

The longitudinal relaxation timeT ₁ and the transverse relaxation timeT ₃ for the inversion levels of the NH₃ molecule have been calculated for NH₃ — NH₃, NH₃ — N₂ and NH₃ — H₂ collisions. The ratioT ₂/T ₁ lies between 1 and 2 which agrees well with the experiment. The phase shift effect onT ₂ and on the collisioninduced line shift δω under the framework of the Mehrotra-Boggs theory have also been evaluated. The change in the line intensity ΔI/I, in four-level double resonance experiments was also calculated, and the significance of higher order interaction terms has been pointed out.     

In vivo determination of 31P spin relaxation times (T1, T2, T1 rho) in rat leg muscle. Use of an off-axis solenoid coil

A probe using a solenoid coil tilted 45 degrees off-axis has been used to study the 31P NMR relaxation characteristics of the resonances arising from phosphorus metabolites in rats in vivo. T1, T1 rho and T2 values have been determined for phosphocreatine and ATP in leg muscle. The ratio of 31P T1(1700ms) to T2(12ms) for ATP was in excess of 200:1 compared with a ratio of 5:1 for 1H T1:T2. Of major significance was the observation that T2 values for phosphocreatine (230ms) were markedly longer than T2 values for ATP (12ms). Thus by use of appropriate delay times in spin echo sequences ATP signals can be nulled, and discrete 31P imaging of phosphocreatine in muscle may be possible provided the overall signal-to-noise is satisfactory.     

A new method for determining relaxation energies by means of aes and xps and its application to silicon compounds

A new method is presented for the determination of the absolute dynamic relaxation energy R_D from experimental Auger parameters, the static dielectric constant and the plasmon energy of the solids. The relaxation energies of the Si 1s and 2p core levels in Si, SiC, SiO₂, Si₃N₄ and Na₂SiF₆ are investigated by comparing the experimental values with theoretical results from a semiempirical dielectric theory. Both the experimental and theoretical results are valid only for the least-bound Si 2p state. The calculated relaxation shifts ΔR_D^ea(1s) and ΔR_D^ea(2p) are in reasonable agreement with the experimental values, and describe the extraatomic polarization effect well also for a deep level.     

A new method for multi-exponential inversion of NMR relaxation measurements

The NMR technique has been widely applied to petroleum well logging and rock core analysis since the 1990s when NUMAR introduced a reliable NMR logging tool to the oil industry. It has been playing an important role for prospecting and exploiting resource of oil and gas for the last ten years. In an oil well, NMR can provide parameters of reservoir and fluid properties, such as porosity, pore size distribution, bound water volume, bulk volume of free water, permeability, in-situ fluid dif…     

A method for measuring relaxation times for collision processes in the surface layers of conductors and semi-conductors

Microwave (～9.9 gHz) conductivity of solid cylindrical samples was investigated using a perturbed resonant cavity approach. The Kramers-Kronig relation was used to deduce relaxation times (collision times) for momentum transfer of the current carriers in the samples. Experimental collision times are presented for Cu, Pb, C, Al, In, Cu₂O, CuO, and n-InSb.     

A simulation-based comparison of two methods for determining relaxation rates from relaxometry images

When assessing liver iron content using relaxometry, an average relaxation rate (R1, R2 or R2*) is usually determined from a region of interest or the entire liver. This is commonly performed by fitting the signal decay in individual voxels to an appropriate relaxation function. The voxel-level parameters resulting from the fits are combined to determine the average relaxation rate, and an empirically derived calibration curve is used to convert this single value to iron content. The goal of this study was to compare the precision and accuracy of this voxel-wise fitting to an alternative method that relies on first averaging the signals from all voxels within the region of interest and then determining the relaxation rate from a single fit. Systematic differences were observed when both methods were applied to clinical images. Mathematical simulations were employed to determine which method provided more robust estimates of the true relaxation rate. The mathematical simulations were then expanded to include a range of conditions expected in typical relaxometry images. The results show that voxel-wise fitting skews the relaxation rate estimates and increases variance, particularly when the true relaxation rate is moderate to fast, as it would be in liver with high iron content. The potential impact of these results on clinical decisions is discussed.     

A new method for determining hydrodynamic effects on the collision of two spheres

A sphere falling in a fluid may collide with another sphere falling more slowly if, when the spheres are far apart vertically, the horizontal distance between their centers is less than or equal to a critical radius. Accurate prediction of aerosol particle coagulation requires a good understanding of this process. Previously reported optical techniques for measuring hydrodynamic effects on this phenomenon have inherent difficulties detecting grazing collisions and hence in determining the critical radius. In this work, a novel detection technique is demonstrated and it is shown that the critical radius may be determined from the sound generated by the collision of two spheres in a viscous liquid. The technique is shown to provide a more precise and decisive indication of when hard spheres collide.