Number Of Nuclear Spins Research Articles

Molecular influence on nuclear-quadrupole-coupling effects in laser induced alignment.

We computationally studied the effect of nuclear-quadrupole interactions on the field-free impulsive alignment of different asymmetric-top molecules. Our analysis is focused on the influence of the hyperfine- and rotational-energy-level structures. These depend on the number of nuclear spins, the rotational constants, and the symmetry of the tensors involved in the nuclear spin and external field interactions. Comparing the prototypical large-nuclear-spin molecules iodobenzene, 1,2-diiodobenzene, 1,3-diiodobenzene, and 2,5-diiodobenzonitrile, we demonstrate that the magnitude of the hyperfine splittings compared to the rotational-energy splittings plays a crucial role in the spin-rotational dynamics after the laser pulse. Moreover, we point out that the impact of the quadrupole coupling on the rotational dynamics decreases when highly excited rotational states dominate the dynamics.

Measurement-induced nuclear spin polarization

We propose a nuclear-spin-polarization protocol in a general evolution-and-measurement framework. The protocol works in a spin-star configuration, where the central spin is coupled to the surrounding bath (nuclear) spins by flip-flop interaction of equal strength and is subject to a sequence of projective measurements on its ground state. Then a nondeterministic nuclear spin polarization could be implemented by entropy reduction through measurement. The optimized measurement-interval $\tau_{\rm opt}$ is analytically obtained in the near-resonant condition, which is relevant to the nuclear spins' polarization degree of the last-round measurement, the number of nuclear spins, and the coupling strength between the central spin and nuclear spins. Hundreds and even thousands of randomly aligned nuclear spins at the thermal state could be almost fully polarized with an optimized sequence of less than $20$ unequal-time-spacing measurements. In comparison to the conventional approaches, our protocol is not sensitive to the magnetic-field intensity, and it is robust against the extra counterrotating interaction in the near-resonant situation.

Anisotropy of spin–spin and spin–lattice relaxation times in liquids entrapped in nanocavities: Application to MRI study of biological systems

Spin–spin and spin–lattice relaxations in liquid or gas entrapped in nanosized ellipsoidal cavities with different orientation ordering are theoretically investigated. The model is flexible in order to be applied to explain experimental results in cavities with various forms, from very prolate up to oblate ones, and different degree of ordering of nanocavities.In the framework of the considered model, the dipole–dipole interaction is determined by a single coupling constant, which depends on the form, size, and orientation of the cavity and number of nuclear spins in the cavity. It was shown that the transverse and longitudinal relaxation rates differently depend on the angle between the external magnetic field and cavity main axis.The calculation results for the local dipolar field, transverse and longitudinal relaxation times explain the angular dependencies observed in MRI experiments with biological objects: cartilage and tendon. Microstructure of these tissues can be characterized by the standard deviation of the Gaussian distribution of fibril orientations. The comparison of the theoretical and experimental results shows that the value of the standard deviation obtained at the matching of the calculation to experimental results can be used as a parameter characterizing the disorder in the biological sample.

Thermal electron spin flip in quantum dots

We study a thermally induced spin flip of an electron spin located in a semiconductor quantum dot. This interesting effect arises from an intriguing interplay between the Zeeman coupling to an external magnetic field and the hyperfine interaction with the surrounding nuclear spins. By considering a minimal model, we explain the main mechanism driving this spin flip and analyze its dependence on the strength of the external magnetic field, the number of nuclear spins and the ratio of the electron and nuclear Zeeman energies, respectively. Finally, we show that this minimal model can be applied to experimentally relevant QDs in III-V heterostructures, where we explicitly predict the temperature at which the spin flip occurs.

An improved semiclassical theory of radical pair recombination reactions

We present a practical semiclassical method for computing the electron spin dynamics of a radical in which the electron spin is hyperfine coupled to a large number of nuclear spins. This can be used to calculate the singlet and triplet survival probabilities and quantum yields of radical recombination reactions in the presence of magnetic fields. Our method differs from the early semiclassical theory of Schulten and Wolynes [J. Chem. Phys. 68, 3292 (1978)] in allowing each individual nuclear spin to precess around the electron spin, rather than assuming that the hyperfine coupling-weighted sum of nuclear spin vectors is fixed in space. The downside of removing this assumption is that one can no longer obtain a simple closed-form expression for the electron spin correlation tensor: our method requires a numerical calculation. However, the computational effort increases only linearly with the number of nuclear spins, rather than exponentially as in an exact quantum mechanical calculation. The method is therefore applicable to arbitrarily large radicals. Moreover, it approaches quantitative agreement with quantum mechanics as the number of nuclear spins increases and the environment of the electron spin becomes more complex, owing to the rapid quantum decoherence in complex systems. Unlike the Schulten-Wolynes theory, the present semiclassical theory predicts the correct long-time behaviour of the electron spin correlation tensor, and it therefore correctly captures the low magnetic field effect in the singlet yield of a radical recombination reaction with a slow recombination rate.

Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics

We have performed a systematic calculation for the non-Markovian dynamics of a localized electron spin interacting with an environment of nuclear spins via the Fermi contact hyperfine interaction. This work applies to an electron in the s -type orbital ground state of a quantum dot or bound to a donor impurity, and is valid for arbitrary polarization p of the nuclear spin system, and arbitrary nuclear spin I in high magnetic fields. In the limit of p=1 and I=1/2, the Born approximation of our perturbative theory recovers the exact electron spin dynamics. We have found the form of the generalized master equation (GME) for the longitudinal and transverse components of the electron spin to all orders in the electron spin--nuclear spin flip-flop terms. Our perturbative expansion is regular, unlike standard time-dependent perturbation theory, and can be carried-out to higher orders. We show this explicitly with a fourth-order calculation of the longitudinal spin dynamics. In zero magnetic field, the fraction of the electron spin that decays is bounded by the smallness parameter \delta=1/p^{2}N, where N is the number of nuclear spins within the extent of the electron wave function. However, the form of the decay can only be determined in a high magnetic field, much larger than the maximum Overhauser field. In general the electron spin shows rich dynamics, described by a sum of contributions with non-exponential decay, exponential decay, and undamped oscillations. There is an abrupt crossover in the electron spin asymptotics at a critical dimensionality and shape of the electron envelope wave function. We propose a scheme that could be used to measure the non-Markovian dynamics using a standard spin-echo technique, even when the fraction that undergoes non-Markovian dynamics is small.

Molecular imaging using hyperpolarized 13C

MRI provides unsurpassed soft tissue contrast, but the inherent low sensitivity of this modality has limited the clinical use to imaging of water protons. With hyperpolarization techniques, the signal from a given number of nuclear spins can be raised more than 100 000 times. The strong signal enhancement enables imaging of nuclei other than protons, e.g. (13)C and (15)N, and their molecular distribution in vivo can be visualized in a clinically relevant time window. This article reviews different hyperpolarization techniques and some of the many application areas. As an example, experiments are presented where hyperpolarized (13)C nuclei have been injected into rabbits, followed by rapid (13)C MRI with high spatial resolution (scan time <1 s and 1.0 mm in-plane resolution). The high degree of polarization thus enabled mapping of the molecular distribution within various organs, a few seconds after injection. The hyperpolarized (13)C MRI technique allows a selective identification of the molecules that give rise to the MR signal, offering direct molecular imaging.

Silvanus Thompson Memorial Lecture Molecular imaging using hyperpolarized C-13

MRI provides unsurpassed soft tissue contrast, but the inherent low sensitivity of this modality has limited the clinical use to imaging of water protons. With hyperpolarization techniques, the signal from a given number of nuclear spins can be raised more than 100 000 times. The strong signal enhancement enables imaging of nuclei other than protons, e.g. C-13 and N-15, and their molecular distribution in vivo can be visualized in a clinically relevant time window. This article reviews different hyperpolarization techniques and some of the many application areas. As an example, experiments are presented where hyperpolarized C-13 nuclei have been injected into rabbits, followed by rapid C-13 MRI with high spatial resolution (scan time <1 s and 1.0 mm in-plane resolution). The high degree of polarization thus enabled mapping of the molecular distribution within various organs, a few seconds after injection. The hyperpolarized C-13 MRI technique allows a selective identification of the molecules that give rise to the MR signal, offering direct molecular imaging. (Less)

Electron paramagnetic resonance spectroscopic study of synthetic fluorapatite: Part III. Structural characterization of sub-ppm-level Gd and Mn in minerals at W-band frequency

Room-temperature, single-crystal W-band (~94 GHz) electron paramagnetic resonance (EPR) spectra of a flux-grown fluorapatite (AP30-0) containing 0.8(1) ppm Gd and 0.9 ppm Mn disclose the presence of two even-isotope Gd 3+ centers (electron spin number S = 7/2 and nuclear spin number I = 0) and a 55 Mn 2+ center (S = I = 5/2). The relative abundance of the two Gd 3+ centers (corresponding to recently established centers “a” and “b” containing Gd 3+ ions at the Ca2 and Ca1 sites, respectively) in AP30-0 has been estimated to be 0.20, indicating that “a” in this sample arises from the presence of ~0.2 ppm Gd at the Ca2 site. In addition, high-resolution W-band spectra of this sample at ~120 and ~77 K disclose the 155 Gd and 157 Gd spectra of “a,” in which these isotopes (I = 3/ 2) are only ~0.02 ppm in abundance. To the best of our knowledge, this is the first-ever demonstration of structural characterization of sub-ppm-level trace elements in minerals and their synthetic analogs. Moreover, the fact that the Gd 3+ and 55 Mn 2+ centers in AP30-0 are detected despite the multiplicity of lines arising from their complex fine structures, hyperfine structures, and magneticsite splittings, suggests that the W-band EPR technique is potentially capable of characterizing trace elements with a single unpaired electron (S = 1/2) and zero nuclear spin (I = 0) at even lower concentrations. The spin-Hamiltonian parameters of the 55 Mn 2+ center, including matrices g, D, A, and P, and high-spin term of type S4, have been determined by optimization using the single-crystal W-band EPR spectra of a Gd-doped fluorapatite containing 3.0(4) ppm Mn. The principal-axis directions of D and the pseudo-symmetry axes calculated from the S4 parameters confirm that this center corresponds to occupancy of 55 Mn 2+ ions at the Ca1 site. Also, the optimized parameters suggest that the Mn 2+ -substituted Ca1 site in the flux-grown fluorapatite has rhombic (i.e., triclinic) local symmetry [e.g., D/g e β e = 436.2(6) G, E/g e β e = 1.1(1) G], slightly different from the trigonal symmetry of the ideal Ca1 site.

Local realistic model for the dynamics of bulk-ensemble NMR information processing.

We construct a local realistic hidden-variable model that describes the states and dynamics of bulk-ensemble NMR information processing up to about 12 nuclear spins. The existence of such a model rules out violation of any Bell inequality, temporal or otherwise, in present high-temperature, liquid-state NMR experiments. The model does not provide an efficient description in that the number of hidden variables grows exponentially with the number of nuclear spins.

Dissipation by nuclear spins in macroscopic magnetization tunneling.

Magnetic systems are currently considered attractive candidates in which to look for quantum phenomena such as the tunneling of the total magnetization of a small (\ensuremath{\sim}100 \AA{} diameter) particle out of a metastable easy direction or between degenerate easy directions. The effect of nuclear spins as a dissipative environment for such a particle is considered and shown to be significant. Two dimensionless parameters characterize the dissipation: a coupling strength varying as the number of nuclear spins, and the ratio of the nuclear and electronic Larmor frequencies.

Molecular hyperfine-structure calculations using an uncoupled representation

Matrix elements and a computational procedure are presented for the calculation of hyperfine splitting of rotational energy levels of a molecule containing an arbitrary number of nuclear spins. The uncoupled representation is used to obtain a more direct and unambiguous procedure. Matrix elements are given for the quadrupole, spin-spin, spin-rotation and Stark-effect interactions. Results of calculations are discussed for the case of three equivalent spins of I = 1. Example calculations are given for Stark splittings of two MASER states of acetonitrile.

Distribution of Atomic Nuclear Spins

I HAVE previously pointed out1 that the distribution of atomic nuclear spins appears to be entirely different in the two types of odd atomic weight nuclei, namely, class A, those possessing an odd nuclear proton, and class B, those possessing an odd nuclear neutron. Since then quite a number of nuclear spins have been added to those known, data now being available for sixty-four elements, among which are seventy odd isotopes and seven even atoms. Improved distribution curves can thus be drawn, as in the accompanying diagram (Fig. 1). The full lines show the spin values known with certainty, and above these (dotted) are included the spins about the value of which there is yet some doubt (generally occasioned by the observation of fine structure in terms with J values insufficient to permit full fine structure multiplicity to be reached).