Angular dependence of spin densities on protons of CH2 group

Spin densities on protons of the CH₂ group of planar radicals have been calculated by the valence bond method as a function of the valence angle H-C-H. The five-electron model was used for the calculation.     

Quantum coherence and decoherence of protons and muons in condensed matter

The coherence in quantum superposition states of protons (and chemically similar particles, the positive muons) has been studied in some condensed matter environments. It is shown that if the proton systems and the experimental techniques used to study them are carefully selected, it is possible to observe quantum delocalization states of single particles and to understand the mechanisms for their loss of coherence. Quantum correlated two- and multiparticle states of protons lose coherence very fast when coupled to condensed matter environments, but new sub-femtosecond techniques have made them accessible to experimental studies. The degree of decoherence can be measured as function of time and the decoherence mechanisms can, at least in certain cases, be identified. Although less clean than in corresponding studies of quantum optical systems, these studies can be seen as a first step towards understanding the conditions for preservation of quantum correlation and entanglement in massive systems. Some consequences and some suggestions for future work are discussed. Received 28 August 2002 Published online 7 January 2003     

Effects of resveratrol and its analogs on scavenging hydroxyl radicals: Evaluation by EPR spin trapping method

Resveratrol (3,4′,5-trihydroxy-trans-stilbene) and six analogs, polyhydroxystilbenes, were synthesized. Their effects on scavenging hydroxyl radicals were studied by electron paramagnetic resonance (EPR) spin trapping method. The EPR signal intensity of the spin adduct of hydroxyl radical to 5,5-dimethyl-1-pyrroline N-oxide was detected and used as a standard for the evaluation of the effect of the seven compounds on scavenging hydroxyl radicals. While all seven compounds exhibited hydroxyl radical-scavenging activity, some of them proved to be more effective than resveratrol in this model. Another stable but low-intensity spin adduct was also observed by EPR. A possible assignment is proposed.     

On the calculation of spin densities

Methods are presented for calculating the expectation value of the spin density for the state resulting from spin-projection of an anti-symmetrized spin-orbital product. It is found that the spin densities for projected and unprojected states differ in the coefficients of the various spatial terms, and that these coefficients can be determined from the properties of the spin algebra. It is shown how the coefficients needed for the spin density are related to those previously derived by other workers for spin-free operators. Illustrative cases of the formalism are examined in detail to show how the calculated z component of the spin density depends upon the total spin as well as upon its z component.     

Energy losses of muons, pions, protons, and deuterons channeled in Si

The energy loss of positive muons, pions, protons, and deuterons channeled in Si crystals has been investigated by computer simulation. The model considers the individual trajectories of particles inside the target and calculates the electronic energy loss for each particle history. The results show important differences in the energy loss distributions, stopping powers, and straggling values for low and intermediate energies, as a consequence of channeling effects.     

The spin turning in ferromagnetic Gd studied by positive muons

We have studied the muon precession frequency in a ferromagnetic single crystal of Gd metal. The overall features of our findings are compatible with earlier results on polycrystalline material. In the temperature region between 245 and 220 K where the Gd magnetization starts to turn away from the c-axis, we observe an increase in the muon depolarization rate, and a complex precession signal which can be separated into two frequency components meaning that spin turning does not occur simultaneously in different parts of the sample (domains). From these more detailed data follows that previously obtained values forB _fc andB _dip can not both be correct. Two explanations for our new result are possible: EitherB _fc undergoes a change around 230 K which is directly coupled to the spin turning angle, or the value of the dipolar field contribution used in the earlier evaluation is too low. This imposes some uncertainty as to the value of the angle at the onset of spin turning derived fromSR frequencies.     

Spin densities in some odd alternant radicals including linear polyene radicals

An approximate unrestricted Hartree-Fock method is used to calculate spin densities in the odd alternant radicals cyclohexadienyl, benzyl, perinaphthenyl and triphenylmethyl and the linear polyene radicals from allyl to C₁₉H₂₁. The results agree quite well with the exact calculations and with empirical estimates as well as with experimental data on hyperfine splitting constants and E.S.R. second moments.     

Spectral densities and nuclear spin relaxation in solids

We investigate the properties of ten spectral densities relevant for nuclear spin relaxation studies in solids. This is preceded by a brief review of nuclear spin relaxation in solids which includes a discussion of the appropriate spin-dependent interactions and the various relaxation rates which can be measured. Also, the link between nuclear spin relaxation and dielectric relaxation is discussed. Where possible and/or appropriate each of the spectral densities is expressed as a continuous distribution of Bloembergen-Purcell-Pound (or Debye) spectral densities 2ξ /(1 + ξ² ω²) for nuclear Larmor angular frequency ω and correlation time ξ. The spectral densities are named after their originators or the shape of the distributions of correlation times or both and are (1) Bloembergen-Purcell-Pound or δ-function, (2) Havriliak-Negami, (3) Cole-Cole, (4) Davidson-Cole, (5) Fang, (6) Fuoss-Kirkwood, (7) Bryn Mawr, (8) Wagner or log-Gaussian, (9) log-Lorentzian, and (10) Fröhlich or energy box. The Havriliak-Negami spectral density is related to the Dissado-Hill theory for dielectric relaxation. The spectral densities are expressed in a way which makes them easy to compare with each other and with experimental data. Many plots of the distributions of correlation times and of the spectral densities vs. various correlation times characterizing the distributions are given.     

Generation of spin currents and spin densities in systems with reduced symmetry

We show that the spin-current response of a semiconductor crystal to an external electric field is considerably more complex than previously assumed. While in systems of high symmetry only the spin-Hall components are allowed, in systems of lower symmetry other non-spin-Hall components may be present. We argue that, when spin-orbit interactions are present only in the band structure, the distinction between intrinsic and extrinsic contributions to the spin current is not useful. We show that the generation of spin currents and that of spin densities in an electric field are closely related, and that our general theory provides a systematic way to distinguish between them in experiment. We discuss also the meaning of vertex corrections in systems with spin-orbit interactions.     

McLachlan spin densities in even alternant ions

This paper reports some new wave functions for the ground state of the hydrogen molecule ion which give lower values for the mean energy than do previously published functions of comparable complexity. The wave functions were optimized first by the local-energy method and then by the variation principle. With wave functions of as high quality as those discussed here, the two optima were found to be very similar. The variation-principle optima, however, still gave better expectation values for one-electron operators.     

Relaxation of protons by radicals in rotationally immobilized proteins

Proton spin-lattice relaxation by paramagnetic centers may be dramatically enhanced if the paramagnetic center is rotationally immobilized in the magnetic field. The details of the relaxation mechanism are different from those appropriate to solutions of paramagnetic relaxation agents. We report here large enhancements in the proton spin-lattice relaxation rate constants associated with organic radicals when the radical system is rigidly connected with a rotationally immobilized macromolecular matrix such as a dry protein or a cross-linked protein gel. The paramagnetic contribution to the protein-proton population is direct and distributed internally among the protein protons by efficient spin diffusion. In the case of a cross-linked-protein gel, the paramagnetic effects are carried to the water spins indirectly by chemical exchange mechanisms involving water molecule exchange with rare long-lived water molecule binding sites on the immobilized protein and proton exchange. The dramatic increase in the efficiency of spin relaxation by organic radicals compared with metal systems at low magnetic field strengths results because the electron relaxation time of the radical is orders of magnitude larger than that for metal systems. This gain in relaxation efficiency provides completely new opportunities for the design of spin-lattice relaxation based contrast agents in magnetic imaging and also provides new ways to examine intramolecular protein dynamics.     

Influence of V on the Fe site spin and charge densities in BCC-Iron

Using the Mössbauer effect we studied the influence of substituting iron atoms by vanadium atoms on the Fe site hf field and isomer shift for a series of Fe-V alloys containing up to 18 at% V. We found that the two qualities are correlated with each other as well as that the average hf field H? is correlated with the average number of V atoms in the vicinity of the Fe nuclei, N?. Based on the former correlations we were able to determine the hyperfine coupling constants to be equal to: a) 1735 kOe/s-el for itinerant s-like electrons, b) 3240 and 3450 kOe/s-el for the s-electrons localized in the first- and second-neighbour shell, respectively and c) 3090 kOe/s-el, the average value. Using the estimated hf coupling constants and based on the H? ? N? correlation we calculated the disturbance of the spin or charge density per one V atom per unit cell, η, to be equal to 0.048. The present results are being compared with those obtained previously for other substitutes and they are discussed in terms of Friedel's and Stearns' models.     

Radio-frequency spin resonance of positive muons in α-iron at high temperatures

Resonant transitions between the Zeeman levels of positive muons implanted into α-iron foils have been observed above the Curie temperature by applying a 17.8 MHz transverse radio-frequency field and varying the longitudinal external field. Resonance signals of free and trapped muons are detected.     

Positive muons in single crystal sodium fluoride: A simple spin system

We report on the relaxation of positive muons (μ ⁺) stopped in a single crystal of sodium fluoride at 15±0.2K. At this temperature theμ ⁺ is believed to be static, and the observed time dependence of theμ ⁺ spin polarization is seen to deviate from the familiar Kubo-Toyabe form at late times. Specifically these data exhibit oscillations in the long time tail, which are attributed to hyperfine transitions between theμ ⁺ and neighboring spins. Quantitative comparison of these data to exact quantum mechanical calculations indicates that most of the time dependence can be explained by considering only interactions with the first shell (i.e., two fluorine and two sodium nuclei), and suggests strongly that the muon occupies a site along the <110> axis, midway between two fluorine nuclei.     

Shell effects on state densities with given numbers of excited protons and neutrons

A new method is introduced to calculate particle-hole state densities taking into account the complete structure in both the proton and neutron shells. The results are given for three nuclei: ²⁰⁸Pb, ¹⁷²Yb and ¹¹⁷Sn. They are compared with previous formulae and with two other expressions derived in the present paper. Strong shell effects are displayed and discussed.