Electronic states of the c is - and trans - H3ONO molecules: a CASPT2 study

The CASPT2 calculations for the S₀, T₁, S₁, T₂, and S₂ states of the cis- and trans-CH₃ONO molecules predict the energy levels and geometries of the cis- and trans-isomers in the different states. The CASPT2 adiabatic (T ₀) and vertical (T _v) excitation energies are in good agreement with available experimental data (for the S₁ cis- and trans-isomers). The CH₃O-NO dissociation potential energy curves were calculated at the CASPT2//CASSCF level, and the CASPT2 calculations were performed for the transition states along the T₁, S₁, and T₂ dissociation paths. For the repulsive S₂ state the calculations predict the T _v values larger than 5.4 eV and dissociation products of CH₃O (1²A″) + NO (X²Π).     

Nuclear spin lattice relaxation and electric field gradient in liquid indium

We have measured the nuclear spin lattice relaxation time in liquid indium from 130°C to 300°C to be: 1/T ₁=(1.98 × 0.0082T) × 10³ sec^-1. The relaxation rate consists of two significant parts: (1/T ₁) _K from the nuclear magnetic hyperfine interaction, and (1/T ₁) _Q from the nuclear quadrupole interaction. We calculate (1/T ₁) _K from the the modified Korringa relation using a correction factor of order unity for electron-electron interactions. The hyperfine term is linear in T and accounts for the second term in 1/T ₁. Within experimental error the remaining rate, (1/T ₁) _Q , is temperature independent, and theoretically varies as the product of the square of the electric field gradient, q, and τ_c, a typical time between field gradient fluctuations. Making use of the x-ray RDF, we construct a simple model for liquid indium and calculate the ionic and electronic contributions, q _I and q _E, to the electric field gradient, to be q _I=1.4 × 10²⁴/cm³ and q _E=8.5 × 10²⁴/cm³. The calculation of q _E assumes covalent bonding between nearest neighbours. Taking q _I and q _E to be of opposite sign, we find that the correlation time τ_c is 1.6 × 10^-13 sec. When we further identify τ _c with the correlation time for diffusion in a three-dimensional random walk, we are able to calculate the r.m.s. jump distance, Δr _D, involved in self-diffusion, Δr _D=0.38 Å. This value is consistent with the x-ray peak width of 0.38 Å which we used earlier to calculate the electric field gradient.     

Implications of time-reversal symmetry for the band structure of single-wall carbon nanotubes

When electron states in carbon nanotubes are characterized by two-dimensional wave vectors with the components K ₁ and K ₂ along the nanotube circumference and cylindrical axis, respectively, then two such vectors symmetric about a M-point in the reciprocal space of graphene are shown to be related by the time-reversal operation. To each carbon nanotube there correspond five relevant M-points with the following coordinates: K ₁⁽¹⁾ = N/2R, K ₂⁽¹⁾= 0; K ₁⁽²⁾ = M/2R, K ₂⁽²⁾= −π/T; K ₁⁽³⁾= (2N −M)/2R, K ₂⁽³⁾= π/T; K ₁⁽⁴⁾= (M + N)/2R, K ₂⁽⁴⁾= -π/T, and K ₁⁽⁵⁾= (N − M)/2R, K ₂⁽⁵⁾= π/T, where M and N are the integers relating the chiral, C _h , symmetry, R, and translational, T, vectors of the nanotube by N R = C _h + M T, T = |T|, and R is the nanotube radius. The states at the edges of the one-dimensional Brillouin zone, which are symmetric about the M-points with K ₂ = ±π/T, are shown to be degenerate due to the time-reversal symmetry.     

The Evolution of Interfacial Strength as a Way to Characterize a Low-Temperature Limit of the Surface Glass Transition of an Amorphous Polymer

The evolution of autoadhesive strength, σ, with healing temperature, T _h, at the symmetric amorphous polystyrene (PS)?PS interfaces of the samples with vitrified bulk has been used to characterize a low-temperature limit of the surface glass transition temperature T _g ^surface(low). The existence of a linear relationship between the square root of σ and T _h has been found for both polydisperse and monodisperse polymers. By the extrapolation of straight lines σ ^1/2 ? T _h to σ ^1/2 = 0, the values of T _g ^surface(low) have been determined and compared with those of a high-temperature limit of T _g ^surface, T _g ^surface(high), measured earlier. The differences between T _g ^surface(low) and T _g ^surface(high) have been found to be insignificant, 10–20°C. Using an average value of the shift of T _g ^surface(low) with healing time, t _h, the quasi-equilibrium value of the surface glass transition temperature of amorphous PS T _∞ ^surface has been estimated to be 10–15°C.     

Dynamic contrast-enhanced magnetic resonance imaging parameters independent of baseline T10 values

A baseline T₁₀ value is typically needed for dynamic contrast-enhanced (DCE-) MRI studies. However, an assumed baseline T₁₀ has to be used when T₁₀ measurements for patients are not available. In this work, we systematically investigate the dependence on T₁₀ of the commonly used DCE-MRI parameters (K^trans, k_ep, v_e and IAUC) as well as several newly defined parameters [the normalized ratios (NRs) of k_ep, K^trans and v_e, which are measures of relative changes in these parameters between two time points] for a spoiled gradient-echo pulse sequence using simulations and in vivo studies. Effects of various factors on the T₁₀ dependence, such as the true T₁₀ value, flip angle and the potential changes in T₁₀ due to treatment, were also assessed using simulations. We found that DCE-MRI parameters k_ep and the NR of k_ep are largely independent of T₁₀, especially when larger flip angles are used (e.g., 30–40°). Their estimations therefore do not require any knowledge of T₁₀. The NRs of K^trans, v_e and IAUC also exhibit independence to T₁₀, but only when T₁₀ remains constant between pre- and posttreatment. The estimation of parameters themselves (K^trans, v_e and IAUC) is highly dependent on the T₁₀ value.     

NMR investigations of molecular motions inp-n-hexyloxybenzylidene-p′-n-propylaniline

Proton spin-lattice relaxation times,T ₁, have been measured in the smectic phases, S _G ² , S _G ¹ and S_A, and in the nematic phase of HxBPA, in the temperature range, 220K<T<360 K. In the S _G ¹ and S _G ² phases,T ₁ has been measured at 15 and 40 MHz. The (S _G ¹ →S _G ² ) and (S _G ² →S _G ¹ ) transitions are clearly seen as discontinuities inT ₁. The former transition is seen to be due to possible freezing or change of hydrocarbon chain motions of the molecule. Our data in the S _G ¹ phase have been fitted to a model in which anisotropic rotational diffusion of the end hydrocarbon chains as also that of the rigid part of the molecule are considered. In the nematic phase, at 351 K, the observed behaviour ofT ₁, measured in the frequency range, 5 to 40 MHz, agrees well with the theoretical predictions of Uklejaet al and Freed, who take into account long range collective order fluctuations and local reorientations. Using these theories, the correlation time for short range reorientations has been calculated from our results to be 4.3 × 10⁻¹⁰ and 1.1 × 10⁻⁹ s respectively.     

Nuclear Spin-Lattice Relaxation of 82BrFe

The field dependence of the nuclear spin-lattice relaxation (SLR) of cold implanted ⁸²Br (T ≤ 25 mK) in α-Fe single crystals was investigated with nuclear magnetic resonance of oriented nuclei (NMR/ON) at low temperatures as experimental technique. The SLR at the lattice sites with the hyperfine fields found by earlier NMR/ON experiments was measured as a function of the applied external magnetic field B _ext parallel to the three principle axes [100], [110] and [111] of the iron single crystal. The data were evaluated with the full relaxation formalism in the single impurity limit and for comparison also with the often employed model of a single exponential function with an effective relaxation time T ₁′. With a phenomenological model the high field values of the relaxation rates r _{∞, [100]′} = 6.6(2) · 10⁻¹⁵ T²sK⁻¹, r _{∞, [110]} = 5.4(2) · 10⁻¹⁵ T²sK⁻¹ and r _{∞, [111]} = 5.2(1) · 10⁻¹⁵ T²sK⁻¹ were obtained.     

Study on the phase transitions by nuclear magnetic resonance of α-type RbAl(SO4)2·12H2O and β-type CsAl(SO4)2·12H2O single crystals

The thermodynamic properties, spin–lattice relaxation times, T₁, and spin–spin relaxation times, T₂, of the ²⁷Al, ⁸⁷Rb, and ¹³³Cs nuclei in MAl(SO₄)₂·12H₂O (M=Rb and Cs) crystals were investigated, and the two crystals were found to lose H₂O with increases in temperature. From our results for T₁ and T₂, we conclude that the discontinuities near T_d in the T₁ curves of the two crystals correspond to structural changes. In both crystals, below T_d the water molecules surrounding the Al³⁺ and M⁺ nuclei form distorted octahedra, whereas above T_d the water molecules around the Al³⁺ and M⁺ nuclei form regular octahedra and the environment of the Al³⁺ and M⁺ nuclei has cubic symmetry. Further, the T₁ for the ²⁷Al and ⁸⁷Rb nuclei in RbAl(SO₄)₂·12H₂O below T_d were found to increase with increasing temperature, whereas the T₁ for the ²⁷Al and ¹³³Cs nuclei in CsAl(SO₄)₂·12H₂O were found to decrease. It is possible that this difference is due to the different characteristics of α- and β-type crystals.     

Dynamical Correlation Functions for an Impenetrable Bose Gas with Neumann or Dirichlet Boundary Conditions

Abstract

We study the time and temperature dependent correlation functions for an impenetrable Bose gas with Neumann or Dirichlet boundary conditions ψ(x ₁, 0)ψ ^?(x ₂ , t) _±,T . We derive the Fredholm determinant formulae for the correlation functions, by means of the Bethe Ansatz. For the special case x ₁ = 0, we express correlation functions with Neumann boundary conditions ψ(0, 0)ψ ^?(x ₂ , t) _+,T , in terms of solutions of nonlinear partial differential equations which were introduced in [1] as a generalization of the nonlinear Schrödinger equations. We generalize the Fredholm minor determinant formulae of ground state correlation functions ψ(x ₁)ψ ^?(x ₂) _±,0 in [2], to the Fredholm determinant formulae for the time and temperature dependent correlation functions ψ(x ₁, 0)ψ ^?(x ₂ , t) _±,T , t ∈ R, T ≥ 0.     

Electronic spectra of mono-substituted chromates

The electronic spectra of monosubstituted chromate ion derivatives, CrO₃X^-, where X^-=F^-, Cl^-, Br^- and IO₃ ^-, have been measured at liquid helium temperature, employing a variety of sample forms. The observed electronic transitions correlate simply and directly with those of CrO₄ ^2-, the lowest-lying transitions being only very weakly perturbed. Of particular interest is that the lowest excited state ¹ E^a retains the peculiarities of the ¹ T ₁ parent state of CrO₄ ^2-. The sharp line spectrum observed in Cr₂O₇ ^2- between 18 000 and 19 000 cm^-1 is identified as ¹ E^a (¹ T ₁ in T _d) ←¹ A ₁ in a single O₃CrO⁼ chromophore. It is suggested that the observed features of the low-lying absorption bands can be explained by assuming that two spin-triplet states [³ E, ³ A ₂] are located a few hundred wave numbers above the sharp 0-0 line of ¹ E^a ←¹ A ₁.     

Specific heat behavior of high temperature superconductors in the pseudogap regime

We consider the competition between the one dimensionalization effect due to a magnetic field and the hopping parameters in quasi-one-dimensional conductors. Our study is based on a perturbative renormalization group method with three cut-off parameters, the bandwidth E₀, the 1D-2D crossover temperature T^*₁, which is related to the hopping process t₁, and the magnetic energy . We have found that the renormalized crossover temperatures T^*₁ and T^*₂, at which the respectively hopping processes t₁ and t₂ become coherent, are reduced compared to the bare values as the field is increased. We discuss the consequences of these renormalization effects on the temperature-field phase diagram of the organic conductors.Received: 5 March 2003, Published online: 23 July 2003PACS: 64.60.-i General studies of phase transitions - 75.30.Fv Spin-density waves - 72.15.Gd Galvanomagnetic and other magnetotransport effects - 74.70.Kn Organic superconductors     

Exchange interactions in a trigonal chromium (III) pair

The theory of exchange interactions in the excited state of a trigonal chromium(III) pair which occurs in Cs₃Cr₂Cl₉, and first nearest neighbours in ruby, is extended to the singly excited ² T ₁, ² T ₂ and ² E(t ₂ ³) pair states. The multiplet splitting is described by an effective hamiltonian which includes trigonal field, spin-orbit coupling, first-order Zeeman effect and bilinear and biquadratic exchange. Previous calculations on the important single-ion intensity mechanism for ² E pair states are incorrect. The corrected electric dipoles for ² E and also for ² T ₁ and ² T ₂ pair states are presented.     

Possible manifestation of spin fluctuations in the temperature behavior of the resistivity of Sm<Subscript>1.85</Subscript>Ce<Subscript>0.15</Subscript>CuO<Subscript>4</Subscript> thin films

A pronounced step-like (kink) behavior in the temperature dependence of resistivity ρ(T) is observed in the optimally doped Sm_1.85Ce_0.15CuO₄ thin films around T _sf = 87 K and attributed to the manifestation of strong-spin fluctuations induced by Sm³⁺ moments with the energy ħω_sf = k _B T _sf ≃ 7 meV. The experimental data are found to be well fitted by the residual (zero-temperature) ρ_res, electron-phonon ρ_e-ph(T) = AT, and electron-electron ρ_e-e(T) = BT ² contributions in addition to the fluctuation-induced contribution ρ_sf(T) due to thermal broadening effects (of the width ω_sf). According to the best fit, the plasmon frequency, impurity scattering rate, electron-phonon coupling constant, and Fermi energy are estimated as ω_p = 2.1 meV, τ ₀ ⁻¹ = 9.5 × 10⁻¹⁴ s⁻¹, λ = 1.2, and E _F = 0.2 eV, respectively. The text was submitted by the authors in English.     

Approximant crystals of icosahedral Mg–(Ga,Al)–Zn alloys

The zero field cooled (ZFC) and field cooled (FC) low-field magnetic moment m of a dense frozen ferrofluid containing Fe₅₅Co₄₅ particles of size 4.6nm in hexane exhibits irreversibility at temperatures T?T _b≈ 30?K. FC in μ ₀ H ≤ 1?T gives rise to shifted minor hysteresis loops below T _b. At T _c≈ 10?K, sharp peaks of m ^ZFC and of the ac susceptibility χ ′, a kink of the thermoremanent magnetic moment m ^TRM, a sizeable reduction of the coercive field H _c, and the appearance of a spontaneous moment m ^SFM indicate a phase transition with near mean-field critical behaviour of both m ^SFM and χ ′ . These features are explained within a core-shell model of nanoparticles, whose strongly disordered shells gradually become blocked below T _b, while their soft ferromagnetic cores couple dipolarly and become superferromagnetic (SFM) below T _c.     

NMR relaxation times and proton motion in HxWO3

The relaxation timesT ₁,T _1q,T _1D, andT ₂ for¹H in the tetragonal-A phase of H_xWO₃ have been measured over the temperature range 190 to 490 K. The¹H relaxation behaviour appears to be governed by diffusion over inequivalent jump distances, approximating to a short range planar diffusion and a long range isotropic diffusion. Parameters for the latter motion are estimated asE _a = 68 kJ/mol and ₀=2.5×10^–13 s. The powder X-ray diffraction pattern for this phase of H_xWO₃ has been studied over the temperature range 300–470 K. The tetragonal distortion diminishes with temperature and H_0.43 WO₃ becomes cubic at about 435 K. Volumetric studies of hydrogen evolution show that decomposition accelerates at approximately this temperature.     

Solutions for the T = 0 quantum spin glass transition in a metallic model with spin-charge coupling

We solve several low temperature problems of an infinite range metallic spin glass model. A compensation problem of T 0 divergencies is solved for the free energy which helped to extract the quantum critical behaviour of the spin glass order parameters as a function of δJ = J – J_c (T = 0). The critical value J_c(T = 0) = 3/16p_F^?1 of the frustrated spin coupling J, which separates spin glass from nonmagnetic (spin liquid) phase, is determined exactly in the static saddle point solution for a semielliptic metallic band model in terms of the density of states at the Fermi level. In addition to the replica-overlap order parameter 〈Q^ab〉, a ≠ b, the diagonal 〈Q^aa〉 is confirmed as order parameter by the result 〈Q^aa〉 _SP ～ (δJ)^β, β = 1, and its susceptibility χ^aaaa ～(-δJ)^?γ with γ = 1/2 at T = 0. The value for γ agrees with the one for the transverse field Ising spin glass. The low γ decay of 〈Q^aa〉, ～ T is obtained exactly in the whole quantum disordered phase including the critical value.     

Improved Estimation of Protein Rotational Correlation Times fromN Relaxation Measurements

In the study of protein backbone dynamics by¹⁵N relaxation measurements, an initial estimation of the isotropic global correlation time, τ_m, is usually obtained from the averageT₁/T₂ratio of nuclear spins that do not exhibit slow internal motion and withT₂values not significantly shortened by chemical or conformational exchange processes. Different methods have been used for identification of the rates of internal motion. However, the number of nuclear spins included in the τ_mestimation is often larger than the number that ultimately can be fitted to a single-order parameter,S², implying that some nuclear spins involved in the initial τ_mestimation actually have an effective internal correlation time, τ_e, not as fast as assumed. As a consequence, τ_mis underestimated, since internal motion reduces theT₁/T₂ratio. This situation becomes more obvious if the molecule has a large τ_mvalue because the reduction inT₁/T₂ratio arising from internal motion is more significant than for molecules with smaller τ_mand the same degree of internal motion. This Communication describes a more reliable method for identifying nuclear spins which should be excluded from the τ_mestimation because of insufficiently rapid internal motion. This results in an improved τ_mvalue, giving a much better agreement between the number of nuclear spins fitted successfully to a single-order parameter,S², and those used in the τ_mestimation.     

Luminescence from Ti2+ ions in LiF crystals

Luminescence of Ti²⁺: LiF crystals in the wavelength range 650–900 nm excited using laser radiation is reported. The values of 10Dq and the Racah B parameter obtained from the present results indicate that in LiF the ¹ E, ¹ T ₂, and ³ T ₂ energy levels are almost at the cross-over point in the Tanabe-Sugano diagram. In consequence photoluminescence from all three energy levels to the ground state is observed. At low temperature (T 14 K) the emission is mainly due to sharp emission lines with weak vibronic structure due to the ¹ E, ¹ T ₂³ T ₁ transitions of Ti²⁺ ions. The ³ T ₂³ T ₁ broad-band emission is weak at low temperature, becoming stronger at 300 K due to a phonon-assisted tunnelling process, similar to that observed in Cr³⁺: garnets [1]. The excitation spectrum of these lines is a broad peak at 590 nm due to absorption in the ³ T ₁³ T ₂ transition.     

Investigation of the^3 He(\vec d,p)^4 He reaction between 1 and 13 MeV

High-precision measurements of the cross section, the vector analyzing poweriT ₁₁ and the three tensor-analyzing powersT ₂₀,T ₂₁, andT ₂₂ of the³He(d, p)⁴He reaction have been performed in the energy range between 1.0 and 13.0 MeV in steps of 1 or 2 MeV. Angular distributions of the cross section have been obtained between 22.5° and 157.5° in the laboratory system. The polarization observables have been measured between 10° and 170°.     

Gamow-Teller transitions from 58Ni to discrete states of 58Cu

Under the assumption that isospin is a good quantum number, symmetry is expected for the transitions from the ground states of T = 1, T _z = ±1 nuclei to the common excited states of the T _z = 0 nucleus situated between the two nuclei. The symmetry can be studied by comparing the strengths of Gamow-Teller (GT) transitions obtained from a (p, n)-type charge-exchange reaction on a target nucleus with T _z = 1 with those from the β-decay of the T _z = - 1 nucleus. The A = 58 system is the heaviest for which such a comparison is possible. As a part of the symmetry study, we measured the GT transitions from ⁵⁸Ni (T _z = 1) to ⁵⁸Cu (T _z = 0) by using the zero-degree (³ He, t) reaction at 150 MeV/nucleon. With the achieved resolution of 50 keV, many hitherto unresolved GT states have been identified. The GT transition strengths were obtained for states up to 8 MeV excitation, i.e., near to the Q window limitation ( Q _EC = 9.37 MeV) of the β-decay from ⁵⁸Zn (T _z = - 1) to ⁵⁸Cu. The strength distribution is compared with that from shell-model calculations. Received: 24 November 2001 / Accepted: 30 January 2002