MICROSCOPIC CALCULATION OF VISCOSITY COEFFICIENT IN HEAVY NUCLEI

A realistic calculation of the viscosity coefficients for ²³⁶U from ground equilibrium shape to saddle point is presented based on the linear response theory, in which the single particle spectra and wave function are provided by generalized Nilsson model. The dependence of viscosity coefficients γ_δ2δ2, γ_δ3δ3, γ_δ4δ4, γ_δ2δ3, γ_δ2δ4, γ_δ3δ4, on the collective variables δ₂, δ₃, δ₄ is studied at various values of the nuclear temperature with the smearing width Γ=0.1hω₀.     

Molecular field theory analysis of R3Co11B4 compounds

The temperature dependence of magnetization of the R₃Co₁₁B₄ compounds has been analysed using the two-sublattice molecular field theory. The molecular field coefficients, n_CoCo, n_RCo, n_RR, have been calculated by a numerical fitting process. The analytic form of the exchange field H_R(T) varying with temperature for each of the R₃Co₁₁B₄ compounds is presented, and some results are discussed.     

Molecular field theory analysis of R2Fe17C (R=PR,Nd, Gd,Tb, Dy,Ho, Er)

The temperature dependence of magnetization is analysed for R₂Fe₁₇C via the two-sublattice molecular field theory. The molecular field coefficients n_FF, n_RF and n_RR are obtained, by which T_C was calculated. Using the least-squares method, the fitted-form of H_R(T) varying with temperature for each compound is presented. The results are analysed. In addition, the parameters F=M_Fe²(0)n_FF/T_C was calculated for each R₂Fe₁₇C. By F, some phenomena different from the normal view were explained.     

A numerical analysis of the heavy-ion reaction based on the linear response theory

Taking the relative distanceR and the deformationδ of each nucleus as the collective variables, we solve the two dimensional coupled dynamical equations of motion with friction in the framework of the linear response theory. In solving the equations of motion, we approximately replace the inertia tensor with the hydrodynamical one and use the modified liquid-drop one as the collective potential energy. As the frictional coefficients we use the microscopically calculated ones in the previous paper. The calculation is done for the reaction of²⁸Si+²⁰Ne, in which the incident energy of²⁰Ne is 120 MeV. Results show that our microscopically calculated friction gives the large value of energy dissipation which amounts to the “completely damped” collision. Besides it, growths of the oblate deformation in the entrance channel and the prolate deformation in the exit channel are clearly seen. They give a large influence on the time development of the energy dissipation. We compare our calculated results with the experimental data for the reactions of 120 MeV²⁰Ne with²⁷Al. The agreement between them is found to be reasonably good.     

Nonlinear optical properties of nanospherical layer in the presence of an electric field

The linear and nonlinear optical properties in a spherical nanolayer quantum system subjected to an uniform applied electric field directed with respect to the z-axis have been theoretically investigated within the compact-density matrix formalism and the iterative method. The dependence of the optical absorption coefficients (ACs) and refractive index (RI) changes on the core radius R₁, on the inner radius of the clad R₂, and on the applied electric field F has been investigated detailedly. The results show that the optical ACs and RI changes of the nanospherical layer have been strongly affected by these factors. Moreover, the outcome of the calculation also suggests that all the factors mentioned above can give rise to blue-shift or red-shift significantly.     

Effect of anions on the phase stability of γ-FeOOH nanoparticles and the magnetic properties of gamma-ferric oxide derived from lepidocrocite

The effect of anions such as Cl⁻, SO₄²⁻, and HPO₄²⁻ on the phase stability of FeOOH (α or γ) during precipitation is investigated. Oxidation of Fe(OH)₂·xH₂O from FeCl₂ solution with high Cl⁻ concentration ([Cl⁻]/[Fe]=R_Cl≥8) or (NH₄)₂Fe(SO₄)₂ (FAS) with [HPO₄²⁻]/[Fe]=R_P≥0.02 yields phase-pure γ-FeOOH. In the medium ranges of R_Cl and R_P, mixed phases of α-FeOOH and γ-FeOOH are obtained. Replacement of OH⁻ by Cl⁻ with the bridging cations or strongly bonded HPO₄²⁻ ions in the matrix of the intermediate phase (Fe_x²⁺Fe_y³⁺(OH)_2x+2y−nz·xH₂O(A)_zⁿ⁻, where A is anions such as Cl⁻, SO₄²⁻, HPO₄²⁻, etc.), promoted the lower density γ-FeOOH. However, the particles are less developed and have poor crystallinity as evidenced from transmission electron microscope and thermogravimetry-differential thermal analysis of the precipitates. Whereas, monophasic, uniformly sized, nano-lath shaped particles with high aspect ratio >10 are obtained when morphology-controlling cation additives such as Pt⁴⁺, Pd²⁺ or Rh³⁺ are present in FeCl₂ (R_Cl≥8) solution. Preferential adsorption of additives on (0k0) and (h00) planes limits the growth in the perpendicular directions leading to high aspect ratios. The effect of these additives are suppressed by the phosphate ion, a strong complexing ligand, giving rise to fibrous aggregate with the length of individual particles as small as 10-30 nm. While most of the Cl⁻ ion is removed from the final precipitates on washing, phosphate remained as HPO₄²⁻ as evidenced from IR absorption spectra. Maghemite obtained by dehydroxylating γ-FeOOH contains randomly distributed micropores bringing in the relaxation effects of spins on the surface atoms as deciphered from Mössbauer spectroscopy. This leads to the low σ_s (44-48 emu/g) and H_c (120-130 Oe) for γ-Fe₂O_3−δ particles. Whereas nearly pore-free single crystalline particles obtained by reduction followed by reoxidation has high value of σ_s (73 emu/g) and H_c (320 Oe), which decreases to 30 emu/g and 75 Oe, respectively, for nanoparticles obtained from phosphate stabilized lepidocrocite. The mobility of iron ions and counter mobility of vacancies during the topotactic transformation of γ-FeOOH to magnetite to γ-Fe₂O_3−δ renders the particles pore-free.     

N2-broadening coefficients in the ν2 and ν4 bands of PH3

N₂-broadening coefficients are measured for 61 transitions of PH₃ in the ^QR branch of the ν₂ band and the ^PP, ^RP, ^SP, and ^PQ branches of the ν₄ band, using a tunable diode-laser spectrometer. The recorded lines with J values ranging from 1 to 16 and K from 0 to 11 are located between 1008 and 1106 cm⁻¹. The collisional widths are determined by fitting each spectral line with a Voigt profile, a Rautian profile, and a speed-dependent Rautian profile. The latter models provide larger broadening coefficients than the Voigt model. These coefficients have also been calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to the electrostatic contributions. The theoretical results are in good agreement with the experimental data and reproduce the J dependence of the broadenings, but their decrease at high J values is overestimated for the ^QR (J, K) transitions.     

Author index

The penumbra of the profile function describing the nuclear collisions of relativistic heavy ions is related to the cross section for their producing a specific target-nucleus γ-ray, σ_γ. The analysis assumes that the diffuse-edge diffraction model suffices to calculate the inelastic cross sections to the particle-stable states of the target nucleus. When the deformation lengths, $\text{δ}{}_{\mathrm{L}}\text{≡ β}{}_{\mathrm{L}}\text{R}$, characterizing all important excitations are available from other experiments and the γ-branching of these states is also known, the only unknown quantity determining σ_γ is found to be the ratio of the diffuseness parameter of the profile function, d, to its radius, $\text{R}$. The most reliably determined values of $\text{d}\text{R}$, for the target ⁴⁰Ca, imply a rather wide penumbra, consistent with microscopic calculations.     

Description of the nuclear surface by moments

The parameters proposed by W. D. Myers to describe the radial shape dependence of the nuclear surface are shown to be as useful as they are natural. For spherical nuclei, the central radiusC, the charge radiusR, the quadratic radiusQ are redefined, and it is shown how they are interrelated by Myers' surface widthb, flair γ₃, crookedness γ₄, and the higher shape parameter γ₅. All these quantities are calculated for some special charge distribution functions. (For symmetric distributions, possessing a symmetry center atC, the odd surface momentsb ³γ₃ andb ⁵γ₅ vanish.) The connection of the surface moments Г_μ =b ^μ γ _μ with the volume momentsF _k that have been extracted by K. W. Ford and J. G. Wills from muonic atoms, is indicated.     

N2-broadening coefficients in the ν2 and ν4 bands of PH3 at low temperature

N₂-broadening coefficients have been measured for 41 transitions of PH₃ at −100 °C in the ^QR branch of the ν₂ band and the ^PP, ^RP, and ^SP branches of the ν₄ band, using a tunable diode-laser spectrometer. The recorded lines with J values ranging from 1 to 13 and K from 0 to 10 are located between 1026 and 1093 cm⁻¹. The collisional widths are determined by fitting each spectral line with a Voigt profile, a Rautian profile, and a speed-dependent Rautian profile. The latter models provide larger broadening coefficients than the Voigt model. These coefficients have also been calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to the electrostatic contributions. By comparing broadening coefficients at room and low temperatures, the temperature dependence of these broadenings has been determined both experimentally and theoretically.     

Comparison of analytical and numerical analysis of the reference region model for DCE-MRI

This study compared three methods for analyzing DCE-MRI data with a reference region (RR) model: a linear least-square fitting with numerical analysis (LLSQ-N), a nonlinear least-square fitting with numerical analysis (NLSQ-N), and an analytical analysis (NLSQ-A). The accuracy and precision of estimating the pharmacokinetic parameter ratios K_R and V_R, where K_R is defined as a ratio between the two volume transfer constants, K^trans,TOI and K^trans,RR, and V_R is the ratio between the two extracellular extravascular volumes, v_e,TOI and v_e,RR, were assessed using simulations under various signal-to-noise ratios (SNRs) and temporal resolutions (4, 6, 30, and 60 s). When no noise was added, the simulations showed that the mean percent error (MPE) for the estimated K_R and V_R using the LLSQ-N and NLSQ-N methods ranged from 1.2% to 31.6% with various temporal resolutions while the NLSQ-A method maintained a very high accuracy (< 1.0×10^− 4 %) regardless of the temporal resolution. The simulation also indicated that the LLSQ-N and NLSQ-N methods appear to underestimate the parameter ratios more than the NLSQ-A method. In addition, seven in vivo DCE-MRI datasets from spontaneously occurring canine brain tumors were analyzed with each method. Results for the in vivo study showed that K_R (ranging from 0.63 to 3.11) and V_R (ranging from 2.82 to 19.16) for the NLSQ-A method were both higher than results for the other two methods (K_R ranging from 0.01 to 1.29 and V_R ranging from 1.48 to 19.59). A temporal downsampling experiment showed that the averaged percent error for the NLSQ-A method (8.45%) was lower than the other two methods (22.97% for LLSQ-N and 65.02% for NLSQ-N) for K_R, and the averaged percent error for the NLSQ-A method (6.33%) was lower than the other two methods (6.57% for LLSQ-N and 13.66% for NLSQ-N) for V_R. Using simulations, we showed that the NLSQ-A method can estimate the ratios of pharmacokinetic parameters more accurately and precisely than the NLSQ-N and LLSQ-N methods over various SNRs and temporal resolutions. All simulations were validated with in vivo DCE MRI data.     

Hydrogen line broadening in the ν2 and ν4 bands of phosphine at low temperature

Using a tunable diode-laser spectrometer, we have measured H₂-broadening coefficients of PH₃ at low temperature (173.2 K) for 27 lines in the ^QR branch of the ν₂ band and in the ^PP and ^RP branches of the ν₄ band. The recorded lines with J values ranging from 2 to 11 and K from 0 to 9 are located between 1016 and 1093 cm⁻¹. The collisional widths are determined by fitting each spectral line with a Voigt profile and a speed-dependent Rautian profile which provides slightly larger broadening coefficients than the Voigt model. These coefficients have also been calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to the weak electrostatic contributions. Except for three ^QR(J,K) lines, where K = J, the calculated broadening coefficients are in good agreement with the experimental data. By comparing the results obtained at room and low temperatures, the temperature dependence of linewidths has been determined both theoretically and experimentally.     

Oscillator strength of electron-type color centers in KCl single crystals irradiated with electrons and protons

The absorption spectra of KCl single crystals irradiated with electrons and protons at energies of 15 and 100 keV and a particle flux ranging from 5×10¹² to 10¹⁵ cm^?2 are investigated. The absorption bands attributed to simple (F, F _a, K) and complex (M, R ₂, R ₄, N) color centers are identified in the spectra. The correlation dependences of the absorption coefficients for M, R ₂, and R ₄ centers on the absorption coefficient of F centers and the correlation dependences of the absorption coefficients for R ₂ and R ₄ centers on the absorption coefficient of M centers are established. The oscillator strengths are calculated for M, R ₂, and R ₄ color centers.     

The analysis of surface processes on solid electrons by combined modulated ellipsometric and reflectometric experiments

The response of reflectometric and ellipsometric parameters to small changes in the properties of the metal-solution interphase is analysed by the use of linear approximation expressions. It is shown that the changes in R₆ and R_⊥ are generally closely related, and the ratio (δR/R_⊥ /δR/R_⊥∥ may be insensitive to the value of n?_film. On the other hand, the ratio δΔ/(δR/R_⊥)₆ is shown to have always good sensitivity to ^n?film. For two surface processes on solid electrodes, gold surface oxidation and hydrogen adsorption on platinum, it is demonstrated that the information extracted from the combined measurements of Δ and R transients is more detailed and informative compared with the evidence obtained by reflectometry alone. A fast component is resolved in the process of gold surface oxidation, and shown to result optically in an apparent metallic film, which probably reflects changes in the properties and structure of the metal surface atoms induced as the oxygen uptake commences.     

Multispectrum analysis of the ν9 band of C2H6: Positions, intensities, self- and N2-broadened half-width coefficients

Line positions, intensities, Lorentz self- and N₂-broadened half-width coefficients have been measured for ^PQ₃, ^PQ₂, ^PQ₁, ^RQ₀, ^RQ₁, ^RQ₂, and ^RQ₃ sub-band transitions in the ν₉ fundamental band of ¹²C₂H₆. A multispectrum nonlinear least-squares fitting technique was used to fit up to 17 high-resolution (∼0.00156 cm⁻¹), room temperature absorption spectra of pure (99.99% chemical purity) natural sample of ethane and lean mixtures of the high-purity ethane diluted with N₂. A Bruker IFS 120HR Fourier transform spectrometer located at the Pacific Northwest National Laboratory (PNNL), in Richland, Washington was used to record the data. A standard Voigt line shape was assumed to fit all the data since no line mixing or other non Voigt line shapes were required to fit any of the spectra used in the analysis. Short spectral intervals (∼2-2.5 cm⁻¹) of all 17 spectra covering a specific ^PQ or ^RQ sub-band were fit simultaneously. For the first time in an ethane band, pressure-broadened half-width coefficients were determined for the torsional-split components. However, for better reliability of the retrieved coefficients for the weaker components (transitions with large intensity ratios of 4:1 or 3:1 for most K levels between the strong and weak components), constraints were used such that the half-width coefficients of both torsional-split components for a given J were identical for a specific broadening gas. No pressure-induced shift coefficients were necessary to fit the spectra to their noise level. The present study revealed for the first time the dependence of self- and N₂-broadened half-width coefficients upon the J, K quantum numbers of the transitions in ethane. A number of transitions belonging to the ν₉+ν₄−ν₄ and the ν₉+2ν₄−2ν₄ hot bands were also observed in the fitted regions and measurements were made when possible.     

Canonical realizations of the lie algebras gl(n, R) and sl(n, R) I. Formulae and classification

The generators of the Lie algebra of the general linear group GL(n, R) and of the special linear group SL(n, R) are, recurrently, expressed through polynomials in the quantum canonical variables p_t and q_t. These realizations are skew-Hermitian, the Casimir operations are realized by constant multiples of identity element and, in dependence on the number of the canonical pairs used, they depend on d(d?1 for sl (n,R)), d = 2, …, n, free real parameters.     

Evidence for dipole-quadrupole-octupole mixing in the 902 keV 2 → 2 transition in W

From known conversion coefficients and angular correlations combined with the γ-ray decay deduced from the ¹⁸¹Ta(p, 2n¹⁸⁰W reaction it is found that the 1007 → 104 keV (2⁻ → 2⁺) transition in ¹⁸⁰W has mixing parameters δ₁ = −0.16 ± 0.07 and δ₂ = −0.64 ± 0.17 for M2/E1 and E3/E1, respectively     

(p, γ) reaction studies on 60Ni

The γ-ray spectra from the ⁶⁰Ni(p, γ)⁶¹Cu reaction were measured for 27 isolated resonances. From these studies the J^π assignment of the compound states in ⁶¹Cu were made. Moreover, a value for the El photon strength function k(El) = 1.03 × 10^?9 MeV^?3 was obtained from seven l = 0 resonances to the 16 low-lying states. This value was then compared with the theoretical estimates of El strengths as predicted from the s.p. and giant dipole resonance models. The distribution of partial radiative widths about their mean value was determined from a Monte Carlo technique and was found to be consistent with the Porter-Thomas distribution when the Γ_{γ, ij} were divided by the E_γ⁵ energy dependence.Values for the coefficients of the correlation R between Γ_{λ, p} and Γ_{λ, γj} and T between Γ_{λ, yj} and $\text{Γ}{}_{\mathrm{\lambda ,\; \gamma ?}}$ where f ≠ j, were computed with the values R = 0.14 and T = 0.39, respectively. Also the correlation coefficients C(〈 Γ_{λ, yj}〉, I₃He, d, j) and $\text{C(〈Γ}{}_{\mathrm{\lambda ,\; y?}}\text{〉 I}{}_{\mathrm{<mtext>d,\; n</mtext><mtext>,\; ?</mtext>}}\text{)}$ yielded the values ρ = 0.87 and ρ = 0.80 respectively. All these correlations which are found to be statistically significant, imply that the (p, γ) reaction in ⁶⁰Ni is partly due to direct capture such as given by valence and doorway state contributions.     

Influence of chemical bond length changes on the crystal field strength and “ligand-metal” charge transfer transitions in Cs2GeF6 doped with Mn and Os ions

Detailed study of dependence of the crystal field strength 10Dq and lowest charge transfer (CT) energies for different interionic distances in Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺crystals is presented. The calculations were performed using the first-principles discrete-variational Dirac-Slater (DV-DS) method. As a result, the functional dependencies of 10Dq and lowest CT energy on the metal-ligand distance R were obtained without any fitting or semiempirical parameters. It was shown that 10Dq depends on R as 1/Rⁿ, with n=4.0612 and 4.3874 for Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺, respectively. Two approximations (linear and quadratic) are obtained for the dependence of the lowest CT energy on R; CT energy decreases when R increases with dE(CT)/dR=−638 and −1080 cm⁻¹/pm for Cs₂GeF₆:Mn⁴⁺ and Cs₂GeF₆:Os⁴⁺, respectively, if the linear approximation is used. These values can be used for estimations of the lowest CT energies for Mn⁴⁺ and Os⁴⁺ ions in other hosts with fluorine ligands. Estimations of the electron-vibrational interaction (EVI) constants, Huang-Rhys parameters, and Stokes shifts for all the above-mentioned crystals were performed using the obtained 10Dq and E(CT) functions.     

Low and room temperature measurements and calculations of O2-broadening coefficients in the ν3 band of CS2

O₂-broadening coefficients have been measured for 16 lines in the P and R branches of the fundamental ν₃ band of ¹²C³²S₂ at room and low temperatures (298.0, 273.2, 248.2, 223.2, and 198.2 K), using a tunable diode laser spectrometer and a low temperature cell. These lines from P(62) and R(64) are located in the spectral range 1519-1547 cm⁻¹. The collisional half-widths are obtained by fitting each observed profile with the Voigt and Rautian lineshape models. The broadening coefficients have also been calculated at all experimental temperatures using a semiclassical calculation performed by considering in addition to the electrostatic quadrupole-quadrupole interaction, a simple anisotropic contribution. Finally, from all the results, the parameter n of the temperature dependence of the broadening coefficients has been determined both experimentally and theoretically.