Corrections to Kramers’ formula for the fission rate of excited nuclei

A Kramers?? formulas with corrections of the first and second infinitesimal orders, R _F and R _S , are derived from the integral Kramers?? formula. In these corrections, we consider higher derivatives of the potential and the distance between the saddle and scission points in R _F . The rates R _F and R _S are compared with the results of dynamic simulations R _D . It is shown that R _F and R _I agree with R _D equally well. The calculations are performed for different forms of the potential. Although the corrections are derived for the overdamping mode they can be used for the case of medium friction.     

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.     

Effective Rayleigh range of Gaussian array beams propagating through atmospheric turbulence

The analytical expressions for the effective Rayleigh range z_R of Gaussian array beams in turbulence for both coherent and incoherent combinations are derived. It is shown that z_R of Gaussian array beams propagating through atmospheric turbulence depends on the strength of turbulence, the array beam parameters and the type of beam combination. For the coherent combination z_R decreases due to turbulence. However, for the incoherent combination there exists a maximum of z_R as the strength of turbulence varies. The z_R of coherently combined Gaussian array beams is larger than that of incoherently combined Gaussian array beams, but for the coherent combination case z_R is more sensitive to turbulence than that for the incoherent combination case. The larger the beam number is, the longer z_R is, and the more z_R is affected by turbulence. For the coherent combination z_R is not monotonic versus the relative beam separation distance, and the effect of turbulence on z_R is appreciable within a certain range of the relative beam separation distance.     

Spectral features of radiation from Nordström and Kerr-Newman white holes

Unlike the Schwarzschild white hole, Nordström and Kerr-Newman white holes cannot explode right down from the space time singularityR=0. For example a charged white hole has to commence explosion (i.e., comes into existence) with a radiusR ₀=R _c (2?R _c /R _b )^?1 whereR _c is the ‘classical radius’ andR _b is the final radius attained when the stationary state is reached. That means charged and rotating black holes also cannot hit the singularityR=0 and perish. Here the explosion is decelerated by the presence of charge and rotation and hence the radiation emitted would be not as energetic as in the Schwarzschild case where its energy is infinitely large for emission fromR=0.     

Quantum fluctuations and the universal kinetic inductance of granular superconducting films

The same mean-field theory for an array of Josephson junctions that describes the onset of superconductivity at normal state resistance R_N^(c) yields the kinetic inductance, L, for R_N<R_N^(c). The predicted universal behavior of L, as a function of R_N/R_N^(c), provides a further test of the theory of quantum fluctuations.     

Elastic properties of the RIV-RIII rotator phases of alkanes

A model free energy has been constructed to describe the R_IV-R_III rotator phase transition in alkanes in terms of the elastic strains and order parameter. The conditions for the R_IV-R_III phase transition are discussed. From the free energy, the order parameter and the elastic strains are determined. The model free energy describes the first or second order character of the R_IV-R_III transition depending on the strength of the coupling. The elastic properties in the vicinity of the R_IV-R_III transition are discussed on the basis of a free energy expansion. The temperature dependence of the elastic constants is calculated on both sides of the transition. The coupling between the order parameter and elastic stains is shown to have a crucial influence on the phase behavior and the order of the transition.     

Systematics of diatomic molecular transition moments: Encouraging progress—II

Literature absolute transition moments for A-X(0-0) bands have been compiled and used to obtain “best” values of R_e for some 90 transitions. Correlations were sought between R_e and various molecular parameters such as multiplicity, average internuclear separation, etc. None was found. The A-X (and related) R_e have been plotted for isoelectronic molecules against the nuclear charge difference and fitted with simple curves which seem to approach the R_e axis with zero slope. Both of these results are in accord with theory. The concept of isovalence has been clarified to allow for the orbital structure of molecules. It appears that the heavier of two isovalent hydrides has the greater R_e. Graphs of R_e for groups of isovalent molecules can be fitted with simple curves.     

Feasibility of using limited-population-based average R10 for pharmacokinetic modeling of osteosarcoma dynamic contrast-enhanced magnetic resonance imaging data

Retrospective analyses of clinical dynamic contrast-enhanced (DCE) MRI studies may be limited by failure to measure the longitudinal relaxation rate constant (R₁) initially, which is necessary for quantitative analysis. In addition, errors in R₁ estimation in each individual experiment can cause inconsistent results in derivations of pharmacokinetic parameters, K^trans and v_e, by kinetic modeling of the DCE-MRI time course data. A total of 18 patients with lower extremity osteosarcomas underwent multislice DCE-MRI prior to surgery. For the individual R₁ measurement approach, the R₁ time course was obtained using the two-point R₁ determination method. For the average R₁₀ (precontrast R₁) approach, the R₁ time course was derived using the DCE-MRI pulse sequence signal intensity equation and the average R₁₀ value of this population. The whole tumor and histogram median K^trans (0.57±0.37 and 0.45±0.32 min⁻¹) and v_e (0.59±0.20 and 0.56±0.17) obtained with the individual R₁ measurement approach are not significantly different (paired t test) from those (K^trans: 0.61±0.46 and 0.44±0.33 min⁻¹; v_e: 0.61±0.19 and 0.55±0.14) obtained with the average R₁₀ approach. The results suggest that it is feasible, as well as practical, to use a limited-population-based average R₁₀ for pharmacokinetic modeling of osteosarcoma DCE-MRI data.     

Use of fat suppression in R₂ relaxometry with MRI for the quantification of tissue iron overload in beta-thalassemic patients

Purpose

To assess the performance and results of R₂ relaxometry using a fat-suppressed (FS) multiecho sequence and compare these to conventional R₂ relaxometry in estimating tissue iron overload.

Materials and Methods

Relaxation rate values (R₂=1/T2) of the liver, spleen, pancreas and vertebral bone marrow (VBM) were estimated in 21 patients with β-thalassemia major, using a respiratory-triggered 16-echo Carr-Purcell-Meiboom-Gill (CPMG) spin-echo sequence before (R₂) and after (R₂ FS) the application of chemically selective fat suppression.

Results

Hepatic and splenic R₂ FS values correlated with respective R₂ values (r=0.98 and r=0.96, P<.001), whereas correlations between R₂ FS and R₂ values for pancreas and VBM were not statistically significant. Bland–Altman plots show disagreement between R₂ and R₂ FS values, particularly for pancreas and VBM. Hepatic, pancreatic and VBM R₂ FS values correlated with serum ferritin (r=0.88, P<.001; r=0.51, P<.003; and r=0.75, P<.002, respectively). Hepatic R₂ FS values correlated with splenic R₂ FS (r=0.77, P<.03), pancreatic R₂ FS (r=0.61, P<.006) and VBM R₂ FS values (r=0.70, P<.001), whereas pancreatic R₂ FS values correlated also with VMB R₂ FS values. On the contrary, among the R₂ values of the above tissues, obtained without fat suppression, only hepatic R₂ values correlated with serum ferritin, whereas no correlation was documented between hepatic and pancreatic or VBM R₂ values. The application of fat suppression did not improve breathing or flow artifacts.

Conclusion

Application of fat suppression in the standard CPMG sequence improved the capability of MRI in noninvasive quantification of iron, particularly in lipid-rich tissues, such as vertebral bone marrow (VBM) and pancreas.     

Contribution of the inhomogeneous waves in angular-spectrum representations

Angular-spectrum representations of wave fields separate naturally into two parts, V_h(R,t) containing only homogeneous plane waves and V_i(R,t) containing only inhomogeneous plane waves. Some properties of V_i(R,t) are presented here. We conclude that, for some problems, V_i(R,t) has several unphysical properties, and that under certain specified conditions, V_i(R,t) can not be neglected compared to V_h(R,t), even far from the sources of the field.     

The influence of CO adsorption on the galvanomagnetic and magnetic properties of evaporated nickel films

The influence of CO adsorption on the ordinary Hall coefficient, R_HO, the extraordinary Hall coefficient, R_HE, the perpendicular magnetoresistivity ΔR_{mag O} and the saturation magnetization, B_S, of Ni films with thicknesses between 1 and 200 nm has been studies as a function of the CO coverage at 77 and 273 K. There is a maximum in ΔR_HE at a coverage of about half a monolayer. ΔR_HO, ΔΔR_{mag O} and ΔB_S exhibit an oscillating behaviour.     

Optical properties of excitons in semiconductor superlattices and microcavities

The optical response of Mott–Wannier excitons is investigated in semiconductor superlattices and microcavities. p-Polarized light is considered to calculate the reflectivity R_pand dispersion relation of the collective normal modes in superlattices accounting for extrinsic Morse potential wells, andR_p in microcavities. Results of R_pexhibit well-defined peaks of the exciton bound states in the Morse potentials for both transverse and longitudinal modes. Comparisons ofR_p with experimental reflectivity data of light for semiconductor microcavities exhibit good qualitative agreement as well as Rabi splitting.     

Non-coherent scattering in subordinate lines: A unified approach to redistribution functions

Within the scope of the quantum-mechanical result of Omont, Smith and Cooper, we have derived a laboratory-frame redistribution function for the scattering of radiation in subordinate lines where both atomic levels are radiatively broadened. This new function, denoted as R_V(x′, n′; x, n), is the correct counterpart of Hummer's redistribution function R_IV. Moreover, it follows from the formalism developed here that R_V contains all known redistributions R_i(i=I, II, III, IV) as special cases and we may therefore speak in some sense of a unified redistribution function. A simple method has been tested for the evaluation of R_V and our numerical examinations of the properties of R_V served, among others, as an independent verification of the results obtained by Reichel and Vardavas for R_III and R_IV. Finally, it is shown in the conclusion to this paper that the function R_V, discussed here, can be applied not only to the radiative redistribution, but also to a more general case of a collisional redistribution in subordinate lines.     

Nuclear vibron model with 2 and 3 clusters for heavy nuclear molecules

An algebraic vibron model for two- and three-cluster nuclear molecules is presented, where all clusters are deformed. It is shown that if the clusters are deformed a minimum can be obtained for r ≠ 0, even in the relative vibrational limit U _R (4) ? U _R (3) for the case of two clusters, and U _R (7) ? U _R (3) ? U _R (3) for three clusters. By using coherent states, the geometrical mapping is discussed.     

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.     

Beam quality of radial Gaussian Schell-model array beams

Taking the Rayleigh range z_R and the M²-factor as the characteristic parameters of beam quality, the beam quality of radial Gaussian Schell-model (GSM) array beams is studied. The analytical expressions for the z_R and the M²-factor of radial GSM array beams are derived. It is shown that for the superposition of the cross-spectral density function z_R is longer and the M²-factor is lower than that for the superposition of the intensity. For the two types of superposition, z_R increases and the M²-factor decreases with increase in beam coherence parameter, and both z_R and the M²-factor increase with increase in inverse radial fill-factor. For the superposition of the cross-spectral density function, z_R increases and the M²-factor decreases with increase in beam number, while for the superposition of the intensity both the z_R and M²-factor are independent of the beam number.     

Stability of the long-period stacking order in Mg3ln AND Mg3(In1−yCdy) alloys

The stability of the stacking ordered structures of close-packed layers in Mg-In alloys near Mg₃In and pseudo-binary alloys Mg₃(In_1?yCd_y) for 0 ? y ? 1 is studied from a standpoint based on the pseudopotential theory. An expression of the structure-dependent energy for an arbitrary type of layer stacking is given by the method described in the previous papers [1,2]. The numerical results explain well the observed trends in the composition and pressure dependences of stacking sequence; the orders of appearance of stacking variants are 3R → 12R → 2H with an increasing Mg-content for Mg-In alloys near Mg₃In, 12R → 18R → 2H with an increasing Cd-content for Mg₃(In_1?yCd_y) and 12R → 18R → 24R with an increasing pressure for Mg₃ln. Speaking in detail, however, the present calculation fails to reproduce a 12R-structure (β₁-phase) at 25% In in the Mg-In system, an 18R-structure of Mg₃(In_0.65Cd_0.35) and an 18R-structure of Mg₃In found under pressure of 20–55 kb, although the energy differences are small in all the cases. From the analysis of components of the structure-dependent energy, it is concluded that the favorable type of layer stacking is determined predominantly by a contribution from the band-structure energy term of a state with the disordered arrangement of constituent atoms and also that an energy required to the alternation of stacking of layers is apparently smaller than the ordering energy. If a specific layer sequence is characterized by a hexagonality, the alloys vary their sequences in such a way that the hexagonality increases from zero (3R) to unity (2H) as the electron-to-atom ratio of the alloys decreases from 2·3 to 2·0.The Ewald and Madelung constants are calculated for various types of layer structure. Both constants change linearly with hexagonality, without regard to period, symmetry and layer sequence.     

Non-coherent scattering in subordinate line—V: Solutions of the transfer problem

We present several examples of the numerical solution of the radiative transfer in subordinate lines. Using a simplified physical model that yields the line source function analogous to the usual two-level-atom form modified by the presence of the redistribution function R_v in the scattering integral, we have solved the transfer problem for isothermal, plane-parallel atmospheres, both finite and semi-infinite. For finite atmospheres, we have found substantial differences between the solutions with R_v and those with complete redistribution. On the other hand, for semi-infinite atmospheres the complete redistribution appears to be a good approximation, at least for a_l?a_u (damping parameters for the lower and upper levels, respectively). It is shown that the effect of R_v becomes more pronounced with increasing ratio a_u/a_l. Finally, it is demonstrated that an approximate form for R_v analogous to that of Kneer for R_II serves as a very good approximation for computing the line profiles, particularly in the line wings.     

The scattering effects of the redistribution function RIII(x′, n′; x, n) on spectral line formation

The effects of frequency and angular redistribution on line formation are examined in static isothermal atmospheres for scattering described by the redistribution function R_III(x′, n′; x, n). For an optically thin atmosphere, it is found that the emergent line intensities obtained using R_III are essentially the same as R_I and R_II. In the case of a semi-infinite atmosphere, the emergent line intensities obtained using R_III, whether angle-averaged or angle-dependent, did not differ substantially from the complete redistribution results.     

Micropatterning of perfluoroalkyl self-assembled monolayers for arraying proteins and cells on chips

Organosilane self-assembled monolayers (SAMs) with perfluoroalkyl groups (R_f) on glass surfaces were used for arraying proteins and cells on chips. Quartz crystal microbalance measurements confirmed the inhibition of protein adsorption on R_f-SAM-modified surfaces and showed efficient adsorption on hydroxyl-, carboxyl-, and amino group-modified surfaces. The characteristics of R_f-modified surfaces were evaluated using solvent contact angle measurement and Fourier transform infrared (FTIR) spectroscopy. The R_f surface was highly water- and oil-resistant, as inferred from the contact angles of water, oleic acid, and hexadecane. Specific peaks of IR spectra were detected in the region from 1160 to 1360 cm⁻¹. Etching with dry plasma completely exfoliated the R_f-SAM, exposing the underlying intact glass surface. Modification conditions were optimized using contact angle and FTIR measurements. After dry plasma processing, the contact angles of all solvents became undetectable, and the IR peaks disappeared. Micrometer scale protein and cell patterns can be fabricated using the proposed method. Protein adsorption on micropatterned R_f-SAM-modified chips was evaluated using fluorescence analysis; protein adsorption was easily controlled by patterning R_f-SAM. PC12 and HeLa cells grew well on micropatterned R_f-SAM-modified chips. Micropatterning of R_f-SAM by dry plasma treatment with photolithography is useful for the spatial arrangement of proteins and cells.