A level-density-dependent imaginary potential for heavy ions

Under the assumption that compound-nucleus formation is the only channel competing with elastic scattering, an L-dependent imaginary potential is defined with the help of the compound-nucleus level density. For the latter an expression is used which seems to be accurate enough for excitation energies of several tens of MeV and with a substantial part of rotational energy. Associated with a double-folded real part, this imaginary potential is shown to reproduce well the elastic scattering data of eight systems of medium size (total mass between 36 and 72) at various energies not very high above the Coulomb barrier. The results are equivalent to those obtained with a folding real potential and a Woods-Saxon imaginary potential with parameters adjusted for each set of data with the advantage that our approach only needs two parameters to fit the data for a wide range of energies for each scattering system.     

原子吸收限附近完整晶体内的能流方向

研究了原子吸收限附近对称劳厄和布拉格情况下完整晶体内的能流方向．发现在对称劳厄情况下，只有当原子散射因子的虚部对衍射的贡献可以与实部的贡献相比较时，晶体内与色散面上某一结点相对应的能流会偏离色散面的实部的法向；而在对称布拉格情况下，即使在原子散射因子的虚部对衍射的贡献可以忽略时，在所谓的“全反射”区内也会偏离．当衍射仅由原子的虚部引起时，这种偏离在对称劳厄情况下最大，而在对称布拉格情况下最小． 关键词：     

Complex microscopic optical potential between two nuclei based on Dirac-Brueckner theory for nuclear matter

The real and imaginary parts of the optical-model potential between two nuclei are calculated in the energy density formalism. The energy density is derived from the Dirac-Brueckner approach to nuclear matter. In this approach, both free NN scattering and the saturation properties of nuclear matter can be explained starting from a realistic NN interaction. The relativistic features incorporated in the Dirac-Brueckner approach make the real part of the optical potential less attractive than that obtained in a non-relativistic calculation while the imaginary part is enhanced. The comparison of the calculated differential cross section for elastic ¹²C-¹²C scattering with the experimental data suggests that the enhancement of the imaginary part due to the relativistic treatment is favourable while its repulsive contribution to the real part is unfavourable.     

Standard deviations of chemical reaction rates and validity ranges of the statistical theory

Validity ranges of the statistical theory of chemical reactions are discussed. On the basis of the quantum mechanical scattering theory, the rate of the chemical reaction of the complex-formation mode is formulated. The interaction matrix elements between resonance states and scattering continua are regarded as stochastic variables. The expectation value of the reaction rate is shown to coincide with the prediction of the conventional statistical theory if the condition of overlapping resonance is fulfilled. The standard deviation is found to be inversely proportional to the number of resonance states involved in the width of the collision energy. High density of vibrational energy levels of the collision complex serves to suppress the standard deviation and to make the statistical theory accurate. The condition for the conventional statistical theory to hit the correct value with probabilities more than 99% is obtained as a relation between the number of vibrational modes and the depth of the potential energy well of the collision complex.     

Microwave radiative transfer in scattering atmosphere: Effects of complex permittivity of ice spherical crystals

This paper presents the effects of ice particle's complex permittivity uncertainties on the scattering properties and upwelling brightness temperatures of cloudy atmospheres at the Advanced Microwave Sounding Unit-B (AMSU-B) channel frequencies of 89, 150 and 183 GHz. We investigated the mean deviations of ice particle's optical efficiencies and asymmetry parameters due to the uncertainties in the real and imaginary parts of its complex permittivities. We assumed that the true values of ice particle's permittivity are, respectively, within ±20% for the imaginary part and ±5% for the real part of the permittivity values given by the model of Hufford. Microwave radiative transfer calculations were performed to estimate the absolute errors of brightness temperatures due to uncertainties in ice particle's permittivities. Ice particles were taken to be spherical and their diameters were chosen in the range of 40-4000 μm. Gamma-size distribution was employed in computing volume scattering properties and the effective diameters were 70, 100 and 150 μm with an effective variance being 0.25. We found that ±20% uncertainty in the imaginary part of ice particle's permittivity resulted in only about 10% mean deviations in the absorption efficiencies at the three AMSU-B channel frequencies. However, an uncertainty of ±5% in the real part resulted in more than 15% mean deviations in both scattering and extinction efficiencies, especially significant at the frequency of 183 GHz. The absolute variations of the emerging brightness temperature from the cloudy atmosphere due to uncertainties in the permittivity were found to be more than 1 K, which is already significant compared with the sensitivities achieved with today's technology for millimeter wave radiometers.     

Heterodyne coherent anti-Stokes Raman scattering (CARS) imaging

We have achieved rapid nonlinear vibrational imaging free of nonresonant background with heterodyne coherent anti-Stokes Raman scattering (CARS) interferometric microscopy. This technique completely separates the real and imaginary responses of nonlinear susceptibility chi(3) and yields a signal that is linear in the concentration of vibrational modes. We show that heterodyne CARS microscopy permits the detection of weak vibrational resonances that are otherwise overshadowed by the strong interference of the nonresonant background.     

The real part of the amplitude of proton-deuteron scattering at an energy 3 GeV

Measurement of the differential cross-sections of the proton-deuteron scattering at 3 GeV is described. Measurement was performed in the region of angles 2.5° to 11.5°. Analysis of the experimental data shows that besides the imaginary scattering amplitude a real part of the scattering amplitude is also required to describe proton-deuteron scattering at 3 GeV energy; the magnitude of the real part is 28% of the imaginary part.Behová 7, Praha 1, Czechoslovakia.We gratefully acknowledge the assistance of the JINR staff and their valuable services.     

The elastic scattering of proton on proton at an energy of 8 GeV

The paper describes the measurement of the differential cross-section for pp scattering at an energy of 8 GeV. The results of the paper agree well with the assumption that there exists a real part of the scattering amplitude that is 33% of the imaginary part.     

Electron excitation in atoms and molecules by neutron-nucleus scattering

The quantum theory of electron stimulated desorption developed in two preceding papers is presented in a WKB like form and is applied to the desorption of hydrogen and oxygen from tungsten. Retunnelling processes are taken into account and manifest themselves in an imaginary part in the potential of the desorbing particles. This imaginary part together with a non zero width of the wavepacket leads to quantum effects in the motion of the desorbing particles modifying the corresponding classical results of the reduction factor and of the energy conservation. The modifications turn out to be quite large for hydrogen as well as for oxygen increasing the reduction factor by several orders of magnitude. The isotope effect also is changed appreciable. The parameters of the model are determined from corresponding experimental data such as vibrational levels of the adsorbates, the energy distribution of the desorbing particles and the reduction factor.     

Ambiguity on the imaginary potentials in the Dirac formalism for the elastic and the inelastic scattering of nucleons

The Dirac formalism for the elastic scattering of nucleons has been extended to a coupled channel formalism taking into account collective excited states. Calculations for the scattering of 500 MeV protons on ⁴⁰Ca shows large second-order effects on the elastic scattering. The imaginary scalar potential and the imaginary vector potential can be varied widely without giving so large effects on the elastic scattering. This large ambiguity is not limited to this case.     

Studies on the vibrational excitation differential cross sections of non-resonant e-N2 scattering using augmented polarization potentials

Distributed spherical Gaussian (DSG) correlation-polarization model potentials with higher-order terms and exact exchange effects in single-configuration Slater determinant are taken into account for low-energy vibrational excitation e-N₂ scattering system. The integrodifferential coupled channel equations are solved using a combination of linear-algebraic and R-matrix-propagator algorithms. Analytic Born completion is used to calculate high-order scattering matrix elements in order to obtain convergent differential cross sections. The energy range is set to 4–15 eV which is not tested by the present theoretical method before. The overall agreement of theoretical results with the latest experiments emphasizes the importance of higher-order correlation-polarization potentials and rigorous exchange effects in vibrational excitation scattering.     

Temperature dependence of the dielectric constant and I.R. reflection spectrum of LiNBO3 by Raman scattering

The temperature and frequency dependence of the dielectric constant, ?_xx, and the reflection coefficient associated with LiNbO₃ in the far infrared (i.r.) was obtained from Raman scattering measurements. The Raman spectrum associated with the E symmetry vibrational mode was carefully studied in the temperature range of 77 to 1190 K. The first order scattering intensity was related to the imaginary part of the dielectric constant and the Kramers-Kronig relation was used to obtain the dielectric constant.     

Effect of nonpolar optical phonon scattering on free-carrier absorption in heavily doped n-type germanium

The effect of nonpolar optical phonon scattering on the free-carrier absorption in n-type semiconductors such as germanium has been investigated quantum mechanically in quantizing magnetic fields. It is assumed that the energy band of electrons in semiconductors is nonparabolic and the dominant scattering mechanism for electrons in solids is that of nonpolar optical phonon scattering. When the radiation field is polarized parallel to the magnetic field, the absorption coefficient will be of complex value due to the interaction of the radiation field and the optical phonon field with electrons in semiconductors. Results show that real and imaginary parts of the absorption coefficient oscillate quite considerably with the magnetic field in the high fields for the heavily doped n-type Ge. Both real and imaginary parts of the absorption coefficient appear as positive and negative values when changing the magnetic field. In low magnetic fields, the imaginary part of the absorption coefficient disappears. However, if the density of electrons increases, the imaginary part of the absorption coefficient will increase with the magnetic field in low fields. Moreover, it is also shown that the amplitudes of oscillations for the real and imaginary parts of the absorption coefficient do not vary in a regular trend with the density of electrons.     

Coupled channel description of O+Nd scattering around the Coulomb barrier using a complex microscopic potential

Angular distributions of elastic scattering and inelastic scattering from 2⁺₁ state are measured for ¹⁶O+^142,144,146Nd systems at several energies in the vicinity of the Coulomb barrier. The angular distributions are systematically analyzed in coupled channel framework. Renormalized double folded real optical and coupling potentials with DDM3Y interaction have been used in the calculation. Relevant nuclear densities needed to generate the potentials are derived from shell model wavefunctions. A truncated shell model calculation has been performed and the calculated energy levels are compared with the experimental ones. To simulate the absorption, a ‘hybrid’ approach is adopted. The contribution to the imaginary potential of couplings to the inelastic channels, other than the 2⁺₁ target excitation channel, is calculated in the Feshbach formalism. This calculated imaginary potential along with a short ranged volume Woods–Saxon potential to simulate the absorption in fusion channel reproduces the angular distributions for ¹⁶O+¹⁴⁶Nd quite well. But for ¹⁶O+^142,144Nd systems additional surface absorption is found to be necessary to fit the angular distribution data. The variations of this additional absorption term with incident energy and the mass of the target are explored.     

A microscopic model analysis of the 90Zr(p,n) IAS transition

Direct reaction (p, n) data to the isobaric analogue of the ground state of ⁹⁰Zr is analysed within a DWA using a complex effective two-nucleon transition interaction, the real part of which has been used in many previous inelastic scattering analyses. Using collective model form factors in the ansatz for the imaginary part of the transition interaction and allowing for virtual resonance excitation, the differential cross sections from the scattering of 18.5–45 MeV protons are well reproduced. The parameters of the required complex interaction have a smooth energy variation similar to that required by a microscopic model analysis of proton inelastic scattering to collective states in nuclei.     

Real parts of scattering amplitudes and Regge phenomenology

High energy scattering amplitudes are computed using the Harari model for the imaginary parts and fixed t dispersion relations for the real parts. This procedure induces a corrective term to the real part of the Regge amplitudes whose effects are investigated in π-nucleon and K-nucleon charge exchange reactions.     

An optical potential description of 16O + 28Si elastic scattering

The differential cross sections for ¹⁶O + ²⁸Si elastic scattering at seven energies between 21 and 35 MeV in the centre of mass are described well over the whole angular range from 20° to 180° by an optical potential whose real part consists of a double-folded potential supplemented by a phenomenological model-independent correction term. This surface correction is predominantly attractive and has structure which depends only weakly on the energy. The associated imaginary potentials imply surface transparency and have detailed structure which varies rapidly with energy. However there is a systematic trend for the absorptive region to extend to larger radii as the energy increases. A simple parameterization of this trend allows the main features of the excitation function for 180° scattering to be reproduced.     

Coupling to the elastic channel in electron impact spectroscopy: A simple second born model and its application to excitation of the 61P1 state of mercury and to the excitation of molecules

The matrix element in the infinite channel close coupling approximation responsible for coupling to the elastic channel in electron impact inelastic encounters is investigated. The contribution from the imaginary part of the energy denominator in the elastic coupling matrix element for dipole allowed transitions is shown to yield large angle differential cross sections in good agreement with experiment. This coupling mechanism predicts that the shape of the inelastic differential cross section will be dominated by the shape of the elastic cross section in the large angle high energy limit. In fact the coupling matrix element exhibits a dependence on incident energy, k², and momentum transfer, K, of the form 1/kK² which is in agreement with the theoretical predictions of Huo and means that in the limit of high incident energy the non-first-Born elastic coupling will dominate the angular dependence of the inelastic differential cross section at large scattering angles. In the case of molecular electron impact spectra it is shown that the analog of the Massey—Moore coherence features depending on the symmetry of the states involved in the excitation process will also occur in the coupling contribution. It is suggested that this new mechanism for producing coherent features in inelastic differential cross sections may be the explanation of the coherent features observed experimentally by Karle and Swick.It can be concluded on the basis of the results obtained here that the coupling to the elastic cross section provided by the imaginary contribution from the second Born energy denominator is sufficient to explain presently available experimental data on the large angle differential cross section and spin polarization. The simple coupling model was found to be inadequate to explain the small angle differential cross section in the range 10° < θ < 30° even at incident energies as high as 400 eV. The calculations also showed significant differences between first and second Born calculations at zero scattering angle. No conclusion can be drawn about this observation as all the omitted terms should make significant contributions in the small angle region. It is important to again emphasize that the large angle scattering even in the limit of high incident electron energy will be completely dominated by the coupling to the elastic channel^{7, 11}. On the basis of this work it appears that the coherent structure in the large angle inelastic differential cross section observed by Swick and Karle^{12, 13} at incident electron energies in the keV region may well be due to coupling to the elastic channel.     

Low‐noise,vibrational phase‐sensitive chemical imaging by balanced detection RIKE

We perform a back‐to‐back comparison between two nonlinear vibrational imaging techniques: stimulated Raman scattering (SRS) and balanced detection Raman‐induced Kerr effect (BD‐RIKE). Using a compact fiber‐based laser system for generation of pump and Stokes signals, we image polymer beads as well as human hepatocytes under the same experimental conditions. We show that BD‐RIKE, despite the slightly lower signal levels, consistently offers an improved signal‐to‐noise ratio with respect to SRS, resulting in significantly higher image quality. Importantly, we observe that such quality is not affected by the static birefringence of the sample, which makes BD‐RIKE a robust and attractive alternative to SRS. We also highlight a unique advantage of the technique, which is its capability to easily access both the real and imaginary parts of the nonlinear susceptibility, thus allowing for vibrational phase imaging. The phase information can be readily obtained from BD‐RIKE with minimal experimental effort and provides an additional chemical selectivity channel for coherent Raman microscopy. Copyright © 2014 John Wiley & Sons, Ltd.     

Quasimolecular nuclear optical potentials

A theory is presented to calculate potentials for the elastic nuclear heavy-ion scattering in a phenomenological way. The density properties of finite nuclei are derived with a schematic ansatz for the interaction energy between nuclear matter. The same interaction energy is applied to the calculation of the real part of the heavy-ion potential, which is of the quasimolecular type. The imaginary part is connected with the outflow time of nuclear matter out of compressed regions of overlapping nuclei. The resulting cross section for the elastic O¹⁶-O¹⁶ scattering reproduces the experiment up to 30 MeV quite well. An effective compression modulus of the S³² compound system can be deduced from the scattering experiment. It results to be about 200 MeV.