An interaction potential for heavy-ion scattering

The long-range part of the nucleus-nucleus interaction is taken to be given by folding the density distribution of one nucleus with the real part of the single-nucleon optical potential of the other. Analytic approximations are derived for the folded potential and its derivative in the case where the density distribution and single-nucleon optical potential have Saxon-Woods form factors of equal surface thickness. The approximations are generalised to the case of different surface thicknesses and are compared with a previous parametrisation due to Broglia and Winther. The variation with mass number of the central density of the Saxon-Woods matter distribution required to obtain the correct normalisation is shown to be large and an expression for the variation is given. Some calculations are performed on various elastic scattering data using the “quarter-point recipe” of Frahn's diffraction theory. The parameters required to fit the quarter-points of the elastic cross sections are shown to be consistent with their accepted values. It is shown, however, that the quarter-point recipe leads to a larger radius for ²⁰⁸Pb than for ²³²Th. The positions and heights of the pure Coulomb barrier (L = 0) are evaluated for various nuclei. The barrier radii are found to be sufficiently large to suggest that an interaction of the folded type should be reasonable in this region.     

三维光晶格中玻色凝聚气体基态波函数及干涉演化

基于Gross-Pitaevskii方程，运用有效化学势概念，研究了囚禁在组合势(由磁阱和三维光 晶格组成)中玻色凝聚气体在三维光晶格中的分布规律，并由此得到玻色凝聚气体的归 一化基态波函数.在取消组合势和仅取消光晶格而保留磁阱的两种情况下，运用传播子方 法求解出玻色凝聚气体密度分布的解析表达式.取消组合势后，理论计算所得到的玻色凝聚 气体聚随时间的演化规律与Greiner等的实验结果相一致.仅取消光晶格而保留磁阱时，研 究表明玻色凝聚气体的干涉模式呈现周期性的振荡行为.此外，在磁阱为各向异性的情况下 ， 关键词： 玻色凝聚气体 磁阱 光晶格 干涉模式     

Calculation of error probability in an optical communication channel in the presence of intersymbol interference,using a characteristic function method

In this paper the error rate of an optical channel is calculated. The channel considered consists of a laser or light emitting diode as the optical source and a glass fibre as transmission medium. The transmitted optical pulses are spread in the fibre causing intersymbol interference. The receiver is assumed to be an avalanche photodiode which is considered as a p-n junction and a random multiplier whose electron probability distribution function is known, and a filter. In calculating the probability of error, their characteristic functions are multiplied and the probability density function of all the noises put together is truncated to a finite interval and described in a trigonometric series form. The total characteristic function is related to the Fourier coefficients of the periodic probability density function, resulting in an expression that is then used, for a given bit rate, to determine the worst case and average probability of error as functions of transmitted power or signal-to-noise ratio, for different amounts of intersymbol interference.     

Microscopic study of ~7Li-nucleus potential

A microscopic approach is employed to study the optical potential for the 7Li-nucleus interaction system without any free parameters.It is obtained by folding the microscopic optical potentials of the constituent nucleons of 7Li over their density distributions.We employ an isospin-dependent nucleon microscopic optical potential,which is based on the Skyrme nucleon-nucleon effective interaction and derived using the Green's function method,as the nucleon optical potential.The harmonic oscillator shell model is used to describe the internal wave function of 7Li and obtain the nucleon density distribution.The 7Li microscopic optical potential is used to predict the reaction cross-sections and elastic scattering angular distributions for the target range from 27Al to 208Pb and energy range below 450 MeV.Generally,the results can reproduce the measured data reasonably well.In addition,the microscopic optical potential is comparable to a global phenomenological optical potential by fitting the presently existing measured data.     

Multipole structure of static continuous matter distributions in general relativity

A mass skeleton is defined for a static extended body in a gravitational field. It is a scalar-valued distribution on a tangent space, and is equivalent to that part of the reduced multipole moment structure which describes the mass density of the body. An explicit form is given for this distribution in terms of the mass density and the scalar potential of the field. It is deduced that the mass skeleton and the scalar potential are not completely independent. The smoothness of the mass distribution imposes certain weak restrictions on those scalar potentials which are compatible with a given mass skeleton.Dedicated to Achille Papapetrou on the occasion of his retirement.     

On the nuclear matter approach to the heavy-ion optical potential

A simple theory of the heavy-ion optical potential oV, based on the local density approximation, is presented. The colliding ions are described locally as two slabs of nuclear matter. The real part of the energy density of the two slabs is derived from the properties of nuclear matter, and for the imaginary part the “frivolous model” is applied. Results for oV in the case of two slabs are presented and compared with results of other calculations. Arguments are given in favour of using the frivolous model in the optical potential and the VUU calculations for heavy-ion collisions.     

Detection of nano-interfacial space charge field at metal–organic film interface by SHG and surface potential

At the metal–organic film nano-interface, surface polarization phenomena are observed, due to the displacement of excess charges from metal to the films as well as alignment of polar dipoles. Surface potential method has been employed to examine these surface polarization phenomena, and the distribution of space charges and distribution of electronic density of states have been determined. However, for further understanding of the nanometric interface phenomena, it is very helpful to develop an experimental method that can detect electrical and optical phenomena induced by the space charge formation. In this paper, it is shown that optical second harmonic generation measurement is effective through our experiment on phthalocyanine films deposited on Al and Au electrodes.     

Electron-acceptor luminescence from a non-Maxwellian distribution of photoexcited electrons in GaAs

Distribution functions are calculated for photoexcited electrons in GaAs, under conditions of continuous, monochromatic excitation. The lattice temperature is taken to be 1.2 K and the excitation intensity such that the density of photoexcited carriers is insufficient for the distribution to be affected by intercarrier scattering. A Boltzmann equation approach is used to take account of the effects of, injection of electrons into the conduction band, at an energy below the threshold for longitudinal optical phonon emission, scattering by acoustic phonons, via the deformation potential and piezoelectric interactions, and recombination. The equation is solved numerically using an iterative technique and the distribution functions are found to differ significantly from a Maxwellian form. Emission spectra due to conduction band to neutral acceptor transitions are derived from the computed distribution functions and are compared with recent experimental results.     

The nuclear self-energy and related quantities in the semiclassical approximation

By using our recently developed semiclassical model for the imaginary part of the optical potential, we calculate here the polarization and correlation contributions to the real part via the dispersion relation. As underlying nonlocal mean-field potential, the semiclassical Hartree-Fock potential evaluated with the Gogny D1 effective interaction or the Perey-Buck potential is employed. With this full self-energy or second-order mass operator we calculate consistently depths, radial dependence and volume integrals of the single-particle potential, rearrangement energies and effective masses, the momentum distribution, mean free paths of a nucleon in a nucleus, and single-particle level densities. We obtain depths which are in excellent agreement with experiment including the Fermi anomaly: the effective mass exhibits a strong bump at the Fermi and the nuclear surface and the single-particle level density at the Fermi energy is enhanced by 65% yielding almost the correct average experimental value.     

Nuclear matter approach to the heavy-ion optical potential

An energy-dependent local potential for heavy-ion (HI) scattering is derived from Reid's softcore interaction using the Brueckner theory. The Bethe-Goldstone equation in momentum space is first solved with the outgoing boundary condition for two colliding systems of nuclear matter with the relative momentum K_r per nucleon. The Fermi distribution is assumed to consist of two spheres without double counting of their intersection separated by the relative momentum K_r. The angle-averaged Pauli projection function is given in the form of a one-dimensional integral. Secondly the optical potential for HI scattering is evaluated using the energy-density formalism. The energy density is calculated for two limiting cases: (i) the sudden approximation in which the spatial distribution of the two HI is described by an antisymmetrized cluster wave function, and (ii) the adiabatic limit represented by an antisymmetrized two-centre wave function. The complex HI potential is defined in terms of the energy density from nuclear matter so that both volume elements in the finite and the infinite systems have the same nucleon and kinetic energy density. This method is applied to the ¹⁶O + ¹⁶O, ⁴⁰Ca + ¹⁶O, and ⁴⁰Ca + ⁴⁰Ca potentials. The calculated results are compared with phenomenological potentials. Though in principle our approach can generate an imaginary part for the HI potential, the magnitude is too small. Reasons and possible improvements of this point are discussed.     

双折叠模型对相互作用势实部的计算

用双折叠模型计算了核核碰撞的相互作用势, 其中核子-核子相互作用势采用M3Y-Reid和M3Y-Paris形式, 交换部分考虑了有限力程的密度依赖的核子-核子相互作用, 程序用于重离子散射光学势实部的计算. 回顾了折叠模型的普遍特征和讨论了理论计算过程, 对各种类型的核子-核子相互作用下计算的相互作用势进行比较, 发现双折叠模型对大部分系统相互作用势的实部取得了满意的结果. 因此这个工作为重离子相互作用势的折叠计算提供了很好的方法.     

α-Cluster Optical Potential Model of <Superscript>40</Superscript>Ca

Elastic scattering of α + ⁴⁰Ca is analyzed in the framework of the optical model. We adopted an independent α-cluster model to generate the α-cluster and matter density of ⁴⁰Ca. We proposed a parametrized form for the α-cluster density and fixed its parameters according to the available experimental data about the α-particle and ⁴⁰Ca nuclei. The obtained α-cluster density of ⁴⁰Ca is used to generate the real part of the optical potential. The single folding procedure is used to generate this real optical potential with two different effective α–α interactions. The real calculated potential supplied with an imaginary Woods–Saxon squared potential is used to analyze 20 sets of experimental data in the energy range between 18 and 166 MeV. We found that our model is successful in reproducing the data for energies above 40 MeV and still doubtful for lower energies.     

Theory of kaonic atoms

A nonlocal energy-dependent self-consistent kaon-nucleus optical potential is derived for kaonic atoms. Energy level shifts and widths are calculated for several light nuclei, and the results are compared with experiment. The sensitivity of the results to changes in parameters of the nuclear matter distribution is studied. Nonlocality and off-energy-shell effects are examined.The optical potential is derived by means of a Brueckner-type many-body theory with the independent pair approximation for the kaon and the nucleon. The two-body interaction on which the optical potential depends is represented by separable potentials of the Yamaguchi form. Coupled channels ($\text{K}\text{N}$ and Σπ) are used for the I = 0 states, which are dominated by the $\text{Y}{}_0{}^1$ resonance, and only a single channel ($\text{K}\text{N}$) is used for the I = 1 state.Calculations are carried out in three levels of approximation of the nonlocal energy-dependent optical potential. In no approximation is the potential found to be proportional to the nuclear density. Indeed, the real part of the potential changes sign in the nuclear surface. Sensitivity of the results to variations in the nuclear matter distribution is investigated and found to be on the order of experimental error. Nonlocality and off-energy-shell effects are estimated to be at least as large as this error, so that these effects must be included if one wishes to extract information about the nuclear surface from the existing experimental data. The use of correct nucleon wavefunctions and binding energies is similarly found to be essential in the calculation.     

一种新颖的表面空心微光阱阵列

提出了采用四台阶相位光栅与微透镜阵列组合产生一种新颖的表面空心微光阱阵列的方案，研究了表面空心微光阱阵列的光强分布，计算了相应的光学囚禁势，并讨论了该微光阱阵列在原子分子光学中的潜在应用.研究表明当用1W的YAG激光照射时，在1cm²面积上可产生近10⁴个空心光阱，每个光阱具有较小的囚禁体积和较大的有效光强及其强度梯度，对⁸⁵Rb原子的光学囚禁势可达190μK.如此深的光阱足以囚禁冷原子或冷分子，并可用于实现全光型原子或分子玻色-爱因斯坦凝聚，甚至制备新颖的光学晶格等. 关键词： 空心光阱 冷原子或冷分子 光学晶格     

Approximate solutions of the Liouville equation. II. Stationary variational principles

Stationary variational functionals for the Laplace transform of the Liouville distribution are constructed. The value of the functional is the autocorrelation function that one wishes to compute. It is shown that the functionals may be transformed to a renormalized form. Trial functions not involving the potential explicitly give rise to time-dependent autocorrelation functions determined only by equilibrium spatial correlation functions. Another class of functionals is constructed by independently varying the parity symmetric and antisymmetric parts of the distribution function. Trial functions need only be assumed for one of these—the optimum value of the other one is given exactly. This procedure is used to improve the simplest known theories for velocity and density autocorrelation functions.Work supported by a grant from the National Science Foundation.     

On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids

It is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density. We derive the explicit form that the functional takes for a system of hard rods, and propose an approximate one for hard spheres. Attractive interactions are also considered in mean-field approximation. In all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated.     

On the stability of neutron matter calculations

The problem of the stability of usual Hartree-Fock calculations of neutron matter with effective two-body interactions is investigated by using the second order variational equations. Sufficient conditions for instability are derived, which can be checked easily for a given effective potential. Numerical calculations are performed and neutron matter is found to be unstable against density fluctuations.     

Energy dependence of the rotational enhancement factor in the level density

The one-shell SU(3) energies are given and the corresponding level density is calculated approximately by use of a distribution function for the SU(3) quantum numbers. The calculation is extended to include many shells by a renormalization procedure and an effective one-shell interaction. The traditional level density is then obtained from the related mean-field hamiltonian which corresponds to a deformed harmonic oscillator potential. Various rotational enhancement factors are considered. Numerical results, are obtained and comparisons between the SU(3) and the traditional level densities allow the first computation of the energy dependence of the rotational enhancement factor. A transition from axial to spherical level density is found. A simple parametrization is suggested in terms of a deformation-dependent half-value energy and a transition width.     

First- and second-order statistics of partially coherent, high-numerical-aperture optical fields

The intensity probability distribution as well as the cross-spectral density of partially coherent optical fields generated through high-numerical-aperture illuminations are analyzed, and novel effects, not apparent in paraxial optical fields, are described. It is shown that the intensity probability distribution significantly differs from what can be expected from a small-angle analysis, and the number of degrees of freedom for the distribution is higher. It is further shown that the cross-spectral density of a high-angle optical field is a function of the coordinate difference along the propagation direction of the field.