Inelastic proton scattering to the lowest 1+ state in58Ni

A microscopic, antisymmetrized Distorted Wave approximation is used in an analysis of the inelastic scattering of 17.8 MeV protons from⁵⁸Ni in which the 1⁺ (2.90 MeV) state is excited. Two step resonance amplitudes complement the usual direct reaction transition amplitudes in this analysis. In particular, resonance amplitudes associated with the virtual excitation of a giant dipole and of a giant octupole resonances are considered, and are essential for the model to fully explain the experimental data.     

Muffin‐tin potentials in EXAFS analysis

Muffin‐tin potentials are the standard tool for calculating the potential surface of a cluster of atoms for use in the analysis of extended X‐ray absorption fine‐structure (EXAFS) data. The set of Cartesian coordinates used to define the positions of atoms in the cluster and to calculate the muffin‐tin potentials is commonly also used to enumerate the scattering paths used in the EXAFS data analysis. In this paper, it is shown that these muffin‐tin potentials are sufficiently robust to be used to examine quantitatively contributions to the EXAFS data from scattering geometries not represented in the original cluster.     

Inelastic shadowing effects in multiple scattering

The projectile-nucleon scattering amplitudes used as input into multiple scattering theories of projectile-nucleus scattering naturally include the effects of coupling to inelastic (i.e., production) channels. We employ a multichannel separable potential to describe the projectile-nucleon interaction and show that within the fixed nucleon framework we can obtain the nuclear elastic scattering amplitude. This includes terms outside the conventional formalisms, corresponding to intermediate propagation in the inelastic channels both above and below inelastic threshold. We refer to this as inelastic shadowing. In a two-channel approximation, we show that knowledge of the projectile-nucleon elastic scattering phase shifts plus specification of the inelastic threshold energy are sufficient to determine the off-shell coupled-channel transition matrix, implying that the nuclear amplitude can be calculated within this model without any detailed information about the inelastic channels. We study this solution quantitatively for some model problems and for pion scattering, with the general result that inelastic shadowing can be significant whenever the elementary interaction has important channel coupling. For pion scattering in the energy regime characterized by strongly absorptive resonances, we find, for example, that the effect of inelastic shadowing is much more important than that due to two-nucleon correlations.     

46.8MeV的p+12C非弹性散射

在Glauber多重散射理论框架下，使用跃迁密度方法和三种N湮没势，计算了46.8MeV的反质子在¹²C上的非弹性散射微分截面. 理论曲线与实验数据符合得较好. 关键词： Glauber理论 反质子 非弹性散射 湮没势 跃迁密度     

Two-component description of dynamical systems that can be approximated by solitons: The case of the ion acoustic wave equations of plasma physics

A new approach to the perturbative analysis of dynamical systems, which can be described approximately by soliton solutions of integrable non-linear wave equations, is employed in the case of small-amplitude solutions of the ion acoustic wave equations of plasma physics. Instead of pursuing the traditional derivation of a perturbed KdV equation, the ion velocity is written as a sum of two components: elastic and inelastic. In the single-soliton case, the elastic component is the full solution. In the multiple-soliton case, it is complemented by the inelastic component. The original system is transformed into two evolution equations: An asymptotically integrable Normal Form for ordinary KdV solitons, and an equation for the inelastic component. The zero-order term of the elastic component is a single-soliton or multiple-soliton solution of the Normal Form. The inelastic component asymptotes into a linear combination of single-soliton solutions of the Normal Form, with amplitudes determined by soliton interactions, plus a second-order decaying dispersive wave. Satisfaction of a conservation law by the inelastic component and of mass conservation by the disturbance to the ion density is determined solely by the initial data and/or boundary conditions imposed on the inelastic component. The electrostatic potential is a first-order quantity. It is affected by the inelastic component only in second order. The charge density displays a triple-layer structure. The analysis is carried out through the third order.     

Theory of nuclear reactions and decays with allowance for antisymmetrization effects

On the basis of an explicit implementation of the projection-operator method and with due regard to antisymmetrization effects, formulas are constructed for the amplitudes of elastic and inelastic nuclear reactions induced by nucleons and composite particles and for the widths with respect to the nucleonic, alpha-particle, and cluster decays of nuclei. It is shown that equations governing the behavior of elastic-scattering form factors represent generalizations of the equations of the resonating-group model and coincide, provided that ground-state correlations are taken into account, with the analogous equations in the theory of open Fermi systems. It is demonstrated that the nonretarded part of the effective potential of nucleus-nucleus interaction coincides with the Hartree-Fock potential, which has a deep attractive character in accordance with the Levinson theorem, and that the retarded part of the effective potential is determined by the fragmentation of the initial states of colliding nuclei into compound states. It is revealed that the use of different elastic-form-factor representations associated with taking into account antisymmetrization effects leads to the same results for the amplitudes of elastic and inelastic nuclear reactions. The formulas obtained here for the amplitudes of direct inelastic nuclear reactions are found to differ significantly from the corresponding formulas of the distorted-wave method in the Born approximation. Problems that are concerned with the emergence of potential optical resonances for elastic form factors and with their relation to the shell-model wave functions for a compound system are investigated. A new regime of interpolation for the amplitudes of cluster form factors from the shell to the asymptotic region of a decaying nucleus is found. Implications of this interpolation for the calculated alpha-particle and cluster widths and for understanding the nature of superfluid correlations in nuclei are analyzed.     

Extended X-ray-absorption fine structure of mixed-coordination systems

An analysis method of the extended x-ray absorption fine structure (EXAFS) for mixed-coordination systems (MCS) is provided to determine structure parameters of the same type of atoms located at different coordination sites and proportion of them. It's demonstrated that if the effects of different sites on EXAFS amplitudes are ignored, the coordination numbers gotten from EXAFS analyzing must be wrong mostly. The method has been well tested by analyzing a known structure Gd₃Ga₅O₁₂ (GGG) crystal in which the Ga atoms have two different coordination sites. Li₂O-ZnO-GeO₂ glass system is also analyzed by means of the EXAFS method for MCS. Two different coordination sites for Ge atoms in the glasses. are found and the occupancies of them and the structure parameters are determined.     

Peculiarities of the correlation functions, X-ray and neutron scattering in BaTiO3

Based on molecular-dynamics (MD) simulations, we have calculated the static and dynamic correlation functions in a BaTiO₃ crystal. The static correlation functions have been used to study the peculiarities of diffuse scattering in barium titanate showing the experimentally observed anomalous planes. Based on time-dependent pair correlation functions, we have calculated the phonon spectra of BaTiO₃ and studied the central peak of inelastic scattering. The phonon frequencies calculated by the MD method agree well with those obtained previously in the quasi-harmonic approximation. We show that the central peak of inelastic scattering is associated mainly with the soft optic mode and has the same symmetry. The large anisotropy in the displacements of atoms in the soft mode allows the presence of peculiarities in both X-ray scattering and EXAFS spectroscopy to be explained. The characteristic shape of the EXAFS spectra is shown to be explained by the quasi-one-dimensional motion of the oxygen ions in the cubic lattice of BaTiO₃. Our calculation of triple correlation functions shows that the titanium atom in the described model oscillates around the cubic cell center. Explaining the experimental data that have caused disagreement about the nature of the phase transition in BaTiO₃ using the developed model gives grounds to treat the phase transition in barium titanate as a displacive one.     

Pressure effects on EXAFS Debye-Waller factor and melting curve of solid krypton

The pressure effects on atomic mean-square displacement, extended X-ray absorption fine structure (EXAFS) Debye-Waller factor and melting temperature of solid krypton have been investigated in within the statistical moment method scheme in quantum statistical mechanics. By assuming the interaction between atoms can be described by Buckingham potential, we performed the numerical calculations for krypton up to pressure 120?GPa. Our calculations show that the atomic mean-square displacement and EXAFS Debye-Waller factor of krypton crystal depend strongly on pressure. They make the robust reduction of the EXAFS peak height. Our results are in good and reasonable agreements with available experimental data. This approach gives us a relatively simple method for qualitatively calculating high-pressure thermo-physical properties of materials. Moreover, it can be used to verify future high-pressure experimental and theoretical works.     

Elastic and inelastic scattering of high-energy particles on the deuteron

The scattering amplitudes on the deuteron at small momentum transfers are described, taking into account the shadow corrections. In the framework of Regge pole theory, the inelastic shadow corrections are expressed in terms of the amplitudes of inelastic processes. The validity limit of the formulae thus obtained is discussed.     

具有交叉对称的李模型下的非弹性振幅

在具有交叉对称的李模型中,写出了非弹性振幅的积分方程组,它们是Omne氏型的。在已知弹性振幅时,这积分方程组是可解的。在适当地写出这方程组时,可证明非齐次项是小的(在某些区域内),因而使解也有取小值的可能。     

Structure of the deformed terms of the rotational-model optical potential (II)

The microscopic optical matrix potential (OMP^m) for rotational nuclei is constructed. The structure of the non-diagonal elements of OMP^m is investigated and compared with the deformed part of the phenomenological optical potential (OMP^p) employed in analyses of nucleon inelastic scattering data. The deformed form of OMP^p relates the real parts of the phenomenological form factors. This relation is shown to be approximately satisfied by the microscopic form factors. It is proved that the decay amplitudes of complicated compound states to similar channels are correlated, which we call the similar channels effect (SCE). Some channels are similar since the rotational states of the target are obtained from the same intrinsic state. The commonly used deformed imaginary part of OMP^p at very low energies (few MeV or Iess) may be justified as being due to the similar channels effect.     

High-energy approach for heavy-ion scattering with excitations of nuclear collective states

A phenomenological optical potential is generalized to include the Coulomb and nuclear interactions caused by the dynamical deformation of its surface. In the high-energy approach, analytical expressions for elastic and inelastic scattering amplitudes are obtained, where all the orders in the deformation parameters are included. The multistep effect of the 2⁺ rotational state excitation on elastic scattering is analyzed. Calculations of inelastic cross sections for the ¹⁷O ions scattered on different nuclei at about tens of MeV/nucleon or higher are compared with experimental data, and the important role of the Coulomb excitation is established. The text was submitted by the authors in English.     

On the structure of planar field theory

Universality of the ω intercept has been recently questioned, on the basis of new and precise high-energy data for theK _L ⁰ total cross-sections and regeneration amplitudes on various nuclei. These data are re-analysed within the framework of Glauber's theory, with special attention to the contribution of inelastic intermediate states. They are shown to be completely understandable using standard values for all parameters, including the ω intercept. The analysis determines the characteristics of inelastic collisions of Kaons in nuclei: the diffractive terms could have been deduced from other sources, but this is the first evaluation of ω-exchange terms in nuclei.     

On the role of indirect processes in the inelastic excitation of low lying 0+ states

Using simple microscopic form factors, we have studied the indirect excitation of low lying 0⁺ states by inelastic scattering through the lowest 2⁺ states in the case of α scattering from ²⁴Mg and ²⁸Si and ³He scattering from ⁴⁶Ti. Scaling amplitudes according to the inelastic scattering and B(E2) data we found that only for α scattering from ²⁴Mg was the indirect excitation small. For the other cases studied, our estimate yields indirect cross sections which were significant in comparison with the data, although this has been well described by the direct one-step process alone. The shape of the indirect cross section may be either strongly oscillatory or flat, depending on the radius of the real optical potential.     

Analysis of Three Annihilation Potential andp+ 12C Inelastic Scattering

The inelastic scattering of antiproton (p_lab=600MeV/c) by ¹²C leading to the excitation of the three normal parity T=0 levels is studied in the framework of Glauber model. The transition densities obtained from fitting to the electron scattering data and the three annihilation potentials derived from analysis of pp scattering data are used in the calculation. The inelastic angular distribution for exciting the three lowest normal parity T=0 states in ¹²C at 4.44MeV(J^π=2⁺), 7.66MeV(J^π=0⁺), and 9.63MeV(J^π=3^-) by 600MeV/c antiproton are calculated by selecting potential parameter suitably. The results are seen to be in fairly good agreement with the available experimental data. The results are given by using the elementary two-body amplitudes comparatively.     

遗传算法在EXAFS谱图解析中的应用

扩展Ｘ射线吸收精细结构（ＥＸＡＦＳ）谱是研究物质原子近邻结构和表面结构的有力工具。ＥＸＡＦＳ谱的解析通常采用标准样品比较法或最小二乘曲线拟合方法。但前者对标样的要求很高，而后者则参数初值难以确定，且结果有时不唯一。本文提出一种ＥＸＡＦＳ曲线拟合的新方法一遗传算法，并对单配位层Ｃｕ样品的ＥＸＡＦＳ谱图进行了解析，取得满意的结果。     

On the neglecting of higher‐order cumulants in EXAFS data analysis

The cumulant expansion is one of the most powerful and useful methods for EXAFS data analysis, in which the higher‐order cumulants allow to consider deviations from a simple Gaussian distribution. In this work, analytical expressions have been derived to show the effects of neglecting higher‐order cumulants in EXAFS analysis by the ratio method. The errors in the best‐fitting procedure owing to the omission of the higher‐order cumulants, as well as of the coordination number, can be determined.     

The effect of compound states on collective-state singularities in the optical potential

From an exact form of the self-energy of a nucleon in a nucleus, which is equivalent to the optical potential, two approximation schemes, which are both based on a weak-coupling picture, are presented. They lead to expressions which can be interpreted physically as the coupling of a dressed single-particle (single-hole) state to the exact particle-hole (particle-particle) propagator. The residues of the many poles of the self-energy are divided into two categories: (i) residues which are distributed statistically, and (ii) residues which vary systematically. The first set is interpreted as compound nuclear structure and its influence on the single particle motion is investigated. The second set leads to intermediate structure. This structure is further investigated within an extension of the random phase approximation where all particle and hole lines are dressed by compound nuclear effects. In this way the spreading width of intermediate resonances, which is found to be the imaginary part of the pole position in the self-energy, is calculated. The escape width for these resonances is obtained by solving the Lippmann-Schwinger equation in which the calculated self-energy appears. This width depends on the structure of the continuum as well as on the residues of the poles of the self-energy. It is shown that these residues are complex, one of the reasons for this being that corrections to the vertex for the excitation of a collective state, appear. The similarity between the complex form factors introduced in the macroscopic model for inelastic scattering and the complex vertex functions above, is discussed. It is also pointed out that the results obtained here may be used in a phenomenological analysis.