Effective probabilities in a new approach to analyzing angular distributions in elastic heavy-ion scattering

A new approach proposed previously to analyze angular distributions in elastic heavy-ion scattering is generalized to cases where total partial probabilities (that is, those that are summed over all channels) of the enhancement of “fusion” (in general, complete and incomplete fusion, quasifission, and deep-inelastic collisions) are commensurate with the total partial probabilities of the suppression of “fusion.” This could be done with the aid of effective total partial probabilities, each of these being defined as a linear combination of actual total partial probabilities. It is shown that the probabilities introduced in this way have a specific physical meaning. Indeed, the effective total partial probabilities make it possible to calculate the cross section for “fusion” through the entrance channel and some reference total cross sections for peripheral processes, and a conclusion on whether fusion and peripheral reactions are enhanced or suppressed can be drawn from a comparison of the calculated or measured results for, respectively, the fusion cross section and the total cross section for peripheral reactions with the above two cross sections. It is also found that the enhancement of fusion is accompanied by the suppression of peripheral reactions, and vice versa.     

Incomplete fusion reactions

A review of incomplete fusion reactions is given. The localization of the entrance chanel angular momentum window is discussed for incident energies lower than 10 MeV per nucleon and is found to depend on the target deformation. With deformed target “peripheral” collisions are observed with ? values in the vicinity of ?_cr for complete fusion, while for spherical targets, the ? window is centered around values lower than 0.5 ?_cr. These properties are discussed on the grounds of available theoretical models. All other properties of the reactions such as cross sections, angular distributions, shape of the energy spectra of light ejectiles are discussed to bring additional informations about the reaction mechanism.     

Elastic scattering of35Cl from27Al,58, 62Ni,116, 120, 124Sn and141Pr

Elastic scattering angular distributions for³⁵Cl from²⁷Al,^{58, 62}Ni,^{116, 120, 124}Sn and¹⁴¹Pr have been measured at energies between 100 and 170 MeV. Optical model analyses have been performed to determine reaction cross sections, strong absorption radii and grazing angular momenta. The results are compared with the corresponding quantities extracted by means of the Fresnel scattering model. Near the interaction barrier the quarter point method yields reaction cross sections systematically smaller than the optical model results. The interaction radii, however, do not show significant differences or energy dependencies. These radii are compared with trend formulae for interaction radii, and comparisons with fusion radii are made.     

The influence of precritical scattering on inclusive proton production in relativistic central nuclear collisions

By use of the improved version of our model of transport theory, the effect of precritical scattering on the inclusive cross section for protons produced in central nucleus-nucleus collisions at 800 MeV/N is studied. As a result, we find an enhancement of the inclusive cross section at high transverse momenta by nearly a factor of two, and angular distributions which are more isotropic than for the case without precritical scattering. These features are consistent with the results of a previous investigation of impact parameter integrated inclusive cross sections.     

Competition between inertial and PEP emission in incomplete fusion reactions

We present here a new mechanism of inertial emission of fast particles in incomplete fusion reactions. Analytical formulae for the cross section and the angular momenta associated to these inertially emitted particles (IEP) are derived within some approximations. In a more realistic calculation it is shown that there is a strong competition between this inertial emission and the PEP emission [15], depending crucialy on the interaction between the particle and the target nucleus. Using a proximity potential for this interaction, one gets numerical results in good agreement with experimental data.     

质子滴线核8B的实验研究进展

质子滴线核8B的最后一个质子的分离能只有0.137 5 MeV,被认为是最有可能具有质子晕结构的候选核之一,对其反应机制和奇特结构的研究吸引了人们的关注。针对8B的奇特结构和反应机制研究是一个非常有趣的课题,研究人员在包括反应截面、碎裂产物动量分布宽度、电四极矩、熔合截面及弹性散射等方面开展了大量的工作。但是8B的研究至今仍不够充分,需要从理论和实验上对其进行更深入的研究。     

离线γ技术测量重离子熔合复合核平均角动量

使用离线γ测量技术在质心系25.0—40.5MeV的能区测量了¹²C+⁹³Nb熔合反应产生的二中子和三中子蒸发道的激发函数。由于在相同的激发能下,蒸发道的相对截面比与复合核的角动量有很强的依赖关系,应用统计蒸发程序(CASCADE),从二中子和三中子蒸发道的截面中提取不同能量下的复合核平均角动量和熔合截面。同时从能很好地拟合熔合激发函数的简单耦合道模型(CCFUS)计算中提取复合核的平均角动量。两种方法得到的复合核平均角动量随入射能量的变化相自洽,表明耦合道模型 关键词：     

Opposite sign dimuon events produced in narrow band neutrino and antineutrino beams

On the basis of 315 dimuon events of opposite sign for which the nature (and energy) of the incident neutrino is known, and the momenta and hadronic shower energy are measured, we find a) very similar production by neutrinos and antineutrinos, and therefore confirmation of the GIM model for semileptonic weak interactions, b) energy spectra, excitation functions, angular correlations and transverse momentum distributions which are in remarkable agreement with the hypothesis of charm production and decay, c) evidence against models for which the second muon has a heavy lepton as origin, d) evidence against “bottom” quark production by antineutrinos, e) the amount and the structure function for the strange quark-antiquark sea, and f) an approximate branching ratio, of 0.15 for the muonic decay of the semistable charmed meson.     

Elastic scattering of 11B from 209Bi in the energy range 49.8 ⩽ E ⩽ 84.1 MeV

The elastic scattering of ¹¹B from ²⁰⁹Bi has been measured at laboratory energies of 49.8, 51.3, 52.2, 52.8, 54.3, 55.8, 59.8, 64.8, 69.8, 74.8 and 84.1 MeV. These data have been analyzed using a microscopic optical model and the energy dependence of the real and the imaginary parts of the optical potential at near barrier energies has been determined. The “threshold anomaly” observed in the real part of the potential is found to be consistent with the dispersion relation which connects the real and the imaginary parts of the potential. Inelastic scattering and transfer reactions have also been measured at energies of 51.3, 55.8, 59.8 and 74.8 MeV. DWBA calculations for the 3⁻ state in ²⁰⁹Bi are made. From the measured transfer probabilities, using a semiclassical approach the strength of the form factors have been obtained. The fusion cross sections have been derived at these energies from the corresponding quasi-elastic scattering angular distribution data. The fusion cross sections calculated using the energy dependent barriers extracted from the energy dependent real parts of the potential compare well with, that determined from quasi-elastic scattering data and are also in good agreement with simplified coupled channels calculation for fusion incorporating important inelastic and transfer channels.     

Effect of electron and γ polarization on two-photon bremsstrahlung of electrons in a nuclear field

The cross section for two-photon bremsstrahlung is integrated over the electron scattering angle and the (common) emission angle of the bremsstrahlung photons. Equations are found for the energetic, angular, and polarization distributions of the cross section. The cross section for two-photon bremsstrahlung for the case in which the momenta of the bremsstrahlung photons are parallel can be larger than the corresponding Bethe-Heitler cross section. The probabilities for certain polarization states of the electrons are also analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 13–18, July, 1972.     

Energy dependence of optical-model parameters for the interaction of 6Li and 7Li Ions with 28Si nuclei at low energies

The results of a joint analysis of experimental data (angular distributions for scattering and total reaction cross sections) are presented for the case of the interaction of ^6,7Li ions with ²⁸Si nuclei at energies between 7.5 and 32 MeV. The respective calculations were performed on the basis of a deformed potential of the optical model by using the SPI-GENOA code. The energy dependences of the parameters of the macroscopic optical model and the total cross section for the (^6,7Li+²⁸Si) reactions were obtained over the energy interval from 7.5 to 32 MeV. The calculated angular distributions and total reaction cross sections are in good agreement with experimental data.     

Theoretical Calculations and Analysis of n+208Pb Reaction for Intermediate Energy Neutron

Based on experimental data of total, nonelastic, elastic cross section and elastic scattering angular distributions for n+Pb reactions, a set of neutron optical model potential parameters is obtained in the region of incident neutron energy from 1—300 MeV. The cross sections, angular distributions and energy spectra are calculated and analyzed by optical model, distorted wave Born approximation theory, Hauser-Feshbach theory, exciton model and cascade mechanism inside nuclear. The results indicate that the cross sections can be given for n+ ²⁰⁸Pb reactions which are all in good agreement with experimental data.     

Simple algorithm for quantitative analysis of reflection electron energy loss spectra (REELS)

A detailed comparison of two different physical approaches for quantitative analysis of reflection electron energy loss spectra (REELS) is presented. The Tougaard–Chorkendorff (TC) algorithm [S. Tougaard, I. Chorkendorff, Phys. Rev. B35 (1987) 6570] is analyzed theoretically and applied to experimental spectra of four elemental solids (Si, Cu, Ag, and Au). A closed expression is derived for the quantity retrieved by the TC-algorithm, the so-called “effective” cross section, which was originally only given as a recursive procedure. Single scattering loss distributions are derived from the experimental spectra using the bivariate reversal method [W.S.M. Werner, Phys. Rev. B74 (2006) 075421]. The latter agree satisfactorily with density functional theory (DFT) calculations and other data found in the literature. Using these single scattering loss distributions, the TC “effective” cross section can be perfectly reproduced if the fact is taken into account that the effective cross section is not a single scattering loss distribution and is governed to a significant extent by elastic scattering. On the basis of the above results, a dramatically simplified deconvolution scheme for quantitative analysis of REELS is developed.     

Nonrelativistic dyon-dyon scattering

The nonrelativistic problem of the scattering of two dyons (including the case of electron scattering by magnetic monopoles) is systematically studied, both classically and quantum mechanically, with a view toward the discrimination between various combinations of electric and magnetic charges. We analyze the classical cross section with particular attention to the interesting phenomena which occur for large angle scattering, the “rainbows” and “glory,” where the cross section becomes infinite. Quantum mechanically, we find that these infinities do not occur and that, when the partial wave scattering amplitude is summed, a very elaborate structure emerges for the cross section, which depends sensitively upon the electric and magnetic charges of the particles, as well as on their relative speed. We further discuss a large modification, leading to spin flip and nonflip amplitudes, due to the dipole moments of the particles. Numerical results are presented for a variety of values of these parameters. In principle, these results could be used to distinguish the δ-ray distributions produced by the various species of electrically and magnetically charged particles. Quite apart from the experimental implications of our numerical results, we have made a number of theoretical improvements and extensions. Numbered among these are the consideration of dyons and particles having dipole moments, and the explicit demonstration, based on the methods of angular momentum, that the differential cross section is independent of the choice of singularity line.     

The competition between fusion-fission and deeply inelastic reactions in the medium mass systems

The competition between fusion-fission and deeply inelastic reactions in the Cl + Ni system has been studied by investigating the exit channelQ-value dependence of theZ-distributions of fission-like fragments. TheZ-, kinetic energy- and angular distributions of the fission-like fragments produced in the³⁷Cl +⁶⁴Ni system atE _lab=170, 186 MeV and in the²⁸Si +⁷⁴Ge system atE _lab=176 MeV have been measured by counter telescopes. TheZ-distribution of the³⁷Cl +⁶⁴Ni system was found to be essentially the same as that of the³⁵Cl +⁶²Ni system at the same bombarding energy. It is shown that this result can not be explained by the statistical fusion fission model but is consistent with a deeply inelastic model. A systematic study of the fission-like phenomenon in this mass region indicates that the maximum angular momenta for fusion reactions as well as the minimum angular momenta for DIC can be reproduced by the Bass model in the sliding limit (f=1.0) while the maximum angular momenta for fully energy-damped deeply inelastic reactions are governed by the strong interaction radius as predicted by the successive critical distance fusion model. The significance of these results are discussed.Communicated by V. Metag     

Near-barrier transfer in16O +144, 154Sm

The production of nitrogen and carbon fragments in the reactions induced by¹⁶O on¹⁴⁴Sm and¹⁵⁴Sm targets was studied at two bombarding energies (65 MeV and 72 MeV) around the interaction barrier. The measured angular distributions exhibit the characteristic behaviour of direct transfer reactions, and theQ-value spectra are typically centered at the values predicted by kinematic selectivity. The comparison between fusion and charged-particle transfer cross sections shows that whereas fusion is the most important process at the highest bombarding energy, transfer reactions become comparable or even dominant (as in the¹⁴⁴Sm case) at near-barrier energies. The different transfer probabilities observed for the two systems are analyzed in terms of nuclear deformation.     

中子与裂变核238U反应双微分截面的理论分析

根据中子与原子核U及其同位素反应的总截面,去弹性散射截面和弹性散射角分布的实验数据,获得了入射中子能量0.1—20MeV的一组普适中子与U及其同位素反应的光学模型势参数.应用光学模型,核裂变理论,耦合道理论,扭曲波玻恩近似理论,宽度涨落修正的Hauser-Feshbach理论和预平衡反应的激子模型,计算和分析了中子与²³⁸U反应的所有截面、角分布、能谱和双微分截面.理论计算与实验数据进行了分析比较     

Large-angle scattering of heavy ions: (I). General structure of elastic cross section

Closed-form expressions are derived for the differential cross section of elastic heavy-ion scattering at large angles. The derivation is based on the general form of the elastic partial-wave S-matrix in real l-space. By a generalization of analytic techniques developed in earlier work, it is shown that the large-angle scattering cross section has a universal structure involving combinations of Bessel functions and the Fourier transforms of the rapidly varying parts of the S-matrix, irrespective of their dynamical origin. Anomalous large-angle scattering is attributed to deviations of the S-matrix from its “normal strong-absorption profile”, and general conditions for backward-angle enhancement are given. Our model-independent formulation provides the framework for an “inductive” method of analyzing experimental angular distributions and excitation functions aimed at identifying, as uniquely as possible, the dynamical mechanisms that operate in large-angle heavy-ion scattering. Extensions of the formalism to inelastic scattering and transfer reactions, and applications of the analytic method, will be described in subsequent papers.     

中子与52Cr反应截面的理论分析

根据中子与天然核Cr及其同位素反应的总截面,去弹性散射截面和弹性散射角分布的实验数据,获得了入射中子能量从1MeV—250MeV的一组普适中子与Cr及其同位素反应的光学模型势参数.应用光学模型,扭曲波玻恩近似理论,宽度涨落修正的Hauser-Feshbach理论,和预平衡反应的激子模型,计算和分析了中子与⁵²Cr反应的所有截面、角分布、能谱和双微分截面.理论计算与实验数据进行了分析比较.     

Evidence of incomplete relaxation in the reaction Ag+40Ar at 288 and 340 MeV bombarding energies

The particles emitted in the reaction induced by ⁴⁰Ar on natural Ag at 288 and 340 MeV bombarding energy have been studied. The fragments have been identified in atomic number, their kinetic energy distribution and their angular distributions have been measured. The kinetic energy spectra show two components: a high-energy component related to the beam energy, or “quasi-elastic” component, and a low kinetic energy component, close to the Coulomb energy called “relaxed” component. The relaxed component is present at all angles and for all particles. The quasi-elastic component is present close to the grazing angle for atomic numbers close to that of the projectile. The relaxed cross section increases with atomic number for Z > 9. The increase in cross section is sharper for the lower bombarding energy. The angular distributions are forward peaked, in excess of $\text{1}\text{sin}\text{θ}$ for all the measured atomic numbers. The forward peaking is larger for particles close in Z to the projectile. The results are interpreted in terms of characteristic times associated with a short-lived intermediate complex. The cross sections and angular distributions are satisfactorily reproduced on the basis of a model accounting for a diffusion process occuring along the mass asymmetry coordinate of the intermediate complex.