Scattemng of 14.1 MeV neutrons from 209Bi

Differential cross sections for the elastic and inelastic scattering of 14.1 MeV neutrons from ²⁰⁹Bi have been measured with a time-of-flight system which had an energy resolution of 650 keV. For elastic scattering from ²⁰⁹Bi, an optical-model analysis gave the best-fit potential parameters. The absolute cross sections for excitation of collective (2.66 and 4.36 MeV) states are reproduced by the results of distorted-wave calculations under the assumption of a core (²⁰⁸Pb) excitation model using deformation parameters obtained from (p, p') reactions.     

165Ho fast neutron cross sections

Total neutron cross sections of¹⁶⁵ Ho were measured from 0.1 to 1.5 MeV with resolutions of ? 2.5 keV. The observed total cross sections varied slowly with energy and displayed no significant structure. Differential neutron elastic and inelastic scattering cross sections were determined at intervals of ?50keV from 0.3 to 1.5 MeV. The inelastic excitation of states in¹⁶⁵Ho at; 98, 214, 371, 460, 517, 586, 712, 824, 995, 1104 and 1143 keV was positively observed with probably identification of several additional states. The observed excited structure and the respective cross sections were correlated with known single-particle and collective states and with excited structure postulated from systematics. The measured cross sections were compared with calculated values based upon spherical and deformed optical-potentials, and compound-nuclear processes. Total cross sections were best described by a spherical potential while the differential elastic angular distributions were better represented by deformed-potential calculations. Resonance interference effects were found small and, at the energies of the present experiments, the contribution of direct processes was not large.     

The scattering of fast neutrons from W184

Neutrons with energies of 0.3 to 1.5 MeV are scattered from W¹⁸⁴. Pulsed-beam fast time-of-flight techniques including a magnetic bunching system are utilized to resolve the elastically scattered neutrons from those inelastically scattered. The differential elastic cross section is measured at 50 keV intervals with an ≈20 keV incident neutron energy spread. The differential cross sections for inelastic scattering resulting in the excitation of residual nuclear levels at 111±5, 365±10, 690±40, 900±25, 1000±30, and 1120±30 keV are determined. In all instances the inelastically scattered neutrons are emitted, within experimental error, isotropically. The experimental results are compared with those obtained in previous work and with the predictions of theory.     

光学模型与ADS靶的反应截面

利用核反应中光学模型理论,对质子入射能量从阈能到450MeV,加速器驱动的洁净核能系统的靶材209Bi、208Pb、202Hg、197Au、184W、181Ta与质子的反应进行了研究.给出了两套与实验数据符合很好的光学势参量;预言了质子与Bi、Pb、Hg、Au、W、Ta的反应截面;对现有的实验数据进行了理论验证.     

Elastic scattering of γ-rays from lead for energies from 0.145 to 1.33 MeV

Differential cross sections for elastic scattering of 889 and 1120 keV γ-rays from lead have been measured at angles ranging from 30° to 150°. These results and previously measured differential cross sections at 145, 279, 412, 662 and 1332 keV are compared with theoretical predictions taking into account Rayleigh scattering, nuclear Thomson scattering, and Delbrück scattering. The Rayleigh amplitudes of the K-shell were obtained from the theory of Brown et al., the amplitudes of the other shells from form factors calculated from relativistic HFS wave functions. Discrepancies are found at 145, 889, 1120 and 1332 keV while the experimental data at 279, 412 and 662 keV are in good agreement with the theory. A discussion of possible explanations and consequences is presented.     

Neutron scattering from Bismuth,Strontium and Sodium at 14.8 MeV

Differential cross sections for the elastic and inelastic scattering of 14.8 MeV neutrons from Bi, Sr and Na have been measured with four neutron detectors participating in a time-of-flight system which had an energy resolution of 900 keV for the incident neutrons. The whole procedure was checked by scattering from carbon. For the elastic scattering of Bi, Sr and Na satisfactory optical-model fits were obtained. The absolute cross sections for excitation of collective states are compared to the distorted-wave theory for direct reactions, and a reasonable agreement has been found. The nuclear deformation parameters are extracted and compared to the values from other experiments.     

Elastic and inelastic scattering of nucleons from 16O

Measurements of differential elastic and inelastic cross sections for neutron scattering from ¹⁶O at incident energies 18 to 26 MeV are presented. In addition to cross sections for neutron scattering differential cross sections for proton scattering up to 66 MeV are described in terms of phenomenological optical model potentials. At 24.5 MeV incident energy inelastic scattering up to 11.5 MeV excitation was measured. The elastic and inelastic compound nucleus contributions were examined. Direct inelastic scattering from the normal parity states was calculated using the DWBA and coupled-channel formalisms. The inelastic scattering cross section from non-normal parity state 2⁻ was calculated using the coupled-channel formalism via multi-step processes. Cross sections due to inelastic scattering from some of the states, which are thought to be members of an excited state rotational band were calculated using both vibrational and rotational approaches and were compared.     

Measurement of the fast neutron scattering and total cross sections of141Pr

The differential elastic neutron scattering cross sections of¹⁴¹Pr were measured at the incident neutron energies of 1.2, 1.7 and 1.9 MeV in the angular range between 25 and 150 degrees. At 1.7 MeV the differential inelastic neutron scattering cross sections corresponding toQ=?1122 keV, and at 1.9 MeV the ones corresponding toQ=?1122, andQ=?1295 keV were also determined. In a transmission experiment, the total cross section was measured between 0.50 and 2.42 MeV. The total and differential cross sections were calculated using the nuclear optical model. The calculated results were compared with the experimental data.     

Neutron total and scattering cross sections of some even Mo isotopes and the optical model

Neutron total cross sections of ⁹²Mo, ⁹⁶Mo, ⁹⁸Mo and ¹⁰⁰Mo were measured at intervals of ? 10 keV from 1.6 to 5.5 MeV with resolutions of ≈ 10 keV. Neutron elastic and inelastic scattering cross sections of these isotopes were measured from 1.8 to 4.0 MeV at intervals of 0.2 MeV. Neutron groups corresponding to the excitation of forty states were identified. The experimental results were examined in the context of optical and statistical nuclear models. It was concluded that the real part of the optical potential includes a term proportional to [(N-Z)/A] and suggested that the imaginary part of the potential was shell dependent with decreasing magnitude as N = 50 is approached. Comparison of measured and calculated inelastic neutron excitation cross sections suggested a number of J^π assignments extending previous knowledge.     

Inelastic excitation and the nucleon optical potential

We study nucleon elastic scattering from targets of ⁴⁰Ca and ²⁰⁸Pb in the presence of inelastic excitation to a fairly realistic set of levels. We suggest a method of averaging over the l-dependence of the trivially equivalent local potentials so as to obtain smooth, surface-peaked potentials which yield cross sections in good agreement with exact results in the forward hemisphere. Only slightly poorer agreement is obtained with potentials from simple, analytical formulae derived from the plane wave approximation. We also briefly compare approximate and exact inelastic cross sections.     

Investigation of fast neutron interaction with235U

The angular distribution of neutrons emitted by elastic, inelastic and fission processes on²³⁵U were measured at the incident neutron energies of 1.5, 1.9, 2.3, 4.0, 4.5, 5.0 and 5.5 MeV using nanosecond time-of-flight technique. The differential elastic scattering cross sections and their angular distributions at all the seven energies are presented. The total elastic scattering cross sections, angle and energy integrated cross sections for the inelastically scattered neutrons in energy bands of 200 keV, fission cross sections and the angular distributions of fission neutrons were extracted at 1.5, 1.9 and 2.3 MeV incident neutron energies. The energy distributions of the prompt fission neutrons and of the inelastically scattered neutrons are given at the incoming neutron energies of 1.5, 1.9 and 2.3 MeV; and the average fission neutron energies and the inelastic neutron evaporation temperatures were also evaluated at these energies.     

The excitation of collective nuclear states by high energy particles

The excitation of collective nuclear states by high energy particles is considered within the framework of the Glauber theory. The approach is based on the adiabatic approximation and expansion of the scattering amplitude in powers of the nonsphericity parameter. The formulae for the excitation cross sections of the rotational and one- and two-phonon vibrational states, as well as the elastic scattering cross section with the collective motion included, are obtained. The effect of nucleon correlations in both elastic and inelastic cross sections is also studied. The theoretical predictions are compared to new data on 1 GeV proton scattering by ⁵⁸Ni, ²⁰⁸Pb, ¹²C, ⁴⁰Ca and ³⁹K. A comparison with electron scattering data is simultaneously carried out. The agreement with the experimental data is generally good.     

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.     

Analysis of elastic and inelastic α + <Superscript>24</Superscript>Mg scattering within the <Emphasis Type="Italic">S</Emphasis> matrix model involving regge poles

A generalization of the phenomenological S-matrix model taking into account isolated Regge poles is proposed for simultaneously describing refractive effects in the cross sections for the elastic and inelastic scattering of light nuclei. The cross sections for elastic α + ²⁴Mg scattering are analyzed at energies of 50, 54, 65.7, 81, and 119 MeV. The analysis of the cross sections for elastic scattering is supplemented with an analysis of the inelastic scattering of alpha particles that is accompanied by the excitation of the first excited state (2⁺) of ²⁴Mg nuclei. It is shown that the proposed model makes it possible to describe satisfactorily all of the aforementioned cases of elastic and inelastic scattering, correctly reproducing the refraction Airy structures and anomalous large-angle scattering that are observed at large scattering angles.     

Direct numerical reconstruction of inelastic cross sections from REELS and ISS spectra

The reconstruction of inelastic scattering cross sections faces two problems: the measured signal (energy spectrum) is a multiple scattering signal; the inelastic energy loss is nonuniform over the target depth. In this paper, we present a method for numerical reconstruction of cross sections from characteristic energy loss spectra, which efficiently solves both problems within a multilayer model. It is shown that the inverse problem of cross section extraction in the three-layer model is ill-conditioned, and the method is practically inapplicable to the three-layer model. The direct numerical reconstruction method yields a strongly “noised” result and can be applied only to obtain a priori information on the inelastic cross section form for further fitting. Using a combination of two methods, inelastic scattering cross sections were reconstructed for aluminum from characteristic energy loss spectra at probe beam energies of 5 and 40 keV. It is shown that ionization in solids should be described as a local process and as a collective one using the dispersion formula similarly to the case of excitation plasmons.     

Large-angle scattering of heavy ions: (II). General structure of inelastic cross section

Closed-form expressions are derived for the differential cross section of inelastic heavy-ion scattering at large angles. The inelastic transition amplitude given by the distorted-waves theory for excitation of low-lying collective states is evaluated by an extension of analytic methods developed in the preceding paper for elastic large-angle scattering. The very close relation between the inelastic and elastic cross sections is displayed. In particular it is shown that the angular distributions have a universal form, and that the backward-angle inelastic excitation function has, aside from a slowly varying overall energy dependence, an oscillatory gross structure of diffractive origin which is nearly identical to that of the elastic excitation function, irrespective of the physical mechanism involved.     

Quadrupole moments and nucleon excitation strengths in even-A Sm isotopes

We present a coherent coupled-channel analysis of 7 MeV neutron and 16 MeV proton elastic and inelastic scattering from ^{148, 152, 154}Sm. The optical potential and nuclear deformation parameters are determined so as to fit not only these elastic and inelastic scattering data but also the low-energy neutron scattering properties and the total cross sections over a wide energy range. This analysis provides evidence of the same excitation strengths for both projectiles in the case of ^{152, 154}Sm, and of a smaller excitation strength for the proton than for the neutron in case of ¹⁴⁸Sm. Moreover the quadrupole moments of these deformed optical potentials are in good agreement with those extracted from Coulomb excitation measurements and from nuclear matter distribution calculations.