Many-body field theoretic framework for inelastic pion-nucleus scattering

We consider inelastic scattering of pions from nuclei using many-body quantum field theory methods. We find that, in an inelastic amplitude for small energy transfer, one can separate out effects of particle-hole correlations in the final nuclear state. The ratio of π⁺ and π^? inelastic cross sections can differ substantially from the analogous ratio for free πN scattering.     

Investigation of α-particle scattering from Mg as a test of hauser-feshbach calculations in the continuum region

The elastic and inelastic scattering of α-partieles by ²⁴Mg is investigated at bombarding energies between 15.4 and 19.1 MeV. Particular attention is given to the analysis of the inelastic scattering to the 3⁺ unnatural-parity state at 5.22 MeV. Both energy-averaged angular distributions and fine-energy-resolution excitation functions are used in the analysis. It is found that the inelastic scattering to the (3⁺, 5.22 MeV) state may be interpreted as pure compound nucleus scattering. This fact is used to investigate whether the incoherent addition of a compound nucleus cross section and a direct cross section, as has been done in recent analyses, is a realistic way to describe energy-averaged scattering data which contain both direct and compound contributions.     

Fluctuations in 88Sr(p,p0) and 90Zr(p,p′) in the energy region from 12 MeV TO 13 MeV

The low cross sections in the diffraction minima of elastic proton scattering at 12.5 MeV incident energy and far backward scattering angles for target nuclei with mass numbers A of about 90 were used to investigate compound nucleus effects in the framework of the statistical model. In the case of ⁹⁰Zr(p, p′) energy averaged T^< fluctuations are observed, while in the case of ⁸⁸Sr(p, p₀) resolved structures with a coherence width of Γ = 22 keV are found, which is assumed to be the coherence width Γ^> of overlapping T^> states.     

Interference effects in inelastic proton scattering on 28Si

Interference effects in ²⁸Si(p, p') inelastic scattering are studied in the Coulomb barrier region. The interference occurs between compound contributions and direct inelastic transitions. The asymmetric resonance shape is analysed to extract the intrinsic shape of the excited target nucleus.     

用高能核子非弹性散射研究核力有效势

本文用扭曲波玻恩近似法及多体高能近似法,处理了原子核对高能核子的非弹性散射现象。在具有可靠的靶核激发态波函数的情况下,可利用这些理论处理方法研究核内两核子间的有效势,本文具体就碳核对185MeV入射核子的非弹性散射进行了计算。在计算中利用了粒子-空穴模型核波函数。在采用了具有各种交换性质并包含自旋轨道耦合项的有效势后,用一组合理的位阱参数,由多体高能近似法计算的理论值可与几个微分截面及极化实验曲线同时符合。     

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.     

Proton and neutron contributions to the charge longitudinal response

The charge longitudinal response of nuclei, as measured by inclusive inelastic electron scattering, is investigated in the semiclassical RPA framework. The proton and neutron contributions to the total response are explicitly separated out. It is found that a sizable neutron ejection can be induced by RPA correlations, particularly at low momentum and energy transfer. A comparison of our theory with the experimental data is presented, also in the case of asymmetric nuclei (N ≠ Z). In particular, the differences in the neutron contributions between ³⁰Ca and ⁴⁸Ca are discussed.     

Analisis of inelastic scattering of π-mesons from nuclei within the microscopic optical potential

Cross sections of inelastic scattering of π-mesons from Si, Ni, and Pb nuclei at energy T _lab = 291 MeV are calculated using the distorted wave approximation. The microscopic direct and transition optical potentials are determined by specifying the pion-nucleon scattering amplitude and the nuclear density distribution, where we use the in-medium πN amplitude parameters obtained earlier by analyzing the elastic scattering data for the same nuclei. The cross sections are calculated on the basis of the relativistic wave equation. The deformation parameters of the nuclei are obtained by comparing inelastic scattering cross sections with the appropriate experimental data.     

Excitation of states of medium-mass nuclei in the region of giant resonances in inelastic deuteron scattering

Results are presented that were obtained by measuring a continuum in the inelastic scattering of 37-MeV deuterons on ¹²C, ⁴⁸Ti, and ^58,64Ni nuclei in the angular range 16° ≤ θ ≤ 61°. Broad excitation maxima are found for deuteron scattering angles in the range θ ≤ 21°. The region of a broad maximum includes giant resonances of target nuclei, whose levels are excited quite readily at E _d = 37 MeV. Summation of the inelastic-scattering cross sections over all final states of the excited| nucleus and the use of completeness of the wave functions for these states make it possible to express the total cross section for inelastic (incoherent) deuteron scattering only in terms of the wave functions for the ground state of the target nucleus. The corresponding quasielastic-scattering amplitude is taken in the diffraction approximation. Nucleon correlations in the target nucleus are disregarded. Upon disregarding a small contribution of multiple quasielastic scattering at small scattering angles, the cross section for incoherent deuteron scattering is represented approximately as the product of known factors—the square of the absolute value of the amplitude for diffractive quasielastic scattering and the effective number of target nucleons scattering deuterons. The results of these calculations agree qualitatively with experimental data.     

Nucleon channel coupling in electrodisintegration of nuclei

The process of nuclear excitation above threshold for nucleon decay in high energy electron scattering is considered. On the basis of the particle-hole shell model a formalism is proposed which allows one to describe electroexcitation of nuclei in a unified manner both in the resonance and quasielastic scattering regions. Numerical calculations were made for the ¹²C nucleus taking into account the mixing of proton and neutron configurations (channels) of the particle-hole type in the continuum.     

Multistep scattering in the 160 MeV208Pb(α, α′) reaction

New experimental data has been obtained for the²⁰⁸Pb(α, α′) reaction induced by 160 MeV alpha particles, for inelastic scattering to forward angles. We use these data to investigate the applicability of the multistep scattering theory of Feshbach, Kerman, and Koonin for describing this reaction. The mechanism we study, following the work of Gadioli et al. [1], is of the incident alpha particle remaining intact throughout the scattering process, exciting nucleon particle-hole pairs through multistep process. We conclude that this mechanism, combined with compound nucleus decay at low emission energies, can account for much of the observed data. However, there are indications that other processes also contribute at energies above the compound nucleus emission regime, and we outline future theoretical analyses that are needed.     

Critical scattering and pionic instabilities in heavy ion collisions

We investigate the effect of collective instabilities in heavy ion collisions. The focus is on critical scattering phenomena associated with pionic instabilities. The decay rate Γ of excited many-body systems is calculated in RPA. Γ is shown to give the rate of spontaneous “phonon” pair production. We express Γ as a sum of a collective, Γ_col, and a scattering, Γ_scat, rate. Γ_col is the pair production rate of phonons in unstable states. In the case of pionic instabilities, Γ_col is the condensation rate of π⁺π^? and π⁰π⁰ pairs into unstable states. Γ_scat is the pair production rate of phonons in the particle-hole excitation region and gives the two-body scattering rate in the medium. An effective (density-dependent) two-body cross section is obtained. The difference between critical scattering of external particles in a system near equilibrium and that of constituents of systems far from equilibrium is investigated. A model calculation suggests the existence of pionic instabilities in heavy ion collisions. Growth rates of unstable modes and the effective cross sections displaying critical scattering are calculated. Finally, we estimate Γ_scat and Γ_col.     

Theory of the local field correction in an electron gas

The wave-vector- and frequency-dependent dielectric function ?(k,ω) of an electron gas can be expressed in terms of Lindhard's function and a complex local field correctionG(k,ω) which incorporates all the effects of dynamic exchange and correlation in the system. The general properties ofG(k,ω) are discussed, in particular the static and high-frequency limits. It is shown that for smallk, bothG(k, 0) andG(k, ∞) vary ask ², with different coefficients, but both determined by the average kinetic and potential energies per particle. For largek,G(k, ∞) varies again ask ² and it is argued that the same holds true forG(k, 0), with both coefficients (though different) determined by the average kinetic energy per particle. General formulas for the plasma dispersion relation and damping, involving, respectively, the real and imaginary parts ofG(k,ω), are given. The term in the plasma frequency which is proportional tok ² is given directly in terms of the average kinetic and potential energies per particle, a result true at all temperatures. A calculation of the frequency dependence ofG(k,ω), starting from the exact equation of motion for the particle-hole operator and employing a decoupling approximation introduced previously by Toigo and Woodruff, is presented. Explicit results forG(k,ω) are obtained for smallk and allω. The complete expressions forG(k, 0) andG(k, ∞) in this approximation have been obtained and are plotted.     

Dynamic deformation of light nuclei in excited states

An important property—the dynamic deformation of B* light aligned nuclei—is investigated for the nuclear reactions A(x, y)B* → γ + B ₀ by measuring the y-γ correlations. Dynamic deformation is determined from the orientation tensors of multipolar moments. Normalization constants of the contributions from even-rank orientation tensors are determined from the condition of coincidence between dynamic and static deformations of the B* nucleus for θ _y = 0°. Experimental dynamic deformations of ¹²C(2⁺) nuclei caused by the inelastic scattering of α particles and deuterons are determined, along with the ¹⁰Be(2⁺) nuclei formed in reaction ⁹Be(d, p)¹⁰Be(2⁺). It is shown that the dynamic deformation of the aligned nuclei depends on how they are formed and their structure, and evolves substantially when the angle θ _y is varied.     

Influence of inelastic subbarrier impurity scattering on the nonresonant tunneling transmission of a quasi-one-dimensional tunneling junction with weak structural disorder

The contribution of inelastic subbarrier impurity scattering of tunneling electrons to the nonresonant transmission of a quasi-one-dimensional tunneling junction with weak (low impurity concentrations) structural disorder at temperature T=0 is determined. It is shown that this contribution leads to an increase in the tunneling transmission and conditions are determined for which this increase may be appreciable.     

An effective dynamic interaction for the two-particle propagator

In nuclear structure calculations the collective excitations of the core introduce dynamic effects in the interaction between particles. Under the restriction of including forward-going contributions only, it is shown that the two-particle propagator which yields the spectra and two-particle transfer strengths of nuclei with two nucleons outside a closed shell, can be written in a Dyson-like equation in which a two-particle self-energy or dynamic effective interactionΔ is introduced. An expression forΔ is given in terms of the irreducible vertex part of the Bethe-Salpeter equation and partial summations forΔ using phonon exchange interactions to represent the core-polarization diagrams, are discussed. The single-particle propagators are also dressed with phonon-exchange contributions.     

Evolution of proton shells in 20 ⩽ Z ⩽ 28 and 20 ⩽ N ⩽ 50 nuclei and dispersive optical model

Experimental single-particle proton energies in spherical and nearly spherical 20 ? Z ? 28 medium-mass nuclei and their counterparts evaluated with the aid of data formirror nuclei were analyzed on the basis of the dispersive optical model. The parameters of the dispersive optical potential were extrapolated to the region of unstable nuclei, and the values obtained in this way were then used to predict the single-particle proton energies in the 20 ? N ? 50 nuclei under study. The evolution of the particle-hole energy gap was traced, and features peculiar to single-particle spectra of magic and nonmagic nuclei were revealed by comparing single-particle energies with proton-separation energies.     

Phenomenological determination of the Kaon-neutron total cross-sections at high energy

Recent data on the scattering of neutralK mesons on various nuclei (regeneration amplitudes and totalK _L ⁰ cross-sections) are used to get a precise knowledge of inelastic rescattering of Kaons inside a nucleus, which allows a reliable phenomenological evaluation of the inelastic contributions to the cross-section defects in deuteron. New more accurate values for the Kaon-neutron total cross-section can then be deduced from Kaon-deuteron and Kaon-proton measurements. The total cross-sections \(\sigma _{K^ + p} ,\sigma _{K^ + n} ,\sigma _{K^ - p} ,\sigma _{K^ - n} \) are found to follow a classical Regge pattern, and the corresponding residues are determined.