Pion-Nucleus Scattering and the Interacting Boson Model

A procedure of combining the medium energy scattering theory in the Eikonal approximation with the interacting boson model is proposed to study the pion-nucleus scattering. The channel coupling effects in the excitation of nuclear collective state with ρ^- and ρ⁺ elastic and inelastic scattering are analyzed. The calculated cross sections for the excitation of 2₁⁺ state of ²¹⁸Sn agree with experimental data quite well.     

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.     

Coupled channel approach to the off-shell transition matrix

We propose a coupled-channel separable potential model with the feature that the off-shell elastic transition matrix can be generated directly from the scattering phase shifts. This should be useful in constructing pion-nucleus optical potentials.     

Dispersive treatment of low-energy pion-nucleus forward elastic scattering

The amplitudes for pion-nucleus forward elastic scattering are studied by means of dispersion relations, with emphasis on the low-energy and unphysical regions. The importance of the threshold behaviour of inelastic pion scattering is pointed out, and effective coupling constants, a news-wave parameter and the real part of thep-wave scattering length are determined.     

Charged pion photoproduction from light nuclei

The photoproduction of 0–150-MeV charged pions from light nuclei is studied from a distorted wave impulse approximation (DWIA) approach. The final nuclear states are restricted to a finite set of isospin analogs of excited states of the target nucleus. The final state interactions of the pion with the residual nucleus are incorporated via optical potentials. The elementary photoproduction operator used is that of Blomqvist and Laget which is derived in a general reference frame. To gain insight into the predictive power of this DWIA approach, total and differential cross sections for π^± production from ⁶Li, ⁷Li, ¹⁰B, ¹²C, and ¹⁴N are calculated and compared with available data. It is found that, with a few exceptions, reasonable agreement is obtained between theory and experiment as long as the nuclear wave functions are constrained to fit other electromagnetic and weak processes and the optical potentials are constrained to fit pion-nucleus elastic scattering data. We conclude that, at this stage, using the Blomqvist-Laget operator in a DWIA calculation adequately describes the dynamics of charged pion photoproduction from complex nuclei. We illustrate how this reaction can be used to obtain information on the short range nature of the pion wave function and on nuclear wave functions. Shortcomings of and improvements on this calculation are also suggested.     

Pion-gamma angular correlations: A way to separate reaction contributions in pion-nucleus scattering

We discuss some theoretical aspects of pion-gamma angular correlation measurements following inelastic pion-nucleus scattering in the light of recent progress in understanding the reaction mechanism within the isobar-doorway model. For the simple spin sequence 0⁺ → J^P → 0⁺, it is possible to separate two basic classes of reaction contributions in a model-independent and fairly simple way, based entirely on symmetry considerations. In the limit of infinitely heavy nucleons, these two classes reduce to coupling to the usual transition density and spin density. The method is compared to the related separation of longitudinal and transverse form factors in electron scattering.     

反质子与核的电荷交换反应和非弹性散射

在扭曲波冲量近似下,讨论了反质子与核的电荷交换反应A(p,n)B和非弹性散射A(p,p′)*A.并具体地计算能量为E_p=179.7MeV和46.8MeV下¹²C(p,n)¹²B,¹⁸O(p,n)¹⁸N和¹⁸O(p,p′)¹⁸O的微分截面.用严格的分波法处理扭曲波.非弹性散射的微分截面能符合实验.同时预示了在这些能量下,反质子与核发生电荷交换反应可能出现的微分截面理论结果.     

Low-energy pion-nucleus optical potentials

We discuss the local and non-local pion-nucleus optical potentials. We find that the local potential becomes non-local when two-nucleon correlations are included. The two potentials (including correlations) can be made local through a transformation on the wave function. The new local potentials agree up to quadratic terms when expanded in powers of the density. The influence of finite-range correlations and off-shell pion-nucleon form factors is also investigated.     

Optical Potentials for Elastic and Inelastic Scattering of Non-Electronic Projectiles from Electronic Targets

The usual text book one-particle Green's function possesses a self-energy that is known to be an optical potential for elastic scattering. The introduction of an optical potential reduces the complex many-body scattering problem into a tractable one-body problem. In this work the definition of the Green's functions is extended. The defined inelastic functions are shown to possess self-energies that can be expressed in closed form in terms of the target states. It is proven that these self-energies are optical potentials for inelastic scattering. The properties of these potentials and working equations for the scattering wave functions are discussed. Received January 2, 1996; revised June 7, 1996; accepted for publication June 19, 1996     

The pion optical potential and its application to reaction processes

The gross features of the pion-nucleus interaction are studied within the framework of an optical potential approach. The optical potential is determined by a systematic analysis of the data on pionic atoms and elastic scattering. It is then decomposed into quasi-free and absorption terms through theoretical consideration of the reactive content. A method of calculating the absorption cross section using the optical potential with the above decomposition is proposed. It takes into account not only direct absorption from the elastic channel but also the absorption after the quasi-free processes. The calculated absorption cross sections are in reasonable agreement with the observed ones. The cross sections for inelastic, single-charge-exchange and double-charge-exchange processes are calculated as an extended application of the method. The results are consistent with the available data. Inclusive spectra of pions and protons are also considered in this approach. An application to the (γ, π) reaction is briefly discussed.     

Subthreshold pion spectra in nucleus-nucleus collision

The energy spectra of neutral pion produced in¹²C-¹²C reaction atE _Lab=60, 74 and 84 MeV/nucleon is calculated within a modified thermal model. The nuclear mean field is taken into account through the Brueckner G-matrix effective interaction. Pion reabsorption is included through different energy and density dependence pion-nucleus optical potentials. A-comparison to the experimental data shows a satisfactory agreement of pion spectra over a wide range of pion energy. Modifications are made to the pion-nucleus optical potential of Meherem et al. in order to describe pion spectra as well as pion-nucleus reactions.     

Reaction spectroscopy with even tin isotopes

The two-particle transfer reactions ^{116, 118}Sn(t, p) and the inelastic scattering of 55 MeV protons from ¹¹⁶Sn and 16 MeV protons from ^{116, 118, 120}Sn are analysed for various transitions to collective and non-collective states in the final nucleus using DWBA. Form factors have been calculated with wave functions containing two-quasiparticle excitations of neutrons in open and closed shells as well as 1p-1h transitions from closed proton shells. In the inelastic scattering, generally a Serber-type Gaussian effective interaction was inserted. The results are compared with those obtained on the assumption of two-quasiparticle excitations in a restricted configuration space only. For both types of reaction, reasonable agreement with experimental data is obtained for the angular distribution. In the (t, p) reaction the measured and calculated relative cross sections agree within a factor of two. For the inelastic scattering, apart from relative cross sections the mass dependence of the collective excitations and the influence of four-quasiparticle excitations have been examined. The transition to the collective 2⁺ level in ¹¹⁶Sn was calculated with the proton component of the wave function corrected according to electromagnetic measurements. From inelastic scattering it follows that the transitions to negative-parity states especially are not described satisfactorily by the wave functions used. Cross sections for unobserved higher excited levels have been estimated.     

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.     

The DWIA analysis of the pion photoproduction on carbon

The inclusive pion spectra in the¹²C(γ,π) reaction are calculated in the distorted wave impulse approximation (DWIA). The final state pion-nucleus interaction was constructed within the framework of the multiple scattering theory. The sensitivity of the cross section to the choice of different optical potential variants is investigated.     

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。     

Analysis of elastic scattering of pi-mesons by nuclei within the microscopic optical potential

The microscopic pion-nucleus optical potential defined by the pion-nucleon scattering amplitude and the density distribution function of the target nucleus is applied to obtain the differential cross section of the elastic pion-nucleus scattering based on the solution to the relativistic wave equation. This allow one to account for effects of the relativization and distortion by the potential field. Data on π^±-meson scattering on ²⁸Si, ⁵⁸Ni, and ²⁰⁸Pb nuclei at T _lab = 291 MeV are analyzed and the parameters of the in-medium πN-amplitude are obtained. The parameters are compared with similar parameters for scattering on free nucleons.     

Static potential renormalization in time-dependent fields

We consider the scattering of electrons at a static potential under the influence of an additional time-dependent, homogeneous electric field (‘microwave’). Starting from a plane wave basis, we derive a generalization of the Born (first) order approximation in arbitrary strong oscillating fields. As an example, we evaluate the Friedel density oscillations around a static scatterer whose potential is renormalized by the microwave. The microwave leads to a band of inelastic scattering channels with effective potentials, the shape of which can be ‘tuned’ by the microwave polarization and strength.     

Pion-deutron and pion-nucleus scattering — a review

We review recent developments in the microscopic theory of pion-nucleus elastic scattering. Particular emphasis is placed on the connection which has developed between the sophisticated studies of the three-body πNN system, and the less rigorous (but equally sophisticated) treatments of the pion-nucleus many-body problem. Complete sections are devoted to an examination of the underlying pion-nucleon interaction, and also to the difficult question of the effect of absorption on elastic scattering. Our discussion leads very naturally to a comparison with recent data - both for elastic scattering and reactions.