Binding effects in the optical potential of pionic atoms

We calculate the contribution from nucleon binding to the coefficient Re B₀ in the optical potential of pionic atoms. The relevant Feynman graphs are deduced for nuclear matter. They depend on off-shell values for pion-nucleon scattering lengths a_πN and for the nucleon-binding potential V_NA. Off-shell effects are found to be very important: A pole model for a_πN, extrapolated off-shell, increases binding effects by a factor of three over the use of on-shell values. Two simple models are proposed for the off-shell continuation of V_NA. One leads to attractive, the other to repulsive contributions to Re B₀.     

Improved theoretical pion-nucleus optical potentials

An approach which makes the first order pion-nucleus optical potential theoretically sound is presented. This study should permit higher order improvements to the potential to be more meaningful and the nuclear structure information extracted from pi-nucleus scattering to be more reliable. Based on multiple scattering theory, three optical potentials are constructed and studied in momentum space. These models are the popular Kisslinger potential, the local “Laplacian” potential, and an “improved off-shell potential;” the latter one is derived from absorptive separable pion-nucleon potentials which exactly reproduce on-shell πN scattering. By working in momentum space and explicitly including πN resonances and off-shell effects in the definition of the optical potential, the approach described here is capable of handling any number of pi-nucleon partial waves, is applicable over a very wide energy region, is based on a physical model for off-shell behavior, and is extended easily to include higher order effects. The optical potentials are inserted into two different relativistic wave equations to determine the total cross section and elastic differential cross section for pi-nucleus scattering. It is found that the various models for off-shell πN scattering determine significantly different πC¹² scattering, with the improved off-shell model preferred on theoretical grounds. Also discussed is the importance of properly transforming πN scattering to the pi-nucleus c.m. system, the origin of the shift in the peak position of the π^?C total cross section, and the reason for the increased diffractive nature of the differential cross section at 180 MeV.     

The local field correction to the optical potential at high energy

A key assumption in the derivation of the optical potential for high energy hadron-nucleus scattering is that no target nucleon is struck more than once. The local field (rescattering) amplitude gives the probability for the projectile to strike a target nucleon twice with an intermediate interaction with another nucleon. This rescattering amplitude generates a correction to the basic high energy optical potential, and it must be small for the above assumption to be valid. We evaluate the local field correction to the optical potential using the formalism of Foldy and Walecka. The projectile-nucleon potential is assumed to have a finite range, and the target nucleons are kept sufficiently far apart by a hard core correlation function that there is no overlap between target particles, and all off-energy-shell effects vanish. With a specific form for the high energy behavior of the on-shell projectile-nucleon scattering amplitude, we find that the local field correction vanishes rapidly at high energy.     

Separable energy-dependent approximation to local potentials

An extension of the single-pole separable approximation of a two-body t-matrix in which the effects of several poles are included is made. The simple form for the t-matrix derived from a single separable potential is retained. However, the separable potential is constructed using an energy-dependent superposition of the states corresponding to the various poles. The energy dependence is chosen so as to obtain the correct residue of both the on-shell and off-shell t-matrices at each of these poles, while preserving unitarity. The formalism is specialized to the case of s-wave scattering from an attractive square well. Comparison to the exact s-wave cross section gives good results.     

Impulse-approximation correction in pion-nucleus optical potential

The local density approximation is used in this paper to calculate the first-order pion-nucleus optical potential. TheπN scattering matrix in nuclear medium is computed by employing separableπN scattering matrix. This nuclear-mediumπN scattering matrix, which includes impulse-approximation correction is then used to construct the pion-nucleus optical potential.π-¹²C elastic scattering results obtained by using this potential are compared with the impulse-approximation potential results.     

Large constant terms from soft gluons

The vertex and soft gluon integrals in Drell—Yan and deep-inelastic processes are calculated without approximations, keeping the initial and final quarks on-shell. Asymptotic q²-expansion reveals log²-, log- and constant terms. The latter are small in deep-inelastic scattering but unexpectedly large in Drell—Yan production. Lowest order gluon diagrams provide a reliable approximation for the AF-corrections in deep-inelastic scattering but fail to do so in Drell—Yan processes.     

Optical-model analysis of exotic atom data: (II). Antiprotonic and sigma atoms

Data for antiprotonic and sigma atoms are fitted using a simple optical model with a potential proportional to the nuclear density. The potential strength can be related to the free hadron-nucleon scattering length using a model due to Deloff. A good overall representation of the data is also obtained with a black-sphere model.     

Multiple scattering with a linearized propagator

Scattering by a many-body system is studied within the framework of the “fixed scatterer” approximation and the eikonal approximation formulated in terms of a linearized propagator. If properly treated, the “fixed scatterer” approximation is able to take into account the center-of-mass motion. We specifically study the linearized propagator proposed by Abarbanel and Itzykson. Although for potential scattering the above approximation is essentially equivalent to the Glauber eikonal approximation, its physical implications are quite different when applied to scattering by a composite system. The multiple-scattering series can generally no longer be simply expressed in terms of the individual on-shell scattering amplitudes, and the additivity of phase shifts is shown to break down for overlapping potentials. The implications for phenomenological calculations are discussed. Finally, the above approximation is explicitly applied to high-energy elastic nucleon-deuteron scattering and the results are compared with several variants of the Glauber multiple-scattering formalism.     

On the reconstruction of an optical potential on the basis of experimental data in the WKB approximation

The inverse scattering problem at a fixed energy for a complex-valued potential is solved in the WKB approximation. The method is used to reconstruct the optical potential for elastic ¹⁶O + ¹⁶O scattering at E _lab = 350 MeV. The stability of the solution against small changes in the scattering matrix is studied.     

Off-shell πN amplitudes via a multichannel separable potential

The off-shell pion-nucleon transition matrix is a basic ingredient in theories of pion-nuclear interactions which, in the absence of fundamental theory of πN dynamics, must be obtained by a phenomenological extrapolation from the available on-shell data. As one means of performing such an extrapolation, we explore a multichannel separable potential model with the property that the off-shell elastic scattering amplitude is generated directly from the measured elastic-channel phase shifts. The off-shell πN partial-wave transition amplitudes determined by this procedure are compared with those calculated by Landau and Tabakin using a one-channel absorptive separable potential. We find that the absorptive separable potential approach provides a physically unreasonable off-shell extrapolation at energies where the on-shell amplitude is highly inelastic, and show that the difficulty is a direct consequence of the one-channel nature of that method. The multichannel extrapolation is free of these difficulties.     

Self-consistent calculation of the optical potential and ground-state properties of nuclear matter

On the basis of the Green-function formalism, we performed a self-consistent calculation of the self-energy ∑(k, ω) of a particle interacting with the infinite nuclear medium. The function ∑(k, ω) was mapped out in the energy-momentum plane, and the single-particle energy ω(k), momentum distribution ?(k) and the “on-shell” part of the self-energy, ∑(k, ω(k)), were defined, from which all physical properties followed. In particular we investigated the ground-state properties of nuclear matter in two Λ-approximations of the T-matrix. In one, the intermediate two-particle propagator, Λ₀₀, represented free-particle propagation; in the other, called Λ₁₁, intermediate states included both interacting particles and holes. Pauli principle effects were included in both approximations. The second approximation was expected to be conserving because it included a large part of the rearrangement effects which, we found, contributed ～6 MeV per particle to the average energy and ～28 MeV to the singleparticle energy at zero momentum. The Hugenholtz-van Hove theorem was nearly satisfied, with only 1 MeV separating the chemical potential from the average energy. We also studied, in the Λ₀₀-approximation, the optical potential for the scattering of a particle by a large nucleus; it was directly related to the “on-shell” part of the self-energy. It was found that, below 100 MeV, the real part varied as (?90 + 0.584E) [MeV], and the imaginary part as (2.4 + 0.009 E) [MeV].     

动量空间中能质子-12C弹性散射截面和自旋量的研究

在KMT理论框架下，应用微观的动量空间一级光学势，包括了库仑修正，自旋关联，NN振幅反对称，离壳效应，核子反冲和结合能转换，Lorentz不变的角变换.在整个中能区域系统地计算了质子-¹²C弹性散射微分截面和自旋观测量，并与实验数据及Glauber理论框架下或已有的其他理论计算结果做了比较，其结果显示，在200—1000MeV，该理论与实验结论符合程度较好.     

Coupled-channel R-matrix method on a Lagrange mesh

The coupled-channel R-matrix method on a Lagrange mesh is a very simple approximation of the R-matrix method with a basis. The mesh points are zeros of shifted Legendre polynomials. Bound-state energies and scattering matrices are easily calculated with small numbers of potential values at mesh points. A test with an exactly solvable two-channel potential provides an excellent accuracy over a broad energy range with only 30 mesh points. The efficiency of the method is illustrated for a single channel on α + α scattering and for two channels on the deuteron ground-state energy and on nucleon-nucleon scattering.     

Kroll-Watson-type theorem for potential scattering in a bichromatic laser field

Summary We show that for potential scattering of electrons in a bichromatic laser field a Kroll-Watson type of theorem can be derived in which the scatteringT-matrix element is composed of a renormalized on-shell matrix element for scattering without a field times a generalized Bessel function factor. The radiation field has two components of frequency ω₁ and sω₁ (s=2,3,…) and both components are out of phase by an angle ϕ. Our paper is a generalization of earlier investigations which were performed in the first-order Born approximation.     

Absorptive parts of the hadron-nucleus amplitude and multiparticle production on nuclei

The process of the hadron-nucleus interaction is considered in the framework of Glauber theory. A two-channel model is used for inelastic shadow corrections due to low-mass diffractive jets. It is shown that inelastic hadron-nucleus cross sections are connected with the cuts of a number of hadron-nucleon blobs in the elastic scattering amplitude. The relations derived between contributions to the absorptive part of the amplitude from cuts of different kinds satisfy the Abramovsky-Gribov-Kancheli rules up to a factor which is determined by the ratio of the inelastic and total hadron-nucleon cross sections. The inclusive spectrum in the central region is proportional to $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$. The average charged multiplicity increases with A slower than $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$ due to energy conservation. The results obtained are in good agreement with experimental data on the average multiplicities and distributions of charged particles.     

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.     

Effect of tensor nucleon-nucleon forces on the nucleon-nucleus optical potential

In the approximation of unpolarized nuclear matter, the optical potential for nucleon-nucleus scattering is calculated on the basis of the effective Skyrme interaction with allowance for tensor nucleon-nucleon forces. It is shown that the tensor Skyrme forces make a significant contribution to the imaginary part of the optical potential. The effect of tensor nucleon-nucleon forces on the radial distribution of the imaginary part of the optical potential is investigated by considering the example of elastic neutron scattering by ⁴⁰Ca nuclei at scattering energies of about a few tens of MeV.     

Target-mass effects in hadronic lepton-pair production

Hadronic mass corrections to the Drell-Yan formulae are calculated for on-shell partons and shown to be uniquely determined by the quark distributions extracted from deep inelastic lepton-hadron scattering experiments. It turns out that these corrections are negligible for present day experiments. Arguments in favour of on-shell partons are presented.