Remarks on calculating the pion-nucleus first-order optical potential

It is shown that the factorization approximation should not be used in any serious theoretical effort to calculate the first order optical potential for low energy π-nucleus scattering. In contrast to earlier work, the required off-shell πN t matrix for non-zero total momentum is consistently evaluated using relativistic particle quantum mechanics.     

Folding model analysis of pion elastic and inelastic scattering from 6Li and 12C

π ^±-Nucleus scattering cross sections are calculated applying the Watanabe superposition model with a phenomenological Woods-Saxon potential. The phenomenological potential parameters are searched for π ^± scattering from ⁶Li and ¹²C to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at pion kinetic energies from 50 to 672 MeV. The optical potentials of ⁶Li and ¹²C are calculated in terms of the alpha particle and deuteron optical potentials. Inelastic scattering has been analyzed using the distorted waves from elastic-scattering data. The values of deformation lengths thus obtained compare very well with the ones reported earlier.     

Elastic and charge exchange scattering of pions on3He in the (3,3)-resonance region

The elastic scattering of pions from³He and the single charge exchange reaction³He(π ^?,π ⁰)³H are calculated in the energy domain of the (3,3)-resonance within the framework of Glauber's theory, including spin and isospin degrees of freedom in all orders. It is pointed out that, from the first minimum on, the differential cross section strongly depends on the parametrization of theπN amplitude, especially on its continuation into the unphysical region of momentum transfer. Single and double spin flip contributions prove to be very important in the charge exchange reaction. Within a modified version of Glauber's formalism, directly usingπN phase shifts rather than amplitudes, the³He charge exchange scattering is reexamined. Whereas the shape of the angle-integrated cross section as a function of pion energy is confirmed, the magnitude is still uncertain within a factor of 2.     

The absorptive pion-nucleus optical potential

We calculate s-wave and p-wave absorptive pion-nucleus optical potentials assuming that a pion is absorbed by a pair of nucleons. Employing a model which takes into account both a single nucleon absorption with nucleon-nucleon correlations and rescattering, we obtain simple analytic expressions for Im B₀ sid Im C₀ of the pion-nucleus optical potential. The off-shell effect on the s-wave pion absorption is examined and shown to be strongly modified by short range correlations. The result for the p-wave absorptive part Im C₀ clearly shows the importance of the tensor correlations. The enhanced nn emission after π^? absorption is shown to be related with a large p-wave πN scattering length a₃₃ via the tensor correlations.     

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.     

A density expansion of the pion-nucleus optical potential. II. Second order terms

The second order terms in a density expansion of the pion optical potential V_opt are evaluated quantitatively. The coefficients of these terms are proportional to various combinations of on- and off-shell nucleon-nucleon T-matrices, averaged over the distribution of two nucleon relative momenta in the Fermi sea. The on-shell contributions can be obtained directly from experimental phase shifts, but the calculation of the off-shell-parts requires a model for the nucleon-nucleon potential. We consider a number of realistic local and nonlocal, separable potentials which fit nucleon-nucleon phase shifts, in order to study the variations in V_opt which arise from differences in the off-shell behavior of T. We find absorptive (imaginary) and dispersive (real) contributions to V_opt which are of comparable magnitude. The dispersive part, which leads to a real energy shift associated with the two nucleon absorptive process, has not been previously estimated quantitatively. We compare our results to empirical potentials obtained by fitting energy level shifts and widths in pi-mesic atoms, as well as theoretical estimates based on threshold cross sections for the processes π + N + N ? N + N.     

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.     

Phenomenological local potential analysis of π+ scattering

π⁺-nucleus scattering cross section are calculated by solving a Schrödinger equation reduced from the Klein-Gordon equation. Local potentials are assumed, and phenomenological potential parameters are searched energy dependently for π⁺ scattering from ¹²C, ⁴⁰Ca, and ²⁰⁸Pb to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at 800 MeV/c pion laboratory momentum. The collective model is used to calculate the angular distributions of differential inelastic cross sections for pions leading to the lowest 2⁺ and 3^? states of ¹²C. The deformation parameters and lengths are extracted and compared to the corresponding ones from other works. Local potentials well describe the scattering of pions from nuclei.     

A survey of pion charge-exchange reactions with nuclei

A survey study of the elastic charge-exchange reactions is presented. The charge-exchange cross sections are evaluated in a coupled-channel framework with optical potentials obtained from the Kisslinger and Laplacian models for the pi-nucleon off-shell scattering amplitude. Considerable differences between these two modles are obtained for pion kinetic energies below the pi-nucleon (3, 3) resonance. The effect of two-nucleon correlations is included by calculating the second-order pi-nucleus optical potential. We find that this effect dominates the charge-exchange reactions at energies of about 100 MeV.     

Pion-Nucleus potentials in the energy range of 0–80 MeV

Data for the elastic scattering of 30–80 MeV positive and negative pions by a wide range of nuclei is analysed with an Ericson-Ericson MSU type optical potential. By use of consistent sets of data for π⁺ and π⁻ and of experimental results for total reaction cross sections we obtain for the first time optical potentials that describe well all the data without the need of introducing non-standard charge-dependent effects.     

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.     

Dynamics of pion double-charge-exchange reactions

The (π⁺, π^?) reactions leading to the double isobaric analog state are studied at pion energies 50 to 300 MeV, with¹⁴C as an example. Effects of nuclear structure, nuclear recoil, the reaction pathway and off-shell πN interactions are examined in detail. Our study reveals a very strong dependence of calculated cross sections on off-shell πN dynamics. Consequently, use of a self-consistent off-shell πN theory is essential to studying short-range nucleon-nucleon correlations from double-charge-exchange data. The present study further shows that reaction dynamics other than two successive pion single charge exchanges is needed to account for the experimental data.     

The study of πd scattering in the (3, 3) resonance region on the basis of three-body relativistic equations

The πd scattering in the (3, 3) resonance region is studied on the basis of three-body relativistic equations. The differential and integral cross sections for the πd scattering are calculated with the use of πN collision matrices defined by fitting phase shifts up to 300 MeV on the one hand, and, alternatively, by the solution of the inverse πN scattering problem on the other. It is shown that (i) the effect of taking fully into account relativistic pion kinematics is of the same order as the multiple scattering effect, (ii) the πd scattering is rather sensitive to the off-shell behaviour of the πN scattering matrix and (iii) the main contribution from the multiple scattering to the cross sections comes from the terms with NN rescattering. A comparison with some experimental data is carried out.     

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.     

The dependence of the photodisintegration cross section on the off-shell T-matrix

Nucleon-nucleon scattering phase shifts determine the diagonal element of the transition matrix. The off-diagonal elements are not completely arbitrary but have conditions imposed on them by the range and the tail of the potential. Electromagnetic interaction can also be used to place restrictions on the off-diagonal elements. We find that the cross section of the deuteron photodisintegration is sensitive to the off-shell transition matrix. The integrated cross section can be varied by as much as 30 % or more, and the matrix element for the El transition by a factor of 2. While the matrix element for the photodisintegration depends on the off-shell elements of the T-matrix, it cannot be used to discriminate between alternative off-shell T-matrices. We have constructed classes of different off-shell T-matrices, which produce identical photo-disintegration cross sections and other two-body scattering and bound-state properties.     

Elastic scattering of π− from 12C at 29 MeV

We have measured the differential cross section for π^? elastically scattered from ${}^{12}\text{C at}\text{T}\text{?}{}_{\mathrm{\pi }}\text{=29}\text{MeV}$. The scattered π^? were detected with pion range telescopes. The measured angular distribution is compared with a momentum space optical potential calculation. Derived phase shifts are compared with those obtained from π⁺ data and from momentum and coordinate space calculations.