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.     

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.     

T = 1 excitation mechanism in pion induced reactions on 12C

The cross sections for the reactions π^± → π^±, π⁰ on ¹²C with excitation of the T = 1 states are calculated for the N₃₃¹ energy region. The Chew-Low amplitude for pion-nucleon scattering is used in the framework of impulse approximation which has been supported by recent calculation of pion scattering with excitation of definite nuclear states.     

Coupled-channels analysis of K<Superscript>+</Superscript> scattering from <Superscript>6</Superscript>Li and <Superscript>12</Superscript>C using the Watanabe superposition model

Coupled-channels calculations for the elastic and inelastic scattering of K⁺ at 715 MeV/c by ⁶Li and ¹²C at 635, 715 and 800 kaon Lab momenta have been analysed. The optical potentials of ¹²C and ⁶Li are calculated in terms of the alpha-particle and deuteron optical potentials. Good fits to the experimental data and phenomenological calculations are obtained for ⁶Li and ¹²C nuclei.     

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.     

On the nuclear interaction potential in the reactions with heavy ions

The interaction potential of heavy ions⁴He,⁶Li,¹²C and¹⁶O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of⁶Li from¹²C at laboratory energy of lithium ionsT _L =90.0 MeV. Reasonable agreement with experiment is obtained.     

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.     

Cluster Model Analysis of Pion Elastic and Inelastic Scattering from 12C

Angular distributions of differential cross sections for the ¹²C(π ^±, π ^±)¹²C and ¹²C(π ^±, π ^±)¹²C^* reactions at pion kinetic energy ranging from 50 to 260 MeV have been analyzed with the 3α-particle model of ¹²C. The model provides good fits to a wide range of data. Differential cross sections for inelastic transitions to the (2^?+?; 4.44 MeV) and (3^???; 9.64 MeV) states in ¹²C are computed and the deformation lengths δ ₂ and δ ₃ are extracted. It is found that the extracted deformation lengths are sensitive to the nuclear model used and similar to the corresponding values found with other probes and nuclear models.     

Scattering of <Emphasis Type="Italic">π</Emphasis><Superscript>±</Superscript> mesons on a <Superscript>9</Superscript>Be nucleus in the Δ<Subscript>33</Subscript>-resonance region

Within the Glauber diffraction theory of multiple scattering, the differential cross sections for the elastic and inelastic scattering of π^± mesons are calculated for energies in the range between 130 and 260 MeV. This is the region where the broad Δ₃₃ resonance in the π^±N system occurs, the maximum corresponding to this resonance being at approximately 165 MeV. The wave function for the ⁹Be nucleus was chosen on the basis of the 2αN multicluster model. The sensitivity of the resulting differential cross sections to the target-nucleus wave functions computed with various intercluster-interaction potentials, to the contributions of wave-function components, and to various scattering multiplicities in the Glauber operator Ω is analyzed. A comparison with experimental data and with the results of other calculations is performed, and conclusions concerning the quality of the wave functions used and advantages of the present approach are drawn.     

Backward πd scattering between 140 and 260 MeV

Differential cross sections for elastic scattering of pions by deuterons have been measured for centre-of-mass angles between 130° and 175°, and at laboratory energies 141, 177, and 260 MeV for π⁺, and at 151, 185, and 189 MeV for π^?. At 177 and 260 MeV the cross sections are a factor of 2 lower than the predictions of three-body theories.     

Optical model description of the elastic scattering of 6He from a polarized proton target at 71 MeV/nucleon

The vector analyzing power and differential cross section for the elastic scattering of ⁶He nucleus from polarized protons at 71 MeV/nucleon have been analyzed using the optical model potentials. Different versions of the nuclear potential are constructed using phenomenological potentials and semimicroscopic potentials based upon four different versions of 6He density and three effective nucleon-nucleon interactions. The effects of density dependence and the sensitivity of the cross sections for interactions have been investigated.     

The optical potential for 6Li-6Li elastic scattering at 156 MeV

Elastic scattering of ⁶Li from ⁶Li has been studied for a beam energy of 156 MeV. The experimental differential cross sections have been analysed on the basis of the optical model using various phenomenological forms. The spin-orbit interaction proves to be less significant. A semimicroscopic double-folding cluster model which generates the real part of the optical potential by an antisymmetrized dα cluster wave function of ⁶Li and αα, dd and dα interactions is well able to describe the experimental data.     

Proton optical potentials at intermediate energies from Brueckner theory

We have analysed proton scattering cross sections and polarisations from ⁴⁰Ca and ²⁰⁸Pb at intermediate energies using optical potentials calculated from Brueckner theory with internucleon potentials and ground state densities both different from those used previously. We show that the calculated results are very sensitive to the assumed densities and that agreement with experiment is only obtained using phenomenological densities and is not obtained using shell-model densities. We are not able to obtain agreement with the experimental data with a particular soft-core potential, Urbana V-14.     

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.     

A test of the optical theorem

Forward differential cross sections for π^?p elastic scattering at 1.0, 1.5 and 2.0 GeV/c show that the square of the imaginary parts of the nuclear scattering agrees with the optical theorem prediction within ±3%, when averaged over the three momenta.     

Elastic and inelastic scattering of protons from Li between 25 and 45 MeV

The elastic and inelastic scattering of protons from ⁶Li has been studied at incident energies of 25.9, 29.9, 35.0, 40.1 and 45.4 MeV. The 2.18 MeV (3⁺, T = 0) first excited state of ⁶Li was found to be strongly excited, but the 3.56 MeV (0⁺, T = 1) second excited state was quite weakly excited. Angular distributions for excitation of the 2.18 MeV level were measured at all five energies, while angular distributions for excitation of the 3.56 MeV level were extracted only at 25.9 and 45.4 MeV. To test the applicability of the optical model for the scattering of protons from such a light nucleus the elastic scattering angular distributions have been analyzed using the eleven-parameter search code SEEK. Available polarization angular distributions were included in the analysis. Reasonable fits to the data have been obtained with an average geometry potential. Theoretical estimates of the real part of the optical potential and the inelastic scattering differential cross sections have been made using the microscopic model for proton-nucleus scattering. Both phenomenological and realistic forces have been considered and the necessary nuclear transition densities have been extracted from experimental elastic and inelastic electron scattering data. An estimate of a possible spin-spin term in the optical potential has also been made.     

Elastic scattering of 3He nuclei on 13C nuclei at 50 and 60 MeV and V-W ambiguity in choosing optical potentials

At energies of 50 and 60 MeV, the elastic scattering of ³He nuclei on ¹³C nuclei is investigated at laboratory angles in the range 10°–170°. The measured differential cross sections are analyzed on the basis of the optical model of the nucleus by using Woods-Saxon potentials, including both volume and surface absorption. The potential parameters are determined by fitting the computed cross sections to experimental data. It is found that, even in the region of sensitivity, the values of the real and imaginary parts of the potentials (V and W, respectively) show considerable scatter, with extreme values differing by a factor greater than two. This scatter is explained by the existence of a V-W ambiguity in choosing optical potentials.     

Optical-model analysis of Li elastic scattering

The elastic scattering cross sections of 28 MeV ⁶Li ions from the nuclei ¹¹B, ¹²C and ¹³C were analyzed using the optical model. The analysis has been extended to other ⁶Li elastic scattering data on ¹⁶O (29.8 MeV) and on ¹²C (24.5 and 30.6 MeV) previously measured elsewhere. The fits obtained with the usual six-parameter Woods-Saxon potential are good. Parameter ambiguities were studied and the results of the analysis were compared with the predictions of the folding model.