Elastic hadron scattering on Li isotopes at intermediate energies

The elastic scattering of hadrons (protons, charged pions, and positively charged kaons) on ^6,7,8Li nuclei is analyzed on the basis of Glauber-Sitenko diffraction theory. A few nuclear-wave-function versions found within two-and three-particle potential cluster models are used in the calculations. It is shown that the application of these wave functions in diffraction theory makes it possible to describe adequately the experimental differential cross sections and analyzing powers in hadron scattering at intermediate energies. In this study, particular attention is given to a comparison of the scattering of different particles on the same target nucleus, as well as to a comparison of scattering of particles of the same sort on different target nuclei.     

Calculation analyzing power in the elastic scattering of protons on <Superscript>15</Superscript>C and <Superscript>15</Superscript>N nuclei in the diffraction theory

Shell-model wave functions are used to calculate the vector analyzing power in the elastic scattering of 0.2, 0.6, and 1 GeV protons on ¹⁵C and ¹⁵N nuclei within the Glauber diffraction theory. Single and double collisions are allowed for upon the decomposition of multiple scattering. It is shown that the number of oscillations and the amplitude of the analyzing power increase with rising energy in the same angular range.     

Effect of the structure of neutron-rich <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li isotopes on the characteristics of proton elastic scattering

The differential cross sections of proton elastic scattering from ⁸Li and ⁹Li nuclei in inverse kinematics have been calculated. The cross sections were determined within the Glauber diffraction theory with the wave functions of nuclei in the three-particle α-t-n, α-t-2n, and ⁷Li-n-n models. Comparison with the existing experimental data for E = 700 and 60 MeV/nucleon made it possible to draw a conclusion about the quality of the wave functions and the adequacy of the potentials used for their calculations.     

Analysis of elastic and inelastic hadron scattering on 6,7Li nuclei within diffraction theory

Within Glauber-Sitenko multiple-scattering theory, the differential cross sections for elastic and inelastic proton, positive-pion, and positive-kaon scattering on ^6,7Li nuclei are calculated at incident-hadron energies ranging between 0.143 and 1.0 GeV. The ⁶Li and ⁷Li wave functions are taken in, respectively, the α2N and the αt clustermodel. The resulting cross sections are investigated as functions of the scattered-particle energy, parameters of the model wave functions, and various scattering multiplicities. It is concluded that a partial filling of the diffraction minimum in the cross section is due to the D-wave contribution to the wave function for the ⁶Li target nucleus.     

Effect of the shell structure of nuclei on p 15C and p 15N scattering within diffraction theory

The differential cross sections for elastic proton scattering on ¹⁵C and ¹⁵N nuclei at energies of 150 and 800 MeV were calculated within the diffraction theory of Glauber multiple scattering. Shellmodel wave functions were used in these calculations, and particular attention was given to analyzing the sensitivity of the calculated features to distinctions between the shell structure of the ¹⁵C nucleus and the shell structure of the ¹⁵N nucleus. The calculations were performed in the approximation of double scattering. The multiple-scattering operator was written in a form that permits taking into account collisions with nucleons belonging to different shells. It is shown that the difference in structure between the two nuclei in question leads to substantial distinctions between the differential cross sections for scattering at an energy of 800 MeV and scattering angles larger than 25°.     

Rescattering effects in proton scattering on nuclei 6,8He and 8,9Li in the Glauber theory

The differential cross sections of elastic p^6,8He and p^8,9Li scattering are calculated within the Glauber diffraction theory at intermediate energies of 70 to 700 MeV/nucleon. The calculations are based on realistic three-body wave functions α-n-n (for ⁶He), α-2n-2n (for ⁸He), α-t-n (for ⁸Li), α-t-2n (for ⁹Li), obtained using current nuclear models, and the Glauber operator is expanded into a series of multiple scattering corresponding to the three-body nuclei configuration. The approach allows us to calculate the operator matrix elements with allowance for rescattering on all structural components of the investigated nuclei.     

Short-range correlations in high-energy hadron collisions

High-energy collisions of hadrons on nuclei are studied by means of Glauber multiple scattering theory, using Jastrow correlated wave functions. To this end a cluster expansion is derived, and its convergence properties are studied. Calculations have been carried out for ⁴He and ¹⁶O nuclei, and they are compared with experimental data.     

Characteristics of elastic proton scattering from <Emphasis Type="Italic">A</Emphasis> = 9 Li,Be, and C isobars

Differential cross sections and analyzing powers (A _y ) for elastic proton scattering from ⁹Be at 220 MeV and 1.0 GeV and from ⁹Li and ⁹C at 60 and 700 MeV/nucleon are calculated in the context of the Glauber diffraction theory with the three-body wave functions for the ⁹Be, ⁹Li, and ⁹C nuclei described by the α + α + n, ⁷Li + n + n, and ⁷Be + p + p models. Comparison with the available experimental data is made, which allows some conclusions about the quality of the model wave functions.     

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.     

ELASTIC SCATTERING OF HADRONS FROM NUCLEI AT HIGH ENERGY AND THE SHORT RANGE CORRELATION IN NUCLEI

The effects of short range correlation in nuclei on elastic scattering of hadronsfrom nuclei at high energy are studied by means of Glauber multiple diffraction the-ory, using Jastrow correlated wave functions. To this end, a determinant form ofJastrow correlated wave functions is used. Calculations have been carried out for π^--¹²C elastic scattering at 260 MeV, and they are compared with the experimentdata. The results show that the influence of the short range correlation on the dif-ferent cross section is quite important.     

Vector analyzing power of π+7Li scattering in the region of the Δ33 resonance

Within Glauber diffraction theory, the vector analyzing power iT ₁₁ is calculated at three energies of positively charged pions, 134, 164, and 194 MeV, incident to ⁷Li nuclei. These energy values lie in the region of the Δ₃₃ resonance in π^± N interaction, the resonance maximum being at 180 MeV. The calculation of iT ₁₁ was performed with several model ⁷Li wave functions, including the αt-cluster and shell-model ones. The properties of π⁺⁷Li scattering are found to be sensitive to the structural features of the target nucleus. A comparison of the results of the calculations with experimental data shows that the wave functions in question and the potentials used to calculate them are quite appropriate.     

Interference effects in proton scattering on <Superscript>15</Superscript>N nuclei at intermediate energies

The differential cross section for proton scattering on ¹⁵N nuclei is calculated within Glauber diffraction theory at energies of 0.2, 0.6, and 1.0 GeV. Use is made of the shell-model wave function for the ¹⁵N nucleus. The contribution of single and double collisions to the Glauber operator Ω is taken into account. The sensitivity of the differential cross sections to the contributions of scattering on nucleons from different shells, to the parameters of the elementary pN amplitude, and to the energy of projectile protons is investigated. It is shown that the interference between amplitudes corresponding to different collision multiplicities, as well as between the amplitudes for scattering on nucleons from different shells, determines special features of the cross section.     

Structure of neutron-rich Isotopes <Superscript>8</Superscript>Li and <Superscript>9</Superscript>Li and allowance for it in elastic scattering

The differential cross sections for elastic proton scattering on the unstable neutron-rich nuclei ⁸Li and ⁹Li at E = 700 and 60 MeV per nucleon were considered. The ⁸Li nucleus was treated on the basis of the three-body α-t-n model, while the ⁹Li nucleus was considered within the α-t-n and ⁷Li-n-n models. The cross sections in question were calculated within Glauber diffraction theory. A comparison of the results with available experimental data made it possible to draw conclusions on the quality of the wave functions and potential used in the calculations.     

Elastic and inelastic scattering of π mesons on 7Li nuclei

Within the diffraction theory of multiple scattering, the differential cross sections for elastic and inelastic pion scattering on a ⁷Li nucleus are calculated for the case where the final nucleus is either in the ground or in the first excited state. The nuclear wave function is set to that in the αt cluster model. The sensitivity of the calculated observables to variations in the type of the wave functions for the alpha-particle and the triton cluster and for their relative motion is investigated. Various multiplicities of scattering and rescattering on the clusters constituting the ⁷Li nucleus are taken into account, and their contributions to the cross section are revealed. The results of the calculations are compared with experimental data at E _π=143, 164, and 194 MeV.     

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.     

The antiproton-nucleus elastic scattering and the alpha-cluster model with dispersion

The elastic scattering differential cross sections of intermediate energy antiprotons on¹²C and¹⁶O nuclei and the elastic scattering polarization observables of antiprotons on these nuclei have been calculated on the basis of theα-cluster model with dispersion and multiple diffraction theory. The results of these calculations are compared with the experimental data.     

Comparative analysis of the characteristics of the elastic scattering of protons by lithium isotopes 6, 7, 8, 9Li, performed using Glauber’s multiple diffraction scattering theory

Differential cross sections and vector analyzing powers are calculated for the elastic scattering of protons by lithium isotopes ⁶Li, ⁷Li, ⁸Li, and ⁹Li at energies of 60 and 200 MeV. The calculations are performed using Glauber??s multiple diffraction scattering theory in the two-particle (for ⁷Li) and three-particle (for ^6,8,9Li) models with realistic intercluster interaction potentials. An analysis of the relationship between the differential elastic scattering cross section and various wave functions, calculated using different interaction potentials, is presented for the ^{8, 9}Li isotopes.     

Polarization phenomena in the intermediate energy elastic deuteron scattering from <Superscript>16</Superscript>C and <Superscript>16</Superscript>O nuclei

A model based on the multiple diffraction scattering theory and the α-cluster model with dispersion of target nuclei is proposed for describing the behavior of observables for the elastic deuteron scattering from ¹²C and ¹⁶O nuclei at intermediate energies. Differential cross-sections and analyzing powers calculated within this approach for incident-deuteron energies of 400 and 700 MeV are in a reasonable agreement with experimental data.     

Folding model analysis of the nucleus–nucleus scattering based on Jacobi coordinates

This paper presents the results of scattering of ¹⁶O+²⁰⁹Bi interaction near the Coulomb barrier. The interaction potential between two nuclei is calculated using the double folding model with the effective nucleon–nucleon (NN) interaction. The calculations of the exchange part of the interaction were assumed to be of finite-range and the density dependence of the NN interaction is accounted for. Also the results are compared with the zero-range approximation. All these calculations are done using the wave functions of the two colliding nuclei in place of their density distributions. The wave functions are obtained by the D-dimensional wave equation using the hyperspherical calculations on the basis of Jacobi coordinates. The numerical results for the interaction potential and the differential scattering are in good agreement with the previous works.     

Large-angle quasi-free scattering in 6Li(p,pd)4He at 670 MeV

The ⁶Li(p, pd)⁴He reaction was investigated at 670 MeV by a coincidence experiment with a large-angle scattering geometry. The energy sharing and angular correlation of the reaction products were measured and the momentum distribution of the recoil nucleus was determined for transitions leading to residual nuclei in the ground and excited states. Results were analysed in terms of a simplified distorted-wave impulse approximation using cluster-model and three-body wave functions. The observed momentum distribution of the p-n pair in the p-shell of ⁶Li is in agreement with three-body calculations, while the spectroscopic factor is larger than predicted by theory. Transitions to breakup states of the α-particle also have the characteristics of quasi-free scattering on deuteron clusters.