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Title
Abstract
Figures
Introduction
Comparisons with Data
Conclusions
References
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Physics
Nuclear Physics

Proton scattering observables from Skyrme-Hartree-Fock densities

Profile image of Katharine HenningerKatharine HenningerProfile image of S. KarataglidisS. KarataglidisProfile image of K. AmosK. Amos

Abstract

Proton and neutron densities from Skyrme-Hartree-Fock (SHF) calculations are used to generate non-local (g-folding) proton-nucleus optical potentials. They are formed by folding the densities with realistic nucleon-nucleon interactions. The potentials are then used to calculate differential cross sections and spin observables for proton scattering. Good agreement with data has been found, supporting those found previously when using SHF charge densities in analyses of electron scattering data. That agreement was improved by use of (shell model) occupation numbers to constrain the HF iterations. That, in part, is also the case with analyses of proton scattering data. The g-folding method is extended to exotic nuclei by including data for neutron-rich sd-shell nuclei from the inverse kinematics of scattering from hydrogen.

Figures (17)
(Nomenclature: 4= Ods5/2; 5= Od3/2, 6 = 1s1/2, 7= Of7/2,8 = Ofs/2; 9= 1p3/2, 10 = 1p1/2) TABLE I. Shell-model occupation numbers, as used in the SHF-SM calculations, for the given orbits. where Q is a Pauli blocking operator, and effects of the mean field are incorporated into the auxiliary potentials entering the energy denominator. The centre-of-mass and Fermi momenta are denoted by K and ky, respectively.
(Nomenclature: 4= Ods5/2; 5= Od3/2, 6 = 1s1/2, 7= Of7/2,8 = Ofs/2; 9= 1p3/2, 10 = 1p1/2) TABLE I. Shell-model occupation numbers, as used in the SHF-SM calculations, for the given orbits. where Q is a Pauli blocking operator, and effects of the mean field are incorporated into the auxiliary potentials entering the energy denominator. The centre-of-mass and Fermi momenta are denoted by K and ky, respectively.
data are given. TABLE II. Isotopes considered for the elastic scattering of protons. References for the available FIG. 1. (Color online.) Differential cross sections and analysing powers for the elastic scattering of 65 [(a)] and 200 MeV [(b)] protons from 78Si. The data are compared to the results of calculations made using the shell, SHF, and SHF-SM models.
data are given. TABLE II. Isotopes considered for the elastic scattering of protons. References for the available FIG. 1. (Color online.) Differential cross sections and analysing powers for the elastic scattering of 65 [(a)] and 200 MeV [(b)] protons from 78Si. The data are compared to the results of calculations made using the shell, SHF, and SHF-SM models.
FIG. 2. (Color online.) Differential cross sections and analysing powers for the elastic scattering of 65 MeV protons from ??S. The data are compared to the results of calculations made using the shell, SHF, and SHF-SM models.
FIG. 2. (Color online.) Differential cross sections and analysing powers for the elastic scattering of 65 MeV protons from ??S. The data are compared to the results of calculations made using the shell, SHF, and SHF-SM models.
FIG. 3. (Color online.) As for Fig. [2] but for 29.6 MeV protons.
FIG. 3. (Color online.) As for Fig. [2] but for 29.6 MeV protons.
FIG. 4. (Color online.) As for Fig. 2] but for the elastic scattering of 29.8 MeV protons from *48.
FIG. 4. (Color online.) As for Fig. 2] but for the elastic scattering of 29.8 MeV protons from *48.
FIG. 5. (Color online.) As for Fig. 2] but for the elastic scattering of 28 MeV protons from °°S. The differential cross sections and analysing powers for the elastic scattering of 65 MeV protons from *°Ar are displayed in Fig. Therein, the differential cross-section and analysing power data are compared to the results of the calculations made using a simple packed shell model (b = 1.85 fm), the SHF, and SHF-SM models. Of the three results, the best agreement with the data comes from using the simple packed model. The differential cross section is well reproduced also by the SHF model, while the SHF-SM model does marginally less well. For the analysing power, all three models explain the data reasonably well, though the best agreement is obtained with the packed shell model.
FIG. 5. (Color online.) As for Fig. 2] but for the elastic scattering of 28 MeV protons from °°S. The differential cross sections and analysing powers for the elastic scattering of 65 MeV protons from *°Ar are displayed in Fig. Therein, the differential cross-section and analysing power data are compared to the results of the calculations made using a simple packed shell model (b = 1.85 fm), the SHF, and SHF-SM models. Of the three results, the best agreement with the data comes from using the simple packed model. The differential cross section is well reproduced also by the SHF model, while the SHF-SM model does marginally less well. For the analysing power, all three models explain the data reasonably well, though the best agreement is obtained with the packed shell model.
FIG. 6. (Color online.) As for Fig. 2] but for the elastic scattering of 39 MeV protons from °8S. The shell model used in this case is a packed model. results of calculations made using the packed shell (6 = 1.9 fm), the SHF, and SHF-SM models. All models do equally well in describing the differential cross-section data to 80°. It is in the analysing power that differences emerge, with the packed shell model providing a better description of the data.
FIG. 6. (Color online.) As for Fig. 2] but for the elastic scattering of 39 MeV protons from °8S. The shell model used in this case is a packed model. results of calculations made using the packed shell (6 = 1.9 fm), the SHF, and SHF-SM models. All models do equally well in describing the differential cross-section data to 80°. It is in the analysing power that differences emerge, with the packed shell model providing a better description of the data.
FIG. 7. (Color online.) As for Fig. [6] but for the elastic scattering of 30 MeV protons from 4°S.
FIG. 7. (Color online.) As for Fig. [6] but for the elastic scattering of 30 MeV protons from 4°S.
FIG. 8. (Color online.) Differential cross section for the elastic scattering of 33 MeV protons from 36 Ar. The data are compared to the results of the calculations made using wave functions obtained from the shell, the SHF, and the SHF-SM models.
FIG. 8. (Color online.) Differential cross section for the elastic scattering of 33 MeV protons from 36 Ar. The data are compared to the results of the calculations made using wave functions obtained from the shell, the SHF, and the SHF-SM models.
FIG. 9. (Color online.) Comparison of the differential cross sections obtained from calculations made using the shell, SHF, and SHF-SM models for the elastic scattering of 33 MeV (a) and 65 MeV (b) protons from °° Ar.
FIG. 9. (Color online.) Comparison of the differential cross sections obtained from calculations made using the shell, SHF, and SHF-SM models for the elastic scattering of 33 MeV (a) and 65 MeV (b) protons from °° Ar.
IG. 10. (Color online.) Differential cross section and analysing power for the elastic scattering of 5 MeV protons from *°Ar. The data are compared to the calculations made using a packed hell, the SHF, and the SHF-SM models.
IG. 10. (Color online.) Differential cross section and analysing power for the elastic scattering of 5 MeV protons from *°Ar. The data are compared to the calculations made using a packed hell, the SHF, and the SHF-SM models.
FIG. 11. (Color online.) Differential cross sections for the scattering of 33 MeV protons from 4? Ar and *4Ar. The data [29) are compared to the results of the calculations from the packed shell, SHF, and SHF-SM models.
FIG. 11. (Color online.) Differential cross sections for the scattering of 33 MeV protons from 4? Ar and *4Ar. The data [29) are compared to the results of the calculations from the packed shell, SHF, and SHF-SM models.
FIG. 12. (Color online.) Differential cross section and analysing power for the elastic scattering of 65 MeV protons from 4°Ca. The data are compared to the results of the calculations performed using a packed shell, SHF, and SHF-SM models.
FIG. 12. (Color online.) Differential cross section and analysing power for the elastic scattering of 65 MeV protons from 4°Ca. The data are compared to the results of the calculations performed using a packed shell, SHF, and SHF-SM models.
FIG. 13. (Color online.) Differential cross section and analysing power for the elastic scattering of 65 MeV protons from *#Ca. The data [aah are compared to the results of the packed shell model, SHF, and SHF-SM calculations.
FIG. 13. (Color online.) Differential cross section and analysing power for the elastic scattering of 65 MeV protons from *#Ca. The data [aah are compared to the results of the packed shell model, SHF, and SHF-SM calculations.
FIG. 14. (Color online.) Differential cross section and analysing power for the elastic scattering of 65 MeV protons from *4Ca. The data are compared to the results of the calculations from the packed shell, SHF, and SHF-SM models.
FIG. 14. (Color online.) Differential cross section and analysing power for the elastic scattering of 65 MeV protons from *4Ca. The data are compared to the results of the calculations from the packed shell, SHF, and SHF-SM models.
FIG. 15. (Color online.) As for Fig. [[2]but for the scattering from *°Ca.
FIG. 15. (Color online.) As for Fig. [[2]but for the scattering from *°Ca.
FIG. 16. (Color online.) Differential cross sections for the elastic scattering of 65 MeV protons from all even-even Ca isotopes from 4°Ca to °4Ca. The SHF model was used to obtain the cross sections.
FIG. 16. (Color online.) Differential cross sections for the elastic scattering of 65 MeV protons from all even-even Ca isotopes from 4°Ca to °4Ca. The SHF model was used to obtain the cross sections.

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