Ratio of pion-nucleus reaction cross sections and the neutron density distribution for lead

Allardyce, B.W.; Batty, C.J.; Baugh, D.J.; Friedman, E.; Heymann, G.; Weil, J.L.; Cage, Marvin E.; Pyle, G.J.; Squier, G.T.A.; Clough, A.S.; Cox, J.; Jackson, Daphne F.; Murugesu, S.; Rajaratnam, V.H.

doi:10.1016/0370-2693(72)90638-7

Cited by 8 publications

(5 citation statements)

References 11 publications

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“…This is obtained for a value of y ~ 2/3. In this case we obtain Ar~0.05 fm also for 2~ and this agrees with previous conclusions based on the experimental results of reaction cross sections for high energy pions [26,27]. These values of A r are significantly smaller than the predictions of Hartree-Fock calculations.…”

Section: Summary and Discussionsupporting

confidence: 91%

“…The difference for r m between 48Ca and 4~ was found to be 0.05_+ 0.04 fm and the value of r,-rp in 4SCa is 0.03_+0.08 fm. The results of these recent experiments are also in agreement with the conclusion obtained earlier from the analyses of high energy rc + and ~-reaction cross sections [26,27], that the differences r,-rp in heavy nuclei are quite small compared to values obtained from current Hartree-Fock calculations. This same conclusion was obtained by Leonardi [28] from the analysis of bremsstrahlung weighted cross sections.…”

Section: Introductionsupporting

confidence: 90%

“…same values of al in (7)) found for 48Ca were used also for 2~ and the adjustments required in order to exactly fulfill the constraint (8) were very small. For y~0.7, as found for 48Ca, we obtain r,-rp~O.O5fm for 2~ which is in excellent agreement with the results of the pion reaction cross section experiments [26,27] …”

Section: I Values Of R -Rpsupporting

confidence: 83%

“…taken as the average between the values of 4~ and 42Ca. The value of rn-r p for 48Ca is deduced from the results of References 24 and 25 and that for 2~ is from [26][27][28]. For 41Ca the value of rn-r p is determined using the results of [24] for 4~ and the experimental value for rex.…”

Section: Summary and Discussionmentioning

confidence: 99%

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Coulomb energies and nuclear radii in the energy density formalism

Friedman

Shlomo

1977

Z Physik A

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The relation between Coulomb displacement energies, AEc, and A r=r,-rp, the difference between the rms radii of neutrons and protons in nuclei, is investigated within the energy density formalism (EDF). The variational equation, obtained by minimizing the Coulomb plus symmetry energies, is solved assuming the symmetry interaction is a simple functional of the local nuclear matter density. Varying parameters of the model, rather unique relation between AE c and Ar is obtained (within _+50keV). AE c is independent of rex, the rms radius of the excess neutrons distribution. Using the experimental values of rp and adjusting the model to reproduce the recent data on Ar (Ar~0.05 fm for 4SCa and 2~ which are significantly smaller than those obtained from current Hartree-Fock calculations, the calculated AE c agree with the experimental results. Using the value of Ar~0.05 fm and the experimental values of rex, a small compression (<0.02 fro) of the proton core in the analogue state relative to its parent state emerges, thus contributing an additional electrostatic term to the Coulomb displacement energy. The size of this relative core-compression effect depends on the values assumed for A r and rex , it increases with the decreasing of Ar and the increasing of rex. If Ar~0.05 fm the effect is large enough to remove the long standing Coulomb energy anomaly. The main result of the present work is the correlation between AE c and At, suggesting that the difficulties of current Hartree-Fock calculations in reproducing isotope shifts of rp, the small value of r,-rp and the values of AE c may all be different manifestations of some missing residual p n effective interaction.

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Section: Summary and Discussionsupporting

confidence: 91%

Section: Introductionsupporting

confidence: 90%

Section: I Values Of R -Rpsupporting

confidence: 83%

Section: Summary and Discussionmentioning

confidence: 99%

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Coulomb energies and nuclear radii in the energy density formalism

Friedman

Shlomo

1977

Z Physik A

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“…They also measured reaction cross sections for negative kaons and anti-protons at momenta in the range 20-40 GeV/c. These data have been analysed by Abul-Magd et a1 (1969) and by Batty and Friedman (1972) using the semi-classical approximation. I n the latter analysis an optical potential of the form given by equation (7.5) is used but since the pion-nucleon amplitudes are fairly constant with pion momentum it is not necessary to consider resonance effects or to carry out the fermi-averaging procedure.…”

Section: Elastic Scattering Total and Reaction Cyoss Sectionsmentioning

confidence: 99%

Nuclear sizes and the optical model

Jackson¹

1974

Rep. Prog. Phys.

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The study of the nuclear scattering of strongly interacting elementary particles including nucleons, pions and anti-protons and of composite particles, and the interpretation of this scattering in terms of the optical model, is reviewed. The complications surrounding the interpretation of nuclear size information from scattering data are discussed and an indication is given of the areas of confidence and uncertainty in the determination of size parameters. The current state of knowledge on the nuclear matter distribution and particularly the neutron distribution, as obtained from theoretical approaches, coulomb energy differences and nuclear scattering is reviewed.

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