Extraction of neutron densities from elastic proton scattering byPb206,207,208

Abstract

The method for extraction of neutron and matter densities from data on cross sections and spin observables for elastic p-nucleus scattering is presented. The effective nuclear potential was treated to the 6rst order with respect to the t-matrix and density distributions. To eliminate uncertainties associated with the t matrix, the latter has been determined directly from p-Ca scattering data, where the proton and neutron densities are known sufBciently well. The medium modi6cations in the t matrix have been included by means of density dependent terms added to the free t matrix.The neutron densities to be found were expressed as a Hartree-Fock (HF) distribution plus a small correction expanded in a Fourier-Bessel series with inclusion of only low-frequency components determined by the data. High-frequency components are presented by the HF term. Expressions for the physical observables were linearized in terms of the expansion coefficients, the latter being determined through an iterative procedure from the y criterium. The method enables one to obtain statistical Quctuations in those Fourier components as they are generated by experimental error bars. The normalization and model uncertainties have been also estimated. The extracted densities of ' ' Pb and their differences were compared with the HF results calculated by us with the Skyrme interaction. On the whole, pretty good agreement has been achieved.PACS number(s): 21.10. Gv, 25.40.Cm, 21.30. +y, 27.80.+w

Relativistic nuclear energy density functional constrained by low-energy QCD

“…6. Results obtained with the FKVW interaction are compared with data [62] for the Sn isotopes, and with the empirical value of r n − r p in 208 P b (0.20 ± 0.04 fm from proton scattering data [63], and 0.19 ± 0.09 fm from the excitation of the isovector giant dipole resonance by α-scattering [64]). …”

Relativistic nuclear model with point-couplings constrained by QCD and chiral symmetry

“…In particular, he has shown that there is a very strong linear correlation between the neutron skin thickness in 208 Pb and the individual parameters that determine the asymmetry energy S 2 (ρ): a 4 , p 0 and ∆K 0 . The empirical value of the difference between neutron and proton rms radii r n − r p in 208 Pb (0.20 ± 0.04 fm from proton scattering data [34], and 0.19 ± 0.09 fm from the alpha scattering excitation of the isovector giant dipole resonance [35]) places the following constraints In Fig. 4 we plot the asymmetry energy S 2 (ρ) as function of the baryon density for the three steps of our calculation of the nuclear matter EOS: first, using only chiral one-and two-pion exchange calculated in CHPT, next with the inclusion of leading order isoscalar condensate background nucleon self-energies that arise through changes in the quark condensate and the quark density at finite baryon density, and finally with the non-linear contribution δG (1) V to the vector condensate nucleon self-energy.…”

Neutron skin thickness in the droplet model with surface width dependence: Indications of softness of the nuclear symmetry energy

“…The rms radius of neutron densities in nuclei has been measured with hadronic probes such as proton-nucleus elastic scattering [42][43][44][45] or inelastic scattering excitation of the giant dipole and spin-dipole resonances [46,47]. Antiprotonic atoms are helpful to probe the size of the neutron skin of nuclei from the fact that the nuclear periphery is very sensitive to antiprotons in the normally electronic shell.…”