Electric dipole response of 208Pb from proton inelastic scattering: constraints on neutron skin thickness and symmetry energy

The electric dipole (E1) response of 208Pb has been precisely determined by measuring Coulomb excitation induced by proton scattering at very forward angles. The electric dipole polarizability, defined as inverse energy-weighted sum rule of the E1 strength, has been extracted as 20.1+-0.6 fm^3. The data can be used to constrain the neutron skin thickness of 208Pb to 0.168(+-0.009)_expt(+-0.013)_theo(+-0.021)_est fm, where the subscript "expt" refers to the experimental uncertainty, "theor" to the theoretical confidence band and "est" to the uncertainty associated with the estimation of the symmetry energy at the saturation density. In addition, a constraint band has been extracted in the plane of the symmetry energy (J) and its slope parameter (L) at the saturation density.Comment: 6 pages, 8 figures, revised manuscript submitted to special volume of Eur. Phys. J. A on symmetry energ

E2 strengths and transition radii difference of one-phonon 2+ states of 92Zr from electron scattering at low momentum transfer

Background: Mixed-symmetry 2+ states in vibrational nuclei are characterized by a sign change between dominant proton and neutron valence-shell components with respect to the fully symmetric 2+ state. The sign can be measured by a decomposition of proton and neutron transition radii with a combination of inelastic electron and hadron scattering [C. Walz et al., Phys. Rev. Lett. 106, 062501 (2011)]. For the case of 92Zr, a difference could be experimentally established for the neutron components, while about equal proton transition radii were indicated by the data. Method: Differential cross sections for the excitation of one-phonon 2+ and 3- states in 92Zr have been measured with the (e,e') reaction at the S-DALINAC in a momentum transfer range q = 0.3-0.6 fm^(-1). Results: Transition strengths B(E2;2+_1 -> 0+_1) = 6.18(23), B(E2; 2+_2 -> 0+_1) = 3.31(10) and B(E3; 3-_1 -> 0+_1) = 18.4(11) Weisskopf units are determined from a comparison of the experimental cross sections to quasiparticle-phonon model (QPM) calculations. It is shown that a model-independent plane wave Born approximation (PWBA) analysis can fix the ratio of B(E2) transition strengths to the 2+_(1,2) states with a precision of about 1%. The method furthermore allows to extract their proton transition radii difference. With the present data -0.12(51) fm is obtained. Conclusions: Electron scattering at low momentum transfers can provide information on transition radii differences of one-phonon 2+ states even in heavy nuclei. Proton transition radii for the 2+_(1,2) states in 92Zr are found to be identical within uncertainties. The g.s. transition probability for the mixed-symmetry state can be determined with high precision limited only by the available experimental information on the B(E2; 2+_1 -> 0+_1) value.Comment: 14 pages, 5 figures, submitted to Phys. Rev. C, revised manuscrip

Complete Electric Dipole Response and the Neutron Skin in 208Pb

A benchmark experiment on 208Pb shows that polarized proton inelastic scattering at very forward angles including 0◦ is a powerful tool for high-resolution studies of electric dipole (E1) and spin magnetic dipole (M1) modes in nuclei over a broad excitation energy range to test up-to-date nuclear models. The extracted E1 polarizability leads to a neutron skin thickness rskin = 0.156+0.025 −0.021 fm in 208Pb derived within a mean-field model [Phys. Rev. C 81, 051303 (2010)], thereby constraining the symmetry energy and its density dependence, relevant to the description of neutron stars

Pygmies, Giants, and Skins

Understanding the equation of state (EOS) of neutron-rich matter is a central goal of nuclear physics that cuts across a variety of disciplines. Indeed, the limits of nuclear existence, the collision of energetic heavy ions, the structure of neutron stars, and the dynamics of core-collapse supernova all depend critically on the nuclear-matter EOS. In this contribution I focus on the EOS of cold baryonic matter with special emphasis on its impact on the structure, dynamics, and composition of neutron stars. In particular, I discuss how laboratory experiments on neutron skins as well as on Pygmy and Giant resonances can help us elucidate the structure of these fascinating objects.Comment: Invited Talk given at the 11th International Conference on Nucleus-Nucleus Collisions (NN2012), San Antonio, Texas, USA, May 27-June 1, 2012. To appear in the NN2012 Proceedings in Journal of Physics: Conference Series (JPCS

Studies of the Giant Dipole Resonance in 27^{27}Al, 40^{40}Ca, 56^{56}Fe, 58^{58}Ni and 208^{208}Pb with high energy-resolution inelastic proton scattering under 0∘^\circ

A survey of the fine structure of the Isovector Giant Dipole Resonance (IVGDR) was performed, using the recently commissioned zero-degree facility of the K600 magnetic spectrometer at iThemba LABS. Inelastic proton scattering at an incident energy of 200 MeV was measured on $^{27}$Al, $^{40}$Ca, $^{56}$Fe, $^{58}$Ni and $^{208}$Pb. A high energy resolution ($\rm{\Delta}\it{E} \simeq$ 40 keV FWHM) could be achieved after utilising faint-beam and dispersion-matching techniques. Considerable fine structure is observed in the energy region of the IVGDR and characteristic energy scales are extracted from the experimental data by means of a wavelet analysis. The comparison with Quasiparticle-Phonon Model (QPM) calculations provides insight into the relevance of different giant resonance decay mechanisms. Photoabsorption cross sections derived from the data assuming dominance of relativistic Coulomb excitation are in fair agreement with previous work using real photons.Comment: 15 pages, 15 figure

Low-energy electric dipole response in 120Sn

The electric dipole strength in 120Sn has been extracted from proton inelastic scattering experiments at E_p = 295 MeV and at forward angles including 0 degree. Below neutron threshoild it differs from the results of a 120Sn(gamma,gamma') experiment and peaks at an excitation energy of 8.3 MeV. The total strength corresponds to 2.3(2)% of the energy-weighted sum rule and is more than three times larger than what is observed with the (gamma,gamma') reaction. This implies a strong fragmentation of the E1 strength and/or small ground state branching ratios of the excited 1- states.Comment: 7 pages, 6 figure

Pygmy dipole resonance in 208Pb

Scattering of protons of several hundred MeV is a promising new spectroscopic tool for the study of electric dipole strength in nuclei. A case study of 208Pb shows that at very forward angles J^pi = 1- states are strongly populated via Coulomb excitation. A separation from nuclear excitation of other modes is achieved by a multipole decomposition analysis of the experimental cross sections based on theoretical angular distributions calculated within the quasiparticle-phonon model. The B(E1) transition strength distribution is extracted for excitation energies up to 9 MeV, i.e., in the region of the so-called pygmy dipole resonance (PDR). The Coulomb-nuclear interference shows sensitivity to the underlying structure of the E1 transitions, which allows for the first time an experimental extraction of the electromagnetic transition strength and the energy centroid of the PDR.Comment: submitted to Phys. Rev.