Empirical formulas for the second inverse moment of the photoabsorption cross sections in nuclei are discussed in J. N. Orce, Phys. Rev. C 91, 064602 (2015). In this Comment I point out that the experimental values used are systematically too small i
n heavy nuclei by about 10% because of the neglection of the E1 strength below the neutron threshold. Furthermore, combining recently deduced values of the polarizability in heavy and total photoabsorption data in light nuclei it is demonstrated that the mass number dependence of sigma_(-2) is sensitive to the ratio of volume and surface coefficients of the symmetry energy and parameters different to the ones chosen by Orce may be better suited.
The electric dipole strength distribution in 120Sn between 5 and 22 MeV has been determined at RCNP Osaka from a polarization transfer analysis of proton inelastic scattering at E_0 = 295 MeV and forward angles including 0{deg}. Combined with photoab
sorption data an electric dipole polarizability alpha_D(120Sn) = 8.93(36) fm^3 is extracted. The dipole polarizability as isovector observable par excellence carries direct information on the nuclear symmetry energy and its density dependence. The correlation of the new value with the well established alpha_D(208Pb) serves as a test of its prediction by nuclear energy density functionals (EDFs). Models based on modern Skyrme interactions describe the data fairly well while most calculations based on relativistic Hamiltonians cannot.
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 a
nd 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.
A set of high resolution zero-degree inelastic proton scattering data on 24Mg, 28Si, 32S, and 40Ca provides new insight into the long-standing puzzle of the origin of fragmentation of the Giant Dipole Resonance (GDR) in sd-shell nuclei. Understanding
is provided by state-of-the-art theoretical Random Phase Approximation (RPA) calculatios for deformed nuclei using for the first time a realistic nucleon-nucleon interaction derived from the Argonne V18 potential with the unitary correlation operator method and supplemented by a phenomenological three-nucleon contact interaction. A wavelet analysis allows to extract significant scales both in the data and calculations characterizing the fine structure of the GDR. The fair agreement supports that the fine structure arises from ground-state deformation driven by alpha clustering.
Background: The B(E2) transition strength to the 2+_2 state in 94Zr was initially reported to be larger by a factor of 1.63 than the one to the 2+_1 state from lifetime measurements with the Doppler-shift attenuation method (DSAM) using the (n,ngamma
) reaction [E. Elhami et al., Phys. Rev. C 75, 011301(R) (2007)]. This surprising behavior was recently revised in a new measurement by the same group using the same experimental technique leading to a ratio below unity as expected in vibrational nuclei. Purpose: The goal is an independent determination of the ratio of B(E2) strengths for the transitions to the 2+_(1,2) states of 94Zr with inelastic electron scattering. Method: The relative population of the 2+_(1,2) states in (e,e) reactions was measured at the SDALINAC in a momentum transfer range q = 0.17 - 0.51 fm^(-1) and analyzed in plane-wave Born approximation with the method described in A. Scheikh Obeid et al., Phys. Rev. C 87, 014337 (2013). Results: The extracted B(E2) strength ratio of 0.789(43) between the excitation of the 2+_1 and 2+_2 states of 94Zr is consistent with but more precise than the latest (n,ngamma) experiment. Using the B(E2) transition strength to the first excited state from the literature a value of 3.9(9) W.u. is deduced for the B(E2; 2+_2 -> 0+_1) transition. Conclusions: The electron scattering result independently confirms the latest interpretation of the different (n,ngamma) results for the transition to the 2+_2 state in 94Zr.
Properties of the first excited state of the nucleus 9Be are discussed based on recent (e,e) and (gamma,n) experiments. The parameters of an R-matrix analysis of different data sets are consistent with a resonance rather than a virtual state predicte
d by some model calculations. The energy and the width of the resonance are deduced. Their values are rather similar for all data sets, and the energy proves to be negative. It is argued that the disagreement between the extracted B(E1) values may stem from different ways of integration of the resonance. If corrected, fair agreement between the (e,e) and one of the (gamma,n) data sets is found. A recent (gamma,n) experiment at the HIgS facility exhibits larger cross sections close to the neutron threshold which remain to be explained.
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 pr
oton 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.
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 excita
tion. 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.
A benchmark experiment on 208Pb shows that polarized proton inelastic scattering at very forward angles including 0{deg} 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 r_skin = 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.
The fragmentation of the Isoscalar Giant Quadrupole Resonance (ISGQR) in 40Ca has been investigated in high energy-resolution experiments using proton inelastic scattering at E_p = 200 MeV. Fine structure is observed in the region of the ISGQR and it
s characteristic energy scales are extracted from the experimental data by means of a wavelet analysis. The experimental scales are well described by Random Phase Approximation (RPA) and second-RPA calculations with an effective interaction derived from a realistic nucleon-nucleon interaction by the Unitary Correlation Operator Method (UCOM). In these results characteristic scales are already present at the mean-field level pointing to their origination in Landau damping, in contrast to the findings in heavier nuclei and also to SRPA calculations for 40Ca based on phenomenological effective interactions, where fine structure is explained by the coupling to two-particle two-hole (2p-2h) states.
