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The validity of the Brink-Axel hypothesis, which is especially important for numerous astrophysical calculations, is addressed for 116,120,124Sn below the neutron separation energy by means of three independent experimental methods. The $\gamma$-ray strength functions (GSFs) extracted from primary $\gamma$-decay spectra following charged-particle reactions with the Oslo method and with the Shape method demonstrate excellent agreement with those deduced from forward-angle inelastic proton scattering at relativistic beam energies. In addition, the GSFs are shown to be independent of excitation energies and spins of the initial and final states. The results provide a critical test of the generalized Brink-Axel hypothesis in heavy nuclei, demonstrating its applicability in the energy region of the pygmy dipole resonance., Comment: 6 pages, 4 figures, Phys. Rev. Lett. (in press)

The low-lying dipole strength in the 90,94Zr nuclei was investigated via (p,p′γ) at 80 MeV and (α,α′γ) at 130 MeV. The experiments, made at RCNP, used the magnetic spectrometer Grand Raiden for the scattered particles and the array CAGRA with HPGe detectors for the γ-decay. For 94Zr these are the first data for both reactions and for 90Zr these are the first data with (p,p′γ) and the first ones at high resolution for (α,α′γ). The comparison of the present results for the two nuclei with existing (γ,γ′) data shows that both nuclear probes produce an excitation pattern different than that of the electromagnetic probes. DWBA calculations were made using form factors deduced from transition densities, based on RPA calculations, characterized by a strong neutron component at the nuclear surface. A combined analysis of the two reactions was performed for the first time to investigate the isoscalar character of the 1− states in 90,94Zr. The (p,p′γ) cross section was calculated using values for the isoscalar electric dipole energy-weighted sum rule (E1 ISEWSR) obtained from the (α,α′γ) data. The isoscalar strength for 90Zr was found to exhaust 20 ± 2.5% of the EWSR in the energy range up to 12 MeV. In case of 94Zr, a strength of 9 ± 1.1% of the EWSR was found in the range up to 8.5 MeV. Although an overall general description was obtained in the studied energy intervals, not all proton cross sections were well reproduced using the isoscalar strength from (α,α′γ). This might suggest mixing of isoscalar and isovector components and that this mixing and the degree of collectivity are not the same for all the 1− states below the particle binding energy.

Background: There is renewed interest in electric dipole strength distributions for a variety of reasons including the extraction of the dipole polarizability related to properties of the symmetry energy and a measure for the neutron skin thickness, understanding the structure of low-energy E1 strength in nuclei with neutron excess, and establishing the systematics of the isovector giant dipole resonance (IVGDR). Inelastic proton scattering at energies of a few hundred MeV and very forward angles including 0∘ has been established as a tool for the study of electric and magnetic dipole strength distributions in nuclei. Purpose: The present work aims at a systematic investigation of the electric and magnetic dipole strength distributions in the chain of stable even-mass tin isotopes. Methods: Inelastic proton scattering experiments were performed at the Research Center for Nuclear Physics, Osaka, with a 295-MeV beam covering laboratory angles 0∘–6∘ and excitation energies 6–22 MeV. Cross sections due to E1 and M1 excitations were extracted with a multipole decomposition analysis (MDA) and then converted to reduced transition probabilities with the “virtual photon method” for E1 and the “unit cross section method” for M1 excitations, respectively. Including a theory-aided correction for the high-excitation-energy region not covered experimentally, the electric dipole polarizability was determined from the E1 strength distributions. Results: Total photoabsorption cross sections derived from the E1 and M1 strength distributions show significant differences compared to those from previous (γ,xn) experiments in the energy region of the IVGDR. The widths of the IVGDR deduced from the present data with a Lorentz parametrization show an approximately constant value of about 4.5 MeV in contrast to the large variations between isotopes observed in previous work. The IVGDR centroid energies are in good correspondence to expectations from empirical systematics of their mass dependence. Furthermore, a study of the dependence of the IVGDR energies on bulk matter properties is presented. The E1 strengths below neutron threshold show fair agreement with results from (γ,γ′) experiments on Sn112,116,120,124 in the energy region between 6 and 7 MeV, where also isoscalar E1 strength was found for Sn124. At higher excitation energies, large differences are observed, pointing to a different nature of the excited states with small ground-state branching ratios. The isovector spin-M1 strengths exhibit a broad distribution between 6 and 12 MeV in all studied nuclei. Conclusions: The present results contribute to the solution of a variety of nuclear structure problems including the systematics of the energy and width of the IVGDR, the structure of low-energy E1 strength in nuclei, new constraints to energy density functionals (EDFs) aiming at a systematic description of the dipole polarizability across the nuclear chart, from which properties of the symmetry energy can be derived, and the systematics of the isovector spin-M1 strength in heavy nuclei.

The form factor of the electromagnetic excitation of $^{12}\mathrm{C}$ to its ${2}_{1}^{+}$ state was measured at extremely low momentum transfers in an electron-scattering experiment at the Superconducting Darmstadt Electron Linear Accelerator (S-DALINAC). A combined analysis with the world form-factor data results in a reduced transition strength $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=7.63(19)\phantom{\rule{4pt}{0ex}}{e}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{4}$ with an accuracy improved to 2.5%. In-medium no-core shell-model results with interactions derived from chiral effective field theory are able to reproduce the result. A quadrupole moment $Q({2}_{1}^{+})=5.97(30)\phantom{\rule{4pt}{0ex}}e\phantom{\rule{0.16em}{0ex}}{\mathrm{fm}}^{2}$ can be extracted from the strict correlation with the $B(E2)$ strength emerging in the calculations.

The electric dipole is an important property of heavy nuclei. Precise information on the electric dipole response provides information on the electric dipole polarisability which in turn allows to extract important constraints on neutron-skin thickness in heavy nuclei and parameters of the symmetry energy. The tin isotope chain is particularly suited for a systematic study of the dependence of the electric dipole response on neutron excess as it provides a wide mass range of accessible isotopes with little change of the underlying structure. Recently an inelastic proton scattering experiment under forward angles including 0º on 112,116,124Sn was performed at the Research Centre for Nuclear Physics (RCNP), Japan with a focus on the low-energy dipole strength and the polarisability. First results are presented here. Using data from an earlier proton scattering experiment on 120Sn the gamma strength function and level density are determined for this nucleus.

International audience; We performed experiments to study the low-energy part of the E1 response (Pygmy Dipole Resonance) in $^{90,94}$Zr nuclei, by measuring the (p,p’γ) and (α,α’γ) inelastic scattering reactions at energies Ebeam,p = 80 MeV and Ebeam,α = 130 MeV respectively. The inelastically scattered particles were measured by employing the high-resolution spectrometer Grand Raiden. The gamma-rays emitted following the de-excitation of the Zr target nuclei were detected using both the clover type HPGe detectors of the CAGRA array and the large volume LaBr3:Ce scintillation detectors from the HECTOR+ array. Some preliminary results are presented here.

The electric dipole strength distribution in ^{48}Ca between 5 and 25 MeV has been determined at RCNP, Osaka from proton inelastic scattering experiments at forward angles. Combined with photoabsorption data at higher excitation energy, this enables the first extraction of the electric dipole polarizability α_{D}(^{48}Ca)=2.07(22) fm^{3}. Remarkably, the dipole response of ^{48}Ca is found to be very similar to that of ^{40}Ca, consistent with a small neutron skin in ^{48}Ca. The experimental results are in good agreement with ab initio calculations based on chiral effective field theory interactions and with state-of-the-art density-functional calculations, implying a neutron skin in ^{48}Ca of 0.14-0.20 fm.

The electric dipole strength distribution in ^{48}Ca between 5 and 25 MeV has been determined at RCNP, Osaka from proton inelastic scattering experiments at forward angles. Combined with photoabsorption data at higher excitation energy, this enables the first extraction of the electric dipole polarizability α_{D}(^{48}Ca)=2.07(22) fm^{3}. Remarkably, the dipole response of ^{48}Ca is found to be very similar to that of ^{40}Ca, consistent with a small neutron skin in ^{48}Ca. The experimental results are in good agreement with ab initio calculations based on chiral effective field theory interactions and with state-of-the-art density-functional calculations, implying a neutron skin in ^{48}Ca of 0.14-0.20 fm.

Gamma strength functions (GSFs) and level densities (LDs) are essential ingredients of statistical nuclear reaction theory with many applications in astrophysics, reactor design, and waste transmutation. The aim of the present work is a test of systematic parametrizations of the GSF recommended by the RIPL-3 data base for the case of $^{208}$Pb. The upward GSF and LD in $^{208}$Pb are compared to gamma decay data from an Oslo-type experiment to examine the validity of the Brink-Axel (BA) hypothesis. The E1 and M1 parts of the total GSF are determined from high-resolution forward angle inelastic proton scattering data taken at 295 MeV at RCNP, Osaka, Japan. The total LD in $^{208}$Pb is derived from the $1^-$ LD extracted with a fluctuation analysis in the energy region of the isovector giant dipole resonance. The E1 GSF is compared to parametrizations recommended by the RIPL-3 data base showing systematic deficiencies of all models in the energy region around neutron threshold. The new data for the poorly known spinflip M1 resonance call for a substantial revision of the model suggested in RIPL-3. The total GSF derived from the present data is larger in the PDR energy region than the Oslo data but the strong fluctuations due to the low LD resulting from the double shell closure of $^{208}$Pb prevent a conclusion on a possible violation of the BA hypothesis. Using the parameters suggested by RIPL-3 for a description of the LD in $^{208}$Pb with the back-shifted Fermi gas model, remarkable agreement between the two experiments spanning a wide excitation energy range is obtained. Systematic parametrizations of the E1 and M1 GSF parts need to be reconsidered at low excitation energies. The good agreement of LD provides an independent confirmation of the approach underlying the decomposition of GSF and LDs in Oslo-type experiments.

The gamma strength function and level density of 1- states in 96Mo have been extracted from a high-resolution study of the (p,p') reaction at 295 MeV and extreme forward angles. By comparison with compound nucleus $\gamma$ decay experiments, this allows a test of the generalized Brink-Axel hypothesis in the energy region of the Pygmy Dipole Resonance. The Brink-Axel hypothesis is commonly assumed in astrophysical reaction network calculations and states that the gamma strength function in nuclei is independent of the structure of initial and final state. The present results validiate the Brink-Axel hypothesis for 96Mo and provide independent confirmation of the methods used to separate gamma strength function and level density in $\gamma$ decay experiments., Comment: 6 pages, 4 figures

High-resolution inelastic electron scattering on ${}^{96}$Zr establishes shape coexistence---where two nearby states possess distinct shapes---for this nucleus. Monte Carlo shell-model calculations indicate that the shape change in Zr isotopes is a quantum phase transition.

Type II shell evolution has recently been identified as a microscopic cause for nuclear shape coexistence.Establish a low-lying rotational band in ^{96}Zr.High-resolution inelastic electron scattering and a relative analysis of transition strengths are used.The B(E2;0_{1}^{+}→2_{2}^{+}) value is measured and electromagnetic decay strengths of the 2_{2}^{+} state are deduced.Shape coexistence is established for ^{96}Zr. Type II shell evolution provides a systematic and quantitative mechanism to understand deformation at low excitation energies.

Inelastic proton scattering at energies of a few 100 MeV and forward angles including 0° provides a novel method to measure gamma strength functions (GSF) in nuclei in an energy range of about 5 – 20 MeV. The experiments provide not only the E1 but also the M1 part of the GSF. The latter is poorly known in heavy nuclei. Comparison with gamma decay data (e.g. from the Oslo method) allows to test the generalised Brink-Axel (BA) hypothesis in the energy region of the pygmy dipole resonance (PDR) crucial for the modelling of (n,γ) and (γ,n) reactions in astrophysical reaction networks. From the two test cases studied, 208Pb remains inconclusive in the energy region of the PDR because of large Porter-Thomas fluctuations due to the small level density (LD), while the BA hypothesis seems to hold in case of 96Mo. A fluctuation analysis of the high-resolution data also provides a direct measure of the LD in the energy region of the isovector giant dipole resonance (IVGDR) well above the neutron threshold, where hardly any experimental information is available. This permits an independent test of the decomposition of GSF and LD in Oslo-type experiments.

Inelastic proton scattering at energies of a few 100 MeV and forward angles including 0∘ provides a novel method to measure gamma strength functions (GSF) in nuclei in an energy range of about 5–23 MeV. The experiments provide not only the E1 but also the M1 part of the GSF. The latter is poorly known in heavy nuclei. A case study of 208 Pb indicates that the systematics proposed for the M1-GSF in RIPL-3 needs to be substantially revised. Comparison with gamma decay data (e.g. from the Oslo method) allows to test the generalised Brink-Axel (BA) hypothesis in the energy region of the pygmy dipole resonance (PDR) crucial for the modelling of (n,γ) and (γ,n) reactions in astrophysical reaction networks. A fluctuation analysis of the high-resolution data also provides a direct measure of level densities in the energy region well above the neutron threshold, where hardly any experimental information is available.

We report on our recent electron scattering experiment off 96Zr. The B (E2; 01 +→22 +) transition strength is extracted in a relative analysis and allows the determination of all decay strengths of the 22 + state. The strong collectivity of the 22 + → 02 + transition establishes the 02 + state and the states build on top of it as an isolated deformed band.