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Pb – Pygmy Dipole Resonance, Dipole Polarizability, Neutron Skin and Symmetry Energy – Electric Dipole Response of 208Pb – Pygmy Dipole Resonance, Dipole Polarizability, Neutron Skin and Symmetry Energy – A. Tamii1, I. Poltoratska2, P. von Neumann-Cosel2,Y.Fujita1,T.Adachi1,C.A.Bertulani3,J.Carter4, M. Dozono5,H.Fujita1, K. Hatanaka1,D.Ishikawa1,M.Itoh6,Y.Kalmykov2, T. Kawabata7, A.M. Krumbholz2,E.Litvinova8,9,H.Matsubara5, K. Nakanishi5, R. Neveling10,H.Okamura1,H.J.Ong1, B. ¨ozel-Tashenov8, V.Yu. Ponomarev2,A.Richter2,11, B. Rubio12, H. Sakaguchi1,Y.Sakemi6, Y. Sasamoto13, Y. Shimbara1,Y.Shimizu5,F.D.Smit10, T. Suzuki1,Y.Tameshige14,J.Wambach2,R.Yamada15, M. Yosoi1 and J. Zenihiro5 1Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka 567-0047, Japan 2Institut f¨ur Kernphysik, Technische Universit¨at Darmstadt, D-64289 Darmstadt, Germany 3Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, Texas 75429, USA 4School of Physics, University of the Witwatersrand, Johannesburg 2050, South Africa 5RIKEN Nishina Center, Wako, Saitama 351-0198, Japan 6Cyclotron and Radioisotope Center, Tohoku University, Sendai 980-8578, Japan 7Department of Physics, Kyoto University, Kyoto 606-8502, Japan 8GSI Helmholtzzentrum f¨ur Schwerionenforschung, D-64291 Darmstadt, Germany 9Institut f¨ur Theoretische Physik, Goethe-Universit¨at, 60438 Frankfurt am Main, Germany 10iThemba LABS, Somerset West 7129, South Africa 11ECT*, Villa Tambosi, 1-38123, Villazzano (Trento), Italy 12Instituto de Fisica Corpusular, CSIC-Universidad de Valencia, E-46071 Valencia, Spain 13Center for Nuclear Study, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan 14National Institute of Radiological Sciences, Chiba 263-8555, Japan 15Department of Physics, Kyushu University, Fukuoka 812-8581, Japan Abstract The electric dipole (E1) response of 208Pb has been precisely determined by proton inelastic scattering measurement at very forward angles. The data are quite important for studies of low-lying dipole strength, often called pygmy dipole resonance (PDR), as well as for extracting sum-rule values of the E1 reduced transition probability B(E1). The electric dipole polarizability, which is defined as an inversely energy weighted sum-rule of B(E1), is much focused because of its close correlation to the neutron skin thickness and the symmetry energy of the nuclear equation of state. The determination of the symmetry energy is important for nuclear physics as well as studies of astrophysics e.g. properties and cooling process of a neutron star, X-ray burst, superburst, supernovae, and nucleosynthesis. 1 Introduction Electric dipole (E1) response of nuclei is one of the most fundamental responses of nuclei to external fields. Historically the study of the E1 response has been initiated by Migdal with the prediction of its mean excitation energy.[1] The work influenced the studies of nuclear collective excitations and giant resonances through the discovery of the isovector electric giant dipole resonance (IVGDR or shortly GDR) [2] and theoretical work on incompressible hydro-dynamical model by Goldhaber and Teller.[3] In 1960s and 70s E1 responses in the GDR region have been systematically measured by using (γ,xn) reactions with photon beams produced by positron annihilation in flight method. The data have been compared with the Thomas-Reiche-Kuhn (TRK) sum-rule, which is an energy weighted sum-rule of B(E1). The E1 response below the neutron separation energy (Sn)has been measured by nuclear resonance fluorescence (NRF). The photon beam was produced by bremsstrahlung, tagged photon, or laser backward Compton scattering method. Recently a concentration of E1 strengths around the neutron separation energy has been reported for several heavy nuclei and neutron rich unstable nuclei. The strength are called low-lying dipole strength. Several theoretical models have predicted similar E1 strength concentration around the neutron separation energy, which is called pygmy dipole resonance (PDR), and have drawn much attention in relation to the observed low-lying E1 strength. The PDR is explained as a collective dipole oscillation of neutron skin against isospin- saturated core, in contrast that the GDR is explained as a collective dipole oscillation between neutrons and protons. The PDR strength may have close relation to the neutron skin thickness of the nucleus. In addition, since the PDR is located around the neutron separation energy, its strength distribution can have significant influence on the prediction of the nucleosynthesis in stars through the equilibrium between the (γ,n)and(n, γ) reactions at finite temperature.[4] Electric dipole polarizability, or shortly dipole polarizability, is another promising quantity to study the neutron skin thickness and symmetry energy of the nuclear equation of state. The work by P.-G. Reinhard and W. Nazarewicz has shown that the neutron skin thickness and the dipole polarizability of 208Pb has very strong correlation to each other.[5] Since the dipole polarizability can be determined by an inversely energy weighted sum-rule value of B(E1), one needs to measure the complete E1 strength distribution including the neutron separation energy region up to high excitation energy. The symmetry energy is essential to predict the mass, radius, and internal structure of a neutron star, supernova explosion dynamics, evolution of neutron star binary systems, mechanism of X-ray burst and superburst, neutron star cooling, and nucleosynthesis. Thus determination of complete E1 strength distribution is quite important for nuclear-astrophysics as well as nuclear physics. In this background, we have developed an experimental technique for measuring proton inelastic scatter- ing at zero degrees and forward angles. The method is excellent to experimentally determine the complete B(E1) strength distribution including the PDR, GDR, and dipole polarizability. In this article, we report the experimental method and recent results on the 208Pb nucleus. 2 Proton Inelastic Scattering as a New Probe of E1 Responses: Comparison to Real-Photon Measurements We have developed proton inelastic scattering measurement as a new probe to study the E1 response of nuclei. The overview of the E1 response of heavy nuclei is shown in Fig. 1. Historically the E1 response have been studied mainly by real-photon beam experiments. Figure 2 shows the difference between the two methods. In the upper panel, real photon is used as a beam to excite the target nucleus. A decay gamma-ray or a neutron (or a few neutrons) is detected. In this method, only a partial width, corresponding to the observed decaying channel, is measured. Thus all the decay channels must be measured to determine the total width. The flux of the photon beam decreases with the energy and background events from surrounding material or shields become larger. In the gamma decay measurement of NRF, high-purity germanium detectors are usually used for accurate measurement of the gamma energy. Since the photo-peak is used to measure the gamma energy, the detection efficiency decreases rapidly as the gamma energy increases (usually less than 1%). The gamma-ray cannot be observed if each strength is too small or the level density is too high. In addition, direct decay to the ground state is assumed in the analysis of the strength. The assumption might be reasonable but for accurate determination of the strength, cascade decay contribution must be corrected relying on a statistical decay simulation. The problem is similar to the Pandemonium effect in the beta-decay analysis. For the neutron decay channel, neutron detection efficiency is quite low at several MeV region. Usually the emitted neutrons are themalized by using material and the number of the emitted neutrons is measured. The method allows detection of multiple neutrons but the energy information of the neutrons is lost. Thus the E1 strength data can be obtained for each of the beam energy windows, which is typically around 300 keV. Proton decay channel is usually neglected. For real-photon measurements, one needs several grams of isotopically enriched target, that also limits the applicability of the measurements for specific target nuclides. The E1 strength measurement by inelastic proton scattering measurement is shown in the lower panel of Fig. 2. The target nucleus is bombarded by a proton and is excited by Coulomb interaction with exchanging a virtual photon. The scattered proton is detected. The method is probing only the excitation process and is independent of the decay process. Thus the total E1 excitation strength is observed. One of the essences of the method is to measure the reaction at intermediate energy (300 MeV) and at small scattering angles close to zero degrees, where Coulomb excitation is dominant. The detection efficiency of the scattered proton is close to 100%, and is uniform over the measured excitation energy range of 5-25 MeV. The range well covers the neutron separation energy and the GDR region for most of stable nuclei. Since the proton beam flux is much higher than real gamma-beam, only several mili-grams of enriched target is required. An energy resolution of 20-30 keV is achievable. Properties of the proton inelastic scattering measurement are summarized in comparison to real-photon measurements. • Total E1 strength is measured. The measurement is independent of the decay process or neutron separa- tion energy. No correction of cascade decay or feeding is required. • E1 strength distribution is measured with a uniform and high (∼100%) detection efficiency over the excitation energy range of 5-25 MeV, that covers neutron separation energy and GDR. p p ( , ’) NRF or (γ, xn) NRF (γ, xn) γ detector PDR GDR γ (or xn) core pn skin A * A A (or A-x) (p,p’ ) detector p Strength (Arbitrary) p E1 virtual photon 4 S 8 S 12 16 n p * Excitation Energy (MeV) A A Figure 1: Illustration of E1 response of heavy nuclei. Time The pygmy dipole resonance (PDR) is located around the neutron separation energy (Sn). Historically nu- Figure 2: (upper panel) Principle of the E1response clear resonance fluorescence (NRF), sometimes called measurement by a real-photon beam.
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