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Register a new userConstraining isovector nuclear interactions with giant dipole resonance and neutron skin in $^{208}$Pb from a Bayesian approach
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Jun Xu
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The remaining uncertainties of isovector nuclear interactions call for reliable experimental measurements of isovector probes in finite nuclei. Based on the Bayesian analysis, although the neutron-skin thickness data or the isovector giant dipole resonance data in $^{208}$Pb can constrain only one isovector interaction parameter, correlations between other parameters are built. Using combined data of both the neutron-skin thickness and the isovector giant dipole resonance helps to constrain significantly all isovector interaction parameters, thus serves as a useful way in the future analysis.
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We present and discuss numerical predictions for the neutron density distribution of $^{208}$Pb using various non-relativistic and relativistic mean-field models for the nuclear structure. Our results are compared with the very recent pion photoproduction data from Mainz. The parity-violating asymmetry parameter for elastic electron scattering at the kinematics of the PREX experiment at JLab and the neutron skin thickness are compared with the available data. We consider also the dependence between the neutron skin and the parameters of the expansion of the symmetry energy.
The $^{208}$Pb($p$,$ngammabar p$) $^{207}$Pb reaction at a beam energy of 30 MeV has been used to excite the anti-analog of the giant dipole resonance (AGDR) and to measure its $gamma$-decay to the isobaric analog state in coincidence with proton decay of IAS. The energy of the transition has also been calculated with the self-consistent relativistic random-phase approximation (RRPA), and found to be linearly correlated to the predicted value of the neutron-skin thickness ($Delta R_{pn}$). By comparing the theoretical results with the measured transition energy, the value of 0.190 $pm$ 0.028 fm has been determined for $Delta R_{pn}$ of $^{208}$Pb, in agreement with previous experimental results. The AGDR excitation energy has also been used to calculate the symmetry energy at saturation ($J=32.7 pm 0.6$ MeV) and the slope of the symmetry energy ($L=49.7 pm 4.4$ MeV), resulting in more stringent constraints than most of the previous studies.
In ultraperipheral collisions (UPC) of nuclei the impact of Lorentz-contracted electromagnetic fields of collision partners leads to their excitations. In case of heavy nuclei the emission of neutrons is a main deexcitation channel and forward neutrons emitted in UPC were detected at the Relativistic Heavy-Ion Collider (RHIC) and at the Large Hadron Collider (LHC) by means of Zero Degree Calorimeters. However, the excitation of low-lying discrete nuclear states is also possible in UPC below the neutron separation energy. In this work by means of the Weizsacker-Williams method the data on nuclear resonance fluorescence (NRF) induced by real photons in 208 Pb are used to model the excitations of discrete levels in colliding nuclei. Due to Lorentz boosts one can expect that deexcitation photons with energies up to 40 GeV and 300 GeV are emitted in very forward direction, respectively, at the LHC and at the Future Circular Collider (FCC-hh). Energy, rapidity and angular distributions of such photons are calculated in the laboratory system, which can be used for monitoring of collider luminosity or triggering particle production in UPC.
The reaction cross section $sigma_R$ is useful to determine the neutron radius $R_n$ as well as the matter radius $R_m$. The chiral (Kyushu) $g$-matrix folding model for $^{12}$C scattering on $^{9}$Be, $^{12}$C, $^{27}$Al targets was tested in the incident energy range of $30 lsim E_{rm in} lsim 400 $ MeV, and it is found that the model reliably reproduces the $sigma_R$ in $30 lsim E_{rm in} lsim 100 $ MeV and $250 lsim E_{rm in} lsim 400$ MeV. item[Aim] We determine $R_n$ and the neutron skin thickness $R_{rm skin}$ of ${}^{208}{rm Pb}$ by using high-quality $sigma_R$ data for the $p+{}^{208}{rm Pb}$ scattering in $30 leq E_{rm in} leq 100$ MeV. The theoretical model is the Kyushu $g$-matrix folding model with the densities calculated with Gongny-D1S HFB (GHFB) with the angular momentum projection (AMP). item[Results] The Kyushu $g$-matrix folding model with the GHFB+AMP densities underestimates $sigma_{rm R}$ in $30 leq E_{rm in} leq 100$~MeV only by a factor of 0.97. Since the proton radius $R_p$ calculated with GHFB+AMP agrees with the precise experimental data of 5.444 fm, the small deviation of the theoretical result from the data on $sigma_R$ allows us to scale the GHFB+AMP neutron density so as to reproduce the $sigma_R$ data. In $E_{rm in}$ = 30--100 MeV, the experimental $sigma_R$ data can be reproduced by assuming the neutron radius of ${}^{208}{rm Pb}$ as $R_n$ = $5.722 pm 0.035$ fm. item[Conclusion] The present result $R_{rm skin}$ = $0.278 pm 0.035$ fm is in good agreement with the recent PREX-II result of $r_{rm skin}$ = $0.283pm 0.071$ fm.
Information on the size and shape of the neutron skin on $^{208}$Pb has been extracted from coherent pion photoproduction cross sections measured using the Crystal Ball together with the Glasgow tagger at the MAMI electron beam facility. On exploitation of an interpolated fit of a theoretical model to the measured cross sections the half-height radius and diffuseness of the neutron distribution are found to be 6.70$pm 0.03(stat)$ fm and 0.55$pm 0.01(stat)$$^{+0.02}_{-0.03}(sys)$ fm respectively, corresponding to a neutron skin thickness $Delta r_{np}$=0.15$pm 0.03(stat)$$^{+0.01}_{-0.03}(sys)$ fm. The results give the first successful extraction of a neutron skin with an electromagnetic probe and indicate the skin of $^{208}$Pb has a halo character. The measurement provides valuable new constraints on both the structure of nuclei and the equation of state for neutron-rich matter.
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