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تسجيل مستخدم جديدComment on Neutron Skin of $^{208}$Pb from Coherent Pion Photoproduction
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We argue that the reaction mechanism for the coherent pion production is not known with sufficient accuracy to determine the neutron radius of 208Pb to the claimed precision of 0.03 fm.
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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 exploitat
ion 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.
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 photoprodu
ction 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 symmetry energy and its density dependence are pivotal for many nuclear physics and astrophysics applications, as they determine properties ranging from the neutron-skin thickness of nuclei to the crust thickness and the radius of neutron stars.
Recently, PREX-II reported a value of $0.283pm0.071$ fm for the neutron-skin thickness of $^{208}$Pb, $R_{rm skin}^{^{208}text{Pb}}$, implying a symmetry-energy slope parameter $L$ of $106pm37$ MeV, larger than most ranges obtained from microscopic calculations and other nuclear experiments. We use a nonparametric equation of state representation based on Gaussian processes to constrain the symmetry energy $S_0$, $L$, and $R_{rm skin}^{^{208}text{Pb}}$ directly from observations of neutron stars with minimal modeling assumptions. The resulting astrophysical constraints from heavy pulsar masses, LIGO/Virgo, and NICER favor smaller values of the neutron skin and $L$, as well as negative symmetry incompressibilities. Combining astrophysical data with chiral effective field theory ($chi$EFT) and PREX-II constraints yields $S_0 = 33.0^{+2.0}_{-1.8}$ MeV, $L=53^{+13}_{-15}$ MeV, and $R_{rm skin}^{^{208}text{Pb}} = 0.17^{+0.04}_{-0.04}$ fm. We also examine the consistency of several individual $chi$EFT calculations with astrophysical observations and terrestrial experiments. We find that there is only mild tension between $chi$EFT, astrophysical data, and PREX-IIs $R_mathrm{skin}^{^{208}mathrm{Pb}}$ measurement ($p$-value $= 12.3%$) and that there is excellent agreement between $chi$EFT, astrophysical data, and other nuclear experiments.
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.
We discuss the possibility of extracting the neutron-neutron scattering length $a_{nn}$ and effective range $r_{nn}$ from cross section data ($d^2sigma/dM_{nn}/dOmega_pi$), as a function of the $nn$ invariant mass $M_{nn}$, for $pi^+$ photoproduction
on the deuteron ($gamma dto pi^+nn$). The analysis is based on a $gamma dto pi^+nn$ reaction model in which realistic elementary amplitudes for $gamma pto pi^+n$, $NNto NN$, and $pi Nto pi N$ are built in. We show that $M_{nn}$ dependence (lineshape) of a ratio $R_{rm th}$, $d^2sigma/dM_{nn}/dOmega_pi$ normalized by $dsigma/dOmega_pi$ for $gamma ptopi^+ n$ and the nucleon momentum distribution inside the deuteron, at the kinematics with $theta_pi=0^circ$ and $E_gammasim 250$ MeV is particularly useful for extracting $a_{nn}$ and $r_{nn}$ from the corresponding data $R_{rm exp}$. It is found that $R_{rm exp}$ with 2% error, resolved into the $M_{nn}$ bin width of 0.04 MeV (corresponding to the $p_pi$ bin width of 0.05 MeV$/c$), can determine $a_{nn}$ and $r_{nn}$ with uncertainties of $pm 0.21$ fm and $pm 0.06$ fm, respectively, for the case of $a_{nn}=-18.9$ fm and $r_{nn}=2.75$ fm. The requirement of such narrow bin widths indicates that the momenta of the incident photon and the emitted $pi^+$ have to be measured with high resolutions. This can be achieved by utilizing virtual photons of very small $Q^2$ from electron scattering at Mainz MAMI facility. The proposed method for determining $a_{nn}$ and $r_{nn}$ from $gamma dto pi^+ nn$ has a great experimental advantage over the previous one utilizing $pi^- dtogamma nn$ for being free from the formidable task of controlling the neutron detection efficiency and its uncertainty.
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