Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Sn</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>116</mml:mn><mml:mo>,</mml:mo><mml:mn>118</mml:mn><mml:mo>,</mml:mo><mml:mn>120</mml:mn><mml:mo>,</mml:mo><mml:mn>122</mml:mn><mml:mo>,</mml:mo><mml:mn>124</mml:mn><mml:mo>,</mml:mo><mml:mn>130</mml:mn><mml:mo>,</mml:mo><mml:mn>132</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mo> </mml:mo><mml:mmultiscripts><mml:mi>Pb</mml:mi><mml:mprescripts/><mml:none/><mml:mn>208</mml:mn></mml:mmultiscripts></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Ca</mml:mi><mml:mprescripts/><mml:none/><mml:mn>48</mml:mn></mml:mmultiscripts></mml:math>

Abstract

The neutron skin thickness $\mathrm{\ensuremath{\Delta}}{r}_{np}$ in heavy nuclei was known as one of the most sensitive terrestrial probes of the nuclear symmetry energy ${E}_{\mathrm{sym}}(\ensuremath{\rho})$ around $\frac{2}{3}$ of the saturation density ${\ensuremath{\rho}}_{0}$ of nuclear matter. Existing neutron skin data mostly from hadronic observables suffer from large uncertainties and their extraction from experiments are often strongly model dependent. While waiting eagerly for the promised model-independent and high-precision neutron skin data for $^{208}\mathrm{Pb}$ and $^{48}\mathrm{Ca}$ from the parity-violating electron scattering experiments (PREX-II and CREX at JLab as well as MREX at MESA), within the Bayesian statistical framework using the Skyrme-Hartree-Fock model we infer the posterior probability distribution functions (PDFs) of the slope parameter $L$ of the nuclear symmetry energy at ${\ensuremath{\rho}}_{0}$ from imagined $\mathrm{\ensuremath{\Delta}}{r}_{np}(^{208}\mathrm{Pb})=0.15$, 0.20, and 0.30 fm with a $1\ensuremath{\sigma}$ error bar of 0.02, 0.04, and 0.06 fm, respectively, as well as $\mathrm{\ensuremath{\Delta}}{r}_{np}(^{48}\mathrm{Ca})=0.12$, 0.15, and 0.25 fm with a $1\ensuremath{\sigma}$ error bar of 0.01 and 0.02 fm, respectively. The results are compared with the PDFs of $L$ inferred using the same approach from the available $\mathrm{\ensuremath{\Delta}}{r}_{np}$ data for $^{116,118,120,122,124,130,132}\mathrm{Sn}$ from hadronic probes. They are also compared with results from a recent Bayesian analysis of the radius and tidal deformability data of canonical neutron stars from GW170817 and NICER. The neutron skin data for Sn isotopes gives $L=45.{5}_{\ensuremath{-}21.6}^{+26.5}$ MeV surrounding its mean value or $L=53.{4}_{\ensuremath{-}29.5}^{+18.6}$ MeV surrounding its maximum a posteriori value, respectively, with the latter smaller than but consistent with the $L={66}_{\ensuremath{-}20}^{+12}$ MeV from the neutron star data within their 68% confidence intervals. We found that $\mathrm{\ensuremath{\Delta}}{r}_{np}=0.17$--0.18 fm in $^{208}\mathrm{Pb}$ with an error bar of about 0.02 fm leads to a PDF of $L$ compatible with that from analyzing the Sn data. To provide additionally useful information on $L$ extracted from the $\mathrm{\ensuremath{\Delta}}{r}_{np}$ of Sn isotopes, the experimental error bar of $\mathrm{\ensuremath{\Delta}}{r}_{np}$ in $^{208}\mathrm{Pb}$ should be at least smaller than 0.06 fm aimed by some current experiments. In addition, the $\mathrm{\ensuremath{\Delta}}{r}_{np}(^{48}\mathrm{Ca})$ needs to be larger than 0.15 fm but smaller than 0.25 fm to be compatible with the Sn and/or neutron star results. To further improve our current knowledge about $L$ and distinguish its PDFs in the examples considered, even higher precisions leading to significantly less than $\ifmmode\pm\else\textpm\fi{}20\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ error bars for $L$ at 68% confidence level are necessary.

Topics & Concepts