Bayesian inference of nuclear symmetry energy from measured and imagined neutron skin thickness in ${}^{116,118,120,122,124,130,132}\mathrm{Sn},{}^{208}\mathrm{Pb}$ , and ${}^{48}\mathrm{Ca}$

Journal Article · Wed Oct 14 00:00:00 EDT 2020 · Physical Review C

DOI:https://doi.org/10.1103/physrevc.102.044316· OSTI ID:1837897

Xu, Jun  ^[1]; Xie, Wen-Jie ^[2]; Li, Bao-An  ^[3]

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1. Chinese Academy of Sciences (CAS), Shanghai (China)
2. Yuncheng University (China)
3. Texas A & M Univ., Commerce, TX (United States)

The neutron skin thickness Δr_np in heavy nuclei has been known as one of the most sensitive terrestrial probes of the nuclear symmetry energy E_sym(ρ) around $$\frac{2}{3}$$ of the saturation density ρ₀ 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 ²⁰⁸Pb and ⁴⁸Ca 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 ρ₀ from imagined Δr_np(²⁰⁸Pb)=0.15, 0.20, and 0.30 fm with a 1σ error bar of 0.02, 0.04, and 0.06 fm, respectively, as well as Δr_np(⁴⁸Ca)=0.12, 0.15, and 0.25 fm, with different 1σ 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 Δr_np data for ^{116, 118, 120, 122, 124, 130, 132}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 $$^{+ 26.5}_{-21.6}$$ MeV surrounding its mean value or L = 53 . 4 $$^{+ 18.6}_{ -29.5}$$ MeV surrounding its maximum a posteriori value, respectively, with the latter smaller than but consistent with the L = 66 $$^{+ 12}_{-20}$$ MeV from the neutron star data within their 68% confidence intervals. We found that Δr_np = 0.17 –0.18 fm in ²⁰⁸Pb 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 Δr_np of Sn isotopes, the experimental error bar of Δr_np in ²⁰⁸Pb should be at least smaller than 0.06 fm aimed by some current experiments. In addition, the Δr_np (⁴⁸Ca) 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 ±20 MeV error bars for L at 68% confidence level are necessary.

• Research Organization: Texas A & M Univ., Commerce, TX (United States)
• Sponsoring Organization: USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC)
• Grant/Contract Number: SC0013702; SC0009971
• OSTI ID: 1837897
• Journal Information: Physical Review C, Vol. 102, Issue 4; ISSN 2469-9985
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS