Characterizing the nuclear models informed by PREX and CREX: A view from Bayesian inference

Measurements from the weak charge radius experiments on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mmultiscripts> <a:mi>Ca</a:mi> <a:mprescripts/> <a:none/> <a:mn>48</a:mn> </a:mmultiscripts> </a:math> (CREX) and <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mmultiscripts> <b:mi>Pb</b:mi> <b:mprescripts/> <b:none/> <b:mn>208</b:mn> </b:mmultiscripts> </b:math> (PREX) challenge existing nuclear models. In the post-PREX-CREX era, it is unclear if current models can simultaneously describe weak charge distributions along with accurate measurements of binding energy and charge radii. In this work, we explore the parameter space of relativistic and nonrelativistic models to study the differences between the electric and weak form factors, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi mathvariant="normal">Δ</c:mi> <c:mi>F</c:mi> <c:mo>=</c:mo> <c:msub> <c:mi>F</c:mi> <c:mtext>ch</c:mtext> </c:msub> <c:mo>−</c:mo> <c:msub> <c:mi>F</c:mi> <c:mi>W</c:mi> </c:msub> </c:mrow> </c:math> , in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mmultiscripts> <e:mi>Ca</e:mi> <e:mprescripts/> <e:none/> <e:mn>48</e:mn> </e:mmultiscripts> </e:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mmultiscripts> <f:mi>Pb</f:mi> <f:mprescripts/> <f:none/> <f:mn>208</f:mn> </f:mmultiscripts> </f:math> . We show, for the first time, which aspects of mean-field models are the most important in determining the relative magnitude of the neutron skin in lead and calcium nuclei. We carefully disentangle the tension between the PREX-2/CREX constraints and the ability of the relativistic mean field and Skyrme models to accurately describe binding energies and charge radii. We find that the nuclear symmetry energy coefficient <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msub> <g:mi>S</g:mi> <g:mi mathvariant="normal">V</g:mi> </g:msub> </g:math> and the isovector spin-orbit coefficient <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:msubsup> <i:mi>b</i:mi> <i:mn>4</i:mn> <i:mo>′</i:mo> </i:msubsup> </i:math> play different roles in determining <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mi mathvariant="normal">Δ</j:mi> <j:mi>F</j:mi> </j:mrow> </j:math> of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mmultiscripts> <l:mi>Ca</l:mi> <l:mprescripts/> <l:none/> <l:mn>48</l:mn> </l:mmultiscripts> </l:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mmultiscripts> <m:mi>Pb</m:mi> <m:mprescripts/> <m:none/> <m:mn>208</m:mn> </m:mmultiscripts> </m:math> . Consequently, adjusting <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:msub> <n:mi>S</n:mi> <n:mi mathvariant="normal">V</n:mi> </n:msub> </n:math> or <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:msubsup> <p:mi>b</p:mi> <p:mn>4</p:mn> <p:mo>′</p:mo> </p:msubsup> </p:math> shifts predicted <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:mrow> <q:mi mathvariant="normal">Δ</q:mi> <q:mi>F</q:mi> </q:mrow> </q:math> values toward or away from PREX-2/CREX measurements. Additionally, <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"> <s:msub> <s:mi>S</s:mi> <s:mi mathvariant="normal">V</s:mi> </s:msub> </s:math> and the slope <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"> <u:mrow> <u:mi>L</u:mi> </u:mrow> </u:math> are marginally correlated given the prior constraints of our Bayesian inference, allowing us to infer them separately from PREX-2/CREX data.