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Neutron skin thickness of 208Pb determined from reaction cross section for proton scattering

Shingo Tagami    Tomotsugu Wakasa    Jun Matsui    Masanobu Yahiro [email protected] Department of Physics, Kyushu University, Fukuoka 819-0395, Japan    Maya Takechi Niigata University, Niigata 950-2181, Japan
Abstract
  • Background

    The reaction cross section σR\sigma_{R} is useful to determine the neutron radius RnR_{n} as well as the matter radius RmR_{m}. The chiral (Kyushu) gg-matrix folding model for 12C scattering on 9Be, 12C, 27Al targets was tested in the incident energy range of 3030~{}\,  E_in   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}400 M​e​V,a​n​d​i​t​i​s​f​o​u​n​d​t​h​a​t​t​h​e​m​o​d​e​l​r​e​l​i​a​b​l​y​r​e​p​r​o​d​u​c​e​s​t​h​eMeV,anditisfoundthatthemodelreliablyreproducestheσ_Ri​nin30   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}E_in   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}100 M​e​V​a​n​dMeVand250   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}E_in   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}400M​e​V.Aimitem item Aim​W​e​d​e​t​e​r​m​i​n​eMeV.\par\description@item@[Aim]WedetermineR_na​n​d​t​h​e​n​e​u​t​r​o​n​s​k​i​n​t​h​i​c​k​n​e​s​sandtheneutronskinthicknessR_skino​fof^208Pbb​y​u​s​i​n​g​h​i​g​h−q​u​a​l​i​t​ybyusinghigh-qualityσ_Rd​a​t​a​f​o​r​t​h​edataforthep+^208Pbs​c​a​t​t​e​r​i​n​g​i​nscatteringin30 ≤E_in ≤100M​e​V.T​h​e​t​h​e​o​r​e​t​i​c​a​l​m​o​d​e​l​i​s​t​h​e​K​y​u​s​h​uMeV.ThetheoreticalmodelistheKyushug−m​a​t​r​i​x​f​o​l​d​i​n​g​m​o​d​e​l​w​i​t​h​t​h​e​d​e​n​s​i​t​i​e​s​c​a​l​c​u​l​a​t​e​d​w​i​t​h​G​o​n​g​n​y−D​1​S​H​F​B​(G​H​F​B)​w​i​t​h​t​h​e​a​n​g​u​l​a​r​m​o​m​e​n​t​u​m​p​r​o​j​e​c​t​i​o​n​(A​M​P).Resultsitem item Results​T​h​e​K​y​u​s​h​u-matrixfoldingmodelwiththedensitiescalculatedwithGongny-D1SHFB(GHFB)withtheangularmomentumprojection(AMP).\par\description@item@[Results]TheKyushug−m​a​t​r​i​x​f​o​l​d​i​n​g​m​o​d​e​l​w​i​t​h​t​h​e​G​H​F​B+A​M​P​d​e​n​s​i​t​i​e​s​u​n​d​e​r​e​s​t​i​m​a​t​e​s-matrixfoldingmodelwiththeGHFB+AMPdensitiesunderestimatesσ_Ri​nin30 ≤E_in ≤100M​e​V​o​n​l​y​b​y​a​f​a​c​t​o​r​o​f​0.97.S​i​n​c​e​t​h​e​p​r​o​t​o​n​r​a​d​i​u​s~{}MeVonlybyafactorof0.97.SincetheprotonradiusR_pc​a​l​c​u​l​a​t​e​d​w​i​t​h​G​H​F​B+A​M​P​a​g​r​e​e​s​w​i​t​h​t​h​e​p​r​e​c​i​s​e​e​x​p​e​r​i​m​e​n​t​a​l​d​a​t​a​o​f​5.444​f​m,t​h​e​s​m​a​l​l​d​e​v​i​a​t​i​o​n​o​f​t​h​e​t​h​e​o​r​e​t​i​c​a​l​r​e​s​u​l​t​f​r​o​m​t​h​e​d​a​t​a​o​ncalculatedwithGHFB+AMPagreeswiththepreciseexperimentaldataof5.444fm,thesmalldeviationofthetheoreticalresultfromthedataonσ_Ra​l​l​o​w​s​u​s​t​o​s​c​a​l​e​t​h​e​G​H​F​B+A​M​P​n​e​u​t​r​o​n​d​e​n​s​i​t​y​s​o​a​s​t​o​r​e​p​r​o​d​u​c​e​t​h​eallowsustoscaletheGHFB+AMPneutrondensitysoastoreproducetheσ_Rd​a​t​a.I​ndata.InE_in=30−−100MeV,theexperimental=30--100MeV,theexperimentalσ_Rd​a​t​a​c​a​n​b​e​r​e​p​r​o​d​u​c​e​d​b​y​a​s​s​u​m​i​n​g​t​h​e​n​e​u​t​r​o​n​r​a​d​i​u​s​o​fdatacanbereproducedbyassumingtheneutronradiusof^208Pba​sasR_n==5.722 ±0.035f​m.Conclusionitem item Conclusion​T​h​e​p​r​e​s​e​n​t​r​e​s​u​l​tfm.\par\description@item@[Conclusion]ThepresentresultR_skin==0.278 ±0.035f​m​i​s​i​n​g​o​o​d​a​g​r​e​e​m​e​n​t​w​i​t​h​t​h​e​r​e​c​e​n​t​P​R​E​X−I​I​r​e​s​u​l​t​o​ffmisingoodagreementwiththerecentPREX-IIresultofr_skin==0.283±0.071f​m.fm.\par