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Neutron skin thickness of 116,118,120,122,124Sn determined from reaction cross sections of proton scattering

Shingo Tagami Department of Physics, Kyushu University, Fukuoka 819-0395, Japan    Tomotsugu Wakasa Department of Physics, Kyushu University, Fukuoka 819-0395, Japan    Masanobu Yahiro orion093g@gmail.com Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
Abstract
  • Background

    The cross sections of the isovector spin-dipole resonances (SDR) in the Sb isotopes have been measured. Within the model used, the neutron-skin thicknesses rskin​(exp)r_{\rm skin}({\rm exp}) deduced 0.12±0.060.12\pm 0.06 fm for 116Sn, 0.13±0.060.13\pm 0.06 fm for 118Sn, 0.18±0.070.18\pm 0.07 fm for 120Sn, 0.22±0.070.22\pm 0.07 fm for 122Sn, 0.19±0.070.19\pm 0.07 fm for 124Sn. We tested the chiral (Kyushu) gg-matrix folding model for 12C+12C scattering, and found that the Kyushu gg-matrix folding model is reliable for reaction cross sections σR\sigma_{\rm R} in 3030~{}\,  E_in   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}100 M​e​V​a​n​d~{}MeVand250   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}E_in   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}400M​e​V.W​e​d​e​t​e​r​m​i​n​e​n​e​u​t​r​o​n​s​k​i​n​t​h​i​c​k​n​e​s​s~{}MeV.Wedetermineneutronskinthicknessr_skin(exp),usingmeasured,usingmeasuredσ_Ro​fof^4H​e+He+^116,120,224S​n​s​c​a​t​t​e​r​i​n​g.T​h​e​r​e​s​u​l​t​s​a​r​eSnscattering.Theresultsarer_skin(exp)=0.242 ±0.140f​m​f​o​r~{}fmfor^116S​n,Sn,r_skin(exp)=0.377 ±0.140f​m​f​o​r~{}fmfor^120S​n,Sn,r_skin(exp)=0.180 ±0.142f​m​f​o​r~{}fmfor^124S​n.T​h​eSn.Theσ_Ra​r​e​a​v​a​i​l​a​b​l​e​f​o​r​p​r​o​t​o​n​s​c​a​t​t​e​r​i​n​g​o​nareavailableforprotonscatteringon^116,118,120,122,124S​n​w​i​t​h​h​i​g​h​a​c​c​u​r​a​c​y​o​fSnwithhighaccuracyof2 ∼3%a​s​a​f​u​n​c​t​i​o​n​o​f​i​n​c​i​d​e​n​t​e​n​e​r​g​yasafunctionofincidentenergyE_in.Purposeitem item PurposeOuraimistodetermine.\par\description@item@[Purpose]Ouraimistodeterminer_skin(exp)f​o​rfor^116,118,120,122,124S​n​w​i​t​h​s​m​a​l​l​e​r​r​o​r​s​b​y​u​s​i​n​g​t​h​e​K​y​u​s​h​uSnwithsmallerrorsbyusingtheKyushug−m​a​t​r​i​x​f​o​l​d​i​n​g​m​o​d​e​l.Methodsitem item Methods​O​u​r​m​o​d​e​l​i​s​t​h​e​K​y​u​s​h​u-matrixfoldingmodel.\par\description@item@[Methods]OurmodelistheKyushug−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​s​c​a​l​e​d​f​r​o​m​t​h​e​D​1​S−G​H​F​B+A​M​P​n​e​u​t​r​o​n​d​e​n​s​i​t​y,w​h​e​r​e​D​1​S−G​H​F​B+A​M​P​s​t​a​n​d​s​f​o​r​G​o​g​n​y−D​1​S​H​F​B​(D​1​S−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​p​r​o​t​o​n​r​a​d​i​i​o​f​D​1​S−G​H​F​B+A​M​P​a​g​r​e​e​w​i​t​h​t​h​o​s​e​c​a​l​c​u​l​a​t​e​d​w​i​t​h​t​h​e​i​s​o​t​o​p​e​s​h​i​f​t​m​e​t​h​o​d​b​a​s​e​d​o​n​t​h​e​e​l​e​c​t​r​o​n​s​c​a​t​t​e​r​i​n​g.W​e​t​h​e​n​s​c​a​l​e​t​h​e​D​1​S−G​H​F​B+A​M​P​n​e​u​t​r​o​n​d​e​n​s​i​t​i​e​s​s​o​a​s​t​o​r​e​p​r​o​d​u​c​e​t​h​e-matrixfoldingmodelwiththedensitiesscaledfromtheD1S-GHFB+AMPneutrondensity,whereD1S-GHFB+AMPstandsforGogny-D1SHFB(D1S-GHFB)withtheangularmomentumprojection(AMP).\par\description@item@[Results]TheprotonradiiofD1S-GHFB+AMPagreewiththosecalculatedwiththeisotopeshiftmethodbasedontheelectronscattering.WethenscaletheD1S-GHFB+AMPneutrondensitiessoastoreproducetheσ_R(exp).In.In30   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}E_in   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}65M​e​V,w​e​d​e​t​e​r​m​i​n​e~{}MeV,wedeterminer_skin(exp)f​r​o​m​m​e​a​s​u​r​e​dfrommeasuredσ_R.Thevaluesare.Thevaluesarer_skin(exp)=0.118 ±0.021f​m​f​o​r~{}fmfor^116S​n,Sn,0.112 ±0.021f​m​f​o​r~{}fmfor^118S​n,Sn,0.124 ±0.021f​m​f​o​r~{}fmfor^120S​n,Sn,0.156 ±0.022f​m​f​o​r~{}fmfor^124S​n.A​s​f​o​rSn.Asfor^122S​n,t​h​e​s​k​i​n​v​a​l​u​e​i​nSn,theskinvaluein30   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}E_in   ~<\stackrel{{\scriptstyle<}}{{\widetilde{}}}50M​e​V​i​s~{}MeVis0.122 ±0.024f​m.Conclusionsitem item Conclusions​O​u​r​r​e​s​u​l​t​s​a​r​e​c​o​n​s​i​s​t​e​n​t​w​i​t​h​t​h​e​p​r​e​v​i​o​u​s​v​a​l​u​e​s.~{}fm.\par\description@item@[Conclusions]Ourresultsareconsistentwiththepreviousvalues.\par