Neutron Skins with α-clusters

Transcription

1 Neutron Skins with α-clusters GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt Nuclear Astrophysics Virtual Institute Hirschegg 2015 Nuclear Structure and Reactions: Weak, Strange and Exotic International Workshop XLIII on Gross Properties of Nuclei and Nuclear Reactions Hirschegg, Kleinwalsertal, Austria January 11 17, 2015

2 Outline Introduction Neutron Skins and Neutron Matter Equation of State, Density Dependence of Symmetry Energy, Correlations in Low-Density Nuclear Matter Generalized Relativistic Density Functional Details of grdf Model, Effective Interaction α-clusters on the Surface of Nuclei Application of grdf Model, Nuclei with α-clusters Experimental Test Quasi-Free (p,pα) Knockout Reactions, Kinematics, Cross Sections Conclusions Details: S. Typel, Phys. Rev. C 89 (2014) S. Typel, H.H. Wolter, G. Röpke, D. Blaschke, Eur. Phys. J. A 50 (2014) 17 M.D. Voskresenskaya, S. Typel, Nucl. Phys. A 887 (2012) 42 S. Typel, G. Röpke, T. Klähn, D. Blaschke, H.H. Wolter, Phys. Rev. C 81 (2010) Neutron Skins with α-clusters - 1

3 Introduction

4 Neutron Skins and Neutron Matter Equation of State neutron-rich nuclei development of neutron skin with thickness: r np = S = rn 2 rp 2 Neutron Skins with α-clusters - 2

5 Neutron Skins and Neutron Matter Equation of State neutron-rich nuclei development of neutron skin with thickness: r np = S = rn 2 rp 2 charge radii of nuclei well-known from electron scattering experiments, isotope shifts, etc. (see, e.g., I. Angeli et al., ADNDT 99 (2013) 69) Neutron Skins with α-clusters - 2

6 Neutron Skins and Neutron Matter Equation of State neutron-rich nuclei development of neutron skin with thickness: r np = S = rn 2 rp 2 charge radii of nuclei well-known from electron scattering experiments, isotope shifts, etc. (see, e.g., I. Angeli et al., ADNDT 99 (2013) 69) neutron matter radii less precisely known, suggested experimental approach: parity violation in electron scattering PREX@Jefferson Lab with 208 Pb target (C. J. Horowitz et al., Phys. Rev. C 63 (2001) ) Neutron Skins with α-clusters - 2

7 Neutron Skins and Neutron Matter Equation of State neutron-rich nuclei development of neutron skin with thickness: r np = S = rn 2 rp 2 charge radii of nuclei well-known from electron scattering experiments, isotope shifts, etc. (see, e.g., I. Angeli et al., ADNDT 99 (2013) 69) neutron matter radii less precisely known, suggested experimental approach: parity violation in electron scattering PREX@Jefferson Lab with 208 Pb target (C. J. Horowitz et al., Phys. Rev. C 63 (2001) ) observation of B.A. Brown: strong correlation of neutron skin thickness with derivative of neutron matter equation of state (EoS) d(e/a) dn = p 0 n=n0 n 2 0 at density n 0 = 0.1 fm 3 for 18 Skyrme Hartree-Fock parameter sets (Phys. Rev. Lett. 85 (2000) 5296) Neutron Skins with α-clusters - 2

8 Neutron Skins and Neutron Matter Equation of State neutron-rich nuclei development of neutron skin with thickness: r np = S = rn 2 rp 2 charge radii of nuclei well-known from electron scattering experiments, isotope shifts, etc. (see, e.g., I. Angeli et al., ADNDT 99 (2013) 69) neutron matter radii less precisely known, suggested experimental approach: parity violation in electron scattering PREX@Jefferson Lab with 208 Pb target (C. J. Horowitz et al., Phys. Rev. C 63 (2001) ) observation of B.A. Brown: strong correlation of neutron skin thickness with derivative of neutron matter equation of state (EoS) d(e/a) dn = p 0 n=n0 n 2 0 at density n 0 = 0.1 fm 3 for 18 Skyrme Hartree-Fock parameter sets (Phys. Rev. Lett. 85 (2000) 5296) extension to relativistic mean-field models (S. Typel and B. A. Brown, Phys. Rev. C 64 (2001) ) Neutron Skins with α-clusters - 2

9 Neutron Skins and Symmetry Energy equivalent correlation of neutron skin thickness with slope of nuclear symmetry energy found in investigation guided by principles of effective field theory (R. J. Furnstahl, Nucl. Phys. 706 (2002) 85) Neutron Skins with α-clusters - 3

10 Neutron Skins and Symmetry Energy equivalent correlation of neutron skin thickness with slope of nuclear symmetry energy found in investigation guided by principles of effective field theory (R. J. Furnstahl, Nucl. Phys. 706 (2002) 85) expansion of energy per nucleon in nuclear matter E A (n,β) = E 0(n)+E s (n)β n = n n +n p β = (n n n p )/n with symmetry energy E s (n) Neutron Skins with α-clusters - 3

11 Neutron Skins and Symmetry Energy equivalent correlation of neutron skin thickness with slope of nuclear symmetry energy found in investigation guided by principles of effective field theory (R. J. Furnstahl, Nucl. Phys. 706 (2002) 85) expansion of energy per nucleon in nuclear matter E A (n,β) = E 0(n)+E s (n)β n = n n +n p β = (n n n p )/n with symmetry energy E s (n) essential parameters: symmetry energy at saturation J = E s (n sat ) slope coefficient L = 3n d dn E s n=nsat Neutron Skins with α-clusters - 3

12 Neutron Skins and Symmetry Energy equivalent correlation of neutron skin thickness with slope of nuclear symmetry energy found in investigation guided by principles of effective field theory (R. J. Furnstahl, Nucl. Phys. 706 (2002) 85) expansion of energy per nucleon in nuclear matter E A (n,β) = E 0(n)+E s (n)β n = n n +n p β = (n n n p )/n with symmetry energy E s (n) essential parameters: symmetry energy at saturation J = E s (n sat ) slope coefficient L = 3n d dn E s n=nsat determine L from experimental measurement of r np constraint for neutron matter EoS r np (fm) HFB-8 MSk7 v090 SkP D1S Linear Fit, r = Skyrme, Gogny RMF SkX Sk-T6 HFB-17 SGII D1N SkM* FSUGold DD-ME1 DD-ME2 SLy5 SLy4 SkMP SkSM* SIV MSL0 MSkA BCP Ska DD-PC1 Sk-Rs PK1.s L (MeV) (X. Viñas et al., Eur. Phys. J. A50 (2014) 27) G2 Sk-T4 NL3.s25 RHF-PKO3 SkI2 RHF-PKA1 SV Sk-Gs NL3* NL3 PK1 NL-SV2 TM1 SkI5 G1 NL-RA1 PC-F1 NL-SH PC-PK1 NL2 208 Pb NL1 Neutron Skins with α-clusters - 3

13 Symmetry Energy Parameters many attempts to determine symmetry energy J = S 0 = S v and slope coefficient L experimentally χ Lagrangian and Q. Montecarlo Neutron Matter Neutron-Star Neutron Star Data Observations p & α scattering Neutron Skin charge ex. Antiprotonic Atoms Nuclear Model Fit Heavy Ion Collisions Giant Resonances N A scattering Charge Ex. Reactions Energy Levels Parity Violating e-scattering IVGQR Neutron Skin PDR Neutron Skin Mass Mass n p Emission Ratio Isospin Diffusion GDR PDR N Optical Potential Empirical Dipole Polarizability Parity Violating Asymmetry L (MeV) Hebeler et al. PRL105 (2010) and Gandolfi et al. PRC85 (2012) (R) Steiner et al. Astrophys. J. 722 (2010) 33 Lie-Wen Chen et al. PRC 82 (2010) Centelles et al. PRL 102 (2009) Warda et al. PRC 80 (2009) Möller et al. PRL 108 (2012) Danielewicz NPA 727 (2003) 233 Agrawal et al. PRL109 (2012) Famiano et al. PRL 97 (2006) Tsang et al. PRL 103 (2009) Roca-Maza et al. PRC 87 (2013) Roca-Maza et al. PRC (2013), in press Trippa et al. PRC 77 (2008) (R) Klimkiewicz et al. PRC 76 (2007) (R) Carbone et al. PRC 81 (2010) (R) Xu et al. PRC 82 (2010) PREX Collab. PRL (2012) (X. Viñas et al., Eur. Phys. J. A50 (2014) 27) (J.M. Lattimer, Y. Lim, ApJ. 771 (2013) 51) Neutron Skins with α-clusters - 4

14 Symmetry Energy Parameters many attempts to determine symmetry energy J = S 0 = S v and slope coefficient L experimentally χ Lagrangian and Q. Montecarlo Neutron Matter Neutron-Star Neutron Star Data Observations p & α scattering Neutron Skin charge ex. Antiprotonic Atoms Nuclear Model Fit Heavy Ion Collisions Giant Resonances N A scattering Charge Ex. Reactions Energy Levels Parity Violating e-scattering IVGQR Neutron Skin PDR Neutron Skin Mass Mass n p Emission Ratio Isospin Diffusion GDR PDR N Optical Potential Empirical Dipole Polarizability Parity Violating Asymmetry L (MeV) Hebeler et al. PRL105 (2010) and Gandolfi et al. PRC85 (2012) (R) Steiner et al. Astrophys. J. 722 (2010) 33 Lie-Wen Chen et al. PRC 82 (2010) Centelles et al. PRL 102 (2009) Warda et al. PRC 80 (2009) Möller et al. PRL 108 (2012) Danielewicz NPA 727 (2003) 233 Agrawal et al. PRL109 (2012) Famiano et al. PRL 97 (2006) Tsang et al. PRL 103 (2009) Roca-Maza et al. PRC 87 (2013) Roca-Maza et al. PRC (2013), in press Trippa et al. PRC 77 (2008) (R) Klimkiewicz et al. PRC 76 (2007) (R) Carbone et al. PRC 81 (2010) (R) Xu et al. PRC 82 (2010) PREX Collab. PRL (2012) (X. Viñas et al., Eur. Phys. J. A50 (2014) 27) (J.M. Lattimer, Y. Lim, ApJ. 771 (2013) 51) measurement of neutron skin thickness (e.g. PREX), correlation with L from mean-field calculations: effects of clustering correlations on surface of nuclei? Neutron Skins with α-clusters - 4

15 Correlations in Low-Density Nuclear Matter surface of nuclei: densities much below saturation density nucleon-nucleon pairing correlations essential, usually considered in nuclear structure calculations Neutron Skins with α-clusters - 5

16 Correlations in Low-Density Nuclear Matter surface of nuclei: densities much below saturation density nucleon-nucleon pairing correlations essential, usually considered in nuclear structure calculations equation of state of nuclear matter at very low densities: many-body correlations clusters/nuclei as new degrees of freedom model-independent benchmark: virial equation of state (see, e.g., C. J. Horowitz, A. Schwenk, Nucl. Phys. A 776 (2006) 55) Neutron Skins with α-clusters - 5

17 Correlations in Low-Density Nuclear Matter surface of nuclei: densities much below saturation density nucleon-nucleon pairing correlations essential, usually considered in nuclear structure calculations equation of state of nuclear matter at very low densities: many-body correlations clusters/nuclei as new degrees of freedom model-independent benchmark: virial equation of state (see, e.g., C. J. Horowitz, A. Schwenk, Nucl. Phys. A 776 (2006) 55) incorporate clusters as explicit degrees of freedom in nuclear structure calculations adaption of generalized relativistic density functional (grdf) approach for EoS of nuclear and stellar matter Neutron Skins with α-clusters - 5

18 Correlations in Low-Density Nuclear Matter surface of nuclei: densities much below saturation density nucleon-nucleon pairing correlations essential, usually considered in nuclear structure calculations equation of state of nuclear matter at very low densities: many-body correlations clusters/nuclei as new degrees of freedom model-independent benchmark: virial equation of state (see, e.g., C. J. Horowitz, A. Schwenk, Nucl. Phys. A 776 (2006) 55) incorporate clusters as explicit degrees of freedom in nuclear structure calculations adaption of generalized relativistic density functional (grdf) approach for EoS of nuclear and stellar matter nucleons and clusters treated as quasiparticles with scalar potential S i and vector potential V i interaction by meson exchange, well calibrated parametrisation Neutron Skins with α-clusters - 5

19 Correlations in Low-Density Nuclear Matter surface of nuclei: densities much below saturation density nucleon-nucleon pairing correlations essential, usually considered in nuclear structure calculations equation of state of nuclear matter at very low densities: many-body correlations clusters/nuclei as new degrees of freedom model-independent benchmark: virial equation of state (see, e.g., C. J. Horowitz, A. Schwenk, Nucl. Phys. A 776 (2006) 55) incorporate clusters as explicit degrees of freedom in nuclear structure calculations adaption of generalized relativistic density functional (grdf) approach for EoS of nuclear and stellar matter nucleons and clusters treated as quasiparticles with scalar potential S i and vector potential V i interaction by meson exchange, well calibrated parametrisation study dependence of results on neutron excess and on isovector part of interaction experimental test of predictions? Neutron Skins with α-clusters - 5

20 Generalized Relativistic Density Functional

21 Generalized Relativistic Density Functional grand canonical approach extension of relativistic mean-field models with density-dependent meson-nucleon couplings grand canonical potential density ω(t,{µ i }) Neutron Skins with α-clusters - 6

22 Generalized Relativistic Density Functional grand canonical approach extension of relativistic mean-field models with density-dependent meson-nucleon couplings grand canonical potential density ω(t,{µ i }) chemical equilibrium chemical potentials µ i of particles not all independent Neutron Skins with α-clusters - 6

23 Generalized Relativistic Density Functional grand canonical approach extension of relativistic mean-field models with density-dependent meson-nucleon couplings grand canonical potential density ω(t,{µ i }) chemical equilibrium chemical potentials µ i of particles not all independent selected model features extended set of constituents: nucleons, light clusters ( 2 H, 3 H, 3 He, 4 He) and heavy nuclei experimental binding energies: AME 2012 (M. Wang et al., Chinese Phys. 36 (2012) 1603) extension: DZ10 predictions (J. Duflo, A.P. Zuker, Phys. Rev. C 52 (1995) R23) proton number Z DZ AME neutron number N Neutron Skins with α-clusters - 6

24 Generalized Relativistic Density Functional grand canonical approach extension of relativistic mean-field models with density-dependent meson-nucleon couplings grand canonical potential density ω(t,{µ i }) chemical equilibrium chemical potentials µ i of particles not all independent selected model features extended set of constituents: nucleons, light clusters ( 2 H, 3 H, 3 He, 4 He) and heavy nuclei experimental binding energies: AME 2012 (M. Wang et al., Chinese Phys. 36 (2012) 1603) extension: DZ10 predictions proton number Z DZ AME neutron number N (J. Duflo, A.P. Zuker, Phys. Rev. C 52 (1995) R23) medium modifications of composite particles (mass shifts, internal excitations) scattering correlations considered (essential for correct low-density limit) thermodynamically consistent approach ( rearrangement contributions) model parameters from fit to properties of finite nuclei Neutron Skins with α-clusters - 6

25 Effective Interaction exchange of Lorentz scalar mesons m S = {σ,δ,σ,...} Lorentz vector mesons m V = {ω,ρ,φ,...} Neutron Skins with α-clusters - 7

26 Effective Interaction exchange of Lorentz scalar mesons m S = {σ,δ,σ,...} Lorentz vector mesons m V = {ω,ρ,φ,...} represented by (classical) fields A m with mass m m coupling to constituents: Γ im = g im Γ m scaling factors g im density dependent Γ m = Γ m ( ) = i (N i + Z i )n i with parametrization DD2 (S. Typel et al., Phys. Rev. C 81 (2010) ) meson-nucleon coupling Γ i (ρ) DD vector density ρ [fm -3 ] nuclear matter parameters n sat = fm 3 a V = MeV K = MeV J = MeV L = MeV ω σ ρ Neutron Skins with α-clusters - 7

27 Effective Interaction exchange of Lorentz scalar mesons m S = {σ,δ,σ,...} Lorentz vector mesons m V = {ω,ρ,φ,...} represented by (classical) fields A m with mass m m coupling to constituents: Γ im = g im Γ m scaling factors g im density dependent Γ m = Γ m ( ) = i (N i + Z i )n i with parametrization DD2 (S. Typel et al., Phys. Rev. C 81 (2010) ) scalar potential S i = m S Γ ima m m i with medium-dependent mass shift m i (T,n j ) from microscopic calculations mainly action of Pauli principle dissolution of clusters at high densities meson-nucleon coupling Γ i (ρ) DD vector density ρ [fm -3 ] nuclear matter parameters n sat = fm 3 a V = MeV K = MeV J = MeV L = MeV ω σ ρ Neutron Skins with α-clusters - 7

28 Effective Interaction exchange of Lorentz scalar mesons m S = {σ,δ,σ,...} Lorentz vector mesons m V = {ω,ρ,φ,...} represented by (classical) fields A m with mass m m coupling to constituents: Γ im = g im Γ m scaling factors g im density dependent Γ m = Γ m ( ) = i (N i + Z i )n i with parametrization DD2 (S. Typel et al., Phys. Rev. C 81 (2010) ) scalar potential S i = m S Γ ima m m i with medium-dependent mass shift m i (T,n j ) from microscopic calculations mainly action of Pauli principle dissolution of clusters at high densities vector potential V i = m V Γ ima m + V (r) i with rearrangement contribution V (r) i meson-nucleon coupling Γ i (ρ) DD vector density ρ [fm -3 ] nuclear matter parameters n sat = fm 3 a V = MeV K = MeV J = MeV L = MeV ω σ ρ Neutron Skins with α-clusters - 7

29 Effective Interaction exchange of Lorentz scalar mesons m S = {σ,δ,σ,...} Lorentz vector mesons m V = {ω,ρ,φ,...} represented by (classical) fields A m with mass m m coupling to constituents: Γ im = g im Γ m scaling factors g im density dependent Γ m = Γ m ( ) = i (N i + Z i )n i with parametrization DD2 (S. Typel et al., Phys. Rev. C 81 (2010) ) scalar potential S i = m S Γ ima m m i with medium-dependent mass shift m i (T,n j ) from microscopic calculations mainly action of Pauli principle dissolution of clusters at high densities energy per nucleon E/A [MeV] symmetric nuclear matter χeft (N 3 LO) DD2 neutron matter density n [fm -3 ] χeft(n 3 LO): I. Tews et al., Phys. Rev. Lett 110 (2013) T. Krüger et al., Phys. Rev. C 88 (2013) vector potential V i = m V Γ ima m + V (r) i with rearrangement contribution V (r) i Neutron Skins with α-clusters - 7

30 α-clusters on the Surface of Nuclei

31 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation without light clusters 10-1 particle number density n i [fm -3 ] A heavy = Z heavy = 62.3 p n e T = 5 MeV n = 0.01 fm -3 Y p = radius r [fm] Neutron Skins with α-clusters - 8

32 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation without and with light clusters enhanced cluster probability at surface of heavy nuclei, effects for heavy nuclei in vacuum at zero temperature? particle number density n i [fm -3 ] A heavy = Z heavy = 62.3 p n e T = 5 MeV n = 0.01 fm -3 Y p = 0.4 particle number density n i [fm -3 ] A heavy = Z heavy = 48.2 p n e 2 H 3 H 3 He 4 He T = 5 MeV n = 0.01 fm -3 Y p = radius r [fm] radius r [fm] Neutron Skins with α-clusters - 8

33 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation zero temperature: only α-particles relevant density distribution from ground-state wave function (WKB approximation) Neutron Skins with α-clusters - 8

34 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation zero temperature: only α-particles relevant density distribution from ground-state wave function (WKB approximation) variation with neutron excess of nuclei chain of Sn nuclei Neutron Skins with α-clusters - 8

35 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation zero temperature: only α-particles relevant density distribution from ground-state wave function (WKB approximation) variation with neutron excess of nuclei chain of Sn nuclei variation of isovector interaction modified parametrizations, 208 Pb nucleus parametrization symmetry slope ρ-meson ρ-meson energy coefficient coupling parameter J [MeV] L [MeV] Γ ρ (n ref ) a ρ DD DD DD DD DD DD [ )] Γρ(n) = Γρ(n ref )exp aρ( n n 1 ref Neutron Skins with α-clusters - 8

36 Application of grdf Model finite temperature grdf calculations in spherical Wigner-Seitz cell, extended Thomas-Fermi approximation zero temperature: only α-particles relevant density distribution from ground-state wave function (WKB approximation) variation with neutron excess of nuclei chain of Sn nuclei variation of isovector interaction modified parametrizations, 208 Pb nucleus parametrization symmetry slope ρ-meson ρ-meson energy coefficient coupling parameter J [MeV] L [MeV] Γ ρ (n ref ) a ρ DD DD DD DD DD DD energy per neutron E/A [MeV] DD2 +++ DD2 ++ DD2 + DD2 DD2 - DD2 - - neutron matter [ )] Γρ(n) = Γρ(n ref )exp aρ( n n 1 ref neutron density n [fm -3 ] Neutron Skins with α-clusters - 8

37 Neutron Skin of Sn Nuclei neutron and protons rms radii r n and r p neutron skin thickness r skin = r n r p neutron (proton) rms radius r n (r p ) [fm] neutrons (without α correlations) protons (without α correlations) neutron skin thickness r skin [fm] without α correlations mass number A mass number A Neutron Skins with α-clusters - 9

38 Neutron Skin of Sn Nuclei neutron and protons rms radii r n and r p neutron skin thickness r skin = r n r p neutron (proton) rms radius r n (r p ) [fm] neutrons (without α correlations) neutrons (with α correlations) protons (without α correlations) protons (with α correlations) neutron skin thickness r skin [fm] without α correlations with α correlations mass number A mass number A Neutron Skins with α-clusters - 9

39 Neutron Skin of Sn Nuclei density distributions of neutrons (dashed lines) and α particles (full lines) neutron skin thickness r skin = r n r p Sn 112 Sn 0.20 without α correlations with α correlations α particle density n α (r) [fm -3 ] Sn 120 Sn 124 Sn 128 Sn 132 Sn neutron skin thickness r skin [fm] radius r [fm] mass number A Neutron Skins with α-clusters - 9

40 Neutron Skin of Sn Nuclei density distributions of neutrons (dashed lines) and α particles (full lines) effective α-particle number N α α particle density n α (r) [fm -3 ] Sn 112 Sn 116 Sn 120 Sn 124 Sn 128 Sn 132 Sn effective number of α-particles N α radius r [fm] mass number A Neutron Skins with α-clusters - 9

41 Neutron Skin of Sn Nuclei density distributions of neutrons (dashed lines) and α particles (full lines) effective α-particle number N α experimental test of predictions? α particle density n α (r) [fm -3 ] Sn 112 Sn 116 Sn 120 Sn 124 Sn 128 Sn 132 Sn effective number of α-particles N α radius r [fm] mass number A Neutron Skins with α-clusters - 9

42 Neutron Skin of 208 Pb dependence on symmetry energy slope coefficient L use parametrizations DD2 +++,..., DD2 relativistic Hartree (RH) calculation used in original fit of model parameters (correlation r skin L not linear because no complete refit of model parameters, only of effective isovector interaction) neutron skin thickness r skin [fm] RH without α correlations slope coefficient L [MeV] Neutron Skins with α-clusters - 10

43 Neutron Skin of 208 Pb dependence on symmetry energy slope coefficient L use parametrizations DD2 +++,..., DD2 relativistic Hartree (RH) calculation used in original fit of model parameters relativistic Thomas-Fermi (RTF) calculation for description of nuclei with generalized relativistic density functional underestimate of neutron skin thickness but similar correlation as in RH calculation neutron skin thickness r skin [fm] RH without α correlations RTF without α correlations slope coefficient L [MeV] Neutron Skins with α-clusters - 10

44 Neutron Skin of 208 Pb dependence on symmetry energy slope coefficient L use parametrizations DD2 +++,..., DD2 relativistic Hartree (RH) calculation used in original fit of model parameters relativistic Thomas-Fermi (RTF) calculation for description of nuclei with generalized relativistic density functional underestimate of neutron skin thickness but similar correlation as in RH calculation with α-particles at surface systematic reduction of neutron skin neutron skin thickness r skin [fm] RH without α correlations RTF without α correlations RTF with α correlations slope coefficient L [MeV] Neutron Skins with α-clusters - 10

45 Experimental Test

46 Experimental Study of α-clustering at Nuclear Surface clean probe for α-particles in nuclei: quasi-free (p,pα) knockout reactions Neutron Skins with α-clusters - 11

47 Experimental Study of α-clustering at Nuclear Surface clean probe for α-particles in nuclei: quasi-free (p,pα) knockout reactions experiment at RCNP Cyclotron Facility, Osaka, Japan collaboration with T. Aumann (TU Darmstadt), T. Uesaka (RIKEN) et al. proposal accepted in PAC evaluation March 2014, experiment planned for 2015 Neutron Skins with α-clusters - 11

48 Experimental Study of α-clustering at Nuclear Surface clean probe for α-particles in nuclei: quasi-free (p,pα) knockout reactions experiment at RCNP Cyclotron Facility, Osaka, Japan collaboration with T. Aumann (TU Darmstadt), T. Uesaka (RIKEN) et al. proposal accepted in PAC evaluation March 2014, experiment planned for MeV proton beam targets: 112 Sn, 116 Sn, 120 Sn, 124 Sn proton detection: Grand Raiden α detection: LAS several spectrometer settings p Sn α Neutron Skins with α-clusters - 11

49 Experimental Study of α-clustering at Nuclear Surface clean probe for α-particles in nuclei: quasi-free (p,pα) knockout reactions experiment at RCNP Cyclotron Facility, Osaka, Japan collaboration with T. Aumann (TU Darmstadt), T. Uesaka (RIKEN) et al. proposal accepted in PAC evaluation March 2014, experiment planned for MeV proton beam targets: 112 Sn, 116 Sn, 120 Sn, 124 Sn proton detection: Grand Raiden α detection: LAS several spectrometer settings experimental signatures: dependence of effective α-particle number ( cross sections) on neutron excess N Z localisation of α-particles on surface of nucleus broad momentum distribution p Sn α Neutron Skins with α-clusters - 11

50 Quasi-Free (p,pα) Reactions on Sn 300 MeV kinematics low momentum transfer to residual Cd nucleus Neutron Skins with α-clusters - 12

51 Quasi-Free (p,pα) Reactions on Sn 300 MeV kinematics low momentum transfer to residual Cd nucleus strong correlation of angles/energies of emitted protons and α-particles E lab (p) [MeV] E lab (α) [MeV] θ lab (p) [deg] θ lab (p) [deg] θ lab (α) [deg] θ lab (α) [deg] Neutron Skins with α-clusters - 12

52 Quasi-Free (p,pα) Reactions on Sn 300 MeV θlab(p) [deg] Neutron Skins with α-clusters θlab(α) [deg] p α lab p [MeV/c] 300 θlab(p) [deg] 300 Elab(α) [MeV] Elab(p) [MeV] kinematics low momentum transfer to residual Cd nucleus strong correlation of angles/energies of emitted protons and α-particles select pair of angles, e.g., θlab(p) = 45 and θlab(α) = 60 choose spectrometer settings to cover different ranges of intrinsic α-particle momenta Q within acceptance (p, Grand Raiden: 5%, α, LAS: 30%) θlab(α) [deg] Q [MeV/c]

53 Quasi-Free (p,pα) Reactions on Sn 300 MeV cross sections relativistic distorted-wave impulse approximation Neutron Skins with α-clusters - 13

54 Quasi-Free (p,pα) Reactions on Sn 300 MeV cross sections relativistic distorted-wave impulse approximation factorization d 5 σ dqdω Q dω p = K d2 σ dω p W α( Q) R kinematic factor K Neutron Skins with α-clusters - 13

55 Quasi-Free (p,pα) Reactions on Sn 300 MeV cross sections relativistic distorted-wave impulse approximation factorization d 5 σ dqdω Q dω p = K d2 σ dω p W α( Q) R kinematic factor K half-off-shell p-α scattering cross section d2 σ dω p use parametrized experimental elastic p-α scattering cross section dσ/dω p cm [mb/sr] elastic 4 He(p,p) MeV Yoshimura et al., PRC 63 (2001) cm θ p [deg] Neutron Skins with α-clusters - 13

56 Quasi-Free (p,pα) Reactions on Sn 300 MeV cross sections relativistic distorted-wave impulse approximation factorization d 5 σ dqdω Q dω p = K d2 σ dω p W α( Q) R kinematic factor K half-off-shell p-α scattering cross section d2 σ dω p use parametrized experimental elastic p-α scattering cross section intrinsic momentum distribution W α ( Q) = χ α Cd ( Q) 2 with Q = k α Cd of α-particle in Sn nucleus reduction factor R due to absorption dσ/dω p cm [mb/sr] W α (Q) [fm 3 ] elastic 4 He(p,p) MeV Yoshimura et al., PRC 63 (2001) cm θ p [deg] Sn Q [MeV/c] Neutron Skins with α-clusters - 13

57 Quasi-Free (p,pα) Reactions on Sn 300 MeV cross sections relativistic distorted-wave impulse approximation factorization d 5 σ dqdω Q dω = K d2 σ p dω W α( Q) R p kinematic factor K half-off-shell p-α scattering cross section d2 σ dω p use parametrized experimental elastic p-α scattering cross section intrinsic momentum distribution W α ( Q) = χ α Cd ( Q) 2 with Q = k α Cd of α-particle in Sn nucleus reduction factor R due to absorption Monte Carlo simulation of experiment estimate of count rates dσ/dω p cm [mb/sr] W α (Q) [fm 3 ] elastic 4 He(p,p) MeV Yoshimura et al., PRC 63 (2001) cm θ p [deg] Sn Q [MeV/c] Neutron Skins with α-clusters - 13

58 Conclusions

59 Conclusions many-body correlations essential in low-density nuclear matter formation of clusters/nuclei conditions at surface of heavy nuclei prerequisite for explanation of α-decay generalized relativistic density functional (grdf) for equation of state calculations model with explicit cluster degrees of freedom, quasiparticles with medium-dependent properties effective interaction with density-dependent couplings, well-constrained parameters application of grdf approach to heavy nuclei predicts formation of α-clusters at surface of heavy nuclei reduction of neutron skin thickness affects correlation with slope coefficient of symmetry energy systematic variation of effect with neutron excess of nucleus and with isovector part of effective interaction experimental test of predictions quasi-free (p,pα) knockout reactions experiment with Sn nuclei planned at RCNP, Osaka Neutron Skins with α-clusters - 14