Nucelon self-energy in nuclear matter and how to probe ot with RIBs
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1 Nucelon self-energy in nuclear matter and how to probe ot with RIBs Christian Fuchs University of Tübingen Germany Christian Fuchs - Uni Tübingen p.1/??
2 Outline relativistic dynamics E/A [MeV] relativistic Brueckner- Hartree-Fock nuclear/neutron matter asymmetry β density ρ [fm 3 ] 1.2 effective masses optical potentials Christian Fuchs - Uni Tübingen p.2/??
3 Relativity in nuclear systems? k F /M 1/4 = velocity v 1/4 c only small corrections from relativistic kinematics Christian Fuchs - Uni Tübingen p.3/??
4 Relativity in nuclear systems? k F /M 1/4 = velocity v 1/4 c only small corrections from relativistic kinematics Relativistic dynamics: (RMF, relativisitc Brueckner (DBHF), QCD sum rules) = cancellation of large scalar and vector fields! Σ S = 35 MeV, Σ = +3 MeV Christian Fuchs - Uni Tübingen p.3/??
5 Relativity in nuclear systems? k F /M 1/4 = velocity v 1/4 c only small corrections from relativistic kinematics Relativistic dynamics: (RMF, relativisitc Brueckner (DBHF), QCD sum rules) = cancellation of large scalar and vector fields! Σ S = 35 MeV, Σ = +3 MeV Difficult to observe: fields cancel in mean field potential U s.p. = Σ S + Σ = 5 MeV Christian Fuchs - Uni Tübingen p.3/??
6 Relativity in nuclear systems? k F /M 1/4 = velocity v 1/4 c only small corrections from relativistic kinematics Relativistic dynamics: (RMF, relativisitc Brueckner (DBHF), QCD sum rules) = cancellation of large scalar and vector fields! Σ S = 35 MeV, Σ = +3 MeV Difficult to observe: fields cancel in mean field potential U s.p. = Σ S + Σ = 5 MeV But: add up in large spin-orbit force U S.O. (Σ S Σ ) L S = +75 MeV Christian Fuchs - Uni Tübingen p.3/??
7 Saturation of Nuclear Matter DBHF: realistic NN force, no parameter E B [MeV] V K=? 1 2 ρ/ρ correlated uncorrelated wave r E/A [MeV] Tuebingen (Bonn) BM (Bonn) Bonn A, ps Reid CD Bonn Bonn AV k F [fm 1 ] see e.g. nucl-th/393 Coester line = relativistic! Christian Fuchs - Uni Tübingen p.4/??
8 Saturation mechanism Non-relativistic: tensor force essential 2nd order 1 π exchange: large and attractive Pauli-blocking = saturation Relativistic: tensor force quenched (Banerjee & Tjon NPA 78 (22) 33) cancellation of large scalar and vector fields difference of vector and scalar density = saturation principally similar to RMF theory C.F., Lect. Notes Phys. 641 (24) 119 Christian Fuchs - Uni Tübingen p.5/??
9 QCD sum rules In-medium quark condensates = large scalar & vector fields in nuclear matter Σ S = 8π2 Λ 2 B [ ρ qq ρ qq ] Σ = 8π2 ρ qγ q ρ Λ 2 B Λ B = 4πf π Borel mass Christian Fuchs - Uni Tübingen p.6/??
10 QCD sum rules In-medium quark condensates = large scalar & vector fields in nuclear matter Σ v [MeV] 4 Σ S = 8π2 2 [ ρ qq ρ qq ] Σ s [MeV] Λ 2 B Σ = 8π2-4 ρ qγ q ρ -6 DB CHPT + point-couplings Λ 2 B ρ NM -8 Λ B = 4πf π Borel mass k F [fm -1 ] QCD sum rules + ChPT: Finelli, Weise et al., NPA 735 (24) 449 DBHF: Gross-Boelting, C.F., Faessler, NPA 648 (1999) 15 Christian Fuchs - Uni Tübingen p.6/??
11 Large scalar/vector fields Σ (k) [MeV] Σ Σ S k [MeV] kσ V Bonn A AV 18 Idaho CD Bonn Nijm I Nijm II k [MeV] U s.p. [MeV] k [MeV] Mapping of NN potentials on relativistic operator basis = large scalar/vector fields at tree level (Hartree-Fock) = universal feature of NN interaction Plohl. C.F., van Dalen, nucl-th/5949 Christian Fuchs - Uni Tübingen p.7/??
12 Hadronic many-body theory Relativistic Brueckner: N+OBEP ( V = σ, ω, π, ρ, η, δ) = 2-N correlations in hole-line expansion = self-consistent sum of ladder diagrams Dyson-Equation: G = G + GΣG = + Σ Bethe-Salpeter-Equation: T = V + i V GGQT T T = + Self Energy (Hartree-Fock): Σ(ρ, k) = qɛf < q T (q, k) q >= ΣS γσ + γ kσv = T T Σ Christian Fuchs - Uni Tübingen p.8/??
13 Role of correlations 1 E/A [MeV] Bonn A, DBHF Groningen, DBHF σω, DBHF Bonn A, MFT Groningen, MFT σω, MFT correlations -2-4,5 1, 1,5 2, k F [fm -1 ] Lect. Notes Phys. 641 (24)119 [nucl-th/393] Christian Fuchs - Uni Tübingen p.9/??
14 BHF versus DBHF BHF: 3-body forces necessary (Zuo et al., NPA 76 (22) 418) E/A [MeV] variational Tuebingen (Bonn) BM (Bonn) Reid CD-Bonn Bonn AV 18 AV BF AV 18 +δv AV 18 +δv+3-bf E/A [MeV] 1 5 DBHF Bonn A DBHF Bonn B BHF AV 18 BHF AV BF Skyrme hard (K=38) Skyrme soft (K=2) ChPT var AV 18 +δv var AV 18 +δv+3-bf -25 1,2 1,4 1,6 1,8 2, k F [fm -1 ] ρ/ρ All microscopic EOS are soft! Christian Fuchs - Uni Tübingen p.1/??
15 Nuclear/neutron matter EOS 1 E bind [MeV] neutron matter 5 DBHF DBHF (BonnA) BHF var AV AV BF BF var AV NL BF DDRH Typel NL3 DDRH ChPT Typel BHF ChPT -2 nuclear matter,5,1,15 n B [ fm -3 ],1,2,3,4 n B [ fm -3 ] neutron matter better controlled. Christian Fuchs - Uni Tübingen p.11/??
16 Symmetry energy E(ρ, β) = E(ρ) + E sym (ρ)β 2 + O(β 4 ) + E sym (ρ) = E(ρ, β) β 2 β= = a 4 + p (ρ ρ ρ 2 ) + asymmetry parameter : β = Y n Y p E sym [MeV] SKM* SkLya DBHF var AV 18 NL3 DD-TW DD-ρδ ChPT model a 4 [MeV] Skyrme <3 SkLy 32 RMF DBHF ChPT 34,5 1 ρ / ρ ρ / ρ Christian Fuchs - Uni Tübingen p.12/??
17 Isovector potential U iso (n B, k) = (U n U p )/2β U iso [MeV] DBHF BHF Gogny rel. T-ρ SKM* SkLya RMF.5 ρ, β=.4 ρ, β= k [fm -1 ] k [fm -1 ] BHF: Zuo et al. PRC 72 (25) 145 RIA: Chen, Ko, Li, nucl-th/599, amplitudes from: McNeil, Shepard, Wallace. Christian Fuchs - Uni Tübingen p.13/??
18 Effective nucleon mass Comparison of different approaches = careful! Many different defnitions of effective masses are used! Non-relativistic mass: [ m NR = M + 1 d k dk U s.p. = k [de/d k ] 1 ] 1 parameterizes non-locality in space (k-mass) and time (e-mass) Mahaux et al., Müther, Frick,.. Dirac mass: m D = M + Σ S Relativistic: U s.p. m D E Σ S + Σ Christian Fuchs - Uni Tübingen p.14/??
19 Symmetric nuclear matter m * / M 1,8,6 nonrelativistic mass Dirac mass DBHF (Bonn A) BHF (Bonn A) QHD-I NL3 DD-TW,4, ρ / ρ ρ / ρ DBHF/BHF: larger m NR = less repulsive Christian Fuchs - Uni Tübingen p.15/??
20 Neutron-proton mass splitting BHF: m NR,n > m NR,p RMF: m D,n < m D,p ; m NR,n < m NR,p (ρ + δ) Baran, Di Toro et al., Phys. Rep. 41 ( 5) 335 DBHF with Σ extracted by fit method: m D,n > m D,p Alonso & Sammarunca, PRC 67 ( 3) 5431 DBHF with projection method: m D,n < m D,p de Jong & Lenske, PRC 58 ( 98) 89, van Dalen, C.F., Faessler, NPA 744 ( 4) 227 non-rel. mass in DBHF: m NR,n > m NR,p van Dalen, C.F, Faessler, PRL 95 (25) 2232 Christian Fuchs - Uni Tübingen p.16/??
21 Dirac mass in asym. matter Neutron effective mass [ MeV c -2 ] Y p =. Y p =.5 nuclear matter Y p =.1 Y p =.2 Y p =.3 Y p =.4 Y p =.5 neutron matter,1,2,3,4,5 n B [ fm -3 ] np-mass splitting: m D,n < m D,p Christian Fuchs - Uni Tübingen p.17/??
22 Neutron-proton mass splitting 1 nonrelativistic mass Dirac mass Neutron effective mass [MeV c -2 ] Neutron Fermi momentum Momentum k [fm -1 ] β =. β =.4 β =.6 β = 1. n B =.166 fm Momentum k [fm -1 ] van Dalen, C.F., Faessler, PRL 95 (25) 2232 Christian Fuchs - Uni Tübingen p.18/??
23 Guidance for phenomenology SkLy5: mass splitting m n < m p (in contrast to BHF) 8 6 E th - E exp [MeV] SLy A Christian Fuchs - Uni Tübingen p.19/??
24 Guidance for phenomenology SkLy5: mass splitting m n < m p (in contrast to BHF) new fit, small change of parameters: m n > m p (κ V =.3) 8 6 E th - E exp [MeV] SLy5 Fit B A K. Bennaceur, T. Lesinski, private communication Christian Fuchs - Uni Tübingen p.19/??
25 Summary Christian Fuchs - Uni Tübingen p.2/??
26 Summary Relativisitic dynamics: = large scalar/vector fields ( 3 35 MeV): Difficult ot observe (cancellation) = spin-orbit splitting Christian Fuchs - Uni Tübingen p.2/??
27 Summary Relativisitic dynamics: = large scalar/vector fields ( 3 35 MeV): Difficult ot observe (cancellation) = spin-orbit splitting Ab initio calculations = guidance for high density / extreme isospin regime Christian Fuchs - Uni Tübingen p.2/??
28 Summary Relativisitic dynamics: = large scalar/vector fields ( 3 35 MeV): Difficult ot observe (cancellation) = spin-orbit splitting Ab initio calculations = guidance for high density / extreme isospin regime Predictions: symmetry energy, n/p mass splitting, optical potentials,... Christian Fuchs - Uni Tübingen p.2/??
29 Summary Relativisitic dynamics: = large scalar/vector fields ( 3 35 MeV): Difficult ot observe (cancellation) = spin-orbit splitting Ab initio calculations = guidance for high density / extreme isospin regime Predictions: symmetry energy, n/p mass splitting, optical potentials,... Isovector optical potential: = accessable with RIBs Christian Fuchs - Uni Tübingen p.2/??
30 Summary Relativisitic dynamics: = large scalar/vector fields ( 3 35 MeV): Difficult ot observe (cancellation) = spin-orbit splitting Ab initio calculations = guidance for high density / extreme isospin regime Predictions: symmetry energy, n/p mass splitting, optical potentials,... Isovector optical potential: = accessable with RIBs mass splitting: = IVGDR, RIBs Christian Fuchs - Uni Tübingen p.2/??
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