Spectra from thermal relativistic nuclear field theory Elena Litvinova Western Michigan University In collaboration with H. Wibowo, C. Robin, and P. Schuck Workshop: FRIB and the GW170817 kilonova, NSCL@MSU, July 16-27, 2018
Outline Motivation: to build a consistent and predictive approach to describe the entire nuclear chart (ideally, an arbitrary strongly-correlated many-body system), numerically executable and useful for applications, such as r-process, quantum chemistry, fundamental physics etc. Challenges: the nuclear hierarchy problem, complexity of NN-interaction Approximate non-perturbative solutions: Relativistic Nuclear Field Theory (RNFT). Emerged as a synthesis of Landau-Migdal Fermi-liquid theory, Copenhagen-Milano NFT and Quantum Hadrodynamics; now put in the context of a systematic equation of motion (EOM) formalism and linked to ab-initio interactions Technique: Green functions, EOM, time blocking method Nuclear response to neutral and charge-exchange probes: giant EL, Gamow-Teller, spin dipole etc. (neutron capture, gamma and beta decays, pair transfer, …) Nuclear response at finite temperature: thermal QFT for transitions between nuclear excited states Conclusions and perspectives
Definitions and diagrammatic conventions One-fermion propagator: 1 1’ = Two-fermion propagator (two-times): 1’ 1 = G (2) 2 2’ Three-fermion propagator (two-times): 1’ 1 2 2’ = G (3) 3 3’ Two-fermion (antisymmetrized) interaction: Static self-energy: 2 3 j l = = 1 4 1 1’ Response function Fully correlated part
Exact equations of motion for binary interactions: two-body problem (ph) particle-hole response: Spectra of excitations (*) W = F irr t-dependent (retarded & advanced) term instantaneous term (“bosonic” mean field): Mean field F (0) , where contains the full solution of (*) i ncluding the dynamical term! EOM method: S. Adachi and P. Schuck, NPA496, 485 (1989). J. Dukelsky, G. Roepke, and P. Schuck, NPA 625, 14 (1995). P. Schuck and M. Tohyama, PRB 93, 165117 (2016). etc.
Expansion of the dynamics kernel: F (r;12)irr Uncorrelated terms: Irreducible part of G (4) is decomposed into uncorrelated, singly-correlated and doubly-correlated terms: Singly-correlated terms (up to phases): Doubly-correlated terms (up to phases):
Mapping to the (Quasi)particle-Vibration Coupling (QVC, PVC) Model-independent mapping to the QVC-TBA: “phonon” vertex R (ph) = v v “phonon” propagator = v (pp) v G Generalized QVC meets EOM: ALL correlated terms Original QVC: non-correlated and (preliminary, work in in progress) partly singly-correlated terms All channels Self-consistent closed system of equations are coupled E.L., P. Schuck, in progress
Nuclear response with QVC in time blocking approximation. Higher orders: toward a complete theory Bethe-Salpeter Equation: V Time blocking approximation (TBA): R( ω ) = R 0 ( ω ) + R 0 ( ω ) [V + W( ω )] R( ω ) V.I. Tselyaev, Yad. Fiz. 50,1252 (1989) n = 3: 3p3h correlations Generalized TBA for correlated propagator: 2-phonon: V. Tselyaev, PRC 75, 024306 (2007) n-th order: E.L. PRC 91, 034332 (2015)
The underlying mechanism of NN-interaction : meson exchange Charged mesons: QCD QHD QCD QHD u d d u u d u d u d u d p n u + n d _ − p + d _ − u n p p n u d u d u d u u d d d u Neutral mesons: QCD QHD u u d d u u d d u u d d n u d p 0 + _ _ { σ , ω } u d 0 n p d u u d d d u u d d u u
Response function in the neutral channel (leading order in QVC): relativistic quasiparticle time blocking approximation (RQTBA) Response Interaction Subtraction to avoid double Instantaneous counting (if CDFT-based) meson- exchange: R(Q)RPA Dynamic (retardation): Quasiparticle- vibration coupling in the (resonant) time blocking approximation E. L., P. Ring, and V. Tselyaev, Phys. Rev. C 78, 014312 (2008)
Isospin transfer response function: proton-neutron relativistic quasiparticle time blocking approximation (pn-RQTBA) Response Subtraction Interaction to avoid double counting of ρ (if CDFT-based) Instantaneous free-space meson- coupling exchange: fixed strength: R(Q)RPA (free-space if the Fock term is present) Dynamic (retardation): Quasiparticle- vibration coupling in the (resonant) time blocking approximation C. Robin, E.L., Eur. Phys. J. A 52, 205 (2016)
Dipole response in medium-mass and heavy nuclei within Relativistic Quasiparticle Time Blocking Approximation (RQTBA) Giant dipole resonance (GDR) in stable nuclei Neutron-rich Sn 8 132 Sn 2 / MeV] 6 pygmy 4 - 1 (a) 2 fm 2 Giant S [e pygmy pygmy 0 & 0 5 10 15 20 25 30 35 Experiment* pygmy RQTBA** 8 RQTBA with dipole 130 Sn 2 / MeV] 6 detector response resonances (A. Klimkiewicz) pygmy 4 - 1 (b) 2 fm 2 S [e 0 0 5 10 15 20 25 30 35 E [MeV] ** E. L., P. Ring, and V. Tselyaev, * P. Adrich et al., Phys. Rev. C 78, 014312 (2008) PRL 95, 132501 (2005) 2008-2018: Systematic GMR calculations Pygmy dipole resonance (PDR) systematics (important for EOS) (various multipoles) Neutron matter oscillation 50 50 E1 140 Sn RQRPA 40 E1 140 Sn RQRPA RQTBA 40 S [e 2 fm 2 / MeV] RQTBA 30 2 / MeV] 30 20 2 fm 20 10 S [e 10 0 4 6 8 10 0 4 6 8 10 E [MeV] 0.1 E [MeV] 0.1 neutrons neutrons protons protons r 2 ρ [MeV -1 ] 0.0 -1 ] 0.0 2 ρ [MeV E = 7.18 MeV E = 7.18 MeV -0.1 (RQRPA) r -0.1 (RQRPA) 0 5 10 15 20 0 5 10 15 20 1800 2600 1800 2600 0.04 neutrons protons 0.04 neutrons WS-RPA (LM) RH-RRPA (NL3) WS-RPA (LM) RH-RRPA (NL3) protons 2400 2400 1600 WS-RPA-PC r 2 ρ [MeV -1 ] RH-RRPA-PC 1600 WS-RPA-PC RH-RRPA-PC -1 ] 0.00 2 ρ [MeV 2200 0.00 2200 1400 1400 E = 10.94 MeV E1 208 Pb (RQRPA) 208 Pb E1 208 Pb E = 10.94 MeV E1 208 Pb -0.04 E1 (RQRPA) 2000 r -0.04 2000 1200 1200 0 5 10 15 20 1800 0 1800 5 10 15 20 3500 1000 1000 r [fm] 1000 3500 1000 r [fm] RH-RRPA RH-RRPA σ [mb] RH-RRPA-PC RH-RRPA-PC σ [mb] RH-RRPA RH-RRPA 3000 3000 RH-RRPA-PC RH-RRPA-PC 800 800 800 800 800 800 2500 E0 208 Pb E0 132 Sn 4 /MeV] ISGMR 4 /MeV] ISGMR 2500 E0 208 Pb E0 132 Sn 600 600 600 600 2000 Γ = 1.7 MeV 600 Γ = 2.6 MeV 600 2000 Γ = 1.7 MeV 0.08 Γ = 2.6 MeV 140 Sn neutrons 0.08 400 400 400 protons 400 140 Sn neutrons 1500 0.04 protons 400 1500 -1 ] 400 0.04 r 2 ρ [fm 0.00 -1 ] R [e 2 fm Γ = 2.4 MeV Γ = 3.1 MeV 2 fm Γ = 2.4 MeV Γ = 3.1 MeV 2 ρ [fm 0.00 1000 200 200 1000 200 200 R [e -0.04 E = 4.65 MeV E = 5.18 MeV r E = 4.65 MeV E = 5.18 MeV 200 (RQTBA) (RQTBA) -0.04 200 (RQTBA) (RQTBA) 500 0 0 500 0 -0.08 0 5 10 15 20 0 5 10 15 20 0 -0.08 0 5 10 15 20 0 5 10 15 20 5 10 15 20 25 30 5 10 15 20 25 30 5 0.04 10 15 20 25 30 5 10 15 20 25 30 0.04 0 0 0 0.02 0 5 10 15 20 25 E [MeV] 5 10 15 20 25 E [MeV] 5 10 15 r 2 ρ [fm -1 ] 20 25 E [MeV] 5 10 15 20 25 E [MeV] -1 ] 0.02 0.00 2 ρ [fm E [MeV] E [MeV] E [MeV] E [MeV] 0.00 r -0.02 E = 6.39 MeV E = 7.27 MeV -0.02 E = 6.39 MeV E = 7.27 MeV (RQTBA) (RQTBA) (RQTBA) (RQTBA) [(N-Z)/A] 2 -0.04 -0.04 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0.02 0.02 r 2 ρ [fm -1 ] -1 ] 0.00 2 ρ [fm 0.00 r E = 8.46 MeV E = 9.94 MeV E = 8.46 MeV E = 9.94 MeV -0.02 (RQTBA) (RQTBA) -0.02 (RQTBA) (RQTBA) 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 r [fm] r [fm] r [fm] r [fm] Used for (n, γ ) rates: see talk of Caroline Robin I.A. Egorova, E. Litvinova, Phys. Rev. C 94, 034322 (2016)
Exotic spin-isospin excitations Recent measurements at MSU 28 Si ( 10 Be, 10 B) 28 Al 100 Mo (t, 3 He) 100 Nb Isovector monopole Isovector dipole Isovector spin monopole resonance K. Miki, R.G.T. Zegers,…, E.L., …, C. Robin et al., Phys. Lett. B 769, 339 (2017) Recent developments on spin-isospin response: Superfluid pairing Coupling to charge-exchange phonons Beta decay M. Scott, R.G.T. Zegers,…, QVC-induced ground state correlations (GSC); E.L., …, C. Robin et al., Meson-exchange pn-pairing Phys. Rev. Lett. 118, 172501 (2017) See talk of Caroline Robin
Nuclear systems at finite temperature: Experimental data • J.J. Gaardhøje, C. Ellegaard, B. Herskind, S.G. Steadman, Phys. Rev. Lett. 53, 148 (1984). • J.J. Gaardhøje, C. Ellegaard, B. Herskind, et al., Phys. Rev. Lett. 56, 1783 (1986). • D.R. Chakrabarty, S. Sen, M. Thoennessen et al., Phys. Rev. C 36, 1886 (1987). • A. Bracco, J.J. Gaardhøje, A.M. Bruce et al., Phys. Rev. Lett. 62, 2080 (1989). • G. Enders, F.D. Berg, K. Hagel, et al., Phys. Rev. Lett. 69, 249 (1992). • H.J. Hofmann, J.C. Bacelar, M.N. Harakeh, et al., Nucl. Phys. A 571, 301 (1994). • E. Ramakrishnan, T. Baumann, A. Azhari et al., Phys. Rev. Lett. 76, 2025 (1996). • P. Heckman, D. Bazin, J.R. Beene, Y. Blumenfeld, et al., Phys. Lett. B 555, 43 (2003). • F. Camera, A. Bracco, V. Nanal, et al., Phys. Lett. B 560, 155 (2003). • M. Thoennessen, Nucl. Phys. A 731, 131 (2004). A (relatively) recent survey: D. Santonocito and Y. Blumenfeld, Eur. Phys. J. A 30, 183 (2006). General observations: Broadening of the GDR with temperature “Disappearance” of the GDR at T~5 MeV
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