Quantum Nuclear Many- Body dynamics and related aspects Denis Lacroix GANIL- Caen

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1 Quantum Nuclear Many- Body dynamics and related aspects Denis Lacroix GANIL- Caen Diplôme d Habilita;on à Diriger les recherches 16 Décembre 2010 Collec;ve mo;on Nuclear break- up Fusion, transfer Nuclear reac;ons Open quantum systems Density Func;onal Theories Pairing and shape coexistence Mean- Field and Beyond mean- field theory Fragmenta;on

2 Overall Goal Towards a unified descrip;on of nuclear structure, dynamics and thermodynamics THERMODYNAMIC (Eq. or non equilibrium) (finite or infinite systems) LARGE AMPLITUDE DYNAMICS (From W. Nazarewicz) GROUND STATE VIBRATION

3 Mean- Field Theory General aspects and nuclear physics strategies three- body Mean- field: (DFT/EDF) two- body one- body Self- consistent Mean- field Complex many- body states: Independent par;cles or quasi- par;cle states The two steps nuclear Physics strategy Step 1: Grasp the gross features of atomic nuclei Mean- field years Beyond Mean- field Step 2: incorporate the local fine structure effects

4 Mean- Field Theory and op;mal relevant observables evolu;on Selec;on of trial states with specific rules of varia;on: wave- packet space Ψ + δψ = Ψ + δψ =(1+ α δq α A α + ) Ψ = e P α δq αa α Ψ {A α }: generator of the transforma;on Ψ S = Interest t1 t 0 Ψ i t H Ψds i da α dt = [A α,h] Ehrenfest theorem B α Exact evolu;on A 2 Examples Independent (quasi- )part. states A 1 Relevant space One- body degrees of freedom a i a j

5 Selected success of mean- Field Theory From sta;c to dynamics T=cte T = 2π ω Response func;on (a.u.) Energy (MeV) DL, Ph. Chomaz, NPA636 (1998), NPA648 (1998), PRC58 (1998)

6 Selected success of mean- Field Theory Deep Inelas;c collisions: fusion and transfer b Kinetic Dissipation Nucleus- nucleus poten;al Potential Dissipa;on Comparison with experiments Washiyama, DL, PRC78 (2008). fric;on coefficient PRC56(1997) Very good agreement with experiment Washiyama, DL, Ayik, PRC79 (2009). Ayik, Washiyama, DL, PRC79 (2009)

7 Selected success of mean- Field Theory Break- up and con;nuum emission Advantage: numerous effects are included Drawback: numerous effects are included Experiments try to focus on specific channels Courtesy C. Simenel

8 Break- up and con;nuum emission Experimental mo;va;on: 58 Ni break- MeV/A E fin Forward Time- dependent descrip;on E target E nucleon E init Backward Scarpaci et al., Phys. Lea. B428 (1998) 2p3/2 1f7/2 Selected success of mean- Field Theory Angular distribubon: Kinebc Energy distribubon: DL, Scarpaci, Chomaz NPA 658 (1999) With detector acceptance

9 Beam Energy Configurabon mixing Microscopic theory Challenges beyond mean- field 5 MeV/A Fusion 10 MeV/A 50 MeV/A Transfer Break- up (Nuclear, Coulomb) Pairing Knock- out Direct NN collisions 100 MeV/A Spectroscopic tools

10 Beyond Mean- field in nuclear structure

11 Single Reference (SR)- Mean- Field Towards systema;c studies with mean- field Configura;on mixing within Energy Density Func;onal Mul;- Ref. (MR)- GCM Beyond mean- field Ground state Restora;on of broken symmetries (par;cle number, angular momentum, ) Mean- Field Energy 74 Kr Excited state and spectroscopy but we are star;ng from a func;onal theory framework Formal and prac;cal difficul;es Correlabon Energy

12 Single Reference (SR)- Mean- Field Towards systema;c studies with mean- field Configura;on mixing within Energy Density Func;onal Mul;- Ref. (MR)- GCM Beyond mean- field Ground state M mesh points SIII force Corrected Before correcbon... not corrected. Lacroix et al, PRC79 (2009), Bender et al, PRC79 (2009), Angular momentum Duguet et al, PRC79 (2009) +parbcle number proj.. Problem due to the direct mapping Between Hamiltonian and EDF..... Connected to self- interac;on and self- pairing A solu;on has been proposed (not for ρ α ) corrected Requires a new genera;on of Configura;on mixing code. Bender, Duguet, Heenen, DL arxiv:

13 Correla;on energy Pairing Hamiltonian Exact Projected BCS Towards systema;c studies with mean- field Recent progress for pairing With ρ α Coupling gstrength Projected energy (MR- EDF) Aier correcbon Func;onal form Hupin, DL, Bender, in prep. E N 2π 0 dϕ E SR ρ 0ϕ, κ 0ϕ, κ ϕ0 N N (0, ϕ) E N = E N (ρ N 1, ρ N 12) =E N ({u i,v i }) Generaliza;on? Towards natural orbital based func;onal ρ N 1 = i ϕ i n i ϕ i ρ N 12 = F(n i, ϕ i ) Density matrix Func;onal E N = E(n i, ϕ i ) Correla;on energy Pairing Hamiltonian Exact Projected BCS Coupling strength g DL, PRC (2009) DL, Hupin, PRB(2010) Hupin, DL, arxiv(2010) Future applica;ons: Varia;on aker projec;on Dynamics Thermodynamics

14 Beyond Mean- field in nuclear dynamics

15 First step towards configura;on mixing in nuclear dynamics Configurabon mixing in 11 Be: Lima et al., NPA (2007) GS>= α 2s 1/2 0 + > + β 1d 5/2 2 + > γ GANIL (2003) α 2 = 0,47± 0,04 TDSE 2s Alpha clustering in N=Z nuclei α p 40 Ca GANIL (2000) Experiment Scarpaci et al, PRC (2010) 36 Ar * Theory

16 Stochas;c simula;on of configura;on mixing Applica;on to Deep Inelas;c collisions Dynamics with quantum fluctua;ons MF Sta;s;cal ensemble of mean- field evolu;on Illustra;on: mul;- nucleon transfer reac;ons P P T σ 2 MF σ 2 exp σ 2 exp N ex Yield Mean- field Exp. Mass Washiyama, Ayik, DL, PRC (2009). Ayik, Washiyama, DL, PRC (2009) Towards a quantal descrip;on of low energy nuclear reac;on

17 Beyond mean- field approxima;on from a general perspec;ve The Hamiltonian guidance E = ij i T ja i a j ij ṽ kla i a j a la k ij,kl The truncated BBGKY hierarchy ρ 1 ρ 12 with N- N collisions Pairing Higher order Extended TDHF TDDM P now Stochas;c TDHF now «Quantum Many- Body Dynamics», Simenel, DL, Avez, Ed. VDM Verlag (2010)

18 Nuclear dynamics with pairing correla;ons Two- body nuclear break- up with TDDM P 2n interferometry with 6 He di- neutron correlated 2n center of mass Ini;al correla;on of 6 He di- neutron correlated an;- correlated cigare 2n rel. distance anb- correlated cigare Angular correla;on correlated anb- correlated Assié, Scarpaci,DL et al, EPJA (2009) Assié, DL, PRL (2009)

19 DL, Ayik, Chomaz, Progress in Part. and Nucl. Phys. (2004) Nuclear dynamics with nucleon- nucleon collisions Extended and Stochas;c TDHF Short ;me evolu;on <B> Exact evolu;on <A 2 > <A 1 > Mean- field One Body space Projected dynamics Dissipa;on (Extended TDHF) with projected two- body effect Propagated ini;al correla;on Dissipa;on and fluctua;on Random ini;al condi;on

20 Collec;ve mo;on in nuclei Experimental observa;ons Illustration with the Giant Quadrupole resonances Observabons Mean - field Mean energies Widths Fluctuations (fine structure) Challenges Define appropriate exp. tools (order/ chaos?) Physical interpretation? Schwierczinski et al, PRL (1975)

21 Measuring order in disorder Wavelet method DL, Chomaz, PRC (1999) Theore;cians helping experimentalists Mul;- scales measurement Uncovering experimental scales MeV 0.46 MeV 1.1 MeV - 1 Concealing experiments FWHM DL et al, PLB (2000) Recent improvements: 2D imaging A. Shevchenko et al, PRL (2004), PRC (2009)

22 Description of Giant resonance Mean-field with dissipation and fluctuation Mean-field Coupling to 2p2h states Coupling to ph-phonon Collective energies System 2p-2h decay channels Mean-field Dissipation mean-field +fluctuation +dissipation Environment mean-field Fluct. Both

23 Basic Idea One complex evolution Extension of mean-field for large amplitude motion Stochastic approaches N simpler evolutions The stochastic TDHF illustration Reinhard and Suraud, Ann. of Phys. 216 (1992) Residual interaction in the mean-field interaction picture Statistical assumption N-body Master equation

24 N-body Master equation One-body Master Eq. (ETDHF) Extension of mean-field for large amplitude motion Stochastic approaches Illustration: 1D bose condensate with gaussian two-body interaction. Density Condensate one-body density evolution: t=0 t>0 Quantum jump in Slater-determinant space Quantum jump In single-particle space ρ(r) (arb. units) mean-field average evolution DL, PRC73 (2006) r

25 Self-interacting vs Open Quantum systems N-body Open systems <B> Exact evolution <A 2 > <A 1 > One Body space Mean-field Brownian motion Environment (others) Environment System (one-body) System Toward exact stochastic methods for N-body and Open quantum systems

26 Environment Self-interacting vs Open Quantum systems Approximate and exact formulation System Information reduction Master Eq. (Quantum jump) One-body master Eq. (Quantum jump) STDHF Gardiner and Zoller, Quantum noise (2000) Breuer and Petruccione, The Theory of Open Quant. Syst. (2002). Quantum Monte-Carlo (Exact) Stochastic master Equation Stochastic master equation

27 Self-interacting vs Open Quantum systems Closed systems A 1 A 1 A 2 A 1 A 2 MF Open quantum systems Exact methods + Information reduction Theorem: One can always find a stochastic process for trial states such that evolves exactly over a short time scale. Exact evolution DL, Ann. of Phys. (2007). A 2 Mean-field Illustration: Occupation probability two-level bosonic unstable system trajectories time Non-markovian Stochastic dynamics DL, Phys Rev A (2005), Phys.Rev. E (2008) Hupin, DL, Phys.Rev. C (2010)

28 The Many facets of quantum stochas;c Mean- Field Theory Mean- Field Stochas;c Mean- Field Stochas;c TDHF Quantum Monte- Carlo D = ΦΦ D = ΦΦ D = ΦΦ D = Φ 1 Φ 2 Mean collec;ve dynamics 1- body dissipa;on +ini;al collec;ve fluctua;ons +2- body dissipa;on and fluctua;ons +many- body correla;ons Complexity

29 Where we are: Announced goal: Towards a unified descrip;on of nuclear structure, dynamics and thermodynamics Entrance channel Quasi- elasbc Quasi- fission Transfer Spectator/parbcipant fragmentabon TDHF Dinucleus γ TDSE Mononucleus Thermalizabon γ SMF γ ETDHF STDHF Experiments are complex Complexity in theory is increasing. Fusion evaporabon Fusion fission Fragmentabon Vaporizabon 0-3 MeV/A 3-10 MeV/A 8-10 MeV/A Typical Excitabon energy Fusion barrier (5-30 MeV/A) Fermi- Energy ( MeV/A) Beam Energy

30 Few basic key ques;ons Global phenomenological approach to nuclear reac;ons What are the minimum hypothesis compa;ble with observa;on? 1. To apply transport theories, it is necessary to neglect some aspects of nuclear systems which should not be neglected: - quantum effects are oken poorly treated. - internal correla;ons (real two- body and more)? - nuclear masses (Can we hope to understand nuclear fragmenta;on of clusters if we are not able to predict precisely masses?) 2. Defining the no;on of clusters (n,p,imf,x ) conjointly with mean- field? 3. Defining the internal excita;on and thermaliza;on (in a dynamical problem) 4. Long ;me dynamics?

31 Simple rules for cluster forma;on A schema;c simple experiment A simplified experiment: E Beam ~ E Fermi Example : p+208pb α+x at E B =39 MeV proton E B (A- 1) absorpkon (A) Cluster formakon r c ε k emission (A- 4) Rule 1: cluster creakon Center of mass proper;es of clusters are deduced from nucleons Fermi mo;on (A c =4) ε k A.S. Goldhaber, PLB74(1978). W. Bauer, PRC51 (1995) r c Rule 1 defines the total phase- space for clusters (A f ) (A- Af) ε k (MeV) c.m. properbes α r c (fm)

32 Simple rules for cluster forma;on A schema;c simple experiment Rule 2: energy constraints on cluster escape r c + I- Energy balance: Pb α + Hg If not + V A+Ac (r c ) MeV ε k V B r c (fm) II- Barrier constraint: +

33 Applying the rules ε k (MeV) ApplicaKon to p+208pb Step 1: phase-space r c (fm) P(ε k ) (arb. units) α α+x at E B =39 MeV Step 3: apply the constraint V(r c ) MeV Step 4: propagate the configuration Data Calc. ε k (MeV) Step 2: Fix the potential r c (fm) P(ε k ) (arb. units) proton deuton triton alpha ε k (MeV)

34 Hypothesis step by step: Entrance channel Cluster forma;on Chemical and thermal Freeze- out The HIPSE and nipse code In flight decay Rule 1 Rule 2 Classical dynamics Importance of the reac;on geometry Strong final state Interac;on Large secondary decay effects Importance of Fermi mo;on Random phase- space explora;on Importance of conserva;on laws HIPSE: DL, Van Lauwe, Durand, PRC (2004) Courtesy O. Lopez nipse: DL, Blideanu, Durand, PRC (2005)

35 The HIPSE and nipse code INDRA DATA : Xe + Sn, 25,50,80 MeV/A HIPSE v1.0 released DL, GANIL homepage 86Kr+ 124Sn N/Z All events Isospin effects G. A. Souliobs, et al PLB, 588 (2004) 35. HIPSE calc. 80 MeV/u 50 MeV/u Fluctuations of kinetic energy Parallel velocity Angular distribution Event by event correlations Bimodality Indra Data 86Kr 86Kr+ 112Sn Complete events E* (MeV) Central collisions ΔN/Z Charge distribution Mean kinetic mulbplicity Mean energy 25 MeV/u (Z - Z2)/(Z1+Z2) E* (MeV)1 O. Lopez, D. Lacroix, E. Vient, PRL. - Radioac;f isotopes produc;on - Detector simula;on - hadro- therapy

36 Summary and perspec;ve Development Quantum transport theory Descrip;on of various nuclear reac;on aspects - giant resonances - deep inelas;c collisions - break- up - mul;- fragmenta;on, low energy spalla;on Nuclear structure based on Energy Density func;onal Interdisciplinary research Func;onal Theory Pairing in small supra conductors Open quantum system Theory: stochas;c methods Some ongoing projects Formal and prac;cal aspects of EDF Low energy nuclear reac;on (pairing and config. mixing) Connec;ng nuclei proper;es with their underlying bare interac;on