Report

Ab Initio Description of Nucleon and Deuteron Scattering for Systems with up to A=6 Nucleons «Understanding nuclear structure and reactions microscopically, including the continuum» FUSTIPEN topical workshop, GANIL Caen, March17th 2014. Guillaume Hupin Collaborators: S. Quaglioni (LLNL) P. Navrátil (TRIUMF) R. Roth (TU Darmstadt) J. Langhammer (TU Darmstadt) C. Romero-Redondo (TRIUMF) F. Raimondi (TRIUMF) J. Dohet-Eraly (TRIUMF) Quest for the nuclear interaction Fusion based energy generation LLNL-PRES-XXXXXX This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC Nuclear astrophysics Ab initio NCSM/RGM: formalism for binary clusters S. Quaglioni and P. Navrátil, PRL101 (2008); PRC79 (2009) Ex: n-4He scattering Starts from: A) Y (RGM = å ò d r gv (r ) Aˆn F(vrA-a,a) n Relative wave function (unknown) Antisymmetrizer Channel basis ya(A-a )ya(a )d( r - rA-a,a ) 1 2 Cluster expansion technique Entrance channel Exit channel Schrödinger equation on channel basis: ( A) HY (A) = EY RGM RGM å ò dr n éH v¢v (r¢, r ) - E N v¢v (r¢, r )ù gv (r ) = 0 ë û RGM accounts for: 1) interaction (Hamiltonian kernel), 2) Pauli principle (Norm kernel) between clusters. NCSM accounts for: internal structure of clusters. Together with the same microscopic nuclear interaction. Lawrence Livermore National Laboratory 2 LLNL-PRES-XXXXXX Going around the hard core problem E. Jurgenson, Navrátil, R. J. Furnstahl PRL103 (2009) In configuration interaction methods we need to soften interaction to address the hard core We use the Similarity-RenormalizationGroup (SRG) method H l = Ul H Ul+ Unitary transformations ì dH l ï = éh l , H ù ï dl ë ( ) l û í ï h ( l ) = dUl U + l ïî dl Flow parameter Bare potential Evolution with flow parameter l Evolved potential Preserves the physics Decouples high and low momentum k(fm-1) Induces many-body forces k’(fm-1) Lawrence Livermore National Laboratory k(fm-1) k’(fm-1) 3 LLNL-PRES-XXXXXX Demonstrated capability to describe binary-cluster reactions starting from NN interactions Nucleon-nucleus collisions n-He4 phase-shift NN only n-3H, p-3He, N-4He, n-10Be scattering with N3LO NN (mod. Lee-Suzuki eff. Int.) Nucleon scattering on 3H, 3,4He,7Li,7Be,12C,16O with SRGN3LO 7Be(p,γ)8B radiative capture with SRG-N3LO Deuterium-nucleus collisions d-4He scattering and 6Li structure with SRG-N3LO Lee-Suzuki l dependenteffective interaction Good reproduction, but still incomplete (d,N) transfer reactions 3H(d,n)4He and 3He(d,p)4He reactions with SRG-N3LO Lawrence Livermore National Laboratory n-4He scattering 4 LLNL-PRES-XXXXXX Including the NNN force into the NCSM/RGM approach nucleon-nucleus formalism A-1 ( A -1) æ ö V NNN ç1- å PˆiA ÷ è i=1 ø ( a =1) r ( a¢ =1) ( A -1) FnJ ¢rT¢ Aˆv¢V NNN Aˆv FnJr T = p p r¢ Direct potential: µ SD + + ( A-1) ya( A-1) a a a a y ¢ i j l k a 1 1 SD Exchange potential: µ Lawrence Livermore National Laboratory SD ya( A-1) ah+ ai+ a+j am al ak ya( A-1) ¢ 1 1 SD 5 LLNL-PRES-XXXXXX n-4He scattering: NN versus NNN interactions G. Hupin, J. Langhammer et al. PRC88 (2013) n-4He scattering Three scenarii of nuclear Hamiltonians More spin-orbit NNN vs NN “bare” (NN+NNN-ind) splitting • The NNN interactions influence mostly the P waves. • The largest splitting between P waves is obtained with NN+NNN. • The agreement of the P3/2 phase-shifts between NN-only and NN+NNN forces is accidental. Comparison between NN+NNN -ind and NN+NNN at Nmax=13 with six 4He states. Lawrence Livermore National Laboratory 6 LLNL-PRES-XXXXXX n-4He scattering: study of the RGM convergence in the NNN case G. Hupin, J. Langhammer et al. PRC88 (2013) Convergence with respect to the target polarization Target polarization (g.s., low-lying states) Exp. Convergence of the phase-shifts as a function of the 4He excited states. • We have included the first 6 low-lying states of 4He. • Convergence is difficult to assess. Lawrence Livermore National Laboratory 7 LLNL-PRES-XXXXXX 4He(d,d)4He with NN+NNN interaction G. Hupin, S. Quaglioni and P. Navrátil, work in progress d-4He scattering Comparison of the d-α phase-shifts with different interactions • 6Li loses binding energy with NNN interactions. d-4He(g.s.) scattering phase-shifts for NN, NN+NNNinduced and NN+NNN potential with l=2.0 fm-1. Lawrence Livermore National Laboratory • The largest splitting between 3D3 and 3D partial waves is obtained with 2 NN+NNN. 8 LLNL-PRES-XXXXXX Study of the influence of d* continuum G. Hupin, S. Quaglioni and P. Navrátil, work in progress Comparison of the d-α phase-shifts with different interactions d pseudo states 3S -3D 1 1 channel, 3D2 channel… 7d*+4d’*+7d`* 7d* d (g.s.) d-4He(g.s.) scattering phase-shifts interaction and l=2.0 fm-1 at Nmax=7. Lawrence Livermore National Laboratory with NN+NNN Pseudo-states in each deuteron channels d (g.s.,3S1-3D1, 3D2, 3D3-3G3) 9 LLNL-PRES-XXXXXX To overcome the difficulty: couple NCSM and NCSM/RGM (NCSMC) S. Baroni, P. Navrátil and S. Quaglioni PRL110 (2013) • Methods develop in this presentation to solve the many body problem A) Y (NCSM = å cl Al J p T l Mixing coefficients(unknown) A-body harmonic oscillator states A) Y (RGM = å ò d r gv (r ) Aˆn F(vrA-a,a) n Relative wave function (unknown) Antisymmetrizer • Channel basis Al J p T SD A j 00 ( Rc.m. ) Second quantization ya(A-a )ya(a )d( r - rA-a,a ) 1 2 Cluster expansion technique Can address bound and low-lying resonances (short range correlations) Design to account for the continuum of scattering state (long range correlations) The many body quantum problem best describe by superposition of both A) Y (NCSMC = å cl Al J p T + å ò d r gv (r ) Aˆn F(vrA-a,a) l NCSMC n Lawrence Livermore National Laboratory 10 LLNL-PRES-XXXXXX Including the NNN force into the NCSMC approach nucleon-nucleus formalism ( A -1) r¢( a¢ =1) V NNN A-body compound system … Target and projectile in relative motion Lawrence Livermore National Laboratory 11 LLNL-PRES-XXXXXX n-4He scattering with NCSMC G. Hupin, S. Quaglioni and P. Navrátil, work in progress n-4He scattering Study of the convergence with respect to the # of 4He low-lying states Experimental low-lying states of the A=5 nucleon systems. n-4He scattering phase-shifts for NN+NNN potential with l=2.0 fm-1 and 8 low-lying state of 5He. Lawrence Livermore National Laboratory • The convergence pattern looks good. • The experimental phase-shifts are well reproduced. 12 LLNL-PRES-XXXXXX How n-4He elastic cross-sections compare ? Comparison of the elastic cross-section between NN and NN+3N with 4He (g.s.) ∂σ (θc. m . )[mb/ sr] ∂Ω G. Hupin, S. Quaglioni and P. Navrátil, work in progress 5 NN+NNN N N + N N N -i nd ex pt . 2 102 n- 4 He (g.s.) 0 (NN+3N-induced) 45 90 135 180 θc. m . [deg] Differential cross-section at Eneutron =0.84 MeV between NN+3N-ind and NN+3N. n-4He elastic cross-section for NN+3N-induced, NN+3N potentials compared to expt. and ENDF evaluation . Lawrence Livermore National Laboratory • A better agreement with experiment is obtained with NN+NNN. • The NNN force is essential to get the resonance right. 13 LLNL-PRES-XXXXXX How n-4He elastic cross-sections compare ? G. Hupin, S. Quaglioni and P. Navrátil, work in progress 103 9 8 ∂σ (θc. m . )[mb/ sr] ∂Ω Comparison of the elastic cross-section between NN and NN+3N with 4He (g.s.) 7 NN+NNN N N + N N N -i nd ex pt . 6 5 4 3 n- 4 He (g.s.) 2 0 (NN+3N-induced) 45 90 135 180 θc. m . [deg] Differential cross-section at Eneutron =1.79 MeV between NN+3N-ind and NN+3N. n-4He elastic cross-section for NN+3N-induced, NN+3N potentials compared to expt. and ENDF evaluation . Lawrence Livermore National Laboratory • A better agreement with experiment is obtained with NN+NNN. • The NNN force is essential to get the resonance right. 14 LLNL-PRES-XXXXXX p-4He scattering: NCSM/RGM and NCSMC G. Hupin, S. Quaglioni and P. Navrátil, work in progress p-4He scattering NN+NNN NCSM/RGM and NCSMC • Preliminary calculation, the NCSMC results are obtained with only the 4He ground state. • We can see an improvement in the reproduction of the experimental phase-shifts. Comparison between NCSM/RGM and NCSMC at Nmax=13 and l=2.0 with NN+NNN. Lawrence Livermore National Laboratory 15 LLNL-PRES-XXXXXX Analyzing power and differential cross section G. Hupin, S. Quaglioni and P. Navrátil, work in progress p-4He reaction observables compared to experiment ∂σ (θc. m . )[mb/ sr] ∂Ω 104 p- 4 He (g.s.,0+,0- ,2- ,2- ,1- ,1- ) λ =2.0 fm - 1 , N m ax =13 NCSM C 7.89 M eV 11.99 M eV NCSM / RGM 7.89 M eV 11.99 M eV NCSM C 5.95 M eV 9.89 M eV NCSM / RGM 5.95 M eV 9.89 M eV 103 102 (b) (a) 10 1 A y (θc. m . ) 0.8 0.4 expt . Schwandt et al. 7.89 M eV 11.99 M eV expt . Schwandt et al. 5.95 M eV 9.89 M eV 0 -0.4 -0.8 (d) (c) -1.2 0 45 90 135 θc. m . [deg] Lawrence Livermore National Laboratory 180 45 90 135 180 θc. m . [deg] 16 LLNL-PRES-XXXXXX 4He(d,d)4He with NCSMC d-4He scattering G. Hupin, S. Quaglioni and P. Navrátil, work in progress Effects of the short-range correlation of the compound nuclei on the d-a differential cross-section ∂σ (θc. m . )[mb/ sr] ∂Ω 104 N CSM C 2.935 M eV 8.971 M eV 103 RG M 2.935 8.971 ex pt . 2.935 8.971 N CSM C 6.965 M eV 12 M eV M eV M eV M eV M eV RG M 6.965 M eV 12 M eV ex pt . 6.965 M eV 12 M eV 102 10 d- 4 He (g.s.) 1 0 45 NN-only 90 135 θc. m . [deg] 0 45 90 135 180 θc. m . [deg] d-4He(g.s.) differential cross-section for NN-only potential using NCSM/RGM andNCSMC. • Preliminary results in a small model space (Nmax=9). Lawrence Livermore National Laboratory • The coupling to the compound nuclei addresses some missing correlation. 17 LLNL-PRES-XXXXXX 4He(d,d)4He with NN+NNN interaction G. Hupin, S. Quaglioni and P. Navrátil, work in progress Comparison of the d-a phase-shifts wrt the number of d* pseudo-states before d-4He(g.s.) scattering phase-shifts for NN-only with different numbers of deuteron pseudo-states. Lawrence Livermore National Laboratory • The NCMSC weakens the dependence on the d* pseudo-states. • Residual dependence could be attributed to the missing breakup channel. 18 LLNL-PRES-XXXXXX 4He(d,d)4He with NN+NNN interaction G. Hupin, S. Quaglioni and P. Navrátil, work in progress Comparison of the d-a phase-shifts with different interactions -1.43 d+4He(g.s.) scattering phase-shifts for NN-only, NN+NNN-induced, NN+NNN potential with l=2 fm-1. Lawrence Livermore National Laboratory -1.15 -1.73 • Preliminary results in a small model space (Nmax=9). • The 3D3 resonance is not quite reproduced but the 3N force is helping to get the correct position. 19 LLNL-PRES-XXXXXX First step towards Ab initio many-body calculations of fusion P. Navrátil, S. Quaglioni, PRL108 042503 (2012) 3He(d,p)4He astrophysical S-factor 3H(d,n)4He astrophysical S-factor e- lab screening l =1.5 fm-1 Pseudo excited states Complete picture: includes break-up Calculated S-factors converge with the inclusion of the virtual breakup of the deuterium, obtained by means of excited 3S1-3D1 (d* ) and 3D2 (d’* ) pseudo-states. Lawrence Livermore National Laboratory Evidence of incomplete model (nuclear force) NCSM/RGM results for the 3He(d,n)4He astrophysical Sfactor compared to beam-target measurements. Incomplete nuclear interaction: requires NNN force (SRG-induced + “real”) 20 LLNL-PRES-XXXXXX First step towards Ab initio many-body calculations of fusion J. Dohet-Eraly, S. Quaglioni, P. Navrátil et al. work in progress p-4He bremsstrahlung (preliminary) • Perspective to diagnose plasmas in fusion experiments from t(d,ng)4He radiative transfer reaction • Provides another way to probe cluster wave functions 10 ∂σ [µb/ M eV ] ∂Eγ 8 N N +3N - full, N m ax =7 E γ =1MeV E γ =5MeV 6 4 NCSM/RGM exchange terms of a non-scalar operator most difficult part 2 p- 4 He 0 0 4 8 12 16 E p [MeV ] p+4He(g.s.,0+) bremsstrahlung for NN+NNN potential with l=2 fm-1. Lawrence Livermore National Laboratory Transitions of electric dipole operator between scattering states 21 LLNL-PRES-XXXXXX Conclusions and Outlook We are extending the ab initio NCSM/RGM approach to describe low-energy reactions with two- and three-nucleon interactions. We are able to describe: • Nucleon-nucleus collisions with NN+NNN interaction • Deuterium-nucleus collisions with NN+NNN interaction • NCSMC for single- and two- nucleon projectile Work in progress • Fusion reactions with our best complete ab initio approach • The present NNN force is Evolution of stars, birth, main sequence, death Lawrence Livermore National Laboratory "incomplete”, need to go to N3LO 22 LLNL-PRES-XXXXXX