The role of core excitations in break-up reactions

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The role of core excitations in break-up reactions J. A.

de Diego 3 1 DFA Galileo Galilei, Università di Padova and

Italy; 2 Dpto. de FAMN, Universidad de Sevilla, Apdo.

1 The role of core excitations in break-up reactions J. A. Lay 1, A. M. Moro 2, J. M. Arias 2, R. de Diego 3 1 DFA Galileo Galilei, Università di Padova and INFN, Sezione di Padova, Via Marzolo 8, I Padova, Italy; 2 Dpto. de FAMN, Universidad de Sevilla, Apdo. 1065, E Sevilla, Spain; 3 Centro de Física Nuclear, Universidade de Lisboa, Av. Prof. Gama Pinto 2, P Lisboa, Portugal Trento, 6 th June 2016 J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

2 1 Motivation 2 Structure Halo nuclei with excitations of the core PS discretization method Semi-microscopic model Application to 11 Be, 19 C, and 21 C 3 Reactions Semi-Classical EPM DWBAx XCDCC J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

3 Motivation J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

4 Motivation 11 Be in a single particle model E (MeV) Experimental Be(2 )+n threshold Two-body Continuum Single particle model 1d 5/ /2-1/ Be(0 + )+n threshold 1p 1/2 2s 1/2 J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

5 Motivation c r v c ξ r v x No core excitations 11 Be(1/2 + ) = 1 10 Be(0 + g.s.) ν s 1/2 Core excitations 11 Be(1/2 + ) = α 10 Be(0 + g.s.) νs 1/2 + β 10 Be(2 + ) νd 5/ α 2, β 2 = spectroscopic factors J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

6 Motivation 10 Be* 11 Be 10 Be 11 Be Pb n Pb n x Pure valence excitation Core-excitation mechanism J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

7 Structure Halo nuclei with excitations of the core r v Hamiltonian with core excitation c ξ H p = T( r)+h core (ξ)+v NC ( r, ξ) Model for the core h core (ξ) Selecting the model space which states are included The model for core excitations will determine V NC ( r, ξ) Same formalism for different interaction models: Particle-Rotor model (deformed core) Particle-Vibration From microscopic transition densities J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

8 Weak coupling limit Structure Halo nuclei with excitations of the core r v Hamiltonian with core excitation c ξ H p = T( r)+h core (ξ)+v NC ( r, ξ) We look for a basis including core degrees of freedom Coupling core ϕ I ( ξ) and single particle Y lsj (ˆr) to the total J p n α different possible combinations or channels α = {l,s,j,i} J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

9 Structure Halo nuclei with excitations of the core Generalization of Pseudo-states (PS) discretization method r v Hamiltonian with core excitation c ξ H p = T( r)+h core (ξ)+v NC ( r, ξ) Set of L 2 functions in this scheme: φ i,jp ( r, ξ) = α RTHO i,α [Y (r) lsj (ˆr) ϕ I ( ξ) ] J p i = 1,..,N Total number of functions: N times the number of channels N n α J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

10 Structure PS discretization method Pseudo-states (PS) discretization method Discrete set of L 2 functions: φ n Completeness condition: N φi φ i I To diagonalize the internal Hamiltonian of a projectile H p Matrix elements: H p n,n φ n φ n H p φ n φ n J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

11 Structure PS discretization method Pseudo-states (PS) discretization method Eigenstates of the matrix NxN: ϕ (N) n = N C n i φ i { nb states with ε n < 0 representing the bound states. N-n b,ε n > 0 discrete representation of the Continuum Orthogonal and normalizable. What is the most suitable basis? Lagrange, Sturmian, Harmonic Oscillator? J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

12 Structure PS discretization method Transformed Harmonic Oscillator basis Analytic LST from Karataglidis et al.,prc71,064601(2005) 1 s(r) = 1 m 1 ( 2b 1 ) ( ) m m r + 1 γ r HO vs THO: φ(s) e ( s b) 2 = φ[s(r)] e γ2 2b 2r Correct asymptotic behaviour for bound states. Range controlled by the parameters of the LST. J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

13 THO parameters Structure PS discretization method b is treated as a variational parameter to minimize g.s. energy Then γ b controls the density of states: 40 HO THO THO THO γ=1 fm 1/2 γ=2.48 fm 1/2 γ=5 fm 1/2 30 E (MeV) γ can be also used to look for resonances J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

14 Finding Resonances Structure PS discretization method 6 5 J= spectrum ε (MeV) Be(2 + )+n thr. Resonance N 10 Be(0 + )+n thr. J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

15 Finding Resonances Structure PS discretization method 6 5 J= spectrum ε (MeV) Be(2 + )+n thr. Resonant eigenstates Resonance N 10 Be(0 + )+n thr. J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

16 Spectrum Structure PS discretization method ε (MeV) J= Spectrum N Density of states ρ(k)= < k n > ε (MeV) 0 J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

17 Structure PS discretization method Electromagnetic Transition Probabilities 50 db(e2)/de (e 2 fm 4 /MeV) (without core excitations) THO: contribution THO: contribution THO: total db(e2)/de (e 2 fm 4 /MeV) (with core excitations) ε (MeV) ε (MeV) B(E2) dominated by collective excitation of the core J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

18 PRM drawbacks Structure PS discretization method PRM needs: The core to be a rotor A phenomenological potential based on the following parametres: E(2 + ), β 2, V c, r, a, V so,r so, a so J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

19 P-AMD Structure Semi-microscopic model λ= λ=2 ρ 0 (fm -3 ) proton density 2 + proton density 0 + neutron density 2 + neutron density ρ 2 (fm -3 ) >2 + proton density 2 + ->2 + proton density 0 + ->2 + neutron density 2 + ->2 + neutron density r (fm) r (fm) Densities from Antisymmetrized Molecular Dynamics (AMD) Y. Kanada-En yo et al. Phys. Rev. C 60, (1999) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

20 P-AMD Structure Semi-microscopic model λ= λ=2 ρ 0 (fm -3 ) proton density 2 + proton density 0 + neutron density 2 + neutron density ρ 2 (fm -3 ) >2 + proton density 2 + ->2 + proton density 0 + ->2 + neutron density 2 + ->2 + neutron density r (fm) I VNC λ (r, ξ) I = r (fm) dr [ I ρ λ (r,ξ) I v nn ( r r ] ) JLM interaction Phys. Rev. C 16, 80 (1977). J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

21 P-AMD Structure Semi-microscopic model <0 + V > 10 <2 + V > V (MeV) PRM P-AMD: JLM P-AMD: M3Y V (MeV) 0-10 <2 + V > PRM P-AMD: JLM P-AMD: M3Y r (fm) PRC89, (2014) r (fm) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

22 P-AMD E (MeV) Experimental (5/2) - (3/2) - + Structure Application to 11 Be, 19 C, and 21 C PRM P-AMD 10 + Be(2 )+n thr. 3/2 3/2-5/2-3/2-5/2-0 1/2-1/2-1/2 + 1/2 + 1/2-1/ Be(0 + )+n thr. Renormalization factors λ + = and λ = PRC 70, (2004); PRC 81, (2010); PL B 611, 239 (2005). J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

23 19 C Spectrum Structure Application to 11 Be, 19 C, and 21 C 4 Experimental P-AMD 3 1/2 + E (MeV) C(2 + )+n thr. 0 ( ) 1/2 + 1/ C(0 + )+n thr. PL B 660, 320 (2008); PL B 614, 174 (2005). J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

24 19 C Spectrum Structure Application to 11 Be, 19 C, and 21 C 4 Experimental P-AMD E (MeV) /2 + 1/2 - ( ) 1/2 + 1/ C(2 + )+n thr. 18 C(0 + )+n thr. PL B 660, 320 (2008); PL B 614, 174 (2005) SAMURAI J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

25 19 C Spectrum Structure Application to 11 Be, 19 C, and 21 C 4 3 Experimental Shell-Model (WBP) 1/2 + 1/2 + P-AMD E (MeV) ( ) 1/2 + 1/2 + 1/ C(2 + )+n thr. 18 C(0 + )+n thr. PL B 660, 320 (2008); PL B 614, 174 (2005). J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

26 19 C Spectrum Structure Application to 11 Be, 19 C, and 21 C E (MeV) Experimental 1/2 + 1/2 + WBP 1/2 + 1/2 + P-AMD 1/2 + PRM(1) 1/2 + 1/2 + PL B 660, 320 (2008); PL B 614, 174 (2005). J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

27 19 C Spectrum Structure Application to 11 Be, 19 C, and 21 C 4 3 Experimental WBP P-AMD 1/2 + 1/2 + PRM(1) 1/2 + PRM(2) 1/2 + E (MeV) ( ) 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + PL B 660, 320 (2008); PL B 614, 174 (2005). J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

28 Structure Application to 11 Be, 19 C, and 21 C State Model 0 + (ls)j 2 + s 1/2 2 + d 3/2 2 + d 5/2 1/2 + 1 P-AMD WBP P-AMD WBP P-AMD WBP P-AMD WBP J. A. Lay et al., PRC89, J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

29 21 C Spectrum Structure Application to 11 Be, 19 C, and 21 C E (MeV) Experimental P-AMD Preliminary 1/ C(2 )+n thr. 0 (1/2 + ) 20 C(0 + )+n thr. PRC86, J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

30 Reactions Semi-Classical EPM Reactions Equivalent Photon Method J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

31 19 C MeV/u Reactions Semi-Classical EPM C+ 208 Pb C+ 208 Pb RIKEN RIKEN dσ/dω (mb/sr) dσ/de rel (mb/mev) θ c.m. (deg) E rel (MeV) Coulomb Excitation T. Nakamura et al., Phys. Rev. Lett. 83, 1112 (1999). J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

32 19 C MeV/u Reactions Semi-Classical EPM Semiclassical calculations Equivalent Photon Method Only includes first order Coulomb excitation. Actually this is only a first test before using the basis with DWBAx/XCDCC. dσ λ dω de = 4π3 bu 9 db(e 1) dn E1 de dω J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

33 19 C MeV/u Reactions Semi-Classical EPM T. Nakamura et al., Phys. Rev. Lett. 83, 1112 (1999). dσ/dω (mb/sr) C+ 208 Pb RIKEN E1 E2 Total conv θ c.m. (deg) The reaction is dominated by E1 first order Coulomb excitation as expected J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

34 19 C MeV/u Reactions Semi-Classical EPM dσ/de rel (mb/mev) C+ 208 Pb RIKEN E1 E2 Total conv E rel (MeV) Resonant E2 contribution more important due to its low excitation energy J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

35 Reactions DWBAx Reactions DWBAx J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

36 Reactions DWBAx DWBAx calculations p c ξ r v R r vt r ct target No-recoil approach Only first order excitation. Same results for these energies than XCDCC. A. M. Moro et al. AIP Conf. Proc. 1491, 335 (2012) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

37 Reactions DWBAx i Ψ Ψ v J M JM r vt r c R ξ r ct rvt c ξ target f v r R r ct target T JM,J M if = χ ( ) f ( R)Ψ f J M ( r,ξ) V vt( r vt )+V ct ( r ct,ξ) χ (+) i ( R)Ψ i JM ( r,ξ) Core excitation affects in two ways: ❶ Ψ JM ( r,ξ) = projectile states static deformation effect). Ψ JM ( r,ξ) = [ ] ϕ J l,j,i ( r) Φ I(ξ) JM l,j,i ❷ V ct ( r ct,ξ) can modify the core state dynamic core excitation. J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

38 Reactions DWBAx i Ψ Ψ v J M JM r vt c ξ Only first order plus no-recoil: r R r ct rvt target T JM,J M if T JM,J M val +T JM,J M core f c ξ r R r ct v target ❶ T JM,J M val ❷ T JM,J M core Valence excitations Core excitations They explicitly separates in the calculation A. M. Moro & R. Crespo, Phys. Rev. C 85, (2012) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

39 Reactions 11 Be MeV/nucleon DWBAx RIKEN: N. Fukuda et al., Phys. Rev. C70, (2004) 11 Be SF3 BDC Target Neutron VETO NEUT FDC HOD 10 Be Dipole Magnet Measurement of Break up Cross Sections of 11 Be on 12 C and 208 Pb J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

40 19 67 MeV/u Reactions DWBAx Y. Satou et al., Phys. Lett. B 660, 320 (2008). Microscopic DWBA calculations suggest a 1/2 + transition J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

41 19 67 MeV/u Reactions DWBAx C+p RIKEN P-AMD: total conv. 1 P-AMD: valence conv. 1 P-AMD: core conv. 1 dσ/dω (mb/sr) θ c.m. (deg) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

42 19 67 MeV/u Reactions DWBAx dσ/dω (mb/sr) MeV/u Experimental data 1 XCDCC 2 XCDCC 1 XDWBA s 1/2 d 5/2 DWBA s.p. dσ/dω (mb/sr) MeV/u RIKEN 1 XCDCC 1 XDWBA XCDCC x1.8 2 XDWBA s.p. x θ c.m. (deg) θ c.m. (deg) J. A. Lay et al., Submitted to PRC(R) arxiv: A. M. Moro & J. A. Lay, Phys. Rev. Lett. 109, (2012) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

43 Reactions XCDCC Reactions XCDCC J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

44 Full CDCC Reactions XCDCC XCDCC calculations p c ξ r v R r vt r ct target Including core excitations in CDCC We already showed how to discretize the continuum with core excitations DWBA only valid for intermediate and high energies CDCC also includes the effect of break up in the elastic cross section J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

45 Reactions XCDCC Hamiltonian: H p = T r +V vc ( r,ξ)+h core (ξ) H = H p +V vt (r vt )+V ct ( r ct,ξ) Model wavefunction: p c ξ r v R r ct rvt target Φ( R, r,ξ) = α χ α ( R)Ψ α J M ( r,ξ) Coupled equations: [H E]Φ( R, r,ξ) = 0 [ E ε α T R V α,α ( R) ] χ α ( R) = α,α ( R)χ α αv n ( R) Transition potentials: V α;α ( R) = Ψ α J M ( r,ξ) V vt( r vt )+V ct ( r ct,ξ) Ψ α JM ( r,ξ) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

46 Reactions XCDCC Coupling potentials: CDCC vs. XCDCC p c ξ r v R r ct r vt target Standard CDCC. uses coupling potentials: V α;α ( R) = Ψ α J M ( r) V vt(r vt )+V ct (r ct ) Ψ α JM ( r) Extended CDCC uses generalized coupling potentials V α;α ( R) = Ψ α J M ( r,ξ) V vt( r vt )+V ct ( r ct,ξ) Ψ α JM ( r,ξ) R. de Diego et al, PRC89 (2014) (PS discretization) also for binning Summers et al, PRC74 (2006) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

47 Reactions XCDCC XCDCC calculations for 11 Be+ 197 Au at sub-barrier energies Experiment: TRIUMF (Aarhus - LNS/INFN - Colorado - GANIL - Gothenburg -Huelva - Louisiana - Madrid - St. Mary - Sevilla - York collaboration) V. Pesudo s PhD Thesis Submitted to PRL... J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

48 Reactions XCDCC XCDCC calculations for 11 Be+ 197 Au at sub-barrier energies Inelastic scattering probability:... P inel (θ) = σ inel (θ) σ bu (θ)+σ qel (θ) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

49 Reactions XCDCC XCDCC calculations for 11 Be+ 197 Au at sub-barrier energies Breakup scattering probability:... P bu (θ) = σ bu (θ) σ bu (θ)+σ qel (θ) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

50 Reactions XCDCC Electric B(E1) response of 11 Be The inert-core model of 11 Be cannot reproduce simultaneously the B(E1) to bound and continuum states cannot reproduce simultaneously inelastic and breakup. J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

51 Conclusions P-AMD Accurate semi-microscopic description of even-odd halo nuclei Predictive power for unknown halo nuclei like 19,21 C Could be able to include core excitations from different sources Coulomb dissociation Core excitations may interfere the extraction of B(E 1) distributions through the presence of low lying quadrupole resonances Nuclear Break up The interplay between core and valence contributions is crucial to understand resonant break up of halo nuclei Break up reactions are sensitive to spectroscopic factors of resonant states difficult to populate in traditional transfer reactions Full XCDCC will clarify the effects of core excitations in different observables (elastic, energy distributions, inclusive data) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

52 Conclusions Next steps Apply the P-AMD model with other densities and other halo nuclei Perform full PS-XCDCC calculations with the P-AMD model Use the density distributions of the PS to obtain energy distribution of the cross sections Continue for inclusive observables Compare XCDCC with the recent extension of Faddeev-AGS (A. Deltuva) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

53 Appendix Thank you!! And also to: Theory University of Seville : J. Gómez-Camacho University of Lisbon : R. Crespo University of Surrey : R. C Johnson Yukawa Institute, Kyoto University : Y. Kanada-En yo Experiment IEM-CSIC, Madrid : V. Pesudo, M. J. G. Borge, O. Tengblad S1202 Collaboration (formerly E1104) J.A. Lay et al. (U. Padova) Core excitations Trento, 06/06/ / 52

Workshop on low-energy nuclear reaction dynamics

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