Workshop on low-energy nuclear reaction dynamics

Transcription

1 Workshop on low-energy nuclear reaction dynamics Antonio M. Moro Universidad de Sevilla, Spain May 27, 2014 Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 1/46

2 Outline 1 Many-body versus few-body models 2 Inclusion of core excitation in few-body models Core-excitation in a simple DWBA model. Full CDCC with core excitation (XCDCC). 3 Some implications of nuclear and Coulomb breakup with halo nuclei. 4 Inelastic breakup within a 3-body model. Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 2/46

3 Why do we use few-body models in reactions? Microscopic approach 11 Be Be* n Start from (effective) NN interaction. Complicated many-body scattering problem Few-body approach 11 Be Be n Inert clusters Projectile described with few-body model Phenomenological NA interactions More transparent link between reaction and structure Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 3/46

4 CDCC for deuteron elastic scattering We can only solve a finite number of coupled-equations continuum spectrum must be truncated in energy and angular momentum and discretized). 1 l=0 l=2 ε max (dσ/dω)/(dσ R /dω) Exp. (80.0 MeV) Exp. (79.0 MeV) CDCC: No continuum CDCC θ c.m. φ l,n n=3 n=2 n=1 s waves d waves ε = 2.22 MeV ground state ε min Coupling to breakup channels has a important effect on the reaction dynamics Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 4/46

5 Application of the CDCC method: 6 Li and 6 He scattering The CDCC method has been also applied to nuclei with a cluster structure: 6 Li=α+d 11 Be= Be+n Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 5/46

6 Application of the CDCC method: 6 Li and 6 He scattering The CDCC method has been also applied to nuclei with a cluster structure: 6 Li=α+d 11 Be= Be+n But... to what extent can we ignore the dynamics of the core? 11 Be Be* n Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 5/46

7 Effect of core excitation in scattering observables Elastic scattering (adiabatic recoil model): K. Horii et al, PRC81 (20) Some effects found in 8 B+ 12 C. Transfer (DWBA, CCBA, Faddeev): Winfield et al, NPA 683 (2001) 48, Fortier et al, PLB 461 (1999) 22, Deltuva, Phys.Rev. C 88, (2013) Knock-out: Batham et al, PRC71, (2005) Small effect on stripping; large effect on diffraction Breakup DWBA Crespo et al, PRC83, (2011), A.M.M. et al PRC85, (2012), A.M.M. and J.A. Lay, PRL9, (2012) CDCC Summers et al, PRC74, (2006), PRC76, (2007), R. de Diego et al, arxiv: Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 6/46

8 Core excitation in structure: 11 Be case Strict single-particle model: 11 Be(1/2 + ) = Be(0 + ) ν2s 1/2 n p 1d 5/2 1p 1/2 2s1/2 2s1/2 1p1/2 1p3/2 1s 1/2 1p3/2 1s1/2 core Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 7/46

9 Core excitation in structure: 11 Be case Strict single-particle model: 11 Be(1/2 + ) = Be(0 + ) ν2s 1/2 n p 1d 5/2 1p 1/2 2s1/2 2s1/2 1p1/2 1p3/2 1s 1/2 1p3/2 1s1/2 core Core-excited model: 11 Be(1/2 + ) =a Be(0 + ) ν2s 1/2 +b Be(2 + ) ν1d 5/ Be(1/2 )> = a 1d 5/2 2s 1/2 1p 1/2 1p 3/2 1s 1/2 n p 1p 1s 2s 1p 1/2 3/2 1/2 1/2 + b 1d 5/2 2s 1/2 1p 1/ p 1/2 1p 3/2 n p 1p 1s 1/2 1s 1/2 2s 1/2 3/2 a, b=spectroscopic amplitudes Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 7/46

10 Core excitation in reactions: inert-core picture Ψ JM ( r,ξ)= [ ϕ J l,j ( r) Φ I(ξ) ] JM ϕ J l,j ( r)= valence particle wavefunction Φ I (ξ)= core wavefunction (frozen) 3/ MeV Be( ) x 1d 3/ / MeV Be( 0 + ) x 1d 5/2 11 Be Be 1/2 1 1/ MeV 11 Be Be( 0 + ) x 1p 1/2 Be( 0 + ) x 2s 1/2 Pb n Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 8/46

11 Core excitation in reactions: inert-core picture Ψ JM ( r,ξ)= [ ϕ J l,j ( r) Φ I(ξ) ] JM ϕ J l,j ( r)= valence particle wavefunction Φ I (ξ)= core wavefunction (frozen) 3/ MeV Be( ) x 1d 3/ / MeV Be( 0 + ) x 1d 5/2 11 Be Be 1/2 1 1/ MeV 11 Be Be( ) x 1p 0 + 1/2 Be( 0 + ) x 2s 1/2 Pb n Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 8/46

12 Core excitation mechanism in breakup [ Ψ JM ( r,ξ)= ϕ J l,j,i ( r) Φ I (ξ) ] JM l,j,i 3/ MeV Be( 0 + e[ ) x1d 3/2 ] + f [ Be( ) x 2s 1/2 ] / MeV c[ Be( 0 + ) x1d 5/2 ] + d [ Be( 2 + ) x 1d 5/2] Be* 11 Be 1/2 1 1/ MeV 11 Be Be( 0 + A[ ) x 1p1/2 ] + B [ Be( 2 + ) x 1p 3/2 ] a[ ] Be( 0 + ) x 2s Be( 2 + 1/2 + b [ ) x 1d 5/2] Pb n Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 9/46

13 Core excitation mechanism in breakup [ Ψ JM ( r,ξ)= ϕ J l,j,i ( r) Φ I (ξ) ] JM l,j,i 3/ MeV Be( 0 + e[ ) x1d 3/2 ] + f [ Be( ) x 2s 1/2 ] / MeV c[ Be( 0 + ) x1d 5/2 ] + d [ Be( 2 + ) x 1d 5/2] Be* 11 Be 1/2 1 1/ MeV A[ Be( ) x 1p 1/2 ] + B [ Be( ) x 1p 3/2 ] a[ Be( 0 Be( 2 Be + ) x 2s ] + 1/2 + b [ ) x 1d 5/2] Dynamic core excitation contributes to the inelastic/breakup probabilities 2 + Pb n Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 9/46

14 Evidences of core excitation in nuclear breakup Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla /46

15 Application to 11 Be+ 12 C resonant breakup RIKEN: Fukuda et al, PRC70 (2004), / MeV 5/ MeV 1/ MeV / Be Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 11/46

16 Application to 11 Be+ 12 C resonant breakup RIKEN: Fukuda et al, PRC70 (2004), dσ/dω (mb/sr) MeV (5/2 + ) dσ/dω c.m. (mb/sr) MeV (3/2 + ) θ c.m. (deg) Angular distribution of 5/2 + and 3/2 + resonances extracted by background subtraction. Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 11/46

17 Standard DWBA approach for breakup At intermediate energies the breakup can be treated in 1st order (DWBA): T JM,J M if i Ψ Ψ v J M JM r vt c = χ ( ) r R r ct rvt target f c r R r ct v target f ( R)Ψ f J M ( r) V vt ( r vt )+V ct ( r ct ) χ (+) i ( R)Ψ i JM ( r) χ ( ) f ( R),χ (+) i ( R) describe projectile-target relative motion Ψ i JM ( r),ψf J M ( r) projectile states (inert core): Ψ i JM ( r,ξ)=[ ϕ J l,j ( r) Φ I(ξ) ] JM ; Ψf J M ( r,ξ)= [ ϕ J l,j ( r) Φ I(ξ) ] JM Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 12/46

18 Standard DWBA approach for breakup At intermediate energies the breakup can be treated in 1st order (DWBA): T JM,J M if i Ψ Ψ v J M JM r vt c = χ ( ) r R r ct rvt target f c r R r ct v target f ( R)Ψ f J M ( r) V vt ( r vt )+V ct ( r ct ) χ (+) i ( R)Ψ i JM ( r) χ ( ) f ( R),χ (+) i ( R) describe projectile-target relative motion Ψ i JM ( r),ψf J M ( r) projectile states (inert core): Ψ i JM ( r,ξ)=[ ϕ J l,j ( r) Φ I(ξ) ] JM ; Ψf J M ( r,ξ)= [ ϕ J l,j ( r) Φ I(ξ) ] JM Possible excitations of the core or target ignored Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 12/46

19 Extended DWBA model including core excitation (XDWBA) R.Crespo, A.Deltuva, A.M.M., PRC 83, ( 11); A.M.M. and R.Crespo, PRC85, ( 12) T JM,J M if i Ψ Ψ v J M JM r vt = χ ( ) c ξ Core excitation affects in two ways: r R r ct rvt target f c ξ r R r ct v target f ( R)Ψ f J M ( r,ξ) V vt ( r vt )+V ct ( r ct,ξ) χ (+) ( R)Ψ i JM ( r,ξ) ❶ Ψ JM ( r,ξ)=projectile states static deformation effect). [ Ψ JM ( r,ξ)= ϕ J l,j,i ( r) Φ I(ξ) ] JM ❷ V ct ( r ct,ξ) can modify the core state dynamic core excitation. l,j,i i Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 13/46

20 Structure part: particle-core model for projectile Particle-plus-core Hamiltonian: H proj = T r + h core (ξ)+v vc ( r,ξ) Projectile states expanded in α; JM (ls)j, I; JM basis: Ψ JM ( r,ξ)= R J l,j,i (r)[ [ ] Yl (ˆr) χ s j Φ I(ξ) ] JM l,j,i The unknowns R J l,j,i (r) can be obtained by direct integration of the Schrödinger equation or by diagonalization in a suitable discrete basis (pseudo-state method). Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 14/46

21 Valence-core and core-target interactions in a simple collective model p c ξ r v R r ct rvt target Valence-core: describes bound states, resonances, etc V vc ( r,ξ) V vc (0) (r) δ dv vc (0) 2 dr Y 20(ˆr) Core-target: describes (ideally) elastic + inelastic scattering δ 2 =deformation length operator V ct ( r ct,ξ) V (0) dv (0) ct ct (r ct ) δ } {{ } 2 dr Y 20(ˆr ct ) } {{ } Valence excitation Core excitation Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 15/46

22 Application to 11 Be exclusive breakup 3/ Be(2+)+n 5/ / Be(0+)+n 1/ Be Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 16/46

23 Application to 11 Be: spectroscopic factors State Model 0 + (ls)j 2 + s 1/2 2 + d 5/2 1/2 + (g.s.) PRM SM (WBT) /2 + (1.78 MeV) PRM SM(WBT) /2 + (3.41 MeV) PRM SM(WBT) /2 + 1, 5/2+ 1 dominant Be(gs) nlj configuration 3/2 + 1 dominant Be(2 + ) 2s 1/2 configuration (talk by J.A. Lay) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 17/46

24 Calculations without core excitation 11 Be+ 12 C dσ/de x (mb/mev) Be+ 67 MeV/nucleon p 3/2 -wave d 5/2 -wave Total Total: Convoluted RIKEN Data dσ/dω (mb/sr) /2 + Resonance RIKEN Data CDCC calculation E x (MeV) θ (deg) J.A. Lay et al, PRC85, (2012) (similar results reported by Howell, Tostevin, Al-Khalili, JPG31, S1881 (2005)) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 18/46

25 Application to 11 Be+ 12 C: valence/core interplay dσ/dω (mb/sr) MeV (5/2 + ) total valence core Neither the valence nor core excitation alone describe the shape of the data 5/2 + x-section dominated by s.p. excitation 3/2 + x-section dominated by core excitation mechanism dσ/dω c.m. (mb/sr) MeV (3/2 + ) θ c.m. (deg) A.M.M. and J.A. Lay, PRL9, (2012) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 19/46

26 Application to 11 Be+ 12 C: valence/core interplay dσ/dω (mb/sr) MeV (5/2 + ) total valence core Absolute magnitude overestimated by 40% (?) dσ/dω c.m. (mb/sr) MeV (3/2 + ) θ c.m. (deg) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 19/46

27 Application to 11 Be+ 12 C: valence/core interplay dσ/dω (mb/sr) MeV (5/2 + ) RIKEN data PRM SP1 [0 + x 1d 5/2 ] SP2 [2 + x 2s 1/2 ] Interference effects between valence & core mechanisms are essential to explain the shape. This sensitivity can provide constraints on weights of different configurations. dσ/dω (mb/sr) MeV (3/2 + ) PRM SP1 [0 + x 1d 3/2 ] SP2 [2 + x 2s 1/2 ] Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 19/46

28 Beyond DWBA: full XCDCC calculations Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 20/46

29 Full CDCC calculations with core excitation DWBA only valid for intermediate and high energies. DWBA does not provide elastics (relies on OMP). Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 21/46

30 Full CDCC calculations with core excitation DWBA only valid for intermediate and high energies. DWBA does not provide elastics (relies on OMP). In more general situations, one needs to use a full CC formalism (CDCC) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 21/46

31 Reminder of CDCC: 7 Li scattering in a three-body model Hamiltonian: H= T R + h r + V α (r α )+V t (r t ) Model wavefunction: N Ψ(R, r)=φ gs (r)χ 0 (R)+ φ n (r)χ n (R) n>0 7 Li α t r R r Coupled equations: [H E]Ψ(R, r)=0 [ E εn T R V n,n (R) ] χ n (R)= V n,n (R)χ n (R) n n α r t T Transition potentials: V n,n (R)= drφ n(r) [V α (r α )+V t (r t )]φ n (r) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 22/46

32 Coupling potentials: CDCC vs. XCDCC 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) Summers et al, PRC74 (2006) (bin discretization) R. de Diego et al, arxiv: (PS discretization) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 23/46

33 Application to p( 11 Be,p ) at 64 MeV/u Data: Shrivastava et al, PLB596 (2004) 54 (MSU) dσ/dω c.m. (mb/sr) a) E rel = MeV Standard CDCC (no core excitation) 0 dσ/dω c.m. (mb/sr) 20 b) E rel =2.5-5 MeV θ c.m. (deg) E rel =0 2.5 MeV contains 5/2+ resonance (mostly single-particle excitation) E rel =2.5 5 MeV contains 3/2+ resonance (core excitation important) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 24/46

34 Application to p( 11 Be,p ) at 64 MeV/u Data: Shrivastava et al, PLB596 (2004) 54 (MSU) dσ/dω c.m. (mb/sr) a) E rel = MeV XCDCC: full XCDCC: no deformation in V ct 0 dσ/dω c.m. (mb/sr) 20 b) E rel =2.5-5 MeV Core-excitation gives a large contribution to nuclear breakup! (A.M.M. and R. Crespo, PRC 85, (2012); R.de Diego et al, arxiv: ) θ c.m. (deg) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 24/46

35 Application to p( 11 Be,p ): dependence on incident energy dσ/dω c.m. (mb/sr) dσ/dω c.m. (mb/sr) dσ/dω c.m. (mb/sr) E rel = MeV θ c.m. (deg) E= MeV/nucleon E=64 MeV/nucleon E=200 MeV/nucleon E rel =2.5-5 MeV θ c.m. (deg) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 25/46

36 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) Be+ 197 Elab =31.9 MeV Be+ 197 Elab =39 MeV σ/σ R Exp. (TRIUMF) XCDCC: no continuum Standard CDCC XCDCC Preliminary σ/σ R Exp. (TRIUMF) Standard CDCC XCDCC: no continuum XCDCC: full Preliminary θ c.m. (deg) θ c.m. (deg) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 26/46

37 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) = N inel (θ) N bu (θ)+n qel (θ) 0 11 Be+ 197 Elab =31.9 MeV 0 11 Be+ 197 Elab =39 MeV P bu -1-2 Preliminary Exp. (TRIUMF) EPM (only E1) Standard CDCC XCDCC θ c.m. (deg) P bu -1-2 Preliminary Exp. (TRIUMF) EPM (only E1) Standard CDCC XCDCC θ c.m. (deg) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 26/46

38 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) = N inel (θ) N bu (θ)+n qel (θ) 0 11 Be+ 197 Elab =31.9 MeV 0 11 Be+ 197 Elab =39 MeV P inel -1-2 Preliminary Exp. (TRIUMF) EPM (only E1) Standard CDCC XCDCC θ c.m. (deg) P inel -1-2 Preliminary Exp. (TRIUMF) EPM (only E1) Standard CDCC XCDCC θ c.m. (deg) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 26/46

39 Electric B(E1) response of 11 Be db(e1)/de (e 2 fm 2 /MeV) Palit et al. (GSI) Fukuda et al. (RIKEN) Single-particle model (Capel et al) PRM (Summers et al) Millener et al E rel (MeV) The inert-core model of 11 Be cannot reproduce simultaneously the B(E1) to bound and continuum states cannot reproduce simultaneously inelastic and breakup. Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 27/46

40 Core excitation in Coulomb dissociation at intermediate energies Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 28/46

41 db(e1)/de (e 2 fm 2 /MeV) Fukuda et al. 04 Single-particle model (r 0 =1.236 fm, a=0.62 fm) Single-partilce model x E rel (MeV) Common assumptions: Pure E1 excitation mechanism for smallθ. One-step breakup mechanism. Nuclear effects (eg. absorption) simulated with cutoff in impact parameter. B(E1) fitted with single-particle wfs SF/ANC dσ 2 dωde rel = 16π3 9 c dn E1 (θ,e x ) db(e1) dω de rel Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 29/46

42 XCDCC calculations for 11 Be+ 208 Pb at 69 MeV/u dσ/dω (mb/sr) Be+ 69 MeV/u 3/2-1/2 + 1/2 - Fukuda et al. XCDCC 5/2 + (E rel =0-5 MeV) 3/2 + db(e1)/de (e 2 fm 2 /MeV) Nakamura et al. (RIKEN) Palit et al. (GSI) Fukuda et al. (RIKEN) PRM (Nunes et al) θ c.m. (deg) E rel (MeV) Absorption and nuclear effects account for by n+ 208 Pb and Be+ 208 Pb OMP Confirm dominance of E1 (1/2, 3/2 ) forθ Dynamic core excitation small, but mixing of core states important. Breakup treated to all orders. Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 30/46

43 Application of CDCC to inelastic breakup Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 31/46

44 Application of the CDCC formalism to ELASTIC breakup d+ 12 C proton angular distribution following deuteron breakup n d 4 /dω n dω p (mb/sr 2 ) θ n =15 o Matsuoka (1982) Faddeev CDCC d 12 C p θ p θ n θ > 0 p θ <0 p 12 C(d,pn) 12 Ed =56 MeV θ p (deg) A.Deltuva, A.M.M., E.Cravo, F.M.Nunes, A.C.Fonseca, Phys.Rev. C 76, (2007) (3b observables calculated from CDCC amplitudes with CDCN code by J. Tostevin) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 32/46

45 Failure of DWBA/CDCC for inclusive breakup d 2 σ/dω p de p Ed =25.5 MeV (E p =14 MeV) -1 Pampus et al., NPA311,141( 78) Elastic BU (post DWBA) θ c.m. Pampus et al, NPA311 (1978)141 Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 33/46

46 Formal expression for inelastic breakup (INBU) Inclusive breakup: a(= b+x)+a b+anything Inclusive differential cross section:σ inc b =σ EBU b +σ INBU b Elastic+inelastic breakup contribution to inclusive breakup: a(= b+x)+a b+c(= x+a ) d 2 σ dω b E b = 2π v a ρ(e b ) Ψ c,( ) xa wavefunctions for c=x+astates Ψ (+) exact many-body wavefunction c χ ( ) b Ψc,( ) xa V bx+ V ba U ba Ψ (+) 2 δ(e E b E c ) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 34/46

47 Austern s three-model for INBU Austern, Phys. Rep.154, 125 (1987) (also Hussein&McVoy, NPA445, 124 (1985)) Ψ (+) Ψ 3b (eg. CDCC): Ψ 3b = χ (+),i a φ i a(r bx ) Using completeness of c=x+astates one obtains i dσ INBU dω b de b = 2 v a ϕ x W xa ϕ x ϕ x (r xa ) is x-a wavefunction satisfying [K x + U xa E x ]ϕ x (r x )= χ ( ) b V bx Ψ 3b(+) xb Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 35/46

48 Application of Austern s formula in DWBA In DWBA:Ψ 3b(+) a φ a (r bx ) ϕ x (r xa ) is now obtained from : xb χ (+) [K x + U xa E x ]ϕ x (r x ) χ ( ) b V bx χ (+) a φ a(r bx ) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 36/46

49 Application of Austern s formula in DWBA In DWBA:Ψ 3b(+) a φ a (r bx ) ϕ x (r xa ) is now obtained from : xb χ (+) [K x + U xa E x ]ϕ x (r x ) χ ( ) b V bx χ (+) a φ a(r bx ) d 2 σ/dω p de p Ed =25.5 MeV (E p =14 MeV) J. Lei (PhD thesis) -1 Pampus et al., NPA311,141( 78) Elastic BU (post DWBA) Inelastic BU Total BU θ c.m. (also Pampus et al, NPA311 (1978)141) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 36/46

50 Application to halo nuclei: 11 Be+ 64 Zn at E lab =28.7 MeV 00 Di Pietro et al. Standard CDCC (w/o CE) XCDCC dσ/dω (mb/sr) 500 R. de Diego et al, arxiv: θ lab (deg) Dynamic core excitation enhances breakup, but underestimates inclusive breakup (transfer?, inelastic breakup?) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 37/46

51 Application to halo nuclei: 11 Be+ 64 Zn at E lab =28.7 MeV 11 Be+ 64 Zn Be + X (Elab =28.7 MeV) dσ/dω (mb/sr) Di Pietro et al, PRC85,054607(2012) Elastic BU (CDCC) Inelastic Breakup (post DWBA) Total BU Preliminary! J. Lei (PhD thesis) θ lab (deg) Inelastic breakup overestimated need to go beyond DWBA? Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 38/46

52 Conclusions Current few-body reaction frameworks rely on inert cluster approximations. We have studied the effect of core excitation in the scattering of halo nuclei (core+n), within DWBA and full CC frameworks and found that: For nuclear breakup both the core-excited admixtures in projectile wfs and the dynamic core excitation are essential for an accurate interpretation of the data. For Coulomb dissociation (heavy targets, small angles) dynamic core excitation is small but the core-excited admixtures important for describing absolute normalization (spectroscopic factors, B(E1), etc) These effects should be studied in other processes: transfer, knockout, QFS, etc Other extensions of the CDCC method (eg. inelastic breakup) are in progress and should help to understand incomplete fusion and related problems from a full QM viewpoint. Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 39/46

53 List of collaborators Raquel Crespo, Raúl de Diego, Arnoldas Deltuva (Lisbon, Portugal) Jin Lei, Mario Gomez, José Miguel Arias, Joaquín Gómez-Camacho (Univ. of Sevilla, Spain). José Antonio Lay (Padova) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 40/46

54 EXTRA SLIDES... Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 41/46

55 Core excitation in transfer: 1 H( 11 Be, Be) 2 H example Fortier et al, PLB461, 22 (1999) 1d 5/2 1p 1/2 n p 2s 1/2 1d 5/2 2s 1/2 n 2s 1/2 1p 3/2 1s 1/2 1p 1s 1p 1/2 3/2 1/2 Be(gs) 1p 1/2 1p 3/2 1s 1/2 Transfer experiments provide information on the amount of core excitation In DWBA: 11 Be =a Be(0 + ) ν2s 1/2 +b Be(2 + ) ν1d 5/ σ(0 + ) a 2 ; σ(2 + ) b 2 Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 42/46

56 Core excitation in knock-out experiments Batham et al, PRC71, (2005) Enhancement of diffractive breakup Open questions: How does deformation affect the momentum distributions? Effect in exclusive cross sections? Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 43/46

57 XCDCC calculations for 11 Be+ 64 Zn 11 Be+ 64 Elab =28.7 MeV 1 Di Pietro et al. Standard CDCC XCDCC: no continuum XCDCC: full σ/σ R θ c.m. (deg) B(E1; 1/2 + 1/2 ) σ inel CDCC e 2 fm mb XCDCC e 2 fm mb Exp e 2 fm 2 (not measured) Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 44/46

58 Application to 19 C+p 18 C+n+p 19 E/A=69 MeV (RIKEN), Satou et al., PLB 660 (2008) / MeV 0.59 MeV 18 C+n 5/ / / C The peak in the n-core relative spectrum was interpreted as a 1/2 + 5/2 + 2 transition Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 45/46

59 Application to 19 C+p 18 C+n+p Structure of 19 C: two-body model ( 18 C(0 +,2 + )+n) based on microscopic (AMD) densities of 18 C ( P-AMD) Reaction dynamics XDWBA dσ/dω (mb/sr) RIKEN data P-AMD: 5/2 + 1 P-AMD: 5/ / /2+ 2 E (MeV) Experimental SM (WBP) 5/2 + 3/2 + 1/2 + 3/2 + 5/2 + 5/2 + P-AMD 1/2 + 3/2 + 5/ θ c.m. (deg) 0 (?) 3/2 +5/2+ 3/2 + 5/2 + 1/2 + 1/2 + It is unclear whether the observed cross section corresponds to 5/2 + 1, 5/2+ 2 or even a superposition of both! 5/2 + 3/2 + 1/2 + Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 46/46

60 Application to 19 C+p 18 C+n+p dσ/dω (mb/sr) MeV/u RIKEN data P-AMD: 5/2 + 1 full P-AMD: 5/2 + 1 valence P-AMD: 5/2 + 1 core θ c.m. (deg) The core-excitation mechanism gives the dominant contribution to the cross section. Workshop on low-energy nuclear reaction dynamics A. M. Moro Universidad de Sevilla 46/46