Recent advances in nuclear reaction theories for weakly bound nuclei

Recent advances in nuclear reaction theories for weakly bound nuclei Antonio M. Moro Universidad de Sevilla, Spain May 25, 215 Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 1/31

Outline 1 Core excitation effects in reactions Static and dynamic core excitations. Implementation in the CDCC framework. Application to nuclear and Coulomb breakup of 11 Be. 2 The problem of inclusive breakup. The Ichimura, Austern, Vincent (IAV) model revisited. Application to deuteron and 6 Li inclusive breakup. Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 2/31

Why do we use few-body models in reactions? Microscopic approach 11 Be n Be* Start from (effective) NN interaction. Complicated many-body scattering problem [Descouvemont and Hussein, PRL 111, 8271 ( 13)] Few-body approach 11 Be Be n Projectile described with few-body model Inert clusters (cluster excitations not included) Phenomenological cluster-target interactions More transparent link between reaction and structure Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 3/31

Standard CDCC approach to the few-body scattering problem Example: 7 Li scattering in a three-body model 3-body Hamiltonian: H= T R + h r + V α (r α )+V t (r t ) Model wavefunction: Ψ(R, r)=φ gs (r)χ (R)+ N φ n (r)χ n (R) n> Coupled equations: [H E]Ψ(R, r)= [ E εn T R V n,n (R) ] χ n (R)= V n,n (R)χ n (R) 7 n n Li α r t R r 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 Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 4/31

Limitations of the standard CDCC 1 Does not provide breakup accompanied by target excitation, eg. d+a p+n+a generalized in Yahiro et al, Prog. Theor. Phys. Suppl. 89 (1986)32 2 Originally limited to two-body projectiles (three-body reactions) recently extended to 3-body projectiles ( 6 He, 11 Li): Matsumoto et al, NPA738 (24) 471, PRC7 (24) 6161(R). Rodriguez-Gallardo et al, PRC72 (25) 247, PRC77 (28) 6469. 3 Projectile described with single-particle /cluster models (ignores mixing of configurations and cluster excitations). 4 Does not provide breakup accompanied by absorption of one of the fragments (incomplete fusion). Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 5/31

Core-excitation effects Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 6/31

Core excitation in breakup: frozen-halo picture Ψ JM ( r,ξ)= [ ϕ J l,j ( r) Φ I(ξ) ] JM l n ϕ J l,j ( r)= valence particle wavefunction Φ I (ξ)= core wavefunction (frozen) Be(I) 11 Be(J) 3/2 + 1 3.41 MeV 111111 111111 111111 Be( ) x 1d 3/2 + 5/2 + 1 1.78 MeV 111111 111111 Be( + ) x 1d 5/2 11 Be Be 1/2 1 1/2 + 1.32 MeV 11 Be Be( + ) x 1p 1/2 Be( + ) x 2s 1/2 Pb n Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 7/31

Core excitation in breakup: frozen-halo picture Ψ JM ( r,ξ)= [ ϕ J l,j ( r) Φ I(ξ) ] JM l n ϕ J l,j ( r)= valence particle wavefunction Φ I (ξ)= core wavefunction (frozen) Be(I) 11 Be(J) 3/2 + 1 3.41 MeV 111111 111111 111111 Be( ) x 1d 3/2 + 5/2 + 1 1.78 MeV 111111 111111 111111 Be( + ) x 1d 5/2 11 Be Be 1/2 1 1/2 + 1.32 MeV 11 Be Be( ) x 1p + 1/2 Be( + ) x 2s 1/2 Pb n Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 7/31

Core excitation mechanism in breakup [ Ψ JM ( r,ξ)= ϕ J l,j,i ( r) Φ I (ξ) ] JM l,j,i n l Be(I) 11 Be(J) 3/2 + 1 3.41 MeV 111111 111111 111111 Be( + e[ ) x1d 3/2 ] + f [ Be( ) x 2s 1/2 ] 2 + 5/2 + 1.78 MeV 1 111111c[ Be( + ) x1d 5/2 ] + d [ Be( 2 + ) x 1d 5/2] Be* 11 Be 1/2 1 1/2 + 1.32 MeV 11 Be Be( + A[ ) x 1p1/2 ] + B [ Be( 2 + ) x 1p 3/2 ] a[ ] Be( + ) x 2s Be( 2 + 1/2 + b [ ) x 1d 5/2] Pb n Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 8/31

Core excitation mechanism in breakup [ Ψ JM ( r,ξ)= ϕ J l,j,i ( r) Φ I(ξ) ] JM l,j,i n l Be(I) 11 Be(J) 3/2 + 1 3.41 MeV 1111111 1111111 1111111 Be( + e[ ) x1d 3/2 ] + f [ Be( ) x 2s 1/2 ] 2 + 1111111 5/2 + 1.78 MeV 1111111 1111111 1 c[ Be( + ) x1d 5/2 ] + d [ Be( 2 + ) x 1d 5/2] Be* 11 Be 1/2 1 1/2 + 1.32 MeV 11 Be A[ Be( ) x 1p 1/2 ] + B [ Be( ) x 1p 3/2 ] + a[ ] 2 + Be( + ) x 2s Be( 2 + 1/2 + b [ ) x 1d 5/2] Pb n How do core transitions and core admixtures affect the inelastic/breakup cross sections? Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 8/31

Full CDCC calculations with core excitation Standard CDCC use 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 (XCDCC) use 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) Ψ α JM ( r,ξ): two-body WF with deformed potential (e.g. PRM, PVM, etc), microscopic transition densities, etc (static/structure effect) The non-central part of V ct (r ct,ξ) gives rise to core excitations/deexcitations (dynamic core excitation). Summers et al, PRC74 (26) 1466 (bins) R. de Diego et al, PRC 89, 6469 (214) (THO pseudo-states) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 9/31

Coulomb barrier breakup at low energies: 11 Be+ 197 Au at 31.9 MeV (.8V b ) Experiment: TRIUMF (Aarhus - LNS/INFN - Colorado - GANIL - Gothenburg -Huelva - Louisiana - Madrid - St. Mary - Sevilla - TRIUMF - York collaboration) Breakup probability: P bu (θ)= σ bu (θ) σ bu (θ)+σ qel (θ) = N bu (θ) N bu (θ)+n qel (θ) Inelastic probability (requires γ-rays coincidences): P inel (θ)= σ inel (θ) σ el (θ)+σ inel (θ)+σ bu (θ) = N inel (θ) N el (θ)+n inel (θ)+n bu (θ) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla /31

Application to 11 Be+ 197 Au at 31.9 MeV (.8 V b ) P inel (θ)= σ inel (θ) σ el (θ)+σ inel (θ)+σ bu (θ) P bu (θ)= σ bu (θ) σ el (θ)+σ inel (θ)+σ bu (θ) Elastic 11 Be+ 197 Au @ Elab =31.9 MeV Inelastic 11 Be+ 197 Au @ Elab =31.9 MeV Breakup 11 Be+ 197 Au @ Elab =31.9 MeV 1 σ/σ R.8.6.4.2 Exp. (TRIUMF) Standard CDCC XCDCC: no continuum XCDCC: full Preliminary 3 6 9 12 15 18 θ c.m. (deg) P inel -1-2 -3 Preliminary TRIUMF data Standard CDCC XCDCC 3 6 9 12 15 θ c.m. (deg) P bu -1-2 -3 Preliminary Exp. (TRIUMF) Standard CDCC (l max =) XCDCC (l max =7) 3 6 9 12 15 θ c.m. (deg) CDCC describes breakup, but overestimates inelastic cross sections. XCDCC accounts well for elastics, inelastic and breakup. Be excitations unimportant (dominance of E1 couplings). Some underestimation remains for breakup (convergence?, non-elastic breakup?) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 11/31

Comparison of E1 probabilities db(e1)/de (e 2 fm 2 /MeV) 1.8.6.4.2 Palit et al. (GSI) Fukuda et al. (RIKEN) Single-particle model (Capel et al) PRM (Summers et al) Millener et al 1 2 3 4 5 E rel (MeV) 11 Be models: Data: Single-particle model: Capel et al, PRC 68, 14612 (23) Deformed-core model: Summers et al, PLB 65, 24 (27) - Nakamura et al, Phys.Lett. B331, 296 (1994), RIKEN - Palit et al, PRC 68, 34318 (23), GSI. - Fukuda et al, PRC 7, 5466 (24), RIKEN. - Millener et al, PRC 28, 497 (1983). The single-particle model assumed in CDCC reproduces the continuum B(E1), but overestimates the B(E1) for the bound state by a factor of 2. The particle-plus-deformed core model assumed in XCDCC reproduces the bound and unbound B(E1) strengths. The XCDCC analysis of the Coulomb-barrier data for 11 Be+ 197 Au supports the B(E1) strength extracted from the Coulomb dissociation experiment 11 Be+ 28 Pb at RIKEN by Fukuda et al. Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 12/31

Dynamic core excitations in 11 Be: spectroscopic factors State Model + (ls)j 2 + s 1/2 2 + d 5/2 1/2 + (g.s.) PRM.857.121 SM (WBT).76.184 5/2 + (1.78 MeV) PRM.72.177.112 SM(WBT).682.177.95 3/2 + (3.41 MeV) PRM.165.737.81 SM(WBT).68.534.167 1/2 + 1, 5/2+ 1 dominant Be(gs) nlj configuration 3/2 + 1 dominant Be(2 + ) 2s 1/2 configuration Dynamic core excitation effects expected for the excitation of the 3/2 + resonance. Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 13/31

Evidence of dynamical core excitations in p( 11 Be,p ) at 64 MeV/u Data: Shrivastava et al, PLB596 (24) 54 (MSU) 3/2 + 1 111111 111111 3.41 MeV 5/2 + 1 111111 111111 1.78 MeV 1/2 1.5 MeV.32 1/2 + 1 11 Be E rel = 2.5 MeV contains 5/2 + resonance (expected single-particle mechanism) E rel =2.5 5 MeV contains 3/2 + resonance (expected core excitation mechanism) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 14/31

Evidence of dynamical core excitations in p( 11 Be,p ) at 64 MeV/u Data: Shrivastava et al, PLB596 (24) 54 (MSU) dσ/dω c.m. (mb/sr) 25 2 15 5 E rel =2.5-5 MeV XCDCC: with core excitations XCDCC: no core excitation dσ/dω c.m. (mb/sr) 3 2 E rel =.-2.5 MeV Core-excitation gives a large contribution to nuclear breakup (A.M.M. and R. Crespo, PRC 85, 54613 (212); R.de Diego et al, PRC 89, 6469 (214)) 2 3 4 θ c.m. (deg) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 14/31

The problem of inclusive breakup revisited Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 15/31

Breakup observables NOT provided by CDCC A g.s. p n ELASTIC BREAKUP (EBU) ("diffraction") 2 H A A* p n p Inelastic breakup n Incomplete fusion + transfer p (A+n)* NON ELASTIC BREAKUP ("stripping") n p COMPLETE FUSION (A+n+p)* CDCC provides only the EBU part How to compute the NEB part? Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 16/31

Why studying inclusive breakup? Surrogate reactions at low energies to extract n + A CN cross sections: E.g.: d+ A p+b Understanding of reaction mechanisms in breakup reactions at Coulomb-barrier energies with weakly-bound nuclei: 6,7 Li, 6 He, etc E.g.: 6,7 Li+A α+x largeαyields Fusion studies: incomplete fusion is part of the NBU cross section Knockout reactions at intermediate energies (stripping): E.g.: 19 C+ 9 Be 18 C+X Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 17/31

Importance of NEB part in knockout reactions 9 Be( 9 Be, 8 Be+X)Y Bazin et al, PRL 2, 23251 (29) CDCC accounts well for the EBU ( diffraction ) part, but this constitutes only a small fraction of the total inclusive breakup. Glauber/eikonal models are used as alternative, but they should be checked against fully quantum-mechanical formalism. Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 18/31

Sume-rule theories for inclusive breakup Baur & co: DWBA sum-rule with surface approximation. Baur et al, PRC21, 2668 (198). Hussein & McVoy: extraction of singles cross section combining the spectator model with sum rule over final states. Nucl. Phys. A445, 124 (1985). Ichimura, Austern, Vincent (IAV): Post-form DWBA. Ichimura, Austern, Vincent, PRC32, 431 (1985). Austern al, Phys. Rep.154, 125 (1987). Udagawa, Tamura (UT): prior-form DWBA. Udagawa and Tamura, PRC24, 1348 (1981). Udagawa, Lee, Tamura, PLB135, 333 (1984). Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 19/31

Sume-rule theories for inclusive breakup Baur & co: DWBA sum-rule with surface approximation. Baur et al, PRC21, 2668 (198). Hussein & McVoy: extraction of singles cross section combining the spectator model with sum rule over final states. Nucl. Phys. A445, 124 (1985). Ichimura, Austern, Vincent (IAV): Post-form DWBA. Ichimura, Austern, Vincent, PRC32, 431 (1985). Austern al, Phys. Rep.154, 125 (1987). Udagawa, Tamura (UT): prior-form DWBA. Udagawa and Tamura, PRC24, 1348 (1981). Udagawa, Lee, Tamura, PLB135, 333 (1984). Most of these theories have fallen into disuse and should be revisited Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 19/31

Formal expression for non-elastic breakup (NEBU) Inclusive breakup: (b+x) +A b+(x+a) } {{ }} {{ } a c Inclusive differential cross section:σ inc b Post-form expression for inclusive breakup: d 2 σ = 2π ρ(e b ) dω b E b v a Ψ c,( ) xa wavefunctions for c x+astates Ψ (+) exact many-body wavefunction c =σ EBU b +σ NEBU b χ ( ) b Ψc,( ) xa V bx+ V ba U ba Ψ (+) 2 δ(e E b E c ) Inclusion of all relevant c = x + A channels is not feasible in general use closed-form models Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 2/31

Austern, Ichimura, Vincent (IAV) model for non-elastic breakup (NBU) 1 Assume b particle is an spectator, and described by some OMP U b χ ( ) b ( k b, r b ) 2 x A wavefunction following breakup a+a b+x+a, and projected onto A gs : Ψ 3b(+) xb [K x + U xa E x ]ϕ x (r x )=(χ ( ) b V bx Ψ 3b(+) xb 3-body total WF (CDCC, Faddeev). ϕ x (r xa ) x-particle WF following breakup. U xa = V xa + iw xa x+a optical potential 3 The asymptotics ofψ x (r x ) gives the EBU part. 4 The NBU part is the loss of flux ( absorption ) in the x+a gs channel: dσ NEBU dω b de b = 2 v a ρ b (E b ) ϕ x W xa ϕ x Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 21/31

Application of IAV model to deuteron inclusive breakup EBU calculated with full 3-body model (CDCC) NBU calculated with IAV model, in DWBA:Ψ 3b(+) χ (+) d (R)φ d(r bx ) [K x + U xa E x ]ϕ x (r x )= χ ( ) b V bx Ψ 3b(+) xb χ ( ) b V bx χ (+) a φ a (r bx ) 93 Nb(d,pX) @ Ed =25.5 MeV dσ/dω p de p (mb/sr/mev) 1.1 Pampus et al. EBU (CDCC) NEB (DWBA) TBU (E p =14 MeV).1 3 6 9 12 15 18 θ c.m. (deg.) Calculations: J. Lei (PhD thesis) Data: Pampus et al, NPA311 (1978)141 Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 22/31

Application to 29 Bi ( 6 Li+,α+X) dσ/dσ R dσ/dσ R dσ/σ R dσ/dσ R 1.1 1.9 1.2 1.8.6.8.4 dσ/dσ R 1.2 1.5 1.5 Elastic scattering 5 15 θ cm (deg.) 1.1 24 MeV 26 MeV 28MeV 32MeV 36MeV 4MeV 1.9 1.5 1.5 1.5 1.5 3MeV 34MeV 38MeV 5MeV OMP CDCC 5 15 θ cm (deg.) dσ/dω (mb/sr) dσ/dω (mb/sr) dσ/dω (mb/sr) dσ/dω (mb/sr) dσ/dω (mb/sr) 5 2 4 2 3 EBU (CDCC) Inclusive α s NEB (FR-DWBA) TBU=EBU+NEB 28 MeV 4 3 MeV 9 36 MeV 12 38 MeV 6 8 18 4 MeV 36 5 MeV 12 6 24 MeV 32 MeV 5 15 θ lab (deg.) 5 2 8 6 4 2 4 24 12 26 MeV 34 MeV 5 15 θ lab (deg.) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 23/31

28 Pb( 6 Li,α+X) 28 Pb( 6 Li, αx) dσ/dω (mb/sr) dσ/dω (mb/sr) 4 2 Signorini Kelly NEB EBU TBU 5 15 8 6 4 2 6 29 MeV 33 MeV 4 2 5 15 2 35 MeV 39 MeV 15 5 Data: - Kelly et al, PRC63, 2461 (2) - Signorini et al, PRC67, 4467 ( 3) 5 15 θ lab Inclusiveαdominated by NEB. 5 15 θ lab EBU only dominates at very small angles (weakly absorbed distant trajectories ). Overall good agreement with data from Signorini et al (Legnaro), but with some global overestimation. Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 24/31

28 Pb( 7 Li,α+X) 28 Pb( 7 Li, α X) dσ/dω (mb/sr) dσ/dω (mb/sr) 4 3 2 6 4 2 29 MeV Preliminary 39 MeV 33 MeV 5 15 θ lab (deg) Kelly et al. Signorini et al. EBU (CDCC) NEB (with remnant) TBU Data: - Kelly et al, PRC63, 2461 (2) - Signorini et al, PRC67, 4467 ( 3) 5 15 θ lab (deg) Poor agreement with existing data may suggest other sources ofα s, e.g. 7 Li+ 28 Pb α+t+ 28 Pb α+α+ 27 Tl 7 Li+ 28 Pb 8 Be+ 28 Pb α+α+ 27 Tl Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 25/31

6 Li+ 29 Bi: incident energy dependence of cross sections 4 6 Li+ 29 Bi 3 σ (mb) 2 σ R (CDCC) 1 V b 25 3 35 4 45 5 E lab (MeV) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 26/31

6 Li+ 29 Bi: incident energy dependence of cross sections 4 6 Li+ 29 Bi 3 σ (mb) 2 1 V b σ R (CDCC) α + d EBU (CDCC) 25 3 35 4 45 5 E lab (MeV) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 26/31

6 Li+ 29 Bi: incident energy dependence of cross sections 4 6 Li+ 29 Bi 3 σ (mb) 2 1 V b σ R (CDCC) α + d EBU (CDCC) NEB-α (d "absorbed") 25 3 35 4 45 5 E lab (MeV) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 26/31

6 Li+ 29 Bi: incident energy dependence of cross sections 4 6 Li+ 29 Bi 3 σ (mb) 2 1 V b σ R (CDCC) α + d EBU (CDCC) NEB-α (d "absorbed") NEB-d (α "absorbed") 25 3 35 4 45 5 E lab (MeV) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 26/31

6 Li+ 29 Bi: incident energy dependence of cross sections 4 6 Li+ 29 Bi 3 σ (mb) 2 1 V b σ R (CDCC) α + d EBU (CDCC) NEB-α NEB-d CF (exp.): Dasgupta et al. 25 3 35 4 45 5 E lab (MeV) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 26/31

6 Li+ 29 Bi: incident energy dependence of cross sections 4 6 Li+ 29 Bi 3 σ (mb) 2 1 V b σ R (CDCC) α + d EBU (CDCC) NEB-α NEB-d CF (exp.): Dasgupta et al. SUM(CF+NEB-α+NEB-d+EBU) 25 3 35 4 45 5 E lab (MeV) σ reac σ α+d (EBU)+σ α (NBU)+σ d (NBU)+σ(CF) Suggests small transfer cross sections (for this reaction!) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 26/31

6 Li+ 28 Pb α+x: comparison of IAV and UT models IAV model relies on post-form DWBA Udagawa and Tamura use a prior-form DWBA sum-rule Only elastic breakup fusion is accounted for (no target excitation) dσ/dω (mb/sr) 3 25 2 15 DWBA post (IAV) DWBA prior (UT) 29 Bi( 6 Li,αX) @ 5 MeV 5 5 15 θ lab (deg) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 27/31

Testing the post-prior equivalence for 29 Bi( 6 Li,α X) ϕ post x x + n x with n x = χ b χ (+) φ a(r bx ) (NO term) =ϕ prior d 2 σ inc = 2 ρ b (E b ) ϕ post x W xa ϕ post x = 2 ρ b (E b ) ϕ prior x W xa ϕ prior x + n x W xa n x + 2Re[ ϕ prior x W xa n x de b dω b v a v a } {{ } } {{ }} {{ }} {{ } UT HMV Interf. IAV a dσ/de (mb/mev) 5 4 3 2 post formula (IAV) prior formula (UT) NO term interference term prior+no+interference 29 Bi( 6 Li,αX) @ 3 MeV - 15 2 α energy in CM (MeV) Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 28/31

Possible applications and extensions Assuming, W xa = W dir xa + Wfus xa, ICF might be computed as dσ NEBU dω b de b = 2 v a ρ b (E b ) ϕ x W fus xa ϕ x Calculations for stripping part in one-nucleon removal cross sections (knockout) at intermediate energies may provide a benchmark for standard semiclassical approaches. Application to more weakly bound (e.g. halo) nuclei should be possible, but might require going beyond (DWBA) in the calculation ofϕ x (eg. CDCC): [K x + U xa E x ]ϕ x (r x )=(χ ( ) b V bx Ψ 3b(+) xb Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 29/31

Conclusions Recent extensions of existing few-body reaction models, including their application to 3-body projectiles and core excitations in the structure and dynamics, are expected to improve our understanding of reactions with exotic nuclei. Core excitation effects have been found to be important for breakup, particularly with light target. Could be important for A(p, pn) quasi-free scattering reactions? Inclusive breakup theories show a promising agreement with existing breakup data, but remaining discrepancies with data might require going beyond DWBA. These theories may provide a promising framework for applications of current interest requiring inclusive breakup cross sections: surrogate reactions, incomplete fusion studies, knockout reactions, etc. Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 3/31

Conclusions Recent extensions of existing few-body reaction models, including their application to 3-body projectiles and core excitations in the structure and dynamics, are expected to improve our understanding of reactions with exotic nuclei. Core excitation effects have been found to be important for breakup, particularly with light target. Could be important for A(p, pn) quasi-free scattering reactions? Inclusive breakup theories show a promising agreement with existing breakup data, but remaining discrepancies with data might require going beyond DWBA. These theories may provide a promising framework for applications of current interest requiring inclusive breakup cross sections: surrogate reactions, incomplete fusion studies, knockout reactions, etc. Everything should be made as simple as possible, but not simpler Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 3/31

List of collaborators Inclusion of core excitation effects with: J.M. Arias, M. Gómez-Ramos (Univ. of Sevilla, Spain). J.A. Lay (INFN/Univ. di Padova) R. Crespo, Raúl de Diego, A. Deltuva (Lisbon, Portugal) Inclusive breakup calculations done with Jin Lei (Univ. of Sevilla, Spain) (PhD thesis). Workshop on Weakly Bound Exotic Nuclei, Natal (Brasil), May 215 A. M. Moro Universidad de Sevilla 31/31