Universidad de Sevilla

Understanding reactions induced by 6 He at energies around the Coulomb barrier Antonio M. Moro Universidad de Sevilla Discussion session at CEA/Saclay workshop CEA Saclay February 29 / 5

The 6 He nucleus Radioactive: 6 He β 6 Li Weakly bound: ǫ b =.973 MeV (t /2 87 ms) 2 + + g.s. 6 He.797.973 β 4 He + n + n g.s. Neutron halo 6 Li Borromean system: n-n and α-n unbound 3 body system: α almost inert Discussion session at CEA/Saclay workshop CEA Saclay February 29 2 / 5

Some recent experimental data SIMILAR EXPERIMENTS AT NOTRE DAME: 6 HE+ 29 BI Aguilera et al, PRL84, 58 (2).5 6 He+ 29 Bi @ 9 MeV.5 6 He+ 29 Bi @ 22.5 MeV σ/σ R σ/σ Ruth.5.5 3 6 9 2 5 8 θ c.m. 3 6 9 2 5 8 θ c.m. (deg) Low statistics Small angular resolution More focused to fusion studies Discussion session at CEA/Saclay workshop CEA Saclay February 29 3 / 5

Sevilla-Huelva-LLN 6 He+ 28 Pb experiment at LLN Elastic scattering E beam = 2 27 MeV (V b 2 MeV) Good angular resolution Clear evidence of disappearance of diffraction peak PH89 PH25 dσ/dω (mb/sr).5 6 He + 28 Pb @ 22 MeV 5 5 θ c.m. (deg) Discussion session at CEA/Saclay workshop CEA Saclay February 29 4 / 5

Sevilla-Huelva-LLN 6 He+ 28 Pb experiment at LLN Breakup: angular and energy distributions of α particles (neutrons not recorded) - Large yield (transfer/breakup?) - α particles post-accelerated 3 dσ/de α (mb/mev) dσ/de α (mb/mev) dσ/de α (mb/mev) dσ/de α (mb/mev) 25 2 5 5 25 2 5 5 3 25 2 5 5 3 25 2 5 5 E=4 MeV E=6 MeV E=8 MeV E=22 MeV θ=(32 o -64 o ) 5 5 2 25 3 E α (MeV) Discussion session at CEA/Saclay workshop CEA Saclay February 29 4 / 5

Extracting information on reaction mechanisms: 6 He+ 28 Pb reaction at LLN SOME QUESTIONS TO BE ADDRESSED:. How does the 6 He continuum affect the elastic distributions? 2. Is the optical model valid to describe the elastic data? 3. Is it possible to describe the elastic and breakup data within a few-body model? 4. What are the mechanisms responsible for the production of α s? 5. Why are the α particles accelerated with respect to beam velocity? Discussion session at CEA/Saclay workshop CEA Saclay February 29 5 / 5

Optical model calculations for 6 He+ 28 Pb Discussion session at CEA/Saclay workshop CEA Saclay February 29 6 / 5

Normal versus halo nuclei How does the halo structure affect the elastic scatterig? 4 He+ 28 Pb @ E=22 MeV 6 He+ 28 Pb @ E=22 MeV.8.8 V =5.89 MeV r =.33 fm, a=.5 fm W =9.84 MeV r i =.33 fm a i =.7 fm σ/σ R.6 σ/σ R.6.4.4.2 V =96.4 MeV r =.376 fm a =.63 fm W =32 MeV r i =.26 fm a i =.42 fm.2 3 6 9 2 5 8 θ c.m. (deg) 3 6 9 2 5 8 θ c.m. (deg) 4 He+ 28 Pb shows typical Fresnel pattern strong absorption 6 He+ 28 Pb shows a prominent reduction in the elastic cross section due to the flux going to other channels (mainly break-up) 6 He+ 28 Pb requires a large imaginary diffuseness long-range absorption Discussion session at CEA/Saclay workshop CEA Saclay February 29 7 / 5

Optical model calculations for 6 He+ 28 Pb A. Sanchez-Benitez et al, Nucl. Phys. A83, 3 (28), J.Phys.(London) G3, S953 (25) O. Kakuee et al, Nucl.Phys. A765, 294 (26) U(r) = V (r) + iw(r) + V C (r) + V pol (r) V (r), W(r): Phenomenological (WS) OMP V pol : analytical Dipole Polarization Potential developed by M.V. Andrés et al, Nucl.Phys. A579, 273 (994)..9.8.7.6.5 Bare OM + DPP Bare OM.4 5 5.5.95 E=4 MeV.8 E=6 MeV.9 5 5.8.6.4 5 5.9 5 5 E=8 MeV.2 E=22 MeV.2 E=27 MeV.8.6.4 2 4 6 8 Discussion session at CEA/Saclay workshop CEA Saclay February 29 8 / 5

Optical model calculations for 6 He+ 28 Pb RADIUS OF SENSITIVITY OF V(R) AND W(R) 6MeV 8MeV 22MeV 27MeV 2.5 -V(r) (MeV) 2..5..5 2.5 -W(r) (MeV) 2..5..5 2 4 6 r (fm) 2 4 6 r (fm) 2 4 6 r (fm) 2 4 6 r (fm) Imaginary part is sensitive to distances well beyond the strong absorption radius Discussion session at CEA/Saclay workshop CEA Saclay February 29 9 / 5

Optical model calculations for 6 He+ 28 Pb Some conclusions from the analysis of the elastic data with OMP: Elastic data can be indeed well reproduced with OMP, but the imaginary part requires a large difuseness long-range absorption effect Imaginary part is sensitive to distances well beyond the strong absorption radius (r ra 2.5 fm). The Dynamic Dipole Polarization Potential can account, but only partially, for the long range absorption. Discussion session at CEA/Saclay workshop CEA Saclay February 29 / 5

6 He+ 28 Pb within a few-body model Discussion session at CEA/Saclay workshop CEA Saclay February 29 / 5

6 He+ 28 Pb within a di-neutron model α y n n Assumptions of the dineutron model: Assume 6 He=α + 2 n (inspired in α + d model for 6 Li) Ignore n-n dynamics 2n-α ground state described by 2S wavefunction with ε bind = S 2n =.97 MeV. Theoretically very applealing, because permits the application of the standard CDCC method Discussion session at CEA/Saclay workshop CEA Saclay February 29 2 / 5

Standard CDCC formalism: coupled-channel equations Hamiltonian: H = T R +T r +v pn (r)+v pt (r pt )+V nt (r nt ) Internal states: {φ gs, φ n } Model wavefunction: 2 H n r p R T Ψ(R,r) = φ gs (r)χ (R) + NX φ n (r)χ n (R) n> Coupled equations: [H E]Ψ(R, r) [E ǫ α T R V α,α (R)] χ α (R) = X α α V α,α (R)χ α (R) Transition potentials: V α;α (R) = Z drφ α (r) h V pt (R + r 2 ) + V nt(r r 2 ) i φ α (r) Discussion session at CEA/Saclay workshop CEA Saclay February 29 3 / 5

Continuum discretization: 2-body case Truncate the continuum spectrum in ε and l: < ε < ε max < l < l max Division into energy intervals (bins) ε i ; i,..., N For each bin, a representative function is constructed by superposition of the continuum states φ l,2 φ l,2 φ l, n=3 n=2 n= l= l= l=2 s waves p waves Breakup threshold d waves ε max ε= ε = 2.22 ground state φ bin l,i (r) = N l,i Z ki+ k i w(k)φ l (k, r)dk i =,..., N Discussion session at CEA/Saclay workshop CEA Saclay February 29 4 / 5

6 He+ 28 Pb within a di-neutron model 6 He+ 28 Pb @ 22 MeV LLN data (PH89) LLN data (PH25) channel (no continuum) CDCC: di-neutron model σ/σ R.5 5 5 θ c.m. (deg) The naive dineutron model fails to describe the elastic data Discussion session at CEA/Saclay workshop CEA Saclay February 29 5 / 5

6 He+ 28 Pb within a di-neutron model.8 3-body: Scattering states Dineutron: ε b =-.97 MeV 2 db(e)/dε (e 2 fm 2 /MeV).6.4.2 db(e2)/dε (e 2 fm 4 /MeV) 2 4 6 8 ε (MeV) 2 3 4 5 6 7 8 ε (MeV) The dineutron model tends to overestimate the coupling to the continuum: we need a more sophisticated model for 6 He α +n +n Discussion session at CEA/Saclay workshop CEA Saclay February 29 6 / 5

6 He+A within a four-body model (3+) Internal states: φ n (x,y) Model wavefunction: projectile Ψ(R,x,y) = φ gs (x,y)χ (R) + NX φ n (x,y)χ n (R) n> y x r r2 R r3 target [H E]Ψ JM = System of coupled equations: [E ǫ α T R V α,α (R)] χ α (R) = X α α V α,α (R)χ α (R) Coupling potentials: V n,n (R) = φ n b V nt + b V nt + b V α,t φ n Discussion session at CEA/Saclay workshop CEA Saclay February 29 7 / 5

Coupling potentials V J Lnj,L n j (R) = LnjJM P 3 k= b V kt ( r k ) L n j JM where Φ JM Lnj( b R, x, y) = P µm L ψ jµn ( x, y) LM L jµ JM Y LML ( b R) multipolar expansion L Q L «V J Lnj,L n j (R) = P Q ( )J j ˆL ˆL W(LL jj, QJ)F Q nj,n j (R) Discussion session at CEA/Saclay workshop CEA Saclay February 29 8 / 5

Form factors F Q nj,n j (R) = ( ) Q+2j j ĵĵ (2Q + ) 3 ββ k= β k β N k ββk N β β k ( ) l xk+s xk +j abk j abk I k δ lxk l xk δ S xk S ( ) xk ˆl lyk ykˆl yk ˆlk ˆl k ĵ abk ĵ Q l yk abk W(l k l k l ykl yk ; Ql xk)w(j abk j abk l kl k ; QS xk) W(jj j abk j abk ; QI k) (sin α k ) 2 (cos α k ) 2 ρ 5 dα k dρ R βjn (ρ)ϕ l xkl yk K k (α k )VQ k(r, y k)ϕ l xkl yk K (α k k )R β j n (ρ) Discussion session at CEA/Saclay workshop CEA Saclay February 29 9 / 5

Multipolar expansion Multipolar expansion V k Q(R, y k ) = 2 R + b V kt ( r k )P Q (z k )dz k bv kt ( r k ) = P Q (2Q + )V Q(R, y k )P Q (z k ) where z k = by k br V J Lnj,L n j (R) = P L Q L Q ( )J j ˆL ˆL W(LL jj, QJ)F Q nj,n j (R) «Discussion session at CEA/Saclay workshop CEA Saclay February 29 2 / 5

Four-body CDCC calculations for 6 He scattering 2-body case: r p n single degree of freedom (inter-cluster relative coordinate r) 2-body Hamiltonian: H = T r + V pn (r) 2-body wavefunction: φ n,β (r) = R n,β (r) [Y l (Ω) χ S ] jm β = {l, S, j} Discussion session at CEA/Saclay workshop CEA Saclay February 29 2 / 5

Four-body CDCC calculations for 6 He scattering 3-body case: 2 degrees of freedom (6 coordinates) 3-body Hamiltonian: α y n n x H = T R + T r + V nn + V nα + V nα + V nnα The 3-body wavefunction can be expressed in different coordinate systems: Jacobi coordinates: {x, y} Hypersherical coordinates: {ρ, Ω x, Ω y, α} ρ 2 x 2 + y 2 tan α = x y φ n,jm (ρ, Ω) = ρ 5/2 N β X β= R nβ (ρ) h Υ l xl y Kl (Ω x, Ω y, α) X S ijm β {K, l x, l y, l, S x, j} Discussion session at CEA/Saclay workshop CEA Saclay February 29 22 / 5

Pseudo-state method vs Binning method Two methods for continuum discretization:. Pseudo-state method: 2-body and 3-body projectiles 2. Binning method: so far, only 2-body projectiles. Discussion session at CEA/Saclay workshop CEA Saclay February 29 23 / 5

Pseudo-state method for continuum discretization. Choose a complete basis for the degree of freedom under consideration Eg: HO basis: {φ HO l,n (r)} ; n =,..., 2. Truncate the basis: n =,..., N 3. Diagonalize the Hamiltonian in the truncated basis {φ HO l,n (r)} N n= Diagonalize H {ϕ l,n (r)} N n= 8 < ǫ ǫ gs < g.s. ǫ n < (n ) Bound excited states : ǫ n > Continuum states Discussion session at CEA/Saclay workshop CEA Saclay February 29 24 / 5

Transformed Harmonic Oscillator Basis M.V. Stoitsov and I.Zh. Petkov, Ann. Phys. 84, 2 (988) The HO basis has incorrect asymptotic behaviour for bound states of finite potentials φ HO i,l (s) exp( s 2 ) Apply Local Scale Transformation s(r) to the HO basis such that: s(r) j r r r r THO basis: φ THO i,l (r) Advantages: q ds dr φho i,l [s(r)]; i =,... Proper asymptotic behaviour for bound states Preserve simplicity and analytic properties of HO basis. Discussion session at CEA/Saclay workshop CEA Saclay February 29 25 / 5

Transformed Harmonic Oscillator Basis Two alternative THO prescriptions. Determinte the LST s(r) from the g.s. of the system: F. Perez-Bernal et al,phys. Rev. A 63, 52 (2) Z r φ gs (r ) 2 dr = Z s φ HO (s ) 2 ds Advantage: the g.s. wavefunction is exactly reproduced for any N 2. Analytic s(r) : s(r) = 2 4 ` m r + γ r 3 m 5 m Advantage: simpler to calculate, flexibility Discussion session at CEA/Saclay workshop CEA Saclay February 29 26 / 5

Bin method: 3-body system Continuum states can be expanded in HH as Ψ κjµ (ρ, Ω, Ω κ ) = X ββ R ββ j(κρ)y ββ jµ(ω, Ω κ ) β incoming channels β outgoing channels κ = 2mε/ h For each incoming channel, the radial part of the bin WF is calculated as R bin njβ(ρ) = s 2 πn β j Z κ2 κ dκe iδ β j(κ) R ββ j(κρ) n {β ε av } Discussion session at CEA/Saclay workshop CEA Saclay February 29 27 / 5

Bin method: 3-body system Continuum states can be expanded in HH as Ψ κjµ (ρ, Ω, Ω κ ) = X ββ R ββ j(κρ)y ββ jµ(ω, Ω κ ) β incoming channels β outgoing channels κ = 2mε/ h For each incoming channel, the radial part of the bin WF is calculated as R bin njβ(ρ) = s 2 πn β j Z κ2 κ dκe iδ β j(κ) R ββ j(κρ) n {β ε av } The basis space for 3-body case is huge!! Discussion session at CEA/Saclay workshop CEA Saclay February 29 27 / 5

Bin method: eigenchannels How to establish a hierarchy among the states for each energy ε and total angular momentum j? ➀ Define eigenstates of the S-matrix for each ε eigenchannels (EC) ➁ Order the EC according to the magnitude of their phase-shifts ➂ Truncate in the number of EC Discussion session at CEA/Saclay workshop CEA Saclay February 29 28 / 5

B(E) and B(E2) in a three-body model db(e)/dε (e 2 fm 2 /MeV).25.2.5..5 Total EC EC 2 EC 3 EC 4 2 4 6 8 2 eigenphase (rad).5.5 2 4 6 8 ε (MeV) Discussion session at CEA/Saclay workshop CEA Saclay February 29 29 / 5

B(E) and B(E2) in a three-body model db(e2)/dε (e 2 fm 4 /MeV) 3 2.5 2.5.5 2 4 6 8 4 Total EC EC 2 EC 3 EC 4 eigenphase (rad) 3 2 2 4 6 8 ε (MeV) Discussion session at CEA/Saclay workshop CEA Saclay February 29 29 / 5

Applications of the four-body CDCC formalism 6 He+ 2 C @ 23 MeV σ/σ Ruth V. Lapoux et al. PRC 66 3468 no continuum n b =2 ε max =3 MeV n b =4 ε max =3 MeV. 5 5 2 25 θ c.m. (deg) Discussion session at CEA/Saclay workshop CEA Saclay February 29 3 / 5

Applications of the four-body CDCC formalism 6 He+ 64 Zn E= MeV E=3.6 MeV LLN no continuum 4-body CDCC LLN No continuum 4-body CDCC,8.8 σ/σ Ruth,6 σ/σ Ruth.6,4.4,2.2 3 6 9 2 5 8 θ c.m. (deg) 3 6 9 2 5 8 θ c.m. (deg) Discussion session at CEA/Saclay workshop CEA Saclay February 29 3 / 5

Applications of the four-body CDCC formalism M. Rodriguez-Gallardo et al., Phys.Rev. C 77, 6469 (28) 6 He+ 28 Pb E=22 MeV E=27 MeV.8 LLN (PH89) LLN (PH25) no continuum 3-body CDCC 4-body CDCC.2 6 He+ 28 Pb @ 27MeV σ/σ Ruth.6 σ/σ Ruth.8.6.4.2.4.2 LLN data no continuum 3-body CDCC 4-body CDCC 4 8 2 6 θ c.m. (deg) 2 4 6 8 θ c.m. (deg) Discussion session at CEA/Saclay workshop CEA Saclay February 29 32 / 5

Breakup cross sections for 6 He+ 28 Pb dσ bu /dε (mb/mev) j=+ j=- j=2+ 2 5 5 2 2 4 6 8 5 5 2 4 6 8 2 5 5 2 2 4 6 8 5 5 2 4 6 8 ε (MeV) 2 5 5 2 2 4 6 8 5 5 2 2 4 6 8 5 5 2 2 4 6 8 5 5 2 4 6 8 ε (MeV) 2 5. 5 2 2 4 6 8 5 5 2 2 4 6 8 5 5 2 2 4 6 8 5 5 2 4 6 8 ε (MeV) EC EC 2 EC 3 EC 4 Discussion session at CEA/Saclay workshop CEA Saclay February 29 33 / 5

TLEP for 6 He+ 28 Pb Real 2,5,5 -,5 2 4 6 8 2 - -,5-2 -2,5 4 MeV 6 MeV 8 MeV 22 MeV 27 MeV -3 2 2 4 6 8 2 Real part: long range behaviour Repulsive around the strong absorption radius. Atractive at large distances (mainly from dipole Coulomb breakup). Imaginary part: shows long range absorption obtained with phenomenological OMP and dineutron model. Imag 2 4 6 8 2 - -2 2 4 6 8 2 R(fm) Discussion session at CEA/Saclay workshop CEA Saclay February 29 34 / 5

TLEP for 6 He+ 28 Pb Real 2.5.5 2 4 6 8 2 -.5 22 MeV - J= J=5 -.5 J= J=5-2 J=2 J=25-2.5 J=3-3 2 2 4 6 8 2 Real part: long range behaviour Repulsive around the strong absorption radius. Atractive at large distances (mainly from dipole Coulomb breakup). Imaginary part: shows long range absorption obtained with phenomenological OMP and dineutron model. Imag 2 4 6 8 2 - -2 2 4 6 8 2 R (fm) Discussion session at CEA/Saclay workshop CEA Saclay February 29 34 / 5

Open problems and work under development: Pseudo-state vs Binning procedure Is there a more efficient method to represent the 3-body continuum? Inclusion of Coulomb in 3-body structure (eg 6 Be) Calculation of neutron-neutron and neutron-α correlations (energy, angle) to compare with new experiments. Transfer within four-body model. Discussion session at CEA/Saclay workshop CEA Saclay February 29 35 / 5

The dineutron model of 6 He revisited Discussion session at CEA/Saclay workshop CEA Saclay February 29 36 / 5

The dineutron model for 6 He revisited Density distribution for α-2n relative motion:. Three-body Dineutron ρ(y)= Ψ(y) 2.. (R =.9 fm; a=.25 fm) 5 5 y (fm) 3-body: r α 2n = 3.25 fm 2-body: r α 2n = 4. fm Discussion session at CEA/Saclay workshop CEA Saclay February 29 37 / 5

The dineutron model for 6 He revisited Density distribution for α-2n relative motion: ρ(y)= Ψ(y) 2.. Three-body Dineutron db(e)/dε (e 2 fm 2 /MeV).8.6.4.2 3-body (*) Dineutron 2 4 6 8 2. (R =.9 fm; a=.25 fm) 5 5 y (fm) 3-body: r α 2n = 3.25 fm 2-body: r α 2n = 4. fm db(e2)/dε (e 2 fm 4 /MeV) 2 3 4 5 6 7 8 E x (MeV) Discussion session at CEA/Saclay workshop CEA Saclay February 29 37 / 5

Improved dineutron model for 6 He 6 Li 6 He α y n x α y n x p n 6 Li=α + d ε α d =.47 MeV 6 He=α + 2 n ε α 2n = S 2n =.97 MeV ε n p = ε d = 2.22 MeV ε n n? In reality, we expect ε n n >!!! Discussion session at CEA/Saclay workshop CEA Saclay February 29 38 / 5

An improved dineutron model for 6 He Our model: determine an effective α- 2 n binding energy: ε b.6 MeV. Three-body Dineutron: ε b =.97 MeV Dineutron: ε b =.6 MeV ρ(y).. (R =.9 fm; a=.25 fm) 5 5 y (fm) 3-body: r α 2n = 3.25 fm 2-body: r α 2n = 3.45 fm Discussion session at CEA/Saclay workshop CEA Saclay February 29 39 / 5

An improved dineutron model for 6 He Our model: determine an effective α- 2 n binding energy: ε b.6 MeV ρ(y).. Three-body Dineutron: ε b =.97 MeV Dineutron: ε b =.6 MeV db(e)/dε (e 2 fm 2 /MeV).8.6.4.2 3-body Dineutron: ε b =.97 MeV Dineutron: ε b =.6 MeV. (R =.9 fm; a=.25 fm) 2 4 6 8 2 5 5 y (fm) 3-body: r α 2n = 3.25 fm 2-body: r α 2n = 3.45 fm db(e2)/dε (e 2 fm 4 /MeV) 2 3 4 5 6 7 8 ε (MeV) Discussion session at CEA/Saclay workshop CEA Saclay February 29 39 / 5

Application to 6 He+ 64 Zn 6 He+ 64 Zn,2 E lab =3.6 MeV,2 E lab = MeV σ/σ Ruth,8,6,8,6,4,4,2 3 6 9 2 5 θ (grados),2 LLN data No continuum Continuum included (THO) 3 6 9 2 5 θ (grados) A.M.M.,K.Rusek, J.M.Arias, J.Gomez-Camacho, M.Rodriguez-Gallardo, Phys.Rev. C 75, 6467 (27) Discussion session at CEA/Saclay workshop CEA Saclay February 29 4 / 5

Elastic scattering in the improved dineutron model 6 He+ 28 Pb at E = 27 MeV.2 6 He+ 28 Pb @ E=27 MeV σ/σ Ruth.8.6 channel: ε b =-.6 MeV CDCC: ε b =-.97 MeV CDCC: ε b =-.5 MeV.4.2 3 6 9 2 5 θ c.m. (deg) Discussion session at CEA/Saclay workshop CEA Saclay February 29 4 / 5

Elastic scattering in the improved dineutron model 6 He+ 97 Au at E = 2-4 MeV E=27 MeV E=29 MeV E=4 MeV σ/σ Ruth.5.5.5 channel CDCC: ε b =-.97 MeV CDCC: ε b =-.6 MeV 3 6 9 θ c.m. (deg) 3 6 9 θ c.m. (deg) 3 6 9 θ c.m. (deg) Discussion session at CEA/Saclay workshop CEA Saclay February 29 42 / 5

Inclusive breakup in the improved dineutron model dσ/dω (mb/sr) dσ/dω (mb/sr) dσ/dω (mb/sr) dσ/dω (mb/sr) 5 5 5 2 5 5 E=4 MeV E=6 MeV E=8 MeV E=22 MeV 3 6 9 2 5 8 θ lab (deg) dσ/de α (mb/mev) dσ/de α (mb/mev) dσ/de α (mb/mev) dσ/de α (mb/mev) 25 2 5 5 3 25 2 5 5 3 25 2 5 5 3 25 2 5 5 E=4 MeV E=6 MeV E=8 MeV E=22 MeV θ=(32 o -64 o ) 5 5 2 25 3 E α (MeV) Discussion session at CEA/Saclay workshop CEA Saclay February 29 43 / 5

6 He+ 28 Pb: breakup What is the mechanism responsible for the production of α s? 6 He+ 28 Pb 4 He + X Discussion session at CEA/Saclay workshop CEA Saclay February 29 44 / 5

6 He+ 28 Pb: breakup What is the mechanism responsible for the production of α s? 6 He+ 28 Pb 4 He + X Direct Breakup (BU) 6 He 4 He 28 Pb E α 4 6 E beam Discussion session at CEA/Saclay workshop CEA Saclay February 29 44 / 5

6 He+ 28 Pb: breakup What is the mechanism responsible for the production of α s? 6 He+ 28 Pb 4 He + X Direct Breakup (BU) Transfer to the Continuum (TC) 4 He 6 He 4 He 6 He 28 Pb E α 4 6 E beam 28 Pb E α E beam Discussion session at CEA/Saclay workshop CEA Saclay February 29 44 / 5

6 He+ 28 Pb: breakup What is the mechanism responsible for the production of α s? 6 He+ 28 Pb 4 He + X Direct Breakup (BU) Transfer to the Continuum (TC) -neutron transfer (NT) 6 He 4 He 4 He 6 He 4 He 6 He 28 Pb 28 Pb E α 4 6 E beam 28 Pb E α 4 5 E beam E α E beam Discussion session at CEA/Saclay workshop CEA Saclay February 29 44 / 5

6 He+ 28 Pb: breakup D. Escrig et al, Nucl. Phys. A792 (27) 2 dσ/dω (mb/sr) dσ/dω (mb/sr) dσ/dω (mb/sr) dσ/dω (mb/sr) 5 5 5 2 5 5 E=4 MeV E=6 MeV E=8 MeV E=22 MeV TC DBU NT 3 6 9 2 5 8 θ lab (deg) dσ/de α (mb/mev) dσ/de α (mb/mev) dσ/de α (mb/mev) dσ/de α (mb/mev) 3 2 3 2 3 2 3 2 E=4 MeV DBU E=6 MeV E=8 MeV E=22 MeV TC DBU (x5) 5 5 2 25 3 E α (MeV) The TC model explains satisfactory the magnitude and energy distribution of the measured α s DBU fails to explain the yield and energy of α s Discussion session at CEA/Saclay workshop CEA Saclay February 29 45 / 5

6 He+ 28 Pb: breakup Our calculations suggest a picture in which the α particles are repelled by the Coulomb field, while the neutrons are transferred to highly excited states of the target (transfer to the continuum) Discussion session at CEA/Saclay workshop CEA Saclay February 29 46 / 5

Conclusions and medium-term wishes 6 He experiments at Coulomb barrier energies provide a beautiful as well as challenging probe to test our understanding of the structure and the reaction mechanisms that arise in the collision of weakly bound nuclei. The CDCC framework can be applied to describe the scattering of three-body systems using an extension of the binning method. Unlike the α-d model of 6 Li, the naive dineutron model is not appropriate to describe the scattering of 6 He. However, a semi-quantitive understanding of elastic and transfer/breakup can be achieved using a modified dineutron model provided the (positive) n-n relative energy is taken into account in the model. In close future we would like to : Calculate more complicated observables, such as neutron-neutron or neutron-α correlations in breakup experiments. Extend these analyses to the scattering of other Borromean nuclei. E.g.: Li+ 28 Pb measured in July 28 at TRIUMF (Vancouver, Canada). Discussion session at CEA/Saclay workshop CEA Saclay February 29 47 / 5

Collaboration Collaborators: J. Gómez-Camacho, J.M. Arias (Univ. de Sevilla) M. Rodríguez-Gallardo (Univ. de Sevilla / Univ. de Lisboa) L. Acosta, I. Martel, F. Pérez-Bernal, A. Sánchez-Benítez (Univ. de Huelva) I. Thompson, J. Tostevin (Univ. de Surrey, Reino Unido) D. Escrig, M.J. Borge (CSIC, Madrid) Discussion session at CEA/Saclay workshop CEA Saclay February 29 48 / 5

Some recent experimental data 6 He experiments at LLN σ/σ Ruth.2.8.6.4 6 64 He+ Zn @ Elab =3.6 MeV.2 E lab = MeV.8.6.4.2.2 LLN data 3 6 9 2 5 θ (grados) A. Di Pietro et al, Phys. Rev. C 69,4463 (24) 3 6 9 2 5 θ (grados) Discussion session at CEA/Saclay workshop CEA Saclay February 29 49 / 5

Optical model calculations for 6 He+ 28 Pb A. Sanchez-Benitez et al, Nucl. Phys. A83, 3 (28) U(r) = V (r) + iw(r) + V C (r) + V pol (r) V pol : analytical Dipole Polarization Potential developed by M.V. Andrés et al, Nucl.Phys. A579, 273 (994)..9.8.7.6.5 Bare OM + DPP Bare OM.4 5 5.5.95 E=4 MeV.8 E=6 MeV.9 5 5.8.6.4 5 5.9 5 5 E=8 MeV.2 E=22 MeV.2 E=27 MeV.8.6.4 2 4 6 8 Discussion session at CEA/Saclay workshop CEA Saclay February 29 5 / 5