Dynamics of the scattering of 11 Li on 208 Pb at energies around the Coulomb barrier
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1 Dynamics of the scattering of 11 Li on 208 Pb at energies around the Coulomb barrier J. A. Lay Departamento de Física Atómica, Molecular y Nuclear; Universidad de Sevilla University of Surrey, 9 th November 2010
2 1 Motivation 2 3 Equivalent Photon Method CDCC Improved dineutron model 4 BU transformation
3 Motivation
4 Motivation
5 Motivation Reactions with Halo (loosely bound) nuclei Large transfer/break-up probability Long range absorption Long range (Coulomb/Nuclear) non-elastic mechanisms Enhancement of the dipole polarizability
6
7 Collaboration Schedule 6 He+ 208 LLN 11 Be+ 120 ISOLDE 208 TRIUMF DONE DONE UNDER ANALYSIS
8 Collaboration Schedule 6 He+ 208 LLN 11 Be+ 120 ISOLDE 208 TRIUMF 8 He+ 208 GANIL 11 Be+ 208 TRIUMF DONE DONE UNDER ANALYSIS JUST MEASURED APPROVED
9 To continue on the understanding of these novel reaction mechanisms To extract more information about 11 Li structure
10 TRIUMF 2008 ; Collaboration E1104 Detectors T1 T2 T3 T4 (10ö -40ö) (30ö -60ö) (50ö -100ö) (90ö -140ö)
11 TRIUMF 2008 elastic ( 11 Li) and break-up ( 9 Li) scattering is measured neutrons are NOT measured 208 Pb 10 0 P bu (θ) 10-1 Preliminary! 10-2 Det. T1 24 MeV Det. T2 24 MeV Det. T MeV Det. T MeV θ Lab (deg)
12 also the elastic scattering of 9 Li Li+ 208 Elab = 29.4 MeV Rutherford OM (C1) Tel 1 (CM): normalized to Rutherford Tel 2 (CM): normalized to Rutherford dσ/dω (mb/sr) θ c.m. (deg) OM Potential needed for CDCC/CRC calculations Calibration of the detectors
13 Equivalent Photon Method CDCC Improved dineutron model Large amount of 9 Li Direct Break-up (e.g. CDCC) n/2n Transfer (e.g. CRC) 9 Li 11 Li 208 Pb v9 Li v11 Li E9 Li 9 11 E11 Li E9 Li E11 Li
14 Equivalent Photon Method CDCC Improved dineutron model dσ/de (mb/mev) E=24 MeV (9/11)E11 Li 1000 θ lab =(12 o -40 o ) 800 E11 Li dσ/de (mb/mev) E=24 MeV (9/11)E11 Li θ lab =(32 o -60 o ) E11 Li dσ/de (mb/mev) E=29.5 MeV Preliminary! Detector 1 (9/11)E11 Li E11 Li dσ/de (mb/mev) E=29.5 MeV Preliminary! Detector 2 (9/11)E11 Li E11 Li E lab ( 9 Li) (MeV) E lab ( 9 Li) (MeV) Present data consistent with a direct break-up mechanism
15 Equivalent Photon Method CDCC Improved dineutron model Theoretical frameworks for Break-up CDCC Semiclassical Equivalent Photon Method
16 Equivalent Photon Method Equivalent Photon Method CDCC Improved dineutron model EPM vs. CDCC Simple and analytical Only Coulomb excitation is included (no nuclear information) Under the conditions: Impact parameter b bigger than interaction radius = small θ λ projectil distance of maximum approach Probability of break-up: P(Ω) = ( Zt e q v ) 2 4 ε 4 ε b de db(e1) df E1 de dω,
17 CDCC Motivation Equivalent Photon Method CDCC Improved dineutron model Coupling to BU (unbound) channels plays an important role in the scattering of loosely bound nuclei { Infinite number of estates. True Continuum: No square-integrable.
18 208 Pb Motivation Equivalent Photon Method CDCC Improved dineutron model 6 He 4b-CDCC: PRC 77, (2008)
19 Improved dineutron model Equivalent Photon Method CDCC Improved dineutron model We only consider: 2n- 9 Li Ψ(x,y) φ(y)ξ(x) We calculate φ(y) using a 2n- 9 Li potential with ε 2n 9 Li ε b ε 2n 9 Li = ε b implies ε n n 0 but ε n n > 0 φ 2n-9Li (y) body calculation dineutron: ε 2n-9Li =-0.37 MeV Standard dineutron model body calculation n- 9 Li separation (fm)
20 Improved dineutron model Equivalent Photon Method CDCC Improved dineutron model We only consider: 2n- 9 Li Ψ(x,y) φ(y)ξ(x) We calculate φ(y) using a 2n- 9 Li potential with ε 2n 9 Li ε b ε 2n 9 Li is determined by adjusting φ(y) to Ψ(x,y) φ 2n-9Li (y) body calculation body calculation dineutron: ε 2n-9Li =-0.37 MeV dineutron: ε 2n-9Li =-0.54 MeV Standard dineutron model 10-3 Improved dineutron model (ε 2n-9Li =0.54 MeV) n- 9 Li separation (fm)
21 B(E1) Motivation Equivalent Photon Method CDCC Improved dineutron model 3 RIKEN GSI standard dineutron model: ε 2n- 9 Li =-0.37 MeV improved dineutron model: ε 2n- 9 Li =-0.54 MeV db/dε (e 2 fm 2 /MeV) ε (MeV) RIKEN: T. Nakamura et al., PRL 96, (2006) GSI: M. Zinser et al., NPA 619, 151 (1997)
22 Equivalent Photon Method CDCC Improved dineutron model Two-body potentials 2n- 9 Li: Improved dineutron model 6 He: A. M. Moro, Phys. Rev. C 75, (2007) 2n- 208 Pb: d- 208 Pb potential Perey y Perey, PR 132, 755 (1963) 9 Li- 208 Pb: 9 Be- 208 Pb potential R. J. Woolliscroft et al., PRC 68, (2003)
23 9 Li+ 208 Pb potentials Motivation Equivalent Photon Method CDCC Improved dineutron model 9 Li MeV 9 Li MeV 1 dσ el /dω C1 9 Be+ 208 Pb C2 8 Li+ 208 Pb C3 7 Li+ 208 Pb Data Target 1.45 mg/cm 2 Preliminary! dσ el /dω Preliminary! C1 9 Be+ 208 Pb C2 8 Li+ 208 Pb C3 7 Li+ 208 Pb Data Target 1.45 mg/cm θ CM (deg) θ CM (deg)
24 BU transformation dσ/de (mb/mev) E=24 MeV (9/11)E11 Li 1000 θ lab =(12 o -40 o ) 800 E11 Li dσ/de (mb/mev) E=24 MeV (9/11)E11 Li θ lab =(32 o -60 o ) E11 Li dσ/de (mb/mev) E=29.5 MeV Preliminary! Detector 1 CDCC ε 2n- 9 Li =-0.54 MeV (9/11)E11 Li E11 Li dσ/de (mb/mev) E=29.5 MeV Preliminary! Detector 2 CDCC ε 2n- 9 Li =-0.54 MeV (9/11)E11 Li E11 Li E lab ( 9 Li) (MeV) E lab ( 9 Li) (MeV)
25 Break-up Cross-section BU transformation MeV MeV P bu (Ω) 10-1 Preliminary! P bu (θ) 10-1 Preliminary! 10-2 Det. T1 Det. T2 Equivalen Photon Method CDCC dineutron model ε 2n- 9 Li =-0.54 MeV 10-2 Det. T1 Det. T2 Equivalent Photon Method CDCC dineutron model ε 2n- 9 Li =-0.54 MeV θ Lab (deg) θ LAB (deg)
26 Elastic Cross-section Motivation BU transformation 208 Elab =24MeV 208 Elab =29.5MeV σ el /σ R only g.s. ε 2n- 9 Li =-0.54 MeV CDCC l max =0 CDCC l max =1 CDCC l max =2 CDCC l max =7 σ el /σ R only g.s. ε 2n- 9 Li =-0,54 MeV CDCC l max =0 CDCC l max =1 CDCC l max =2 CDCC l max = θ CM (deg) θ CM (deg) Departure from Rutherford mainly due to Coulomb dipole couplings
27 BU transformation? What information about the 11 Li structure can be obtained from BU probabilities?
28 Reduced BU probability BU transformation Equivalent Photon Method ( ) Zt e 2 4 P(Ω) = q v ε 4 ε b de db(e1) df E1 de dω ε = 1 sen θ
29 Reduced BU probability BU transformation Collision time t = q (π + 2ε) v Reduced BU probability P(t) = ( 16π 2 9 P(Ω) (Z te) 2 q( v) 3 1 t v 2 q π ) de E db(e1) e Et de
30 Reduced BU probability BU transformation Collision time t = q (π + 2ε) v Reduced BU probability P(t) = ( 16π 2 9 P(Ω) q( v) (Z te) 2 t v q π [ ) = L E db(e1) ] de
31 Reduced BU probability BU transformation The logarithmic derivative does NOT depend on the Beam Energy 1 d P(t) de E E db(e1) de e Et = P(t) dt de E db(e1) de e Et This derivative IS an Average Excitation Energy
32 BU transformation 10 0 Det. T1 E=24 MeV Reduced break-up probability Preliminary! Collision Time (1/MeV)
33 BU transformation 10 0 Det. T1 E=24 MeV Det. T2 E=24 MeV Reduced break-up probability Preliminary! Collision Time (1/MeV)
34 BU transformation Reduced break-up probability Preliminary! Det. T1 E=24 MeV Det. T2 E=24 MeV Det. T1 E=29.5 MeV Collision Time (1/MeV)
35 BU transformation Reduced break-up probability Preliminary! Det. T1 E=24 MeV Det. T2 E=24 MeV Det. T1 E=29.5 MeV Det. T2 E=29.5 MeV Collision Time (1/MeV)
36 BU transformation Reduced break-up probability Preliminary! Det. T1 E=24 MeV Det. T2 E=24 MeV Det. T1 E=29.5 MeV Det. T2 E=29.5 MeV L[EdB(E1)/dE]: RIKEN Collision Time (1/MeV)
37 BU transformation Reduced break-up probability Preliminary! Det. T1 E=24 MeV Det. T2 E=24 MeV Det. T1 E=29.5 MeV Det. T2 E=29.5 MeV L[EdB(E1)/dE]: RIKEN L[EdB(E1)/dE]: GSI Collision Time (1/MeV)
38 BU transformation Reduced break-up probability Preliminary! Det. T1 E=24 MeV Det. T2 E=24 MeV Det. T1 E=29.5 MeV Det. T2 E=29.5 MeV L[EdB(E1)/dE]: RIKEN L[EdB(E1)/dE]: GSI E=24 MeV; CDCC dineutron model Collision Time (1/MeV)
39 BU transformation Reduced break-up probability Preliminary! Det. T1 E=24 MeV Det. T2 E=24 MeV Det. T1 E=29.5 MeV Det. T2 E=29.5 MeV L[EdB(E1)/dE]: RIKEN L[EdB(E1)/dE]: GSI E=24 MeV; CDCC dineutron model E=29.5 MeV; CDCC dineutron model Collision Time (1/MeV)
40 Conclusions Collaborators Conclusions 208 Pb The elastic and breakup of 11 Li on 208 Pb has been measured for the first time at Coulomb barrier energies. The data show a large yield of outgoing 9 Li fragments. 9 Li fragments energies are close to the beam energy (Direct Break-up). Comparison with semiclassical and CDCC calculations, based on a simple dineutron model, explain the breakup data and support the dominance of the dipole Coulomb breakup.
41 Conclusions Collaborators Conclusions 11 Li structure A dineutron model is developed based on the 3b wavefunction. It gives a simple and clear image of the reaction process, accurate whenever r 2n 9 Li is the main degree of freedom. Using a simple transformation of the BU probability, structure information of the projectile can be obtained through B(E1). Ongoing Work An even more accurate 4b-CDCC calculation should be done including BU cross-section.
42 Conclusions Collaborators Collaborators Deparment of Physics and Astronomy, University of Århus D. V. Fedorov A. S. Jensen Instituto de Estructura de la Materia, CSIC, Madrid E. Garrido C. Romero-Redondo Departmento de F.A.M.N., Universidad de Sevilla: J. M. Arias A.M. Moro M. Rodríguez-Gallardo
43 Conclusions Collaborators Collaboration E1104 Universidad de Huelva I. Martel Instituto de Estructura de la Materia, CSIC, Madrid M. J. G. Borge M. Cubero O. Tengblad Departmento de F.A.M.N., Universidad de Sevilla: M. A. G. Alvarez J. P. Fernández-García J. Gómez-Camacho
44 Conclusions Collaborators Collaboration E1104 Other institutions involved: Univ. Lisboa Univ. Chalmers Univ. York Univ. Århus TRIUMF
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