The many facets of breakup reactions with exotic beams
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1 Angela Bonaccorso The many facets of breakup reactions with exotic beams G Blanchon, DM Brink, F Carstoiu, A Garcia-Camacho, R Kumar, JMargueron, N Vinh Mau JAPAN-ITALY EFES Workshop on Correlations in Reactions and Continuum TORINO - Italy 6-8 September 2010 cf Y Suzuki &Co, H Sagawa &Co, T Nakamura &Co
2 Introduction Breakup reactions are a versatile mean of studying both projectile and target nuclear properties In exotic nuclei they are used to study projectile structure via inverse kinematics experiments Also transfer to the continuum from target sometime or projectile fragmentation to study resonance states in unbound nuclei High energy scattering and the eikonal approximation Optical potentials Elastic scattering of halo nuclei and the optical potential including breakup Transfer to the continuum, projectile fragmentation Coulomb breakup All orders vs first order approximation The proton vs neutron case Accuracy of reaction theory and experimental data analysis vs structure theory
3
4 V i (r) Transfer (to the continuum ) (inclusive breakup with final state interaction with the target) b c before x P k 1 v z z V f (r) T k k 2 k 2 -k 1 =k ε f -ε i =mv2 /2 ε opt f >0 for small ε i diffraction and stripping
5 V i (r) Transfer (to the continuum ) (inclusive breakup with final state interaction with the target) b c before x P k 1 v z z V f (r) T k k 2 -k 1 =k ε f -ε i =mv2 /2 ε opt f >0 for small ε i k 2 after diffraction and stripping
6 V i (r) Transfer (to the continuum ) (inclusive breakup with final state interaction with the target) b c before x P k 1 v z z V f (r) T k k 2 -k 1 =k ε f -ε i =mv2 /2 ε opt f >0 for small ε i k 2 after diffraction and stripping
7 V i (r) Transfer (to the continuum ) (inclusive breakup with final state interaction with the target) b c before x P k 1 v z z V f (r) k 2 -k 1 =k ε f -ε i =mv2 /2 ε opt f >0 for small ε i T k 2 after diffraction and stripping k
8 V i (r) Transfer (to the continuum ) (inclusive breakup with final state interaction with the target) b c before x P k 1 v z z V f (r) k 2 -k 1 =k ε f -ε i =mv2 /2 ε opt f >0 for small ε i T k 2 after diffraction and stripping k
9 V i (r) Transfer (to the continuum ) (inclusive breakup with final state interaction with the target) b c before x P k 1 v z z V f (r) k 2 -k 1 =k ε f -ε i =mv2 /2 ε opt f >0 for small ε i T k 2 T+1 after diffraction and stripping k
10 V i (r) Transfer (to the continuum ) (inclusive breakup with final state interaction with the target) b c before x P k 1 v z z V f (r) k 2 -k 1 =k ε f -ε i =mv2 /2 ε opt f >0 for small ε i T k 2 T+1 after diffraction and stripping k
11 V i (r) Transfer (to the continuum ) (inclusive breakup with final state interaction with the target) b c before x P k 1 v z z V f (r) T k k 2 -k 1 =k ε f -ε i =mv2 /2 ε opt f >0 for small ε i P-1 k 2 T+1 after diffraction and stripping
12 JEnders et al 5
13 6
14 V i (r) V f (r) b c Projectile fragmentation n-core final state interaction before x T 14 Be 14 B v z z
15 V i (r) V f (r) b c Projectile fragmentation n-core final state interaction before x T 14 Be 14 B v z z after
16 V i (r) V f (r) b c Projectile fragmentation n-core final state interaction before x T 14 Be 14 B v z z after
17 V i (r) V f (r) b c Projectile fragmentation n-core final state interaction before x T 14 Be 14 B v z z after T
18 V i (r) V f (r) b c Projectile fragmentation n-core final state interaction before x T 14 Be 14 B v z z after T
19 V i (r) V f (r) b c Projectile fragmentation n-core final state interaction before x T 14 Be 14 B v z z Core after T
20 V i (r) V f (r) b c Projectile fragmentation n-core final state interaction before x T 14 Be 14 B v z z Core after T
21 V i (r) V f (r) b c Projectile fragmentation n-core final state interaction before x T 14 Be 14 B v z z Core after T
22 Projectile fragmentation V i (r) n-core final state interaction before x 14 Be 14 B b c v z z V f (r) T 13 Be Core after T
23 Projectile fragmentation V i (r) n-core final state interaction before x 14 Be 14 B b c v z z V f (r) T 13 Be Core after T
24 Projectile fragmentation 11 Be: a simple test case from bound s-state to d-resonance: inelastic excitation to the continuum? 11 Be AMeV
25 Analytical methods for transfer and breakup S ct 2 σ = d 2 b c P el (b c )P tr (b c ); P tr = A 2 A = 1 ih dt ψ f (r,t) V 2 ψ i (r R(t),t) Seaking a clear physical interpretation of DWBA (Brink et al and Copenhagen school since 1978) similar to Alder& Winther for Coulomb excitations
26 Review of basic knowledge of core-target and nucleon-target interaction potentials and cross sections This is necessary to ensure accuracy of absolute cross sections in spectroscopic studies
27 Heavy-ion high energy scattering and the eikonal approximation 14 Be
28 takes into account difference between impact parameter and distance of closest approach validity of the strong absorption model for heavy-ion reactions gives a simple way to treat the core-target interaction in halo nuclei scattering
29
30 Nucleon-target potential AB & F Carstoiu
31 600MeV 303 b
32 Elastic scattering and the optical potential including breakup channel (cf talks on FUSION) Relevant papers in the past
33 PRL in press
34 or P transf
35
36 A Bonaccorso and F Carstoiu Optical potentials of halo and weakly bound nuclei Nucl Phys A706 (2002) 322 AA Ibraheem and A Bonaccorso, Recoil effects on the optical potentials of weakly bound nuclei Nucl Phys A748 (2005) 414
37
38
39
40 Nuclear and Coulomb breakup potentials can be compared by using the parameterization : α 2 1/2γ, γ= 2µε i /ћ β 3 (ε f -ε i )/ ћ v the most relevant parameter is the diffusness whose physical interpretation is decay length of initial state wave function adiabaticity parameter of Coulomb
41
42 Projectile fragmentation and resonances (near threshold) During scattering at low energy a quasi-stationary system is formed (compound nucleus) Link the properties of the unperturbed target nucleus (wave functions of stationary states, underlying potential) to the experimentally measured scattering quantity This is usually s-state (sometime p-state) scattering Higher angular momentum resonances need an energy dependent optical potential ( channel coupling) 24
43 Transfer to the continuum vs Projectile fragmentation: a model for diffractive breakup in which the observable studied is the n- core relative energy spectrum and its resonances diffraction + stripping inclusive breakup exclusive breakup diffraction Knockout S off-shell S on shell Fragmentation
44 TRANSFER Stripping & Diffraction Overlap of momentum distribution (Fourier transforms) Broglia and Winther book INELASTIC Diffraction Fourier transform of the overlap
45 Comparison to R-matrix theory AB, DM Brink, PRC38, 1776(1988)
46 14 B fragmentation on C JL Lecouey LPCC 02-03; Few-Body Systems 34 (2004) 21 GSI-U Datta Pramanik-2004) Unpublished HSimon et al, NPA791 (2007) Be fragmentation on C 14 B fragmentation on H, Kondo et al, proton target 28
47 14 Be T 1/2 =435ms±017 a s =-35fm s 80% a s =-08fm p d 5/2 Nucl Phys A791 (2007) 267
48
49 PRC, in press, v1-nucl-th
50 a s =-08fm
51 In projectile fragmentation reactions it is the lowest angular momentum initial state to dominate the transition process
52
53 Conclusions A time dependent theory for projectile fragmentation reaction has been established which contains the sudden approximation and R-matrix theories as limiting cases 2p correlations and particle-vibration couplings play a fundamental role Importance of coupling to core excited states For the first time the shell ordering of 13 Be has been established theoretically on a firm basis and parity inversion across threshold has been proved to persist for N=9 isotones Much care is needed in analyzing experimental results in order not to draw misleading or unphysical conclusions: sudden approximation vs time dependent, use of Breit-Wigner resonance form (vs exact S-matrix or R-matrix),importance of various initial state components
54 Coulomb breakup All orders vs first order approximation The proton vs neutron case
55 37
56 38
57 39
58 40
59 41
60 Δ ε i a proton halo feels an effective barrier b c 42 1
61 The proton vs neutron case 43 15
62 44 17
63 18 45
64 20 46
65 Accuracy of reaction theory and experimental data analysis vs structure theory
66 48
67 49
68 2nd Topical Meeting, Valencia, Spain Main organizer: Berta Rubio FUTURE: 50
69 Pacheco & N Vinh Mau, PRC 65 (2002) Labiche et al PRC (1999)
70
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