Unbound exotic nuclei studied by projectile fragmentation
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1 . Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 1 / 20Se Unbound exotic nuclei studied by projectile fragmentation G. Blanchon (a), A. Bonaccorso (a), D.M. Brink (b) & N. Vinh-Mau (c) (a)istituto Nazionale di Fisica Nucleare, Sez. di Pisa, and Dipartimento di Fisica, Università di Pisa, Largo Pontecorvo 3, Pisa, Italy. (b) Department of Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, U. K. (c) Institut de Physique Nucléaire, F-91406, Orsay Cedex, France. Seattle 2005
2 Plan of the Presentation 1 Reactions to study halo nuclei Transfer to the continuum Fragmentation reaction 2 Simple time dependent model Inelastic excitation General wave functions (asymptotic form) Simple time dependent model Comparison to the transfer to the continuum Cross section. Determination of the S-matrix. Potential correction 3 Results Comparison between time dependent and sudden approximation Dependence on the binding energy of the initial state Strength of every transition Dependence on the scattering length of the final s-state Add of a complex part to the potential G. Blanchon 4 Conclusions (a), A. Bonaccorso and (a), D.M. outlooks Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 2 / 20Se
3 Reactions to study halo nuclei G. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 3 / 20Se Transfer to the continuum reaction
4 Reactions to study halo nuclei G. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 4 / 20Se Fragmentation reaction
5 Reactions to study halo nuclei Transfer to the continuum Transfer to the continuum Figure: 12 Be (d,p) RIKEN (Korsheninnikov) (1995). Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 5 / 20Se
6 Reactions to study halo nuclei Fragmentation reaction Fragmentation reaction. Figure: (a) LPC GANIL (Lecouey, Orr) (2002). Figure: (b) GSI (U Datta Pramanik) (Surrey conference Jan.2005).. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 6 / 20Se
7 Reactions to study halo nuclei Fragmentation reaction. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 7 / 20Se Figure: (a) GSI (Simon Nucl. Phys. A734 (2004) Figure: (b) RIKEN (Nakamura)(ECT* 2004)unpublished.
8 Simple time dependent model Inelastic excitation. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 8 / 20Se Inelastic excitation. Inelastic-like excitations can be described by the first order time dependent perturbation theory amplitude: A fi = 1 i dt ψ f (t) V 2 (r) ψ i (t) In order to obtain a simple analytical formula we consider the special case in which V 2 (r) = v 2 δ(x)δ(y)δ(z). A fi = v 2 i v dz ψ f (b c, 0, z)ψ i (b c, 0, z)e iqz
9 Simple time dependent model General wave functions (asymptotic form) G. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 9 / 20Se General wave functions (asymptotic form). For the initial state: For the final continuum state: ψ i (b c, 0, z) = C i i l γh (1) l i (iγr)p li (z/r). ψ f (b c, 0, z) = C f k i 2 (h(+) l f (kr) S lf h ( ) (kr))p lf (z/r). l f
10 Simple time dependent model Simple time dependent model. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 10 / 20Se Simple time dependent model. A fi = v 2 dz ψf i v (b c, 0, z)ψ i (b c, 0, z)e iqz I (k, q) = I R + ii I = I e iα S = Se 2iα = e 2i(δ+α) A fi 2 = C 2 I 2 1 S 2.
11 Simple time dependent model Comparison to the transfer to the continuum. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 11 / 20Se Comparison to the transfer to the continuum. Fragmentation: dp in dε f = 2 v2 2 π 2 v 2 C i 2 m 2 k Σ l f (2l f + 1) 1 S lf 2 I lf 2. Transfer: dp t (b c ) dε f 4π k 2 Σ l f (2l f + 1) 1 S lf 2 B lf,l i (G. Blanchon, A. Bonaccorso and N. Vinh Mau, Nucl. Phys. A739 (2004) 259.)
12 Simple time dependent model Cross section.. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 12 / 20Se Cross section. dσ = C 2 S dε f The core survival probability: 0 db c dp in (b c ) dε f P ct (b c ), P ct (b c ) = S ct 2
13 Simple time dependent model Determination of the S-matrix. Determination of the S-matrix. h = t + U. U(r) = V WS + δv. δv (r) = 16αe 2(r R)/a /(1 + e (r R)/a ) 4. V WS = Woods-Saxon potential plus spin-orbit. δv = correction which originates from particle-vibration couplings. (N. Vinh Mau and J. C. Pacheco, Nucl. Phys. A607 (1996) 163.). Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 13 / 20Se
14 Simple time dependent model Potential correction Potential correction.. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 14 / 20Se
15 Results Comparison between time dependent and sudden approximation Comparison between time dependent and sudden approximation.. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 15 / 20Se
16 Results Dependence on the binding energy of the initial state Dependence on the binding energy of the initial state.. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 16 / 20Se
17 Results Strength of every transition Strength of every transition.. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 17 / 20Se
18 Results Dependence on the scattering length of the final s-state. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 18 / 20Se Dependence on the scattering length of the final s-state.
19 Results Add of a complex part to the potential. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 19 / 20Se Introduction of an imaginary part to the potential.
20 Conclusions and outlooks Conclusions and outlooks 13 Be is a signature of the halo state of the neutron. Possibility to use s resonances. One or two step calculation.. Blanchon (a), A. Bonaccorso (a), D.M. Brink Unbound (b) & N. exotic Vinh-Mau nuclei (c) studied ((a)istituto by projectilenazionale fragmentation di Fisica Seattle 2005 Nucleare, 20 / 20Se
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