Knockout beyond the drip line

Transcription

1 Knockout beyond the drip line Angela Bonaccorso 2 INFN Sezione di Pisa Angela Bonaccorso 3 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31 2 In collaboration with R. J. Charity, G. Salvioni, Ravinder Kumar

2 Ouverture Entering the world of exotic nuclei: probing the unbound by walking at the drip line. Experiments with drip line nuclei Extend our understanding of the residual nuclear force. Check the limits of validity of structure models such as the SHELL MODEL or ab initio models. Challenges in breakup reaction theory. Angela Bonaccorso4 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

3 Dynamics of light exotic nuclei Various breakup mechanisms Angela Bonaccorso 5 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

4 Beyond the drip line What if the core breaks up? Proton unbound nuclei via invariant mass method Interest: Two-proton radioactivity vs. 2n-halo by isospin symmetry 5 He, 6 He, 8 He, 12 Be and IMME 6 Li. α. P T v z before Proton unbound nuclei T+1 5 Li α. CM after: α+p 6 Li, 7 Be, 9 C, 13 O studied by knockout of a deeply bound neutron: R. J. Charity & HiRA collabora5on. Angela Bonaccorso 6 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

5 Beyond the drip line What if the core breaks up? Data: R. J. Charity and the HiRA collabora7on, preliminary. Calcula7ons: G. Salvioni & AB Counts (a) Be( Li, Li)X E/A = 36.6 MeV 5 Li g.s. p (b) Be( Be, Be)X Counts 5000 E/A = 65.2 MeV 6 Be g.s. 2p+ Counts (c) Be( C, C)X E/A = 63.8 MeV C g.s. 4p Counts (d) Be( 12 O, O)X E/A = 28.5 MeV O g.s. 2p+ C E* [MeV] Angela Bonaccorso 7 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

6 Beyond the drip line What if the core breaks up? Counts Counts (a) Be( Li, Li)X E/A = 36.6 MeV 5 Li g.s. p+α (b) Be( Be, Be)X E/A = 65.2 MeV 6 Be g.s. 2p+α - 1/2 Counts Counts (c) Be( C, C)X E/A = 63.8 MeV 8 C g.s. 4p+α (d) Be( O, O)X E/A = 28.5 MeV O g.s. 2p+ C P [MeV/c] Angela Bonaccorso 8 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

7 Formalism Here we go... A consistent formalism for all breakup reaction mechanisms The core-target movement is treated in a semiclassical way, but neutron-target and/or neutron-core with a full QM method. AB and DM Brink, PRC38, 1776 (1988), PRC43, 299 (1991), PRC44, 1559 (1991). Early eikonal model: I. Tanihata, Prog. Part. Nucl. Phys. 35, 505 (1995), halo-core decoupling. dσ dξ = C 2 S 0 dp n (b c ) db c P ct (b c ), dξ ξ ε f, k z, P // also ANC = Core parallel momentum P // = Er 2 Mr 2 = = breakup threshold at ε f = 0 C 2 SC 2 i (T r + M r ) 2 M 2 r (T p + ε i ε f ) 2 + 2M r (T p + ε i ε f ), (1) Angela Bonaccorso 9 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

8 Formalism TC Transfer to the continuum: from resonances to knockout reactions First order time dependent perturbation theory amplitude: A fi = 1 i dt < φ f (r) V (r) φ i (r R(t)) > e i(ωt mvz/ ) (2) ω = ε i ε f mv 2 R(t) = b c + vt φ f see ( ) dp n (b c ) = 1 m 1 dε f 8π 3 2 k f 2l i + 1 Σ m i A fi 2 4π Σ jf (2j f + 1)( 1 S jf S jf 2 )F, 2k 2 f F = (1 + F lf,l i,j f,j i )B lf,l i B lf,l i = 1 [ ] kf 4π mv 2 C i 2 e 2ηbc M lf l 2ηb i c ngela Bonaccorso 10 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

9 Formalism TC Exact final continuum wave functions ( ) Final continuum state: φ jf (r) = C f k i 2 (h(+) l f (kr) S jf h ( ) l f (kr))y lf,m f (Ω f )χ s,ms, S jf (ε f ) is an optical model (n-core in fragmentation reactions, n-target in knockout reactions) S-matrix. Angela Bonaccorso 11 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

10 Formalism TC (Improved) ingredients for the method S nt from a perfect optical potential. S ct from folding the above with a realistic core density. Use directly ANC from ab-initio calculations (Nollett-Wiringa) when possible. ngela Bonaccorso 12 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

11 Examples n-target optical potential: AB, F. Carstoiu, PRC61, (2000) n- 9 Be optical potential: A.B & R.J. Charity, PRC89, (2014), data from DOM 96 AB D&G d /d [mb/sr] ( ) c.m. [deg] Angela Bonaccorso 13 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

12 Examples S nt realistic vs eikonal Eikonal S-matrices do not reproduce the n-t free particle cross sections with a realistic potential 3 2 Resonances, trojan horse knockout data p reaction data n reaction data total data elastic react eik elastic eik tot eik σ(barn) E_lab(MeV) ngela Bonaccorso 14 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

13 Examples resonances Transfer to 10 Be resonances: missing mass experiment. Paper in preparation Diana Carbone, AB, Mariangela Bondì, F. Cappuzzello, M Cavallaro et al. MAGNEX Collabora>on: 1n and 2n transfer experimental campaign d /de x (mb/mev) g.s. (0 + ) g.s.* 3.37 (2 + ) 3.37* 5.96 (2 + ) (2 - ) 7.37 (3 - ) (2 + ) 7.37* * 9 Be( 18 O, 17 O) MeV 3 < lab < (4 - ) (2 + ) 9.27* + 9.4* 9 Be(n,nn) 8 Be 9 Be(n, ) 6 He 1n break-up calculation 16 O has a degenerate gs (1d5/2,2s1/2) 17 O has 5/2+ gs and 1/2+ first excited state at E*=0.87MeV Posi>on and widths of p1/2 and d5/2 resonances in 10 Be perfectly reproduced Paper in prepara>on S n S S 2n E x (MeV) Angela Bonaccorso 15 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

14 Examples realistic S ct Use of the simple parametrization P ct (b c ) = S ct 2 = e ( ln 2exp[(Rs bc)/a]), R s r s (A 1/3 p + A 1/3 t ) r s 1.4fm χ I (b c ) = 1 v strong absorption radius Improved S ct 2 = e 2χ I (b c) d 2 b 1 dz 1 dz 2 W I (b 1 b c, z 2 )ρ(b 1, z 1 ) Angela Bonaccorso 16 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

15 Examples realistic S ct Angela Bonaccorso 17 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

16 Examples realistic S ct Angela Bonaccorso 18 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

17 Examples S = S n S p 10 20MeV reaction Sn Sp E (m) inc σ exp [MeV] [MeV] [A.MeV] [mb] 9 C 8 C Ca 35 Ca O 12 O Cl 32 Cl Ar 31 Ar S 27 S Si 23 Si C 9 C Li 5 Li O 13 O Ar 33 Ar Be 6 Be Ni 56 Ni S 31 S Ar 45 Ar Si 33 Si Be 9 Be C 14 C 16 C 15 C A simple coupling scheme σ = C 2 S 0 db cp n(b c)(1 P p(b c))p ct(b c) e P p 1 P p(b c) DPP from phase shift, AB, F. Carstoiu, NPA706, (2002) -typically 10% reduction in the cross sections. Angela Bonaccorso 19 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

18 Examples S = S n S p 10 20MeV Absolute cross sections Ratios σ = dξ dσ dξ σ exp /σ Theo have been used to validate spectroscopic factors C 2 S (=2j+1, in the IPM ) for single particle orbitals from shell model or ab initio calculations, when available. This is similar to what has traditionally been done for transfer. However in transfer the core-target interaction is treated almost exactly thanks to optical potentials fitted to the elastic scattering. C. Barbieri PRL103, (2009) Angela Bonaccorso 20 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

19 Examples S = S n S p 10 20MeV Structure inputs: Shell model and ab initio Variational MonteCarlo SF SM by Mihai Horoi, private communication. SF VMC from R. Wiringa website ANC VMC from Kenneth M. Nollett and R. B. Wiringa, PRC83, (R) (2011). Angela Bonaccorso 21 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

20 Examples S = S n S p 10 20MeV E inc σ exp σ n σ p σ nnop r s A.MeV mb mb mb mb fm 6 Li 5 Li Be 6 Be C 8 C (-1p CB ) (22.3) C 8 B IAS Li 8 Li IAS O 12 O (-1p CB ) (-1p CB ) direct proton Coulomb breakup Angela Bonaccorso 22 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

21 Examples S = S n S p 10 20MeV Parameters for 9 C 8 B, 1+ and 3+ states, treated according to Wiringa as 9 Li 8 Li. r s =1.37 fm. S n ANC WS (* SF ) ANC VMC SF VMC σ th σ exp MeV fm 1/2 fm 1/2 mb mb p 1/ (0.13) p 3/2 1.8 (1.22) (15.6) p 3/ Angela Bonaccorso 23 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

22 Examples The unusual life of 9 C The unusual life of 9 C S n =14.3MeV, S p =1.3MeV; S 2p =1.4MeV B. Blank et al., NPA624 (1997) A.MeV σ(-1p)=48±8mb; σ(-2p)=127±12mb D. Bazin, R.J. Charity et al., PRL 102, (2009) 98 A.MeV σ(-1p)=56±8mb; J. Enders et al., Phys. Rev. C 67, (2003). 78 A.MeV σ(-1p)=54±4mb; σ(-2p)=98±7mb; R.J. Charity et al., private communication A.MeV σ(-1p)=54mb; σ(-2p)=41mb Angela Bonaccorso 24 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

23 Examples Kinematics Kinematics From Eq.2 by the change of variables dtdxdydz dxdydzdz e i(ωt mvz/ ) e ik 1z e ik 2z neutron energies to neutron parallel momenta with respect to core to target k 1 = ε f ε i 1 2 mv 2 ; v k 2 = ε f ε i mv 2 ; v to core parallel momentum P // = Er 2 Mr 2 = = breakup threshold at ε f = 0 ++ (T r + M r ) 2 M 2 r (T p + ε i ε f ) 2 + 2M r (T p + ε i ε f ), (3) Angela Bonaccorso 25 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

24 Kinematical effects Asymmetric spectra Example deformation effects due to n-target interaction and kinematical cut-off. F. Flavigny, A. Obertelli, AB et al., PRL 108, (2012). F. Flavigny, A. Obertelli, AB et al. PRL 108, (2012). (+) Angela Bonaccorso 26 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

25 Kinematical effects Asymmetric spectra Asymmetries at high incident energy Data courtesy of A. Gade Calcula3ons G. Salvioni MSc Thesis in prepara3on. 28S (- 1n) 80.7 d5/2+d3/2 28S (- 1p) s1/2+d3/2 A.MeV 24Si(- 1p) d5/ A.MeV 34Ar (- 1n) s1/2 gs 70 A.MeV 34Ar (- 1n) d3/2+d5/2 Angela Bonaccorso 27 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

26 Kinematical effects Phase space effect Origin of kinematical cut-off (phase space) and deformation effects PRC60(1999) ,PRC44(1991) 1559,AB and GF Bertsch, PRC63(2001) , F. Flavigny, A. Obertelli, AB et al., PRL 108, (2012). (+) Angela Bonaccorso 28 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

27 Connecting reaction with structure. Ex: reduction of spectr. fact. Removal of a deeply bound n/p while the weakly bound p/n is un-touched b c Knock out from a deeply bound state x.. 14 O Core. T before T. 13 O. v z. z a0er Angela Bonaccorso 29 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

28 Connecting reaction with structure. Ex: reduction of spectr. fact. neutron & proton transfer vs breakup F. Flavigny et al., PRL110, (2013) Angela Bonaccorso 30 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

29 Conclusions Conclusions From the point of view of the knockout reaction model: Advances in n-target ( 9 Be) optical potential and S-matrix ( AB RJ Charity). Advances in core-target ( 9 Be) optical potential and S-matrix: single folding ( A.B, RJ Charity, R. Kumar, G. Salvioni). Inclusion of an elementary coupling neutron breakup-no-proton breakup. From the point of view of the structure model: Ab-initio overlaps and ANC. Application to beyond-the-dripline cores. S ct 2 is not interpreted as the probability that the core stays intact but as the function indicating the localization of the reaction for the no-absorption of the residues. Angela Bonaccorso 31 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

30 Conclusions Use of breakup at different incident energies Inclusive breakup reactions are dominated by final state interaction with the target at small incident energy: use as surrogate reaction At intermediate incident energy: strong interplay between projectile and target characteristics: deformed momentum distributions and cutoff effects.... by the valence particle projectile momentum distribution at high incident energy: information on angular momentum of the initial state and possible dynamical core-target excitations Coincidence experiments of breakup particle experiments (using invariant mass method ) are more INdependent on incident energy but possible dependence on the initial state: necessity to link with methods discussed above and angular correlation of the decaying particles... : one the most interesting experiment to make...and interpret? Can enlighten different channels and reaction mechanisms. ngela Bonaccorso 32 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31

31 Conclusions Angela Bonaccorso 33 (INFN Sezione di Pisa) Knockout beyond the drip line Sinaia / 31