Extracting spectroscopic information from ( 18 O, 16 O) two-neutron transfer reactions. Manuela Cavallaro INFN -LNS (Italy)
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1 Extracting spectroscopic information from ( 18 O, 16 O) two-neutron transfer reactions Manuela Cavallaro INFN -LNS (Italy)
2 Direct transfer reactions Select specific degrees of freedom in the complex many-body nuclear system Exploration of the nuclear structure Relation between 1n transfer cross sections and s.p. configurations a-2 A A+2 α transfer and clustering Connection between 2n transfer probabilities and pairing correlations in nuclei a a + A a-2 + A+2
3 Inside nuclear structure by light probes p( 11 Li, 9 33 MeV DWBA Phonon mediated pairing I.Tanihata et al. PRL 100 (2008) G.Potel et al. PRL 105 (2010) nd order DWBA for A Sn(p,t) A-2 Sn P.Guazzoni et al. PRC 83 (2011) G. Potel et al. PRL 107 (2011)
4 Heavy ions The extraction of structure information from 2n transfer cross-sections is not straightforward Experimental difficulties The techniques to extract the optical potential from fits of elastic scattering data fail Coupling with inelastic excitations (CC corrections) Arbitrary scaling factors unhappiness (>>1) to reproduce the exp. angular distributions Sequential multistep transfer Recoil effects Finite range f.f. Only the product of projectile and target S.F. is accessible
5 Inside nuclear structure by heavy probes EFR-CCBA for 74 Ge( 18 O, 16 O) 76 Ge 76 Ge( 16 O, 18 O) 78 Ge (BCS wave-functions) Lemaire and Low PRC16 (1977) 183 Importance of inelastic channels 18 O* 2 + state at 1.98 MeV However still unhappiness factor = 2.3 Need to: go beyond DWBA go beyond BCS build microscopic nucleus-nucleus potentials 2n addition Destructive interference in the 2 + 2n removal Constructive interference in the 2 + 5
6 Our study
7 Why? 12 C( 18 O, 16 O) MeV The ( 18 O, 16 O) reactions are good candidates to show the role of pairing interaction thanks to The presence of a correlated pair of neutrons in the 18 O g.s. w.f. The very low polarizability of the 16 O core 14 C ideal benchmark for considerations on reaction mechanism 1n and 2n transfer yields on different targets ( 9 Be, 11 B, 12,13 C, 28 Si) to analyze the effects of the pair transfer 13 C( 18 O, 17 O) 14 C 1n transfer to ascertain the selectivity of the two processes Absolute cross-section angular distribution
8 The experiment INFN Laboratori Nazionali del Sud Catania 18 O 7+ beam from Tandem accelerator at 84 MeV 12 C and 13 C targets 50 μg/cm 2 Ejectiles detected by the MAGNEX spectrometer Angular setting opt 8, 12, 18 3 lab 24
9 F. Cappuzzello et al., MAGNEX: an innovative large acceptance spectrometer for nuclear reaction studies in: Magnets: Types, Uses and Safety, Nova Publisher Inc., New York, 2011, pp 1-63 MAGNEX: an innovative large acceptance spectrometer Large acceptance: Energy -28%, +20% Angle 50 msr Measured resolution: Energy E/E 1/1000 Angle θ 0.3 Mass m/m 1/160 Quadrupole Dipole Scattering Chamber Focal Plane Detector
10 MAGNEX Ray-Reconstruction ALGEBRIC RAY-RECONSTRUCTION (Differential Algebras) COSY-INFINITY F : P i P f Physical Parameters at the target F. Cappuzzello, et al., NIM A 638, (2011) 74 Geometrical Parameters measured at the FPD
11 MAGNEX Ray-Reconstruction 1. Detailed knowledge of the geometry and magnetic fields F 1 : P f P i 2. Algorithm to transport and invert 3. Measurements at the focal plane (highly performing FPD) Physical Parameters at the target F. Cappuzzello, et al., NIM A 638, (2011) 74 Geometrical Parameters measured at the FPD
12 Entrance window MAGNEX Focal Plane Detector Induction pads Frisch grid (0V) DC wires (750V) Silicon detectors 54 Silicon Detectors E res 5 Proportional Wires ΔE Ion identification φ foc - Ion trajectory + 4 Induction Strip X 1,X 2,X 3,X 4 X foc,θ foc 4 Drift Chamber (DC) Rayreconstruction Cathode (-950V) Y 1,Y 2,Y 3,Y 4 Y foc,φ foc Section view M.Cavallaro et al. EPJ A 48: 59 (2012) D.Carbone et al. EPJ A 48: 60 (2012)
13 Particle Identification Z identification A identification Bρ = p q 2 X foc m q 2 E resid F. Cappuzzello et al., NIMA 621 (2010) 419
14 Momentum and angle reconstruction 27Al(16O,16O)27Al at 100 MeV 13 < lab<20 F-1 Reconstructed physical parameters foc Parameters measured at the FPD M. Cavallaro et al., NIMA 648 (2011) 46-51
15 Results
16 σ (mb) counts 1. Transfer yields In the absense of any pairing correlation between the two transferred neutrons P 2n = (P n ) 2 18 O+ 13 C 7 < θ lab < 13 inelastic 18 O Enhancement of the two-neutron transfer channel The 2n transfer is not a 2 nd order process TRANSFER OF A CORRELATED PAIR stripping 16 O 17 O pick-up B target 12C target 13C target Si target O 19 O Ejectile Mass (a.m.u.) Ejectile Mass (a.m.u.)
17 6.73 (3 - ) 7.34 (2 - ) 2. Energy spectra: 3 < θ lab < 5 13 C( 18 O, 17 O) 14 C 13 1/ 2 1d C gs 5/ 2 5/ 2 2, (2 + ) 8.32 (2 + ) (4 + ) In the ( 18 O, 16 O), the suppression of s.p. states, which would require an uncorrelated transfer of 2n and the breaking of the initial pair in the 18 O g.s., reveals the minor role of the two-step dynamics 12 C( 18 O, 16 O) 14 C d,2s C gs 5/ 2 1/2 2,4 2,4
18 dσ/dω (mb/sr) 3. Angular distributions 18 O + 12 C g.s. (0 + ) 16 O + 14 C g.s. (0 + ) L = E E+00 θ opt = 6 θ opt = 12 θ opt = E E E E E θ cm (deg)
19 Exact Finite Range CRC Sao Paulo Potential (SPP) used in the optical model L.C. Chamon, et al., PRL 79 (1997) 5218 The w.f. used in the form factor calculations generated by a WS potential adjusted to fit the exp. separation energies Deformation parameters for collective excitations S. Raman, et al., At. Data Tables 78 (2000) 1 Calculations by J. Lubian Niteroi Spectroscopic Amplitudes by shell-model in the 1p 1/2, 1d 5/2, 2s 1/2 model space A.P. Zuker, et al., PRL 17 (1969) 983 Calculations by A.Gargano Napoli S.M.Lenzi - Padova
20 1n transfer 13 C( 18 O, 17 O) 14 C Angular distributions Reliability of our basic theoretical approach Coupling scheme
21 12 C( 18 O, 16 O) 14 C 84 MeV Extreme Cluster Model (CRC) Relative motion of the 2n system frozen and separated by the c.m. Only the term with the 2n coupled to S = 0 participates to the transfer No scaling M. Cavallaro, et al., PRC 88 (2013) A 0.89 amplitude is obtained by scaling to the experimental data (0.91 S.A. predicted by shell model for the (p 1/2 ) 2 configuration). Sequential transfer (DWBA) Introducing the 17 O + 13 C intermediate partition Coherent sum Role of interference Not full 2 nd order calculations a posteriori justification
22 12 C( 18 O, 16 O) MeV Cluster model Sequential transfer Independent coordinates Cluster model overestimates the data. (S.A. = 0.30 is extracted by scaling to the data). Need of a larger model space for the cluster wave function. Independent coordinates well reproduce the data Weak nature of the coupling of the two neutrons in the s 1/2 d 5/2 model space for this state Independent coordinates scheme The transfer is described taking into account s.p. information obtained by shell model calculations (p 1/2 s 1/2 d 5/2 )
23 12 C( 18 O, 16 O) MeV Cluster model Sequential transfer Independent coordinates S.A. = 0.55 from cluster configuration Independent coordinates underestimate the cross-section. A larger space is required in the shellmodel calculations (not surprising since one expects to find relevant (d 5/2 d 3/2 ) contributions in the 4 + wave function, excluded in our model space) Independent coordinates scheme The transfer is described taking into account s.p. information obtained by shell model calculations (p 1/2 s 1/2 d 5/2 )
24 Conclusions and Outlooks
25 Conclusions Possibility to measure energy spectra and angular distribution for HI reactions Enhancement of the 2n stripping in the Strong in the energy spectra For the first time, description of the a HI 2n transfer reaction without any unhappiness factor for
26 Outlooks We are close to an operative definition of the for 2n pair states The ( 18 O, 16 O) reaction at 84 MeV is a very powerful tool to give a quantitative indication of the effects of the in the structure of light nuclei A of the response of other nuclei to this probe will provide a major source of information on the nature of such a force Use of heavy-ion induced transfer reactions (e.g. ( 18 F, 16 O) or ( 16 O, 18 F) ) for?
27 C. Agodi, F. Cappuzzello, D. Carbone, M. Cavallaro, A. Cunsolo, A. Foti Dipartimento di Fisica e Astronomia, Università degli Studi di Catania, Italy Istituto Nazionale di Fisica Nucleare Laboratori Nazionali del Sud, Italy Istituto Nazionale di Fisica Nucleare Sezione Catania, Italy R. Linares, J. Lubian, V.N. Garcia IFUFF, Niteroi, Brasil IFUSP, San Paulo, Brasil A. Gargano Istituto Nazionale di Fisica Nucleare Sezione di Napoli S.M. Lenzi Istituto Nazionale di Fisica Nucleare Sezione di Padova F. Azaiez, S. Franchoo, M. Niikura, J.A. Scarpaci IN2P3 Institut de Physique Nucléaire d Orsay, France
28
29 CRC calculations Sao-Paulo optical potential Real part V LE R, E = V F (R)e 4v2 R c 2 L.C.Chamon et. al. PRC 66 (2002) D. Pereira et al. PLB 670 (2009) 330 Double-folding potential V F R = ρ 1 r 1 ρ 2 r 2 v NN (R r 1 + r 2 )dr 1 dr 2 v NN ρ(r) nucleon-nucleon interaction: M3Y wide and systematic dataset Pauli non-locality e 4v2 R c 2 Imaginary part W R = 0.6 V LE (R)
30 Extreme Cluster Model The relative motion of the 2n system is frozen and separated by the c.m. Only the term with the 2n coupled to S = 0 participates to the transfer For the projectile 18 O: The N = 3, L = 0 configuration is used in the 18 O g.s. since the shell model S.A. is The N = 2, L = 0 configuration (S.A.=0.241) is neglected. For the 14 Cg.s.: N=2, L=0 -> S.A.(data)=0.89, S.A.(shell model)=0.91 N=3, L=0 -> S.A.(data)=0.45, S.A.(shell model)=0.41
31 Independent coordinates scheme The 2 nucleons are not restricted to be in the 1s internal motion The transition potential acts separately on each of the transfer nucleons
32 DWBA Sequential transfer Introducing the 17 O + 13 C intermediate partition
33 Transfer yields spectra Ratio between one- and two-neutron transfer cross-sections Be Odd neutron target Even neutron target TRANSFER OF A CORRELATED PAIR σ 1n /σ 2n B 12 C 13 C 28 Si The 2n transfer is not a 2 nd order process Target mass (a.m.u.)
34 F. Cappuzzello et al., MAGNEX: an innovative large acceptance spectrometer for nuclear reaction studies in: Magnets: Types, Uses and Safety, Nova Publisher Inc., New York, 2011, pp 1-63 Large acceptance: Energy -28%, +20% Angle 50 msr MAGNEX Measured resolution: Energy E/E 1/1000 Angle θ 0.3 Mass m/m 1/160
35
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