Cravo, E.

Crespo, R.

Deltuva, A.

GSI Repository

Fewbody theoretical studies of Quasi Free Scattering reactionsR. Crespo1,2, A. Deltuva3, E. Cravo3,4, the R3B collaboration1, and the FAIR@GSI division11Departamento de Fı´sica, Instituto Superior Te´cnico, Univ. de Lisboa, Portugal; 2Centro de Cieˆncias e TecnologiasNucleares, Univ. de Lisboa, Portugal; 3 Centro de Fı´sica Nuclear da Univ. de Lisboa, Portugal; 4Departamento deFı´sica, Faculdade de Cieˆncias da Univ. de Lisboa, PortugalIntroductionProton-induced quasifree scattering nucleon knockoutreactions have been recently measured and are planed infuture experiments of the R3B collaboration aiming ex-tracting spectroscopy of valence and deeply bound nuclei,and pinning down structure correlation effects. To modeland analyze these experiments it is of utmost importanceto have a reliable reaction framework in order to extractmeaning structure information. Few-body reaction frame-works recently developed are a useful tool to interpret thisexperiments.Electron scattering reactions (e,e’p) have been a long-standing tool to obtain information from single-nucleonstructure information of nuclei. Systematic studies haveshown that for a wide range of magic and near magicnuclei, the single particle occupancies are significantlybellow the values expected from the values predicted byindependent-particle shell model calculations (IPSM).Occupancies have also been extracted using nuclearprobes. In particular, single-nucleon (p,2p) and (p,pn)knockout reactions from light target at intermediate havealso been used in the past to obtain information on single-particle occupancies.Proton-induced quasifree scattering nucleon knockoutreactions have been performed recently at GSI in inversekinematics within the R3B program, at around 400 MeVper nucleon. At high incident projectile energies, it is ex-pected the reaction mechanism to be simpler and that onebe able to obtain structure information about inner andouter shells. In particular, one aims to obtain informationabout deviations from single particle occupancies, and cor-relation effects.There are several timely issues associated with singlenucleon (p,2p) and (p,pn) QFS knockout reactions: (i) Akey issue is to disentangle structure correlations from ef-fective dynamical effects. In particular, one needs to getinsight to what extent the reduced factors found by compar-ing the theoretical cross sections with the results extractedfrom the experimental data can, be traced exclusively tostructure correlations or to effective dynamical effects as-sociated with the reaction framework used to interpretedthe data. Thus a tight control on the reaction formalism isneeded; (ii) Another important aspect is to identify clearlythe role of distortion effects to the nucleon-nucleon freescattering; (iii) The recent experiments performed at GSI,have allowed a unique opportunity to perform systematicstudies of knockout reactions along the isotope chain atnearly the same incident energy. The study of the behaviourof calculated observables using a well constrained reactionframework, with respect to angular momentum, mass andbinding will allow to identify and analyse common fea-tures, and identify new physics as experimental deviationsto this systematic. (iv)A reliable assessment of possible dy-namical core excitation effects and nucleon knockout con-tributions from inner shells is also mandatory for the inter-pretation of recent and future experiments at GSI.Reaction studiesThe study of proton-induced quasifree scattering nu-cleon knockout reactions can be addressed by the three-body Faddeev/AGS [1, 2] reaction formalism, which treatsall relevant three-body observables in equal footing [3].According to this reaction framework, one needs to evalu-ate the operators U βα, whose on-shell matrix elements arethe transition amplitudes. These operators are obtained bysolving the three-body Faddeev/AGS integral equationsUβα = δ¯βαG−10 +∑γδ¯βγtγG0Uγα , (1)with α, β, γ = (1, 2, 3), (β = 0 in the final breakup state).In here, δ¯βα = 1− δβα and the pair transition operator istγ = vγ + vγG0tγ , (2)where G0 is the free resolvent G0 = (E + i0 − H0)−1,and E is the total energy of the three-particle system in thecenter of mass (c.m.) frame. For breakup, the solution ofthe Faddeev/AGS equations can be found by iterationUβα =∑γδ¯βγtγ δ¯γα +∑γδ¯βγtγ∑ξG0δ¯γξtξ δ¯ξα + · · · .The successive terms of this series can be considered asterms of first order or single scattering, represented dia-grammatically in Fig. 1, second order or double scatter-ing, represented diagrammatically in Fig. 2 and so on inthe transition operators tγ .In order to model and interpret recent proton-inducedquasifree scattering nucleon knockout reactions by the R3Bcollaboration we have evaluated total cross sections andcore momentum distributions for several isotopes in in-verse kinematics at around 400 MeV making use of theAGS/Faddeev reaction framework:We have analyzed QFS (p,2p), for the case of valenceproton knockout from 12C. In particular, we have studiedthe role of higher order distortions, valence-nucleon rescat-tering contributions and the effect of some approximationsNUSTAR-KR-06 GSI SCIENTIFIC REPORT 2013140 doi:10.15120/GR-2014-1-NUSTAR-KR-06performed by the standard Distorted Wave Impulse Ap-proximation reaction framework. We found that the mul-tiple scattering expansion of the DWIA might differ fromthe corresponding Faddeev/AGS result.We have analyzed the Faddeev/AGS equations in termsof its multiple scattering expansion, and found that at highincident energies that the terms up to second order providethe dominant contribution of the series.We have analyzed QFS (p,pn), for the case of valenceneutron knockout from the halo nuclei 11Be, 15C and alongthe Oxygen isotope chain 17,22,23O. A detailed analyse ofthe role of higer terms distortion and its dependence of thebinding energy and angular dependence of the valence par-ticle was made.Most few-body theoretical reaction studies rely on the amodel of an inert core and a valence nucleon. However, theinternal degrees of freedom might pay an important role asshown in [4], [5]. In order to predict the total cross sec-tions obtained at recent experiments performed at GSI, theeffects of dynamical core excitation were estimated. Alsothe contribution from the knockout of nucleons from thecore were evaluated and found to be important.+Figure 1: Single scattering diagrams for breakup in theFaddeev scattering framework.+ +a)b)c)d)Figure 2: Double scattering diagrams for breakup in theFaddeev scattering framework.References[1] L. D. Faddeev, Zh. Eksp. Theor. Fiz. 39, 1459 (1960) [Sov.Phys. JETP 12, 1014 (1961)].[2] E. O. Alt, P. Grassberger, and W. Sandhas, Nucl. Phys. B 2,167 (1967).[3] R. Crespo, A. Deltuva, M. Rodrı´guez-Gallardo, E. Cravo, andA. C. Fonseca, Phys. Rev. C 79, 014609 (2009).[4] A.M. Moro and R. Crespo, Phys. Rev. C 85, 054613 (2012);R. Crespo, A. Deltuva, A.M. Moro, Phys. Rev. C 83, 044622(2011).[5] A. Deltuva, Phys. Rev. C 88, 011601 (R) (2013).GSI SCIENTIFIC REPORT 2013 NUSTAR-KR-06doi:10.15120/GR-2014-1-NUSTAR-KR-06 FAIR@GSI 141

Fewbody theoretical studies of Quasi Free Scattering reactions

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Fewbody theoretical studies of Quasi Free Scattering reactions

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