structure obtained from quasifree scattering从准自由散射得到的晕核结构课件

. Quasi-free scattering with exotic nuclei collaboration meeting R3B/EXL L.V. Chulkov October 16 2007 Quasi-free scattering. Owen Chamberlain, Emilio Segre, Berkeley, Li(p,2p), 350 MeV, 1952 M. Yosoi et al., Phys. Let. B 551, 255 (2003). M. Yosoi, PhD Thesis, 2003, Kyoto University Study of deep-hole states (s1/2) Cross section DWIA: spectroscopic factor free n-n cross-section distorted proton momentum distribution spectroscopic factor free NN cross section kinematical factor distorted momentum distribution Three particles in the final state: + 9 kinematical variables. Momentum and energy conservation: - 4 kinematical variables. Cross section generally depends on 9-4=5 variables. Feynman diagram for quasi-free scattering in the impulse approximation. Vertex 1 corresponds to the reaction P Q + pe with particle P and Q on their respective mass shells, and the vertex 2 describes the reaction p0 + p1 q0 + q1 in which p0, q0, and q1 have their physical masses. Impulse approximation. How good it is? Problems: Results are model dependent. In particular, sensitivity to the wave function. Final state interactions Passage of the probe and knocked out particle through nuclear matter. . Recipe: Choose proper energy - 200- 500 MeV. Decrease amount of nuclear matter- light nuclei. Use only in-plane evens (p,2p). Separation energies, widths and angular momentum assignment. G. Jacobs and Th. Maris, RMP 45 (1973) 6. Core + valence nucleons model ? 1s 1p 1d 2s Distorted momentum distributions of the knocked out particle. G. Jacobs and Th. Maris, RMP 45 (1973) 6. 1p1s Spectroscopic factors. Experiment in comparison with the Independent-Particle Model and Large-Basis Shell Model. M.B. Tsang et al., PRL 95(2005)222501 Comparison of experimental spectroscopic factors to predictions from IPM (left) and LB-SM (right). Open and closed symbols denote elements with odd and even Z, respec- tively. The solid line indicate perfect agreement. The two dashed lines indicate 20% deviation from the solid line. Conventional and inverse kinematics. Momentum transfer. Comparison of conventional and inverse kinematics for 12C+1H p+p+11B at 400 MeV/nucleon. Proton detectors are at 430 at both sides if the beam. Proton elastic scattering on hydrogen and helium. The task is the investigation of 8He structure by quasi-free scattering on protons. M.V.Zhukov et al., PRC 50 (1994) R1 Sounds simple. But how to see structures inside the nucleus? 8He (0+) Experiment with 4He, 6He and 8He beams. Experimental I.Tanihata +, Phys.Rev.Let. 55(1985) 2676 A.A.Korsheninnikov+,Phys.Rev.Let. 90(2003) 082501 F.Skaza+,Phys.Rev. C73(2006)044301 Theoretical: Y.Suzuki +, Phys.Rev. C41(1990) 736 M.V.Zhukov+, Phys.Rev.C50(1994)R1 not in agreement with K.Markenroth+, Nucl.Phys. A679 (2001) 462 experiment Confirmations of the jj based structure: Liquid hydrogen target and 4He, 6He, 8He beams. 18O 820 MeV/A +9Be target 6,8He (700 MeV/A) GSI, Darmstadt SIS, FRS. ALADIN Neutron and cluster knockout channels can be disentangled . Cross section. Impulse approximation. A.W.Stetz, Phys.Rev. C21 (1980) 1979. 1. - dependence is trivial. 2. Treiman-Yang criteria dependence is vanished 3. s appears only in kinematical factor. 4. Why not integrate on Q? Relativistic invariant expressions:Conventional formalism Not suitable for large-acceptance measurements! We can not reduce the usual fivefold differential cross section even to a threefold differential. CM system of participants Convenient to use when solid angles of the detectors are small. Can not be used when solid angles are big. Internal momentum distribution of clusters. in 6He in 8He 6He in 8He Laboratory system Tetra-neutron in 8He? Curves are obtained from calculated two-body WF: + 2n, + 4n and 6He + 2n with corresponding quantum numbers. 6He +2n h(1)l Jl Test case: 6He beam neutron and 4He knock out. Solid lines and open points are the relativistic-invariant cross sections for the proton scattering on free neutron (left panel) and 4He (right panel), normalized to the experimental data. QFS mechanism is confirmed. Sn = 1.70.2 S = 0.80.1 6He(p,p n)6He(p,p 4He) 8He. Neutron knockout, 4He knockout, and ? knockout ? 8He(p,pn)6He 8He(p,pn)4He 8He(p,p4He)8He(p,p6He) Sn=3.30.3 Sn=0.80.1 S=0.90.1 ? Solid black lines are the cross sections for the proton scattering on a free neutron (top panels) and 4He (bottom panel), normalized to the experimental data. QFS mechanism is confirmed. Red line is the elastic cross section for 6He(p,p) with its r.m.s radius 2.4 fm. Line goes far from the data. 6He knocked out from 8He. 8He(p,p 6He)8He(p,p 6He) S6He=1.30.1 1/2 = 2.4 fm for a free 6He nucleus. 1/2 = 1.8 fm for a 6He cluster. Elastic scattering was calculated in an eikonal approximation: C.Bertulani +,Nucl.Phys. A588 (1995) 667. Effective size of a cluster can be determined. 8He. Summary Knocked out particle Configuration Spectroscopic factor from quasi- free (p,pX) 1. Spectroscopic factors from di-neutron transfer 8He(p,t) 2 n4n+4HeSn = 0.8 0.10.014 (for 6He(2+)+2n) n2n+6HeSn = 3.3 0.32.9 4He 4n+4HeS4He= 0.9 0.1 6He 2n+6HeS6He= 1.3 0.11.0 1 L.V.Chulkov et al., NuclPhys. A759 (2005) 43, 2 N.Keeley et al., Phys.Let. B646 (2007) 232. Theoretical: Y.Kanada-Enyo, preprint nucl-th:0707.2120v1, 2007. The inclusive n and -knockout reveals mainly the 4He + 4n structure, while coincidences the knocked out neutron and fragment point out the importance of the 0p1/2 orbit. The knockout of 6He directly demonstrates the dominance of the 6He+2n structure. As a perspective, the studies of the nucleon knockout from the s-shell allow to go beyond the 4He +4n structure and to investigate, for example, how the separation energy of the s-shell nucleon changes with the increasing number of neutrons. Prototype Experiment in Inverse Kinematics with LAND/ALADIN: 12C(p,2p)11B Sep/Oct 2007 ToF, E tracking Br Charged fragments Photons & Protons ToF, x, y, z projectile tracking Beam cocktail Reaction products after target (40Ar primary beam) 20 m 20O beam Si recoil detector Single layer cube of prototype Si micro-strip detectors installed inside NaI Crystal Ball Target recoil protons from quasi-free scattering reaction 12C(p,2p)11B tracked by Si energy measured in Crystal Ball Proposal- S296. Present Cave C Setup Conventional and inverse kinematics Comparison of conventional and inverse kinematics for 12C+1H p+p+11B at 400 MeV/nucleon. Proton detectors are at 430 at both sides if the beam. E1 (MeV) Monte-Carlo simulation for for 12C+1H p+p+11B assuming = 3 mrad. E2 (MeV) 12C(p,2p). Some simulations. p - shell s - shell Angle versus angle Energy versus angle knocked out scattered Q=-t versus angle 500 MeV/A knocked out scattered Summary Experiments with radioactive beams Radioactive beams and inverse kinematics Low beam intensities Extremely large angular acceptance Experiments with stable beams Proton beams Extremely high beam intensities Very small angular acceptance Perfect angular and energy resolution Experiments with radioactive beams can not compete in the achievable resolution wi