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Roy Lemmon Daresbury Laboratory United Kingdom

Quasi-Free Scattering at ELISe (and R3B) Correlations in Asymmetric Nuclei, Nuclear Matter and Neutron Stars. Roy Lemmon Daresbury Laboratory United Kingdom. Joint R3B/ELISe/EXL Collaboration Meeting, GSI, 12 – 16 April 2010. p. p. p. n. Probing Correlations in Nuclei Experimentally.

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Roy Lemmon Daresbury Laboratory United Kingdom

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  1. Quasi-Free Scattering at ELISe (and R3B) Correlations in Asymmetric Nuclei, Nuclear Matter and Neutron Stars Roy Lemmon Daresbury Laboratory United Kingdom Joint R3B/ELISe/EXL Collaboration Meeting, GSI, 12 – 16 April 2010

  2. p p p n Probing Correlations in Nuclei Experimentally (p,2p) Spectral functions (spectroscopic factors) (e,e’p) • QFS most direct probe of the properties of a nucleon inside the nuclear medium: • validity of mean field/single particle concepts • role of correlations, e.g. LRC, SRC, Tensor • in-medium nucleon-nucleon interaction 2

  3. Mean Field Model of Nuclei Effective interaction • fermion system at low energies • suppression of collisions by Pauli exclusion • independent particle motion • shell structure • mean field approximation Ph. Chomaz

  4. J. Cavedon et al., Phys. Rev. Lett. 49 (1982) 978. Hartree-Fock P. Grabmayr et al., Nucl. Phys. A 494 (1989) 244. Validity of Mean Field Concept of Nuclei Electron Scattering Charge density difference between 206Pb and 205Tl 206Pb and 205Tl differ in IPM by one 3s 1/2 proton Transfer Reactions Only four strong transitions in 208Pb(d,3He) Pickup from 3s1/2, 2d3/2, 1h11/2 and 1d5/2

  5. Breakdown of Mean Field Concept

  6. Quenching in (Near-) Symmetric Nuclei • SFs reduced to 65% of mean field values • Universal quenching with: • mass • isospin asymmetry • only few nuclei studied Reduction in spectroscopic strength relative to mean field -> Long-range, tensor and short-range correlations Review: W. Dickhoff and C. Barbieri, Prog. Nucl. Part. Sci., 52 (2004) 377.

  7. Correlations Beyond the Mean Field • Realistic nucleon-nucleon interaction not just mean field • Induces long range correlations: coupling to surface modes etc. • Induces short range correlations due to hard core and tensor components • Wavefunction includes e.g. high momentum components • SRCs universal in nuclei, LRCs dependent on “surface structure”

  8. K 1 • K 1 K 2 K 1 > KF , K 2 > KF K 2 How to Observe SRCs in Nuclei • A NN pair with “high” relative momentum between the nucleons and small CM momentum. • Remove one high momentum nucleon. Momentum balanced by other nucleon pair – not by rest of nucleus. • Observe by: • inclusive quasielastic scattering: (e,e’) • semi-exclusive quasielastic scattering: (e,e’p) • exclusive quasielastic scattering: (e,e’pp), (e,e’pn). Also (p,2pn)

  9. For 12C 2N-SRC (np, pp, nn) = 20 ± 4.5%. The probabilities for 3-nucleon SRC are smaller by one order of magnitude relative to the 2N SRC. SRCs Measured with Inclusive Quasielastic Scattering K. Sh. Egiyan et al. PRC 68, 014313 (2003) K. Sh. Egiyan et al. PRL. 96, 082501 (2006) The observed “scaling” means that the electrons probe the high-momentum nucleons in the 2(3) -nucleon phase, and the scaling factors determine the per-nucleon probability of the 2(3) N-SRC phase in nuclei with A>3 relative to 3He.

  10. resonance region SRCs Measured with Semi-Exclusive Quasi-elastic Scattering 12C(e,e’p) Strength from CBF theory D. Rohe et al., Phys. Rev. Lett. 93 (2004) 182501.

  11. SRCs Measured with Exclusive Quasi-elastic Scattering R. Subedi et al.,Science 320 (2008) 1476. • 20x more pn than pp/nn • Tensor correlations From (e,e’pN) and (p,2pN) data on symmetric nuclei (JLab, BNL, NIKHEF, Mainz …):

  12. 2N-SRC  5o 1.f 1.7f ~1 fm 1.7 fm o = 0.16 GeV/fm3 Nucleons Our Present Knowledge of Proton Behaviour in Symmetric Nuclei • 805% single particles moving in average potential • 60-70% independent single particle in a shell model potential • 10-20% shell model long range interactions • 205% two-nucleon short-range and tensor correlations: • 18% np pairs • 1% pp pairs • 1% nn pairs R. Schiavilla et al.,Phys. Rev. Lett. 98 (2007) 132501.

  13. High Density Configurations in SRCs J. Arrington, 2004 High density configurations

  14. Situation in Isospin Asymmetric Nuclei ? • Physics: • Mean Field • Long Range Correlations • Short Range Correlations • Two distinct regions to study: • Low missing energy and momentum • Low momentum components in wavefunction • Concerned mostly with changes in mean field and LRCs • valence nucleons • High missing energy and momentum • High-momentum components in wavefunction • Concerned mostly with changes in SRCs • deeply-bound nucleons • Experimental tools: • (p,2p) – R3B • (e,e’), (e,e’p) – ELISe • 2N knockout, e.g. (p,2p+n), (e,e’pn) ?

  15. Isospin Dependence of Mean Field and Residual Interactions • Residual interaction modifications: • Vmonopole interaction : coupling of • proton-neutron spin-orbit partners • partly occupied orbits • new magic numbers 6, 16, 34 … • Mean field modifications: • surface composed of diffuse neutron matter • derivative of mean field potential weaker and spin-orbit interaction reduced T. Otsuka et al. Phys. Rev. Lett.87 (2001) 082502.

  16. Relative importance of long and short-range correlations in asymmetric nuclei • Precision measurements of spectral functions for valence and deeply bound nucleons: (p,2p), (p,pn) Correlations for Valence Nucleons in Asymmetric Nuclei A. Gade et al., Phys. Rev. C 77 (2008) 044306. J. Lee et al., accepted PRL SCGF method using chiral N3LO force C. Barbieri et al., arXiv:0901.1920v1 (2009).

  17. Asy-stiff Brueckner-Hartree Fock (BHF) Self-Consistent Green’s Function (SCGF) E/A(,) = E/A(,0) + 2.S() n(k) Asy-soft = 0.16 fm-3  = 0.2 e.g. 208Pb k [MeV] n(0)  = 0.16 fm-3  = 0.32 fm-3  = 0.16 fm-3  = 0.32 fm-3 n p  = (n-p)/ High-Momentum Components in Asymmetric Nuclei S() (MeV) T. Frick et al. PRC 71 (2005) 014313. Dependence of correlations on density, isospin asymmetry etc. is vital to understand asymmetric matter: EOS, neutron stars etc.

  18. 14-24O(p,2p) @ 400 AMeV: August/September 2010 A. Gade et al., Phys. Rev. C 77 (2008) 044306. O, F and Ne isotopes Region that will be explored in experiment

  19. Summary • QFS a powerful and unique tool to explore correlations and in-medium nucleon properties in asymmetric nuclei • Both valence and deeply bound nucleons can be studied • Strong synergy with studies of nuclear matter and neutron stars • (e,e’p) at ELISe • (p,2p) at R3B • What physics do we want to study ? • Changes in mean field, LRCs, SRCs • Detailed studies of FSIs -> direct detection of A-1 (A-2) system • What physics CAN we study ?!? • luminosity issues • energy issues • Complementarity of (p,2p) and (e,e’p)

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