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Isospin mixing and parity-violating electron scattering

Isospin mixing and parity-violating electron scattering. O. Moreno , P. Sarriguren, E. Moya de Guerra and J. M. Udías (IEM-CSIC Madrid and UCM Madrid). T. W. Donnelly (M.I.T .), I. Sick (Univ. Basel). Summary. Introduction Theoretical framework Results Conclusions. (PWBA).

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Isospin mixing and parity-violating electron scattering

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  1. Isospin mixing and parity-violating electron scattering O. Moreno, P. Sarriguren, E. Moya de Guerra and J. M. Udías (IEM-CSIC Madrid and UCM Madrid) T. W. Donnelly (M.I.T.), I. Sick (Univ. Basel)

  2. Summary IntroductionTheoretical frameworkResultsConclusions

  3. (PWBA) Introduction: parity violation in electron scattering Standard Model coupling constantsNucleon strangeness contentNuclear isospinNeutron distribution in nuclei Interesting for...

  4. PWBA Theoretical formalism: PV asymmetry Jp = 0+ Elastic scatt. N=Z T=0 g.s. Actual asymmetry: Asymmetry deviation:

  5. And equivalently for WNC form factors but using GE, defined as:  Coulomb monopole form factors ratio: Theoretical formalism: Form factors in s.h.o. basis Coulomb monopole operator matrix element: Spherical part of the density matrix in the s.h.o. basis: Coulomb monopole matrix element between two s.h.o. states:

  6. Theoretical formalism: structure of nuclear target HF: Axially deformed Hartree-Fock mean field using a Skyrme nucleon-nucleon effective interaction (SLy4). BCS: pairing interactions treated within BCS approx. with fixed pairing gaps Dp,n=1 MeV. Occupations and number equation recomputed after each HF iteration. Expansion coefficients in s.h.o. basis of the HF+BCS single particle state i: Occupation probability of the HF+BCS single particle state i

  7. Relative error of the asymmetry: Theoretical formalism: kinematics Figure-of-merit (FOM):

  8. Summary of the effects on PV asymmetry under study Theoretical formalism: summary of effects Nuclear isospin mixing Nucleon strangeness Coulomb distortion Nuclear deformation Strong N-N interaction Nuclear mass

  9. Results: elastic electron scattering cross sections Theory (line) vs. experiment (dots)

  10. Results: Isospin mixing & coulomb distortion effects

  11. rs=0 rs=+1.5 -1.5 < rs< +1.5 rs=-1.5 1.5 Results: strangeness

  12. 32S Results

  13. 28Si Results

  14. 24Mg Results

  15. 12C Results

  16.  Momentum transfer (fm-1) Results: optimal kinematic ranges for experiment  Incident energy at 10º (MeV)  Scattering angle at 1 GeV (º)

  17. Results: comparative (A dependence)

  18. Skyrme force Pairing parameters Nuclear deformation Results: influence of the N-N interaction

  19. 208Pb Results PRELIMINARY

  20. Isospin mixing Deformation Pairing Study of PV elastic electron scattering off the N=Z, Jp=0+ nuclei 12C, 24Mg, 28Si, 32S. Conclusions Analysis of experimental feasibility: maximize figure-of-merit & asymmetry deviation. Nuclear ground states obtained from a deformed HF+BCS mean field New features included: COLLECTIVE EFFECTS

  21. Effects on asymmetry deviation under study: isospin mixing, strangeness, Coulomb distortion… Conclusions We find LARGER isospin-mixing-induced PV-asymmetry deviations with respect to previous shell-model calculations Why?  We use 11 major shells and each single quasiparticle state is a mixture of radial quantum numbers n of the s.h.o. basis

  22. PV asymmetry is important in the experimental determination of: - Standard Model coupling constants - Nucleon strange content - Nuclear isospin structure - Neutron distribution in nuclei (PREX experiment) ... Conclusions

  23. Isospin mixing and parity-violating electron scattering O. Moreno, P. Sarriguren, E. Moya de Guerra and J. M. Udías (IEM-CSIC Madrid and UCM Madrid) T. W. Donnelly (M.I.T.), I. Sick (Univ. Basel)

  24. APPENDIX

  25. Theoretical formalism Coulomb multipole operators

  26. Spin-orbit term Theoretical formalism

  27. Spin-orbit term Results

  28. Strangeness contributions to PV electron scattering Isospin-mixing contribution to PV electron scattering GEn 0 G(s) 0

  29.  1 Neutron distribution from PV asymmetry in e- scatt.

  30. Standard Model coupling constants

  31. Nuclear deformations

  32. Multipole (l,j) analysis of isovector contributions Results

  33. Results: strangeness contribution

  34. 208Pb Results

  35. Nucleon form factors GEp, GMp, GEn, GMn: Höhler et al., Nucl. Phys. B 114 (1976) 505 GE(s), GM(s):

  36. Isospin mixing calculation Exact: Approx.: Expectation value of T perp. squared:

  37. % % Results: isospin mixing

  38. Results: densities

  39. Results: form factors

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