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. Introduction Theoretical framework Results Conclusions Summary

3. Introduction: parity violation in electron scattering (PWBA) Standard Model coupling constants Nucleon strangeness content Nuclear isospin Neutron distribution in nuclei Interesting for...

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

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

6. 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  p,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 Theoretical formalism: structure of nuclear target

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

8. Theoretical formalism: summary of effects Summary of the effects on PV asymmetry under study 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. Results: strangeness  s =+1.5  s =-1.5  s =0 1.5 -1.5 <  s < +1.5

12. Results 32 S

13. Results 28 Si

14. Results 24 Mg

15. Results 12 C

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

17. Results: comparative (A dependence)

18. Results: influence of the N-N interaction Skyrme forcePairing parametersNuclear deformation

19. Results 208 Pb PRELIMINARY

20. Conclusions Study of PV elastic electron scattering off the N=Z, J  =0 + nuclei 12 C, 24 Mg, 28 Si, 32 S. 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 Isospin mixing Deformation Pairing

21. Conclusions We find LARGER isospin-mixing-induced PV- asymmetry deviations with respect to previous shell-model calculations Effects on asymmetry deviation under study: isospin mixing, strangeness, Coulomb distortion… 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. Conclusions 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)...

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. Theoretical formalism Spin-orbit term

27. Results

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

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

30. Standard Model coupling constants

31. Nuclear deformations

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

34. Results: strangeness contribution

35. Results 208 Pb

36. Nucleon form factors G Ep, G Mp, G En, G Mn : Höhler et al., Nucl. Phys. B 114 (1976) 505 G E (s), G M (s) :

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

38. Results: isospin mixing %

39. Results: densities

40. Results: form factors