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
Introduction: parity violation in electron scattering (PWBA) Interesting for... Standard Model coupling constants Nucleon strangeness content Nuclear isospin Neutron distribution in nuclei
Theoretical formalism: PV asymmetry PWBA J π = 0 + Elastic scatt. N=Z T=0 g.s. Actual asymmetry: Asymmetry deviation:
Theoretical formalism: Form factors in s.h.o. basis Coulomb monopole form factors ratio: Coulomb monopole operator matrix element: 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:
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 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: kinematics Relative error of the asymmetry: Figure-of-merit (FOM):
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
Results: elastic electron scattering cross sections Theory (line) vs. experiment (dots)
Results: Isospin mixing & coulomb distortion effects
Results: strangeness ρ s =+1.5 ρ s =0 ρ s =-1.5-1.5 < ρ s < +1.5 1.5
Results 32 S
Results 28 Si
Results 24 Mg
Results 12 C
Results: optimal kinematic ranges for experiment Momentum transfer (fm -1 ) Incident energy at 10º (MeV) Scattering angle at 1 GeV (º)
Results: comparative (A dependence)
Results: influence of the N-N N interaction Skyrme force Pairing parameters Nuclear deformation
Results 208 Pb
Conclusions Study of PV elastic electron scattering off the N=Z, J π =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
Conclusions Effects on asymmetry deviation under study: isospin mixing, strangeness, Coulomb distortion We find LARGER isospin-mixing-induced PVasymmetry 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
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)...
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)
APPENDIX
Theoretical formalism Coulomb multipole operators
Theoretical formalism Spin-orbit term
Results Spin-orbit term
Strangeness contributions to PV electron scattering Isospin-mixing contribution to PV electron scattering G En 0 G (s) 0
Neutron distribution from PV asymmetry in e - scatt. 1
Standard Model coupling constants
Nuclear deformations
Results Multipole (l,j) analysis of isovector contributions
Results: strangeness contribution
Results 208 Pb
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) :
Isospin mixing calculation Exact: Approx.: Expectation value of T perp. squared:
Results: isospin mixing % %
Results: densities
Results: form factors