Isospin mixing and parity-violating electron scatteringO. Moreno, P. Sarriguren, E. Moya de Guerra and J. M. Udas

(IEM-CSIC Madrid and UCM Madrid)

T. W. Donnelly (M.I.T.), I. Sick (Univ. Basel)

Introduction

Theoretical framework

Results

ConclusionsSummary

Introduction: parity violation in electron scatteringStandard Model coupling constants Nucleon strangeness content Nuclear isospin Neutron distribution in nucleiInteresting for...

Theoretical formalism: PV asymmetryPWBAJp = 0+N=ZT=0 g.s. Elastic scatt.Actual asymmetry:Asymmetry deviation:

Coulomb monopole form factors ratio:Theoretical formalism: Form factors in s.h.o. basisCoulomb monopole matrix element between two s.h.o. states:Spherical part of the density matrix in the s.h.o. basis:Coulomb monopole operator matrix element:

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 iTheoretical formalism: structure of nuclear target

Theoretical formalism: kinematicsFigure-of-merit (FOM):Relative error of the asymmetry:

Theoretical formalism: summary of effects Summary of the effects onPV asymmetry under studyNuclear isospin mixing Nucleon strangenessCoulomb distortionNuclear deformationStrong N-N interactionNuclear mass

Results: elastic electron scattering cross sectionsTheory (line)vs.experiment (dots)

Results: Isospin mixing & coulomb distortion effects

Results: strangeness

Results32S

Results28Si

Results24Mg

Results12C

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

Results: comparative (A dependence)

Results: influence of the N-N interactionSkyrme forcePairing parametersNuclear deformation

Results208PbPRELIMINARY

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

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

ConclusionsPV 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 scatteringO. Moreno, P. Sarriguren, E. Moya de Guerra and J. M. Udas

(IEM-CSIC Madrid and UCM Madrid)

T. W. Donnelly (M.I.T.), I. Sick (Univ. Basel)

APPENDIX

Theoretical formalismCoulomb multipole operators

Theoretical formalismSpin-orbit term

ResultsSpin-orbit term

Strangeness contributions to PV electron scatteringGEn 0Isospin-mixing contribution to PV electron scatteringG(s) 0

Neutron distribution from PV asymmetry in e- scatt.

Standard Model coupling constants

Nuclear deformations

ResultsMultipole (l,j) analysis of isovector contributions

Results: strangeness contribution

Results208Pb

Nucleon form factorsGEp, GMp, GEn, GMn:Hhler et al., Nucl. Phys. B 114 (1976) 505GE(s) , GM(s) :

Isospin mixing calculationExact:Approx.:Expectation value of T perp. squared:

Results: isospin mixing

Results: densities

Results: form factors

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