Isospin mixing and parity-Isospin mixing and parity-violating electron scatteringviolating electron scattering

O. MorenoO. Moreno, P. Sarriguren, , P. Sarriguren,

E. Moya de Guerra and J. M. UdíasE. Moya de Guerra and J. M. Udías

(IEM-CSIC Madrid and UCM Madrid)(IEM-CSIC Madrid and UCM Madrid)

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

IntroductionIntroduction

Theoretical frameworkTheoretical framework

ResultsResults

ConclusionsConclusions

Summary

Introduction: parity violation in electron scatteringIntroduction: parity violation in electron scattering

(PWBA)

Standard Model coupling constants

Nucleon strangeness content

Nuclear isospin

Neutron distribution in nuclei

Interesting for...

Theoretical formalism: PV asymmetryTheoretical formalism: PV asymmetry

PWBA

J= 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. basisTheoretical 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 GE, defined as:

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 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 targetTheoretical formalism: structure of nuclear target

Theoretical formalism: kinematicsTheoretical formalism: kinematics

Figure-of-merit (FOM):

Relative error of the asymmetry:

Theoretical formalism: summary of effectsTheoretical formalism: summary of effects

Summary of the effects onPV asymmetry under study

Nuclear isospin mixing

Nucleon strangeness

Coulomb distortion

Nuclear deformation

Strong N-N interaction

Nuclear mass

Results: elastic electron scattering cross sectionsResults: elastic electron scattering cross sections

Theory (line)

vs.

experiment (dots)

Results: Isospin mixing & coulomb distortion effectsResults: Isospin mixing & coulomb distortion effects

Results: strangenessResults: strangeness

s=+1.5

s=-1.5

s=0

1.5

-1.5 < s < +1.5

ResultsResults 32S

ResultsResults 28Si

ResultsResults 24Mg

ResultsResults 12C

Results: optimal kinematic ranges for experimentResults: optimal kinematic ranges for experiment

Momentum transfer (fm-1)

Scattering angle at 1 GeV (º)

Incident energy at 10º (MeV)

Results: comparative (A dependence)Results: comparative (A dependence)

Results: influence of the N-N interactionResults: influence of the N-N interaction

Skyrme force Pairing parameters Nuclear deformation

ResultsResults 208Pb

PREL

IMIN

ARY

ConclusionsConclusions

Study of PV elastic electron scattering off the N=Z, J=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 field

New features included: COLLECTIVE EFFECTS

Isospin mixingDeformationPairing

ConclusionsConclusions

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

ConclusionsConclusions

PV asymmetry is important in the experimental determination of:

- Standard Model coupling constants- Standard Model coupling constants

- Nucleon strange content- Nucleon strange content

- Nuclear isospin structure- Nuclear isospin structure

- Neutron distribution in nuclei- Neutron distribution in nuclei (PREX experiment) (PREX experiment)

......

Isospin mixing and parity-Isospin mixing and parity-violating electron scatteringviolating electron scattering

O. MorenoO. Moreno, P. Sarriguren, , P. Sarriguren,

E. Moya de Guerra and J. M. UdíasE. Moya de Guerra and J. M. Udías

(IEM-CSIC Madrid and UCM Madrid)(IEM-CSIC Madrid and UCM Madrid)

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

APPENDIXAPPENDIX

Theoretical formalismTheoretical formalism Coulomb multipole operators

Theoretical formalismTheoretical formalism Spin-orbit term

ResultsResults Spin-orbit term

Strangeness contributions to PV electron Strangeness contributions to PV electron scatteringscattering

GEn 0

Isospin-mixing contribution to PV electron scatteringIsospin-mixing contribution to PV electron scattering

G(s) 0

Neutron distribution from PV asymmetry in eNeutron distribution from PV asymmetry in e -- scatt. scatt.

1

Standard Model coupling constantsStandard Model coupling constants

Nuclear deformationsNuclear deformations

ResultsResults

Multipole (l,j) analysis of isovector contributions

Results: strangeness contributionResults: strangeness contribution

ResultsResults 208Pb

Nucleon form factorsNucleon form factorsGEp, GMp, GEn, GMn:

Höhler et al., Nucl. Phys. B 114 (1976) 505

GE(s)

, GM(s)

:

Isospin mixing calculation

Exact:

Approx.: Expectation value of T perp. squared:

Results: isospin mixingResults: isospin mixing

% %

Results: densitiesResults: densities

Results: form factorsResults: form factors