isospin mixing and parity- violating electron scattering o. moreno, p. sarriguren, e. moya de guerra...
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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)
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IntroductionIntroduction
Theoretical frameworkTheoretical framework
ResultsResults
ConclusionsConclusions
Summary
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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...
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Theoretical formalism: PV asymmetryTheoretical formalism: PV asymmetry
PWBA
J= 0+
N=ZT=0 g.s.
Elastic scatt.
Actual asymmetry: Asymmetry deviation:
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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:
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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
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Theoretical formalism: kinematicsTheoretical formalism: kinematics
Figure-of-merit (FOM):
Relative error of the asymmetry:
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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
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Results: elastic electron scattering cross sectionsResults: elastic electron scattering cross sections
Theory (line)
vs.
experiment (dots)
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Results: Isospin mixing & coulomb distortion effectsResults: Isospin mixing & coulomb distortion effects
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Results: strangenessResults: strangeness
s=+1.5
s=-1.5
s=0
1.5
-1.5 < s < +1.5
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ResultsResults 32S
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ResultsResults 28Si
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ResultsResults 24Mg
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ResultsResults 12C
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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)
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Results: comparative (A dependence)Results: comparative (A dependence)
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Results: influence of the N-N interactionResults: influence of the N-N interaction
Skyrme force Pairing parameters Nuclear deformation
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ResultsResults 208Pb
PREL
IMIN
ARY
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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
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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
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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)
......
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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)
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APPENDIXAPPENDIX
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Theoretical formalismTheoretical formalism Coulomb multipole operators
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Theoretical formalismTheoretical formalism Spin-orbit term
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ResultsResults Spin-orbit term
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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
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Neutron distribution from PV asymmetry in eNeutron distribution from PV asymmetry in e -- scatt. scatt.
1
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Standard Model coupling constantsStandard Model coupling constants
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Nuclear deformationsNuclear deformations
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ResultsResults
Multipole (l,j) analysis of isovector contributions
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Results: strangeness contributionResults: strangeness contribution
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ResultsResults 208Pb
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Nucleon form factorsNucleon form factorsGEp, GMp, GEn, GMn:
Höhler et al., Nucl. Phys. B 114 (1976) 505
GE(s)
, GM(s)
:
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Isospin mixing calculation
Exact:
Approx.: Expectation value of T perp. squared:
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Results: isospin mixingResults: isospin mixing
% %
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Results: densitiesResults: densities
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Results: form factorsResults: form factors