Electro-Magnetic Insights Into the Structure of Nuclei

What Information do Electrons Provide?•Charge Distributions•Model Validity•Matter Distributions•Effective Interactions (Strong)•Currents and Magnetism •Spin Structure•The “Rules of the Game”

What Information do Electrons Provide?•Charge Distributions•Model Validity•Matter Distributions•Effective Interactions (Strong)•Currents and Magnetism •Spin Structure•The “Rules of the Game”

The Electromagnetic Process

Electrons

The interaction is well understoodWeak and does not greatly disturb the hadronic systemReliable matrix elements of the interaction, <A|O|B>First order perturbation calculations are effective

(q,ω)

k

k’

A

ProtonsNeutronsPionsEtc.

Hadrons Elastic, Inelastic

‘Good Old Huygens To The Rescue’

Incident Wavee-ikz

r

dA ∼ ρ(r)tr e –(k-k’)r dV

dσ/dω = σM{∫ρ(r)tr e –(k-k’)r dV}2

k– k’ = q Momentum Transfer

Diffraction Phase Integral Form Factor: F(q,ω)

Densities and Form Factors

ρ(r)tr F(q,ω)

Inverse Transforms

MeasuredDerived

Elastic Scattering

Fit to: RadiusEnergy

Negele, RMP 54, p913)

Nuclear Charge Densities

Negele, RMP 54, p913)

Great Success ???• Agreement over 12 orders of magnitude! Caution:• A priori calculations have ~10-15% difference

with radius• Adjustable parameters: Short range forces;

three body forces; Forced to fit Radius.• Size of the box is fixed and not free.• Good agreement is expected to some degree.

Comparison Theory to Experiment

Ph.D. Theses ofC. Creswell A. Hirsh

Deformed NucleiAn Independent Success

Isodensity Contours of 238U

Negele, RMP 54, p913)

Magnetic Scattering

Interaction with currents and magnetism

Spin of nucleons

Pion currents

Separable because of spin flip

Important at backward angles

Transverse Form Factor of 17O

Results From HO Calculations Curve 1, Individual Multipoles (b=1.8f)

Curve 2, Total Form Factor (b=1.8f)

Curve 3, Total Form Factor (b=1.7f)

M.V.Hynes et. al. Phys. Rev. Lett. 42, 1444 (1979)

a) Curve 1, HO, (b=1.8 f)Curve 2, WS

b) Curve 1, HO (b=1.8 f)Curve 2, MSU Shell Model

c) Curve 1, HO (b=1.8f)Curve 2, HO + Core PolarizationCurev 3, HO + Core Polarization + π exchange

Comparisons With Theoretical Models of 17O

M.V.Hynes et. al. Phys. Rev. Lett. 42, 1444 (1979)

The Mean Field or Shell Model

Evidence:Spins Stripping and pickup reactions; label LBinding energies: stabilityOther valence phenomena

All the evidence is for last orbital in nuclei.

Evidence for deeply bound nucleons in orbits from (e,e’p)Deeply bound energy eigenstatesCharacteristic momentum distributions: specific L-values

qp

pinitial

pinitial =q - p

Separation Energies and Angular Momentum Assignments

Nucleons in the Nuclear Medium• What is the nucleon-nucleon interaction in the

medium?

• Difficult to measure:No accurate models of nuclear matter densitiesCannot separate model uncertainties; interaction

Can electrons give us matter densities as well as charge densities? YES!

Matter Transition Densities

• Symmetries N=Z Nuclei: ΔT=0; Self-conjugate nuclei

• Transitions with very small transverse components: Charge or longitudinal

• Charge independence of N-N interaction

{ρtr(r)}neutrons = {ρtr(r)}protons

Spectrum from 16O(e,e’)

States in 16O

Transition Form Factors and Charge Densities

16O(p,p’) at 135 MeV

Solid curves: Fits to data deriving t-matrix

Dotted: IA, Free interaction

Dashed: Paris Hamburg

Effective InteractionsSolid curves: Empirical interactions

Compared to calculations using:

Paris-Hamburg: kf=0.0 fm-1, dottedkf=0.6 fm-1, triangleskf=1.0 fm-1, pluskf=1.4 fm-1, diamonds

J.J. Kelly, Phys. Rev C, 59 2120 (1989)

1) Non-local density-dependent interaction.

2) Amenable to an accurate local approximation.

3He(e,e’p)

• Structure of 3He• Three body calculations• Reaction models• Short Range correlations• Final state interactions• Relativistic Dynamics

2bbu x-sections; distorted S(pm)

M. M. Rvachev et al., PRL 94, 192302 (2005)

3 regions in pm

ATL

No structure in PWIA -factorized

Factorization broken by FSI

No ATL from Ciofi –factorized calculations

2bbu, 3bbu “distorted” spectral functions

meppepe

6

m dE)K/dddEdE

d()p( σΩΩ

ση ∫=

High Q2; xB ≈ 1⇒ Reduced MEC, Δ contributions

At pm > pF spectral function is much larger for 3bbu than for 2bbu due to correlations (SRC)

Calculations reproduce both 2bbu and 3bbu - confidence

Awaiting calculations by Schiavilla

A History of the Tensor Polarization of the Deuteron

D(e,e’p)n asymmetries; OOPS

Need many observables: kinematics, responses (or asymmetries)

Left-RightLeft-RightUp-Down

Beam helicity

GEp/GMp

' tan2 2

ptE

pM l

pG E EG p M

θ+=

Quadrupole Amplitudes in γ*N→Δ→Nπ°

Multipole fit16 responses measured (out of possible 18) – 12 for first time!!10 bins available for 1.17 ≤ W ≤ 1.35 GeV

0( , ' )p e e p π Q2 = 1.0 (GeV/c)2 W = 1.23 GeV

*

*

*

*

Fitted Multipoles and Models

No model describes all multipole amplitudes (even ImE1+ at the resonance!)Data suggests radial excitation for RoperCan study additional resonances

MAID2003 DMT Sato-Lee SAID Born (baseline)

GEp/GMp at 12 GeV

Super fast quarks

Conclusions

• EM Probe is very robust• Contributes to many facets of studies of

strong interactions• Results are often very subtle • Need considerable theoretical input for

interpretation• “A work in progress”

A History of the Tensor Polarization of the Deuteron

Short Range Correlations

• The structure of nuclei at short distances• Influence: energy, stability, momentum

distributions• Difficult to observe with hadron probes• Modify momentum distributions

p n

Look for back-to-back (p,p) and (p,n) pairs in (e,e’pn) and (e,e’pp) processes.

(q,ω)

Pf

(e,e’pn)

Preliminary Results

300 350 400 450 500 550 600 650

yiel

d r

atio

0

0.02

0.04

0.06

0.08

0.1

0.12 extrapolated(e,e’p)(e,e’pp)

missing momentum [MeV/c]300 350 400 450 500 550 600 650

yiel

d r

atio

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

measured(e,e’p)(e,e’pp)

(e,pn) = ~ 10(e,pp)

States in 16O

Transition Form Factors and Charge Densities