electro-magnetic insights into the structure of nuclei
TRANSCRIPT
![Page 1: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/1.jpg)
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”
![Page 2: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/2.jpg)
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
![Page 3: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/3.jpg)
‘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)
![Page 4: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/4.jpg)
Densities and Form Factors
ρ(r)tr F(q,ω)
Inverse Transforms
MeasuredDerived
![Page 5: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/5.jpg)
Elastic Scattering
Fit to: RadiusEnergy
Negele, RMP 54, p913)
![Page 6: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/6.jpg)
Nuclear Charge Densities
Negele, RMP 54, p913)
![Page 7: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/7.jpg)
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.
![Page 8: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/8.jpg)
Comparison Theory to Experiment
Ph.D. Theses ofC. Creswell A. Hirsh
Deformed NucleiAn Independent Success
![Page 9: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/9.jpg)
Isodensity Contours of 238U
Negele, RMP 54, p913)
![Page 10: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/10.jpg)
Magnetic Scattering
Interaction with currents and magnetism
Spin of nucleons
Pion currents
Separable because of spin flip
Important at backward angles
![Page 11: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/11.jpg)
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)
![Page 12: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/12.jpg)
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)
![Page 13: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/13.jpg)
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
![Page 14: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/14.jpg)
![Page 15: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/15.jpg)
![Page 16: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/16.jpg)
![Page 17: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/17.jpg)
![Page 18: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/18.jpg)
Separation Energies and Angular Momentum Assignments
![Page 19: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/19.jpg)
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!
![Page 20: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/20.jpg)
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
![Page 21: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/21.jpg)
Spectrum from 16O(e,e’)
![Page 22: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/22.jpg)
States in 16O
![Page 23: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/23.jpg)
![Page 24: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/24.jpg)
![Page 25: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/25.jpg)
Transition Form Factors and Charge Densities
![Page 26: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/26.jpg)
16O(p,p’) at 135 MeV
Solid curves: Fits to data deriving t-matrix
Dotted: IA, Free interaction
Dashed: Paris Hamburg
![Page 27: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/27.jpg)
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.
![Page 28: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/28.jpg)
3He(e,e’p)
• Structure of 3He• Three body calculations• Reaction models• Short Range correlations• Final state interactions• Relativistic Dynamics
![Page 29: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/29.jpg)
2bbu x-sections; distorted S(pm)
M. M. Rvachev et al., PRL 94, 192302 (2005)
![Page 30: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/30.jpg)
3 regions in pm
![Page 31: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/31.jpg)
ATL
No structure in PWIA -factorized
Factorization broken by FSI
No ATL from Ciofi –factorized calculations
![Page 32: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/32.jpg)
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
![Page 33: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/33.jpg)
A History of the Tensor Polarization of the Deuteron
![Page 34: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/34.jpg)
D(e,e’p)n asymmetries; OOPS
Need many observables: kinematics, responses (or asymmetries)
Left-RightLeft-RightUp-Down
Beam helicity
![Page 35: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/35.jpg)
GEp/GMp
' tan2 2
ptE
pM l
pG E EG p M
θ+=
![Page 36: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/36.jpg)
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
*
*
*
*
![Page 37: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/37.jpg)
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)
![Page 38: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/38.jpg)
![Page 39: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/39.jpg)
![Page 40: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/40.jpg)
![Page 41: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/41.jpg)
GEp/GMp at 12 GeV
![Page 42: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/42.jpg)
Super fast quarks
![Page 43: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/43.jpg)
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”
![Page 44: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/44.jpg)
![Page 45: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/45.jpg)
A History of the Tensor Polarization of the Deuteron
![Page 46: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/46.jpg)
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
![Page 47: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/47.jpg)
(e,e’pn)
![Page 48: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/48.jpg)
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)
![Page 49: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/49.jpg)
![Page 50: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/50.jpg)
![Page 51: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/51.jpg)
![Page 52: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/52.jpg)
![Page 53: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/53.jpg)
States in 16O
![Page 54: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/54.jpg)
Transition Form Factors and Charge Densities
![Page 55: Electro-Magnetic Insights Into the Structure of Nuclei](https://reader033.vdocuments.mx/reader033/viewer/2022042815/6268ff6ab4e29f7eec41bf30/html5/thumbnails/55.jpg)