Microscope for the Studying Nuclear Structure with s School of Physics Seoul National University November 15, 2004
Outline s Microscope for the s
Smaller, smaller Quest for basic building blocks of the universe The concept of atom by Greeks atom: indivisible, fundamental building block Modern atoms are composed of nuclei and electrons is composed of protons and neutrons Oxygen atom (O) has 8 electrons and a nucleus with 8 protons and 8 neutrons Nucleons (protons and neutrons) are composed of quarks, gluons In naïve quark model, proton has 2 u quarks and 1 d quark. Microscope for the s
Observing atoms, or anything else Optical microscope Send light to the object Re-emitted light is focused/magnified by lenses Human eye detects the light Image recognized in the brain Resolution: λ of visible light ( 1000 angstrom or 100 nm) Electron microscope Send electron beam to the object Scattered electrons are focused/magnified by coils Phosphor screen detects scattered electrons Human eye sees the image Resolution: λ of electron matter wave (typically 0.2 nm) Microscope for the s
Observing Size of the nucleus: a few fm (femto meter, or fermi, 1 fm = 10 15 m) Requires electron beam at higher energies (100 s of MeV) c = 197MeV fm Electron beam is prepared by accelerators Focusing/bending electrons are done by magnets Sophiscated detector system for the electrons. Observe number of scattered electrons as a function of angle and energy Reconstruction of image from the cross section Microscope for the s
Why use electrons? One of elementary particles point-like without internal structure stable particle well-known properties (mass, charge, spin etc) well-known interaction with other elementary particles (e.g. quarks) Relatively easy to prepare (compare to other leptons or quarks) Easy to detect In general, experiments are quite clean compared to those with hadron beams Microscope for the s
from a Point Charge ag replacements e Rutherford-like scattering ( ) dσ dω point e γ Ze ( dσ dω ) Mott = (Zα) 2 cos 2 θ 2 4E 2 sin 4 θ 2 Microscope for the s
Probing the Microscope for the ts e e ρ(x) Fermi s Golden Rule dσ dω = 2π M fi 2 D f M fi : scattering amplitude D f : density of the final states (or phase factor) s
Potential Scattering Amplitude Microscope for the s M fi = = = ψ f V (x)ψ i d 3 x e ik f x V (x)e ik i x d 3 x e iq x V (x) d 3 x Plane wave approximation for incoming and outgoing electrons Born approximation (interact only once)
Form Factor and Charge Distribution Using Coulomb potential from a charge distribution ρ(x), V (x) = Ze2 4πε 0 ρ(x ) x x d3 x M fi = Ze2 e iq x ρ(x ) 4πε 0 x x d3 x d 3 x [ ] = Ze2 e e iq R iq x ρ(x ) d 3 x d 3 R 4πε 0 R = Ze2 e iq R 4πε 0 R d3 R e iq x ρ(x ) d 3 x F (q) = e iq x ρ(x ) d 3 x Microscope for the s
Form Factor and Cross Section For point-like particle, ρ(x ) = δ(x ) and F (q) = 1 Rutherford-like scattering ( ) dσ dω point ( ) dσ (Zα) 2 cos 2 θ = 2 dω Mott 4E 2 sin 4 θ 2 Scattering from a charge distribution ( ) dσ dσ dω = F (q) 2 dω Mott Microscope for the s
Charge Distribution in the Measurement of F (q) (from cross section) Inverse Fourier transform gives ρ(x) Microscope for the s
Probing Inside the For a target with non-zero spin - form factors for charge and magnetization dσ dω lab = α 2 E 2 cos 2 θ [ 2 4E 3 sin 4 θ (G p E )2 + τ ( ) ε (Gp M )2] 1 1 + τ 2 τ Q2 4M 2, 1 ε = 1 + 2(1 + τ) tan2 θ 2 Microscope for the s G p E G p M distribution of charge inside the proton distribution of magnetization inside the proton
ε 1 0.8 0.6 0.4 0.2 0 frag replacements 0 30 60 90 120 150 180 G 2 E + (τ/ε)g2 M 1 0.8 0.6 0.4 0.2 0 0.2 frag replacements Slope - G 2 M G 2 E τ/ε θ e 0 1 2 3 Microscope for the s
Electric and Magnetic Form Factor of the Microscope for the s Conclusion: G p E (Q2 ) = G p M (Q2 )/µ p
New Method to Measure Form Factors Use of polarized electron beam Measure polarization transfer to the proton I 0 P t = 2 τ(1 + τ)g p E Gp M tan θ 2 I 0 P l = (E + E ) τ(1 + τ)(g p M M )2 tan 2 θ 2 G p E G p M I 0 = (G p E )2 + τ ε (Gp M )2 = P t P l (E + E ) 2M tan θ 2 Microscope for the s
Surprise! 1.2 Microscope for the µ p G Ep /G Mp 1 0.8 0.6 0.4 0.2 0 Jones [11] This work VMD [32] PFSA [29] SU(6) breaking + CQ ff [28] Soliton [31] SU(6) breaking [28] CQM [26] 0 1 2 3 4 5 6 Q 2 (GeV 2 ) s
Why? Same object, two different way of looking Current smoking gun Rosenbluth separation Initial assumption: Born approximation (one photon exchange) At large Q 2, two photon exchange needs to be considered k k p p k k Microscope for the s p p
One Possibility µ p R exp 2 1.5 1 0.5 µ p R exp Polarization µ p R exp Rosenbluth 1-0.0762 Q 2 + 0.004896 Q 4 +0.001298 Q 6 1-0.1306 Q 2 + 0.004174 Q 4-0.000752 Q 6 Microscope for the s 1.5 1 0 0 1 2 3 4 5 6 Q 2 (GeV 2 ) µ p R exp Rosenbluth µ p R exp Polarization µ p R exp 1γ+2γ µ p R exp 0.5 0 0 1 2 3 4 5 6 Q 2 (GeV 2 )
s Inside the Quasi-elastic scattering - scattering from the bound protons inside the nucleus Useful tool to investigate nucleon properties inside the nucleus Microscope for the s
Cross Section d 2 [ σ Q 4 ] dωdω = σ Mott q 4 R L(q, ω) + Q2 1 2q 2 ε R T (q, ω) R L (q, ω), R T (q, ω): Response functions Analogy of G p E and Gp M of the free proton R L (q, ω) characterizes charge interaction in the nucleus. Coulomb Sum S L (q) = ω + el dω R L(q, ω) Z G E 2 (Q 2 ) Microscope for the s G E 2 (Q 2 )=([G p E (Q2 )] 2 +(N/Z)[G n E (Q2 )] 2 ) 1+Q2 /4M 2 1+Q 2 /2M 2
By definition, S L (q) = 1 for the free proton Saturation of the Coulomb Sum S L (q) 1 at sufficiently large q Deviation of the at small q Nucleon-nucleon long-range correlations and Pauli blocking at large q Short range correlations and modification of the free nucleon electromagnetic properties inside the nuclear medium Nuclear density dependence ( 4 He to 208 Pb) Related to chiral symmetry restoration in dense nuclear medium Microscope for the s
Measurements For the past twenty years, a large experimental program at Bates, Saclay and SLAC Limited kinematic coverage in q and ω due to machine limitations S L (q eff ) 1.1 1.0 0.9 0.8 0.7 3 He 40 Ca 56 Fe 208 Pb 56 Fe Microscope for the s 0.6 0.5 0.4 200 300 400 500 600 q eff (MeV/c) The figure does NOT include all the existing data. Especially, MIT Bates results are not included. 1100 1200
Controversy R RL (Meas)dω R RL (RFG)dω ts 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1.0 0.8 0.6 0.4 0.2 40 Ca Bates 40 Ca Saclay 238 U Bates 208 Pb Saclay 0.0 200 300 400 500 600 q (MeV/c) Early data shows significant quenching of the CSR. With the addition of forward angle data, Bates claims no significant quenching. Saclay new analysis claims that quenching persists. Microscope for the s
Saclay(France) vs. MIT(US) εrl + q2 2Q 2RT 0.10 0.08 0.06 0.04 0.02 PSfrag replacements q eff = 350 MeV/c ω = 100MeV χ 2 = 21.2 40 Ca Saclay 40 Ca Bates χ 2 = 0.231 Microscope for the s 0.00 0.0 0.2 0.4 0.6 0.8 1.0 ε(ϑ)
New Proposed at JLab 1.2 1.1 1.0 0.9 Microscope for the s S L (q eff ) 0.8 0.7 0.6 0.5 3 He 40 Ca 56 Fe 208 Pb 56 Fe 56 Fe Expected Error on 56 Fe 0.4 200 400 600 800 1000 1200 q eff (MeV/c)
s One of the main tools in nuclear physics research Charge density of the nucleus - Comparison with theoretical model proton (charge and magnetization) New challenge Surprising results on G p E /Gp M from JLab Two photon exchange effect - more study in theory and experiment Nucleons inside the nucleus Change or no change, that is the question. Controversial results on the Coulomb Sum Proposed experiment will give a definitive answer Probing quarks Existence and interaction of quarks Study of the quark spins Microscope for the s