The correlated spectral function of the nucleus e97006 collaboration - PowerPoint PPT Presentation

The correlated spectral function of the nucleus e97006 collaboration HallC TJNAF Basel University Kristoff Normand - Basel - 21 October 2004

Correlated spectral function of the nucleus Experimental study of Short Range Correlations and reaction mechanism Motivations Processes Setup Hydrogen calibrations Quasielastic carbon Spectral Functions Summary Kristoff Normand - Basel - 21 October 2004

Nuclear structure ◦ 1932: Magic numbers (Barlett, Elsasser) ◦ Strong differences with atomic case ◦ 1949: Goeppert Mayer and Jensen ◦ Interaction between nucleons neglected ◦ Independent motion of nucleons in an average potential ◦ Nucleus = ensemble of nucleons ⇒ many body problem ◦ Protons and neutrons ◦ Interaction between nucleons ◦ Realistic potentials ◦ Limits of calculations Kristoff Normand - Basel - 21 October 2004

Nuclear structure ◦ 1932: Magic numbers (Barlett, Elsasser) ◦ Strong differences with atomic case ◦ 1949: Goeppert Mayer and Jensen ◦ Interaction between nucleons neglected ◦ Independent motion of nucleons in an average potential ? ◦ Nucleus = ensemble of nucleons ⇒ many body problem ◦ Protons and neutrons ◦ Interaction between nucleons ◦ Realistic potentials ◦ Limits of calculations Kristoff Normand - Basel - 21 October 2004

Shell Model Independent Particle Shell Model (IPSM) ⇒ Single particle structure of the nucleus E 1p E 1s ◦ Energy shells ◦ Magic numbers ◦ Momentum distribution ◦ Extensively studied −100 0 100 −100 0 100 k (MeV/c) Kristoff Normand - Basel - 21 October 2004

Short Range Correlations 1.0 Mean Field Theory 48 Ca 90 Zr 0.8 16 O 31 P S/(2j+1) 0.6 7 Li 40 Ca 208 Pb 12 C 0.4 0.2 VALENCE PROTONS 0.0 10 1 10 2 target mass Experimental data deviate from 1. ⇒ Short range correlations occur between two nucleons via the repulsive part of the N-N interaction. Various models: Green’s functions, CBF, ... Kristoff Normand - Basel - 21 October 2004

Spectral function S(E, − → k ): probability to find a proton in the nucleus with E and − → k . 0 10 P(k,E) (fm /MeV) k/k =0.75 Momentum distribution: −1 F 10 � ∞ 3 n ( k ) = dE · S ( E, k ) −2 10 0 −3 10 −4 10 Spectroscopic factor: −5 � ∞ 10 0 50 100 150 200 250 300 dk · k 2 · n ( k ) Z = 4 π E (MeV) 0 Nuclear matter spectral function Theoretical nuclear matter predictions Kristoff Normand - Basel - 21 October 2004

Correlated Basis Functions Separation of the correlated and mean field parts. S ( E, k ) = S IPSM ( E, k ) + S corr ( E, k ) → Low energy and momentum part → IPSM -7 10 → Correlated part → 20/22% in the SRC region -8 10 -9 → Nuclear matter for different densities 10 → Local Density Approximation -10 10 → Finite nucleus 0 100 200 300 400 500 600 Kristoff Normand - Basel - 21 October 2004

Spectral function -9 10 -10 10 -11 10 -12 10 -13 10 0 50 100 150 200 250 300 350 ⇒ Correlated strength for large E and k. ⇒ Experimental measurement via electron scattering. ⇒ The strength found at large E and k, will be a signature of short range correlations. Kristoff Normand - Basel - 21 October 2004

Reaction Mechanism E m = E e − E e ′ − T ′ p − T rec e’ (E ,p ) p’ (E ,p ) p e’ e’ p m = − − → → q − − → p ( ,q) ν A−1 p(E,k) e (E ,p ) e e In PWIA: E = E m A − → k = −− → p m dσ = Kσ ep S ( E m , p m ) dE e ′ dE p d Ω e ′ d Ω p Kristoff Normand - Basel - 21 October 2004

Final State Interactions ⇒ rescattering process p’ e’ N’ → SRC close neighbours → Different nuclei, C, Al, Fe, Au q → kinematics choice N e p p’ ⇒ ∆ excitation e’ → π threshold π → simulate large Em ∆ → kinematics choice q e p Kristoff Normand - Basel - 21 October 2004

Kinematics q q Kinematical conventions p’ p’ k k Parallel kinematics Perpendicular kinematics 900 900 900 900 Pm (MeV/c) Pm (MeV/c) 800 800 800 800 700 700 700 700 600 600 600 600 E m P m region accessible 500 500 500 500 400 400 400 400 300 300 300 300 200 200 200 200 100 100 100 100 0 0 0 0 0 0 100 200 300 400 500 600 700 100 200 300 400 500 600 700 0 0 100 200 300 400 500 600 700 100 200 300 400 500 600 700 Em (MeV) Em (MeV) Kristoff Normand - Basel - 21 October 2004

Continuous electron beam Three experimental halls Hall dedicated energy and current Kristoff Normand - Basel - 21 October 2004

Kristoff Normand - Basel - 21 October 2004

SETUP e97006 ⇒ HMS: electrons ⇒ SOS: protons ⇒ e beam: 3.2 GeV/c - p: 2.05-2.75 GeV/c - - p: 0.85-1.7 GeV/c - ⇒ Targets: - angle: 12.5 deg- - angle: 29.0-73.0 deg- - Solid targets: C, Al, Fe, Au - - Cryogenics : H 2 - Kristoff Normand - Basel - 21 October 2004

Hall C Detectors zfp xfp S2X S1X DC2 DC1 gas Cerenkov S1Y Pb-glass S2Y Shower Counter Detector package for both spectrometers Cerenkov Drift chambers Hodoscopes Kristoff Normand - Basel - 21 October 2004

Analysis Monte Carlo Simulation Data reduction ⇒ Modeling of the two spectrometers ⇒ Kinematical information ⇒ De Forest off-shell Cross-section ⇒ IPSM spectral function ⇒ Yield normalisation ⇒ Radiative weight (Makins, Weissbach) - Experimental charge - Efficiencies Outputs for the analysis - Background substraction ⇒ Phase space ⇒ Radiative corrections ⇒ Cross section calculation ⇒ De Forest off-shell Cross-section Checks with hydrogen runs Checks with quasielastic carbon runs Kristoff Normand - Basel - 21 October 2004

Radiative Corrections e’ p’ ⇒ Bremsstrahlung (e and p) q’ ⇒ Radiations emitted by particles q - internal (with nucleus involved) e p - external (with other nucleus) ⇒ Two modifications - cross section of the process - kinematic of the particle ⇒ Need for corrections Kristoff Normand - Basel - 21 October 2004

Elastic scattering at H 2 Checking of experimental setup → No Final state interactions → Unique kinematics → Cross section known → Radiative corrections Allows various checks: ⇒ Offsets of spectrometers ⇒ Proton transmission ⇒ Cross section parametrisation Kristoff Normand - Basel - 21 October 2004

Offsets ⇒ Reconstructed quantities Em, Pm, W ⇒ Beam and Spectrometers offsets E beam P HMS θ HMS φ HMS P SOS θ SOS φ SOS % % rad rad % rad rad -0.1 -0.234 -0.001 0.0007 var. 0.0015 0.0007 0.006 offset psos 0.004 p sos < 1 . 27 : 0 . 00225 0.002 p sos > 1 . 27 : 0 0 . 00225 − 0 . 033 ∗ ( x − 1 . 27) 2 -0.002 -0.004 -0.006 -0.008 0.8 1 1.2 1.4 1.6 1.8 P SOS (GeV) Kristoff Normand - Basel - 21 October 2004

Offsets ⇒ Reconstructed quantities Em, Pm ⇒ Beam and Spectrometers offsets correction applied Kristoff Normand - Basel - 21 October 2004

H2 Checks ratio data/simc 1.04 2500 6000 2000 5000 4000 1500 1.02 3000 1000 2000 500 1000 1 0 0 -0.04 -0.020 0.02 0.04 -0.05 0 0.05 −0.04 0 0.04 theta(rad) phi(rad) 0.98 7000 5000 6000 0.96 4000 5000 4000 3000 3000 2000 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2000 2 1000 2 Q (GeV/c) 1000 0 0 -2 0 2 -10 -5 0 5 10 ytar(cm) p/p(%) ∆ Comparison of cross section ratio Mergell parametrisation Comparison for spectrometers (Nucl Phys A596 367) ⇒ Agreement between simulation and data Kristoff Normand - Basel - 21 October 2004

Carbon quasielastics 16000 4500 4500 4500 14000 1p 4000 4000 4000 4000 Data 12000 3500 3500 3500 10000 10000 3000 3000 3000 2500 2500 2500 8000 SIMC 2000 2000 2000 2000 6000 1s 1500 1500 1500 4000 1000 1000 1000 2000 500 500 500 0 0 0 0 0 0 −400 −200 0 200 400 -400 -300 -200 -100 0 100 200 300 400 0 20 40 60 80 100 0 0 0 20 20 20 40 40 40 60 60 60 80 80 80 100 100 100 Em(MeV) Pm(MeV/c) data/simc = 0.85 IPSM region: ⇒ missing strength to higher E m and P m ⇒ low P m ≤ 300 MeV/c ⇒ low E m ≤ 80 MeV/c Kristoff Normand - Basel - 21 October 2004