The (e,e‘p) reaction:

advantages• access to nuclear structure• probes the nucleon• more information than inclusive• clean definition of reaction

disadvantages:• final state interaction proton-nucleus• 2. detector needed• smaller cross section due to acceptance

(e,e'p) advantages over (p,2p):

• Electron interaction relatively weak:

OPEA reasonably accurate.

• Nucleus is very transparent to electrons:

Can probe deeply bound orbits.

Structure of the nucleus

• nucleons are bound energy (E) distribution shell structure• nucleons are not static momentum (k) distribution

scan/test/nn_pot.agr

repulsive core

attractive part

determined by N-N potential

in average:binding energy: ~ 8 MeVdistance: ~ 2 fm

long-range

short-range

d

rr

early hint on shell structure in the nucleus

particular stable nuclei with Z,N = 2, 8, 20, 28, 50, 82, 126 (magic numbers)

large separation energy ES

“average”(Weizsäcker Formula,no shell structure,bulk properties)

neutron number N40 60 80 100 120 140

2

1

0

-1

-2

28 50 82 126

shell closure

ES -

W.F

Shell structure (Goeppert-Mayer, Jensen, 1949)

expected:many collisions between nucleons,no independent-particle orbits

But:experimental evidence for shell structure

nucleons can not scatter into occupied levels:Suppression of collisions between nucleons

Pauli Exclusion Principle:

Independent Particle Shell model (IPSM)

spectral function S(E, k): probability of finding a proton with initial momentum k and energy E in the nucleus• factorization into energy & momentum part

• single particle approximation: nucleons move independently from each other in an average potential created by the surrounded nucleons (mean field)

Z(E)

EEF

2MEF =

kF2

Z(k)

kkF

occupied emptyoccupied empty

nuclear matter:

6Li

181Ta

89Y58Ni40Ca

24Mg12C

118Sn 208Pb

R.R. Whitney et al., Phys. Rev. C 9, 2230 (1974).

Inclusive Quasielastic Electron Scattering: (e,e’)

compared to Fermi model:fit paramterkF and

getting the bulk features

Moniz et al, PRL 26, 445 (1971)Fit results:

kF width of q.e. peak, 250 MeV/c for medium-heavy nuclei

U. Amaldi, Jr. et al.,

Phys. Rev. Lett. 13,

341 (1964).

The first (e,e'p) measurement: identification of different orbits

Frascati Synchrotron,

Italy12C(e,e'p)

27Al(e,e'p)

moderate resolution:FWHM: 20 MeV

getting the details

Steenhoven et al., PRC 32, 1787 (1985)

shape described by Lorentz function with central energy E + width

incidental remark:5/2state can not be populated by 1-step process, because 1f5/2 state empty in 12C, but seen in (p,2p) electrons are a suitable probe to examine the nucleus

11B

J

3/2

1/2

5/2

3/2

2.12

4.455.02

0+

12Cg.s.

g.s.

NIKHEF: resolution 150 keV

shell model: describes basic properties like spin, parity, magic numbers ...

Momentum distribution:- characteristic for shell (l, j) - Fourier transformation of lj(r) info about radial shape

-100 0 100 200 -100 0 100 200pm [MeV/c]

NIKHEF results

mo

men

tum

dis

trib

utio

n [(

Ge

V/c

)-3/s

r]

Z/IP

SM

IPSM1.0

NIKHEF

65%• definite number of nucleons in each shell (IPSM): 2 j + 1

theory (solid line):Distorted wave impulse approximation (DWIA)solves the Schrödinger equation using an optical potential (fixed by p-12C) (Hartree-Fock, selfconsistent)real part: Wood-Saxon potentialimaginary part: accounts for absorption in the nucleus Correction for Coulomb distortion

well reproduced shape

strength of the transition smaller!

Spectroscopic factor Z

Z = 4 dE dk k2 S(E, k)single particle

state

= number of nucleons in shell

kF

Massenzahl

z /(

2j+

1)

~10 %

Theoretical description:Random Phase Approximation (RPA)considerable mixing between hole states and 2h1p configurations

Long range correlations (LRC): 20 %

Fragmentation of the 1-particle strength due toexcitation of collective modes -- surface vibration-- configuration mixing-- Giant resonances occupation of “empty” states close to the Fermi edge

broadening, fragmentation, excitation

• Short range and tensor correlations (SRC): ~ 15 % repulsive core of NN force leads to scattering between particles at short distances

SRC k

-k

simple picture:max. of the s.f. expected at

2 M(+ 2EB)Em ~

p2m

Consequences:• scattering of nucleons to high lying states• depletion of IPSM shells

occupation of states at large k and large E

Comparison with CBF theory:modified for finite nucleiIm fitted to the width of the state(PRC 41(1990) R24)

deeper bound nucleons (inner shells):less easily excited, broadeningclose to occupation number

+ LRC

for valence nucleons:binding energy excitation energy for vibration

spectroscopic factor:strength of the transition

A A-1

experimentally: identification via momentum distribution

SRC

/(

2j+

1)

NIKHEF results: 208Pb(e,ep)207Tl

LRC

Bindungsenergie [MeV]

LS splitting 2j +1

l - orbits

W.H. Dickhoff, C. Barbieri,Prog.Part.Nucl.Phys. 52,(2004) 377

Some definitions:

spectroscopic factor Z

probability to reach a final state (n,l,j)when a nucleon is removed (added to) the target nucleus

21 A

oA aZ

occupation number n

number of nucleons in the state which might be fragmentated

"background correlated"i

iZn

occupancy o:occupation number relative to completely filled shell

Occupation numbers:difficult to measure• fragmentation: strength is spread over a wide range of Em

• deep-lying states: large width and start to overlap • absolute spectroscopic numbers are model dependent

CERES: Clement et al, Phys.Lett B 183 (1987) 127Combined Evaluation of Relative spectroscopic factors andElectron Scattering

1) input:• difference in charge density from elastic electron scattering (206Pb)(205Tl)assumption:• main contribution in charge difference comes from 3S1/2 state

n + cp

n3S1/2 (206) n3S1/2 (205)] (3S1/2) + cp

n = 0.64 0.06

63%

in agreement with theory for nuclear matter

2) input:• relative spectroscopic factors (from (e,ep)experiment) R(205/208) = Z3S1/2(205)/ Z3S1/2(208) n3S1/2(205)/ n3S1/2(208)

assumption: equal percentage depletion of all shells, nuclei are neighbours similar shell structure

PbZ

TlZPbZnPbn 208

205206208

n(206Pb) = 1.25 0.1n(205Tl) = 0.61 0.1

n(208Pb) = 1.51 0.18 76 7%

P.Grabmayr et al., PRC 49 (1994) 2971

advantage: • only relative spectroscopic factors needed• avoids to sum up fragmented strength

Spectroscopic factors from (d, 3He)

Pick-up reaction should be equivalent to (e,e’p) reaction

problem:very sensitive to the asymptotic tail of the wave function:Z/Z 7 rrms/rrms

reason:- strong interaction are absorptive- only sensitive to the surface

rrms was chosen to fulfill the sumrule nparticles + nholes = 2j+1 (Pick-up and stripping reaction),assuming IPSM

But: sumrule not fulfilled for Em < 10-20 MeV due to SRC

Original data(d,3He) Local/Zero-rangeBSWF chosen to fulfill sumrule

NIKHEF Reanalysis(d,3He) Non-Local/Finite-rangeBSWF from (e,e'p)Kramer et al. NPA 679 (2001) 267

100

Depletion in other systems:atoms (Ne,Ar) : 0.001 0.018:increases from the inner to outermost shellsnuclei : 0.2 0.3L3He : 0.40.5

interactionincreases

large repulsive core in the interatomic potential:Lennard-Jones potential:strong repulsive core long-range attraction simple spin-independent function of the atomic distance

momentum/kF

mom

entu

m d

istr

ibut

ion

Liquid 3He drops

0.4 quasi hole strength

0 0.5 1 1.5 2

0.8

0.6

0.4

0.2

0.0

1.0

IPSM

Effect of correlations on the binding energy

Without correlations no bound nuclei!

kineticenergy

binding energy: <T> + <V> difference of 2 large values

bindingenergy

potentialenergy

Cr, C: Operator for SRC and tensor correlations

(Feldmeier, Neff)

c12_spectheocomp_nice.agr

k < kF: single-particle contribution dominatesk kF: SRC already dominates for E > 50 MeVk > kF: single-particle negligible

IPSM

consequence: search for SRC at large E, kmethod: (e,e’p)-experiment

kF

CBF

spectral/c12_momtheocomp_nice1.agr

Modern many-body theories:• Correlated Basis Function theory (CBF) O. Benhar, A. Fabrocini, S. Fantoni, Nucl. Phys. A505, 267 (1989)• Green’s function approach (2nd order) H. Müther, G. Knehr, A. Polls, Phys. Rev. C52, 2955 (1995)• Self--consistent Green’s function (T = 2 MeV) T. Frick, H. Müther, Phys. Rev. C68 (2003) 034310

signature of SRC:additional strength at high momentum

c12_benh_mom1s_nicesh

in the IPSM region:

k4que01_ipsmben250.eps

Q2 = 1.5 (GeV/c)2

200 MeV/c < pm < 300 MeV/c

data on 12CIPSM*0.85 CBF

radiation tail

Spectral function containing SRC:good agreement with data

Missing strength already at moderate pm

compared to IPSM

Em = Ee Ee Tp TA-1

in PWIA:direct relation between measured quantities and theory:

(e,ep)-reaction: coincidence experimentmeasured values: momentum, angles

pm = q pp

missing momentum:

|E| == Em k == pm

reconstructed quantites: missing energy:

e

e

pp = k + q

MA

initial momentumk

q

electron energy: Ee

proton: pp’

electron: ke’ Ee’ = |ke’|

performance HMS SOS

momentum range (GeV): 0.5-7.4 0.1-1.75acceptance (%): 10 ± 15 p = po (1 + )solid angle (msr): 6.7 7.5target acceptance (cm): 7 ± 1.5

HMS

SOS

Q Q Q D

D

D

e

e

p

0.8-6 GeV

0.1-1.75 GeV/c

0.5-7.4 GeV/c

target

superconducting magnets,quadrupole: focussing/defocussing

collimator

detectorsystem

detector systemSetup in HallC:

ironmagnets

EmPm_allkins.eps

Data at high pm, Em measured in Hall C at Jlab:• targets: C, Al, Fe, Au• kinematics: 3 parallel 2 perpendicular

k qk q

high Em- region: dominated by resonance

Covered Em-pm range:

perpendicular kinematics parallel kinematics

kinp1

kinp2

kin3,qpi

kin5

kin3,qpi

kin4

Extraction of the spectral function:

• Binning of the data (Em,pm)ij:

Em= 10-50 MeV, pm= 40 MeV/c

dde dp dEe dEp

= K ep S(Em,pm) TA

e-p c.s..

only in PWIA possible, care for corrections later

exp. c.s.:

dde dp dEe dEp

= K ep S(Em,Pm)ij Tp( )ij

(Nij Niju.g.)

L Pij

phase space from M.C.

=

e & p:

FWHM:0.5ns

2ns

Nij

Niju.g.Nij

u.g.

LuminosityEfficiency,dead time ...

• radiative corrections:

redistribution of events in den (Em,pm) bins

[S(Em,pm)ij]derad = S(Em,pm)ij Nijnorad

Nijrad

spectral functionfor M.C. needed

simulated events

Em

pm

Iteration-process

pm = 490 MeV/ccontrolling/adjusting

the spectral fct.via histograms

Fit to exp. spectral function

M.C.data

Monte Carlo simulation of Hall C:

tracks all particles from the reaction vertex to last scintillator in the spectrometer and back

• diff. reactions: (e,e’), (e,e’p), [(e,e’p), [(e,e’), (e,e’K) also on nuclei: spectral functions, cross sections• internal + external bremsstrahlung: (e,e’p): contains interference term (Ent et al., Phys. Rev. C64 (2001) 054610)• Coulomb corrections• Rastering of the electron beam + correction • multiple scattering, energy loss• forward and backward transfer matrix, offsets reaction kinematics Focal plane variables target variables• spectrometer resolution• different collimators (also slits)• different kind of targets (solid targets, cryo targets)• normalization for a given luminosity

spectra (PAW ntuples) to compare with (corrected) data

Extraction of the spectral function:

only valid in PWIA:

exp. W.Q.: dde dp dEe dEp

= K ep S(Em,pm) TA

K : kinematical factorep : cross section for moving bound nucleon (off-shell)TA : nuclear transparency

nexp(pm) = dEm S(Em, pm)• momentum distribution:

• strength = „spectroscopic factor“ in the correlated region

ZC = 4 dpm pm2 dEm S(Em,pm)

>kF

• q || k (parallel)• high q• different nuclei (C, Al, Fe, Au)

distortion of the spectral function

corrections small (C. Barbieri)

perpendicular kinematics: large correction

• FSI (rescattering)

• contribution of the higher-resonance

non-PWIA contribution:

onset of the resonance region clearly visible

solution: cut

e

e

k

N

N

p

p

1) FSI: (e,ep) + (p,pN)

rekonstructed Em,pm E, k

nucleus

reducing FSI due to choice of kinematics:

1) Calculation of rescattering process in a microscopic picture

(C. Barbieri)

Considering 2-step process:(e,ep) + (p ,pN)1 1 f 2

e

r1r2

p

1

p1

pf

N2

N2

e

V

p(r1) K cc1 S(k,E) (r1 r2) N(r2) (r2 )

d6resc

dpf dk= dr1

Vdr2

VdT1

propagationprobability of p

in medium(e,ep)

1 (p ,pN)1 f 2

Sresc(Em,pm) = d6resc

dpf dkcc1Rescattered strength:

Corrected exp. spectral function: for each (Em,Pm) bin

pN

S(Em,Pm) = Sexp(Em,Pm) - Sresc(Em,Pm) ~

1/E2

|r1 - r2|2

Resonances: mainly transverse response, qknon-parallel kinematics in the acceptance of the detector setup

contribution for large Em m

e

ek

p

2) Pion electroproduction

• Simulation with MAID• Calculation taking the response functions of MAIDreactions:e + n = e’ + p’ +

e + p = e’ + p’ +

MAID: unitary isobar modelresonant + non-resonant Terme

Maid2000: 8 ResonanzenMaid2003: 13 with W up to 2 GeV

fit to available data+ input from theoy

Calculation:C. Barbieri

ck5k4k3_e01trec5n_cc1on_nice.agr

Modern Many-Body theories:approaches to avoid divergences• Correlated Basis Function (CBF) O. Benhar, A. Fabrocini, S. Fantoni, Nucl. Phys. A505, 267 (1989)• Greens function (2. Ord.) H. Müther, G. Knehr, A. Polls, Phys. Rev. C52, 2955 (1995) • Self consistent Greens function (T = 2 MeV) T. Frick, phD thesis, Uni Tübingen, 2004 T. Frick, H. Müther, Phys. Rev. C68 (2003) 034310 T. Frick et al., Phys. Rev. C 70, 024309 (2004)

Theoretical treatment of SRC:main problem:Divergence of realistic NN-Potentials at small distances usual Hartree-Fock approach:unbound states use of effective potentials, usually fitted to data in IPSM region contains no SRC!

O.Benhar et. al, Nucl.Phys.A579,493,1994O. Benhar, A. Fabrocini, S. Fantoni, Nucl. Phys. A505, 267 (1989)

Correlated Basis Function Theorie (CBF)

correlations already contained in the ground state (0. Ord.)

V = ( fp(rij) Opij) p.w.

p=1..8i>j

Minimizing of <E>g.s via FHNC, Var. M.C.

Ansatz for nuclear matter

+ corrections of 2. Ord.

spectral function S(E,k)

occupancy

variationalmethod

CBF

k (fm-1)

0.9

CBF withouttensor correlations

Local density approximation (LDA)

theory does not contain the shell structure, i.e. no LRC

for finite nuclei:

dr S(E, k)[] (r)R

0

S(E,k)[] for different densities

S(E,k) = S1p(E,k) + Scorr(E,k)

Shell structureof nucleus

k< kF

E <EF

SRC + Tensorin basis states included

dominant for k> kF

Green’s function-approach (2. Ord.)H. Müther, A. Polls, W.H. Dickhoff: Phys.Rev.C 51, 3040 (1995)Kh. Gad, H. Müther: Phys. Rev. C66, 044301 (2002)

N-N potential G-Matrix (nuclear matter)

Dyson Eq.: g = gHF + gHF g g: 1-particle Green’s fct.

Bethe Goldstone Equ.

HF (2p1h) (2h1p)

plane wave

h1 h2 p1h1p1 p2

oscillator wave fct.

S(E,k) = Im g(E,k) /

Self energy

contains SRC + LRC for finite nuclei

ck4k3_e01trec7nd_cc1on_ovbenhmueth_nice.agr

Self consistent Greens function approach at finite temperature

T. Frick, phd thesis, Uni Tübingen, 2004T. Frick, H. Müther, Phys. Rev. C68 (2003) 034310T. Frick et al., nucl-th/0406010

for nuclear matter: Translation invariance, no shell structure (k2/2M), no LRC complictated calculation possible

Self consistent: nucleon distribution potential due to interacting nucleipropagator is dressed (complete spectral function, no approximation)ladder diagrams and self energy inserts in all orders

solution for finite temperature only: T = 2 MeV experiment: T = 0

T < Tcrit: pair instabilities due to transition to superfluid phase (Superposition of NN-pairs with opposite spin + momentum)

comparison with 12C: 1/2NM

ck4k3_e01trec7nd_cc1on_ovfrick_nice2.agr

T. Frick et al., Phys. Rev. C 70, 024309 (2004)

ck4k3_e01trec7nd_cc1on_ovfrickcomp410_nice2

LRC

• missing strength at low Em

• shift of the max. of exp. S.F. to smaller Em

Frick et al.,

Phys. Rev. C 70, 024309 (2004)

Em dependence of the spectral function:

SRC k

-k

simple picture:max. of the s.f. expected at

2 M

Em = pm2

momdistrpara_e01theofrickup_nice_cc

eep/auswert/ana_prg/output/c12_kin3/plots

nexp(pm) = dEm S(Em, pm)40MeV

(pm)

integration limits chosen such that1-particle + resonance region eliminated

in the correlated region:

Integrated strength in the covered Em-pm region:

ZC = 4 dpm pm2 dEm S(Em,pm)

230MeV/c

670

contains half of the total strength

region used for integral

76240

80 350

3.5

7.5

800

0

1.5

6.5 1.3

Em(MeV)

pm

(MeV

/c)

2

1.7

300

Strength distribution in % (from CBF)

exp. CBF theory G.F. 2.order selfconsistent G.F.

0.61 0.64 10 % 0.46 0.61

contribution from FSI: -4 %

• 10% of the protons in 12C at high pm, Em found• first time directly measured

“correlated strength” in the chosen Em-pm region:

Rohe et al.,Phys. Rev. Lett. 93, 182501 (2004)

experimental area

in total(correlated part)

22 % 12% 20%

12C

comparing to theory leads to conclusion that 20 % of the protons are beyond the IPSM region

Comparison of the results C to Al, Fe, Au• shape of the s.f.: C, Al, Fe: quite similar

Au : contribution of (broad) resonances to the correlated region• max. of the s.f.: similar to C Au : shift to larger Em (particulary at large pm) (consequence of the resonance contribution)• correlated strength: (normalized to Z = 1) C, Al, Fe Au : increasing

nuc_ratiocomp_up2increase of the strength from

12C to 197Au: 1.7

nuccomp_para

im non-relativistic limit: only transversal componentsi.e. mainly perpendicular kinematics

• Meson exchange currents (MEC):

contact term -in-flight

virtual resonances

N N

C. Barbieri: work in progress

Other reaction mechanism?

• contribution of FSI in Au: ~ 10 %

• Isobaric currents

• asymmetric nuclear matter:

number of neutrons > number of protons

20-30 % more correlated strengthfor p-spectral function

occ

upa

ncy

Frick et al.,PRC 71, 014313 (2005)

reason: larger contribution of the tensor force in n-p interaction

for Au: (118 : 79): = 0.2

A

ZN

Inclusive electron scattering (e,e’): xB > 1

= quasielastic scattering on the nucleons probing its momentum distribution

large xB large pm

0 0.5 1 1.5 2 2.5 3 3.5 4xB

4.0

3.0

2.5

2.0

1.5

1.0

0.5

Q2

1.0

0.8

0.6

0.4

0.2

0

pm

(G

eV

/c)

xB = Q2

2M

Bjorken variable:

momentum distribution at high pm is similar

Ratios of cross section from two nuclei should scale

at corresponding (Q2, xB) combination

Compare with simple nucleus with known momentum distribution

3He (pm > 250 MeV/c): 0.080+0.016 (2N-SRC) : 0.0018±0.0006 (3N-SRC)

xB = 1: (q).e. scattering on nucleonxB = 2: 2-N system 2-N correlationenxB = 3: 3-N system 3-N correlationen :xB = A: elastic scattering on nucleus (A MN)

p

-p 2N - SRC

p

pp

-p2p

3N - SRC

“Star” “2- Body”

M. Sargsian et al.,PRC 71, 044614 (2005)

3 A(x,Q2)A He(x,Q2) = r(A/3He) as a function of xB

In xB > 2 region:mainly “2 - Body” configuration (M.Sargsian et al., PRC 71, 044615 (2005))

2N-SRC

3N-SRC

Single particle (%) 2N SRC (%) 3N SRC (%)

56Fe 76 ± 0.2 ± 4.7 23.0 ± 0.2 ± 4.7 0.79 ± 0.03 ± 0.25

12C 80 ± 02 ± 4.1 19.3 ± 0.2 ± 4.1 0.55 ± 0.03 ± 0.18

4He 86 ± 0.2 ± 3.3 15.4 ± 0.2 ± 3.3 0.42 ± 0.02 ± 0.14

3He 92 ± 1.6 8.0 ± 1.6 0.18 ± 0.06

2H 96 ± 0.7 4.0 ± 0.7 -----

Fractions

Nucleus

K.Egiyan et al., PRC68, 014313 (2003)

taking the calculated 2N and 3N SRC strength in 3He,gives absolute numbers,= occupancies

Note: (2+3 SRC) Fe

(2+3 SRC) C= 1.2

Scaling onset: xB = 1.5, Q2>1.5 GeV2

pm 250 MeV/c

(NM/D)exp = 5.5 0.8

Correlated Glauber Theorie

a 2(N

M) large sensitivity to

2-N correlations

xB

Benhar, Fabrocini, Fantoni, Sick,PLB 343 (1995) 47

only half of the correlated strength at k large

Information from inclusive electron scattering:at D, heavy nuclei nuclear matter (NM)

Compare d, NM momentum distribution:

[197 MeV/c]

CBF theory

(NM/D)CBF = 5.0

Pandharipande,Sick,deWitts Huberts, RMP 69 (1997) 981

(e,e’p)-experiment: access to the interior of the nucleus

nuclear radius

pm=50MeV/c

pm=160MeV/c

2p-state in 90Zr

den Herder et al.,

Phys. Lett. B 184, 11 (1987)

large pm small r

radial sensitivity

r (fm)

measured

“IPSM”-part

correlated part

charge density distribution in 12C

Müther, Sick PRC 70, 041301(R) (2004)

exp.

theory

MAMI

threshold for 2-nucleonemission

K.I. Blomqvist et al., Phys. Lett. B 344, 85 (1995).

Settings 1-5: parallel kinematics (pm < 400 MeV/c)Settings 6,7: perpendicular kinematics (pm > 400 MeV/c)

N. Liyanage et al., PRL 86, 5670 (2001)

calculation: Ryckebuschdescribes only half of the yield at high Em

16O(e,e‘p) at Q2 = 0.8 (GeV/c)2 in Hall A

parallel kinematicsalso LT separation,even at moderate pm~150MeV/cdata exceed the DWIA calculationof Kelly

Other methods to look for SRC:

1-particle region

not only (e,e’...): only transverse response Watts et al., PRC 62 (2000) 014616 p strong interaction, less radiation corrections Tang et al., PRL 90 (2003) 042301

SRC << 1-particle contribution:better selection needed: • detection of the correlated pair:(.,.pp),(.,.np)suppression of , MEC, FSI in superparallel kinematics:

• choice of one particular shell: (L=0), requires good energy resolution

k-k

q

LT-separation?• sensitive to non-PWIA contributions: L klein, T groß• might help to get info about reaction mechansm

• smaller cross section• additional detector

onlycentral SRC dominated by

tensor correlation

Groep et al.,PRC 63 (2001) 14005

3He(e,e’pp)n

MEC

Faddeev calculationBochum-Krakow group

12C(e,e’pp), Em < 70 MeV 0.6fm HC

FHNCVMC

G-Matrix

Blomqvist et al.,PLB 421 (1998) 71

p3 =

superparallel

MAMI MAMI

NIKHEF

PWIAFSIfull

parallel kinematics

Experiment E97-111 in Hall A (Jlab)4He(e,e’p) : in parallel and perpendicular kinematics 0+ ground state: only central SRCTheoretical prediction: Experimental result:

0 2 4 6 8k(fm-1)

n(k

) (f

m3)

S. Tadokoro et al., Prog. Theor, Phys. 79 (1987)732

measurement

Location of the minimums sensitive to SRC

calculation: J.-M. Laget,Analysis: B. Reitz

• no minimum ! FSI• MEC+IC contribution small• good agreement with full theory

Photoabsorption 12C(pn): wide angular range

Watts et al.,PRC 62, 14616 (2003)

calculation:Orlandini,Sarra

compared to momentum distribution using harmonic oscillator wave functions

Tang et al.,PRL 90 (2003) 042301

12C(p,p’p+n)

n

p

pn

pup

BNL

c.m. momentum of thep-n pair is zero

7Li(e,e'p) Spectroscopic Strength

7Li(e,e'p) Spectroscopic Strength

spectroscopic strength0+ 2+ 0+ + 2+

---------------------------------------------Exp 0.42(4) 0.16(2) 0.58(5)---------------------------------------------VMC 0.41 0.19 0.60MFT 0.59 0.40 0.99---------------------------------------------

0+

2+

3/2 -

6Hep3/2

p1/2 p3/2

f5/2 f7/2

7Li

everything understood?

W.H. Dickhoff, C. Barbieri,Prog.Part.Nucl.Phys. 52(2004) 377

Picture of SRC and LRC

Summary spectroscopic factors

q 0.45 GeV/c (NIKHEF) q 1.0 GeV/c (JLab)

Difference of 5 – 10 % (relativistic description?)or problem with DWIA ?

H. Gao et al., PRL 84, 3265 (2000)

q dependence of spectroscopic factors for 16O(e,e’p) ?

1p1/2 Z=0.71,0.72

1p3/2 Z=0.71,0.67

Z~62% Z~70%