Impulse Approximation limitations to the (e,e’p) reaction on 208PbIdentifying correlations and

relativistic effects in the nuclear medium

E06-007, March 3 – March 25, 2007

K. Aniol, A. Saha, J. M. Udías, G. Urciuoli

Spokespersons

Students: Juan Carlos Cornejo, Joaquin Lopez, + ?

Outline

1) What will be done?

2) Physics Motivation

3) Experimental Preparations

4) Invitation for students and Post Docs

5) Call for shift workers and run coordinators

What will be done? 208Pb and 209Bi(Kin04)

Kinematicsq[GeV/c]

Eo

[GeV]ω[GeV]

Ee

[GeV]

θe

[degrees]

Pp

[GeV]

θp

[degrees]

pm

[GeV/c]

Kin01 1.000 2.649 0.433 2.216 21.44 0.989 54.101 0.000

Kin02 1.000 2.649 0.433 2.216 21.44 0.989 59.830 0.100

Kin03 1.000 2.649 0.433 2.216 21.44 0.989 48.371 0.100

Kin04 1.000 2.649 0.433 2.216 21.44 0.989 65.625 0.200

Kin05 1.000 2.649 0.433 2.216 21.44 0.989 42.576 0.200

Kin06 1.000 2.649 0.433 2.216 21.44 0.989 71.440 0.300

Kin07 1.000 2.649 0.433 2.216 21.44 0.989 36.762 0.300

Kin08 1.000 2.649 0.433 2.216 21.44 0.989 77.299 0.400

Kin09 1.000 2.649 0.433 2.216 21.44 0.989 30.902 0.400

Kin10 1.000 2.649 0.433 2.216 21.44 0.988 83.222 0.500

Kin11 1.000 2.649 0.433 2.216 21.44 0.988 24.980 0.500

Kin12 1.400 2.649 0.745 1.904 30.60 1.388 43.816 0.000

Kin13 1.750 2.649 1.045 1.604 39.81 1.738 35.936 0.000

What will be done? 208Pb and 209Bi(Kin04)

Investigate states near the Fermi surface

Based on s-FACTORs, the 4 lowest levels are predominantly single-proton hole states 3s½, 2d3/2, 1h11/2, and 2d5/2, and the 3474 level is predominantly the 1g7/2 single-proton hole state.

207Tl

Ex J config

0. 1/2+ 3s1/2

0.351 3/2+ 2d3/2

1.348 11/2- 1h11/2

1.683 5/2+ 2d5/2

3.474 7/2+ 1g7/2

209Bi

Ex J config

0 9/2- 1h9/2

Physics Motivation

How well do we understand nuclear structure ?

The underlying physical picture Dense system of fermions whose motions to first order can be treated as independent particles moving in a mean field Electromagnetic interactions Best probes for investigating the validity of the independent particle picture because they are sensitive to a large fraction of the nuclear volume

Realistic microscopic calculations of the spectroscopic factors are not possible for medium-heavy (A>20) nuclei. Approximations are made that build on top of the shell model (mean field or independent particle picture) that is still the basic building block upon which most calculations of complex nuclei rely

Deviations from independent particle motion for orbits near the Fermi surface are attributed to effects beyond mean field (correlations) which reveal their presence in two ways:

(i) Changes in the occupation and spectroscopic factors with respect to mean-field predictions(kin01-kin07, 0 to 300 MeV/c in pmiss )

(ii) Changes in the momentum distribution of particles, especially at high momentum and binding energies (kin08-kin11, 400 to 500 MeV/c in pmiss)

V.R. Pandharipande, I. Sick and P.K.A. deWitt Huberts, Independentparticle motion and correlations in fermions systems, Reviews of Modern Physics 69 (981) 1997

Physics Motivation

•The (e,e’p) reaction at quasielastic kinematics and in exclusive conditions, for the outermost shells, becomes one of the most powerful and cleanest test of the mean field and the correlations needed to supplement it

•208Pb is the most suitable candidate to employ the mean field prediction, and thus it has been measured in the past in order to measure spectroscopic factors

•The reaction has been measured in the past, mainly in parallel kinematics and for moderate values of Q2. Spectroscopic factors have been measured

Physics Motivation

Still open issues: (i) possible dependence on Q2 of the spectroscopic factors?

12C(e,e’p) data over wide range of Q2.There appears to be a Q2 dependence to the spectroscopic factors observed in this reaction[2]. This interpretation has been disputed and the Q2 dependence attributed to analysis methods of SRC[3]208Pb(e,e'p) has been studied in the past at low momentum transfers and spectroscopic factors in the range of 0.6 to 0.7 have been reliably extracted from parallel kinematics [4,5,6] at low Q2

A measurement at several high values of Q2 will directly address the question of momentum transfer dependence of the spectroscopic factors

data [4], theory [5].

Kin01, kin12, kin13

•Shell model (mean field) calculations: the shape of the cross-section is well described, but the measured spectroscopic factors are below the mean field prediction. How large/small must be the spectrocopic factors?

About 30% depletion is observed for states near the Fermi level. This cannot be explained only with short-range correlations

Shape at moderate pm and parallel kinematics is well understood

Long range correlations are predicted to be visible at large pm

Open issues: (ii) Long range correlations and cross-sections at high pm (> 300 MeV/c)

If long range correlations are the reason for the small spectroscopic factors, then they should produce a large effect at high missing momentum. An experiment was performed at NIKHEF-K to measure the large momentum

region, but the kinematics was far from XB=1. Additional strength was indeed

found, but this can be explained either via long-range correlations [Bobeldijk,6] or by relativistic effects in the mean field model [Udias,7].

I. Bobeldijk et al., PRL 73 (2684)1994

xB = 0.18

E. Quint, thesis, 1988, NIKHEF

J. M. Udias et al. PRC 48(2731) 1994

J.M. Udias et al. PRC 51(3246) 1996

Excess strength at high pmiss

open issues: (iii) Are there any other signatures of relativistic dynamics in nuclei besides the spin

orbit force?It seems that TL-observables (that change sign when the cross-section is measured when the knocked out proton is at both sides of the transferred momentum) are sensitive to dynamical relativistic effects

A measurement at both sides

of q will directly measure ATL

and address the possible dynamical relativisitc effects. Yet such a measurement for 208Pb has never been attempted

kin01-kin07, for 0<pmiss<300 MeV/c

nucleon wave functions dominated by the mean field

Pb + C spectra,

Kin01,

pmiss = 0 MeV/c

Ee = 2.649 GeV

GEANT simulation

Experimental Preparations

Emiss for Pb + C,

Pmiss = 200 MeV/c

kin04

GEANT simulation

Experimental Preparations

Emiss, Pb+C

Pmiss = -400 MeV/c

kin09

GEANT simulation

Experimental Preparations

Determine spectroscopic factors from the low pm kinematics (kin01 to kin07). Expected data were extracted with the peak fitting procedure after averaging the theory over the acceptance with a detailed GEANT simulation

Experimental Preparations

ATL for all the shells added up, compared with the acceptance averaged simulations

Non relativistic dynamics

Relativistic dynamics

Experimental Preparations

208Pb(e,e’p)207Tl(all 5 shells)

Long range correlations are needed to explain the 30% depletion. If correlations are excluded, neither Nonrel. or Rel. theory can produce large strength at high pmiss. This is in contrast to the ambiguous signature at xB << 1 of former experiment at NIKHEF-K

With correlations

Without correlations

Look at large pmiss for correlations.

xB = 1

(II) Mahaux and Sartor (SF=0,6)

(I) Ma and Wambach (SF=0,7)

We compare to theoretical predictions after acceptance averaging. We do not attempt to separate the five shells in this region nor to

compute ATL. If cross-sections are higher than the

mean field prediction, the improved statistics might eventually allow for shell separation and ATL measurement

Target Issues Cold Lead in diamond sandwichE03-011 has demonstrated that a 0.5 mm lead foil sandwiched between two 0.15 mm diamond foils at cryogenic temperatures can withstand currents up to 80 uA and calculations indicate that they can operate at 100 μ A. Thinner (0.2mm) lead foil is not a problem

Experimental Preparations

Direct cooling of target block using cryogen flow from loop2.

Target block contains 2 Pb targets and a Bi target.

Will the diamond structure survive weeks of bombardment? High thermal conductivity is due to diamond structure.

Call for shift workers, run coordinators

http://curriculum.calstatela.edu/faculty/djm/E06007.html

Requesting a 5 shift minimum or comparable contribution to be listed as an author on publications.

Cryotarget operators will be needed because cryogen will be drawn from the ESR.