ELECTRON INDUCED REACTIONS IN HEAVY, MEDIUM AND LIGHT NUCLEI after 100 years of relativity

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ELECTRON INDUCED REACTIONS IN HEAVY, MEDIUM AND
LIGHT NUCLEI (after 100 years of relativity)

• Overview of the model
• Exclusive scattering (unpolarized)
• Exclusive scattering (polarizations)
• Factorization
• Conclusions

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OVERVIEW OF THE MODEL (ingredients)
Even simpler Impulse Approximation
Simple One photon exchange
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Kinematical overview
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Unpolarized and in plane
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One-photon exchange approximation yields, for the
most general case
Rs proportional to Wmn
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Complex nuclei!!!. If we can not treat them
exactly, lets be simple!!!!. Take the simplest
ingredients Mean Field

• Solve a Dirac-like equation
• Bound state Phenomenological s-w lagrangeans
• (Serot and Walecka model) at mean field level
• Final State Phenomenological S-V potentials (B.
  Clark, E.D. Cooper et al.)
• Current operator free prescription, cc1, cc2
  or whatever
• Relativistic, FSI and Impulse App. RDWIA

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Wave functions and free currents in 4x4 space
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Reasonably good agreement with data in parallel
kinematics
Only RL and RT contribute in this kinematics
Relativistic analyses provide larger scale
factors, due to Darwin term (Udias et al., PRC
51 (1995) 3246) 41 E. Quint et al. (1988). 42
I. Bobeldijk et al. PRL 73 (1994) 2684.
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No parallel kinematics, in plane, constant q-w,
unpol Introducing TL
Data at 0.3 (GeV/c)2 from Chinitz et al. PRL
67 (1991) 568 (b)
Data at 0.2 (GeV/c)2 from Spaltro et al. PRC 48
(1993) 2385 (c)
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Introducing TL (II)
This kinematics allows to measure
RTL Nonrelativistic theoretical predictions (red
dashed curves) were in trouble with data.
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Other responses separated and no surprises nor
special sensitivity to relativistic (dynamical)
effects
Data at 0.2 (GeV/c)2 from Spaltro et al. PRC 48
(1993) 2385 (c)
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16O(e,ep)15N experiment at Q20.8 (GeV/c)2, J.
Gao et al. PRL 84 (2000) 3265, see also K. Fissum
et al.PRC (2004)
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Q2-dependence of the spect. factor?
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Get rid of scale factor ambiguity use ATL
Quite insensitive to the ingredients of the
model, and also to pionic MEC (E. Amaro et al.
(2003), but watch out for isobar current)
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High momentum strength?. Data from NIKHEFK,
I.Bobeldijk et al. PRL73 (1994) 2684. Theory from
PRC53 (1996) R1488
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What are we looking forward to?

• Many more high quality data points for
• 16O(e,ep)15N at Q2 of 0.8 GeV/c2
• (exp. E00102, already performed), measured
• unpolarized cross-sections and ATL
• A measurement on 208Pb(e,ep)207Tl under the
• same conditions of the oxygen experiment (x1).
• A proposal is around....

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A current topic (mostly in light nuclei)
factorization
To get factorization we need, first, to go from
To
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Factorization?. Recall

• Requires same effective operator as for free
  nucleons
• Requires additional approximations to the
  relativistic impulse approximation, is an special
  case EMA (J. Vignote et al 2004), diagonal
  approximation (Frullany and Mougey 1985),
  Glauber central (C. Cioffi et al. 2004)
• In any case one has to assume that the sum on
  angular momentum components is the same than for
  free spinors. This means neglecting LS coupling
  (but read next...)
• Even with all these prerequisites, there are
  observables that do not FACTORIZE AT ALL, EVER,
  for instance, RTL, Py.

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From the EMA (bare) hadronic tensor
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It can be written in a compact way
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No every observable factorizes though, even in
the best case
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Small effect in cross-section at moderate pm
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But large effects on ATL
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Small effect for light nuclei. At least in
parallel kinematics at moderate pm
Data from Mainz A1, Florizone et al.
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But failure of factorization will clearly be seen
in ATL at Q2 larger than, say, 0.5 (GeV/c)2
Data M.M. Ravchev, PRL 94 (2005) 192302
Theory relativized wave function from Fadeev
with AV8 interaction. Optical potential from
folding model fitted to 4He(p,p) data
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Induced polarizations a probe of FSI
Left Py in 12C at Q2 of 0.5 (GeV/c)2 measured at
BATES, Woo et al, PRL 80 (1998) 456. Up, Py from
4He at Q2 of 0.8 (GeV/c)2 measured at JLAB , S.
Strauch et al. PRL 91 (2003) 052301
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Recoil transferred polarizations a robust
observable
First data in 16O, S. Malov et al., PRC62
(2000) 057302 Statistics too poor to constrain
the ingre- dients of the models A proposal to
acquire more statistics is still deferred
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Superratio on 4He. A controversial
interpretation?
S. Strauch et al. PRL 91 (2003) 052301, Theory
has been aceptance-averaged
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What have we learnt from exclusive measurements??

• Relativistic impulse approximation simple and
  capable of explaining many different experimental
  results, including polarization measurements
• To constrain the parameters (FSI, current
  operator, bound state wave function) of the
  (somewhat phenomenological) model (or to rule it
  out!!) we need more experiments with
• improved statistics
• larger A coverage (208Pb, 40Ca, 4He)
• x1
• many different Q2 values