THE K NUCLEUS MICROSCOPIC OPTICAL POTENTIAL AND CALCULATIONS OF THE CORRESPONDING DIFFERENTIAL ELAST

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THE K-NUCLEUS MICROSCOPIC OPTICAL POTENTIAL AND
CALCULATIONS OF THE CORRESPONDING DIFFERENTIAL
ELASTIC AND TOTAL REACTION CROSS SECTIONS

• V.K.LUKYANOV, E.V.ZEMLYANAYA, K.V.LUKYANOV
• Joint Institute for Nuclear Research, Dubna
  141980, Russia
• K.M.HANNA
• Math. and Theor. Phys. Dep., NRC, Atomic Energy
  Authority, Cairo, Egypt

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On the Kaon interaction with nuclei
- weaken KN interaction
puud nudd
- strong K-N interaction

• Comparison of total cross sections at T
  0.2-1.0 GeV
• ?KN 10 mb ?NN 50 mb
  100 mb
• The mean free path in nuclear matter
• lKN 5-6 fm lNN 1-1.5 fm
  0.8 fm
• Thus a folding potential is available for KA
  interaction

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Relativization approach for K A scattering

• klab gt mK 0.494 GeV
• The semi-relativistic wave equation with
  UUoptUc
• k relativistic momentum in c.m. system
• relativistic correction factor
• -
  (non)relativistic reduced mass, M1 ?1m1

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Microscopic optical potential (OP)

• Microscopic OP obtained in ) from the optical
  limit of the Glauber theory
• ?k/E - relative velocity in the system
• the KN total cross section
• Re FK(0)/Im FK(0) with FK , the KN
  amplitude
• ?(q) unfolded nuclear form factor

?
) Phys.At.Nucl. 69 (2006) 240
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The KN scattering amplitude

• The KN scattering amplitude is parameterized as
  follows
• For example, in the case of klab0.8 GeV/c one
  has

K
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Input values for K 12C,40Ca
Relativistic momentum in c.m. system Correlation
factors
(r1)
(r2)
Ingemarsson, 1974
Faldt, Ingemarsson, Mahalanabis, 1992
(r3)
(r4)
Goldberger, Watson, 1964
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Calculated microscopic OP (at ?r1)
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Differential elastic cross sections K40Ca (0.8
GeV/c)
?r 367 mb ?r(?r1) 245 mb
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Differential elastic cross sections K 12C
?r(?r1) 93 mb ?r 125 129 - 129 mb ?rexp
140 155 mb
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Role of the U2/2E corrections in the full OP
?r(635) 125 128 mb ?r(715) 129 132
mb ?r(800) 129 131 mb
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Effect of density distributions on cross sections
?r(635) 125 1 mb ?r(715) 129 1
mb ?r(800) 129 1 mb
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The surface term (-gr dU/dr) of OP
g 0 ?r 130 mb g 0.06
?r 140 mb g 0.13 ?r 153 mb
?rexp 155 mb
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Effect of (-gr d(Im U)/dr) on cross sections
g 0 ?r 125 mb g 0.07 ?r 140 mb
?rexp 140 mb

g 0 ?r 129 mb g 0.1 ?r 149 mb
?rexp 150 mb

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Summary

• Microscopic model of OP doesnt use free
  parameters
• Relativistic effects are very important to get
  the agreement with the existing experimental data
• Problem is still open on the in-medium effects
  on KN amplitude
• Model can be improved by addition the surface
  terms to optical potential
• Model is proved to be a workable one for
  predictions of the KA scattering cross sections.

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Thank you!