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V.K.LUKYANOV, E.V.ZEMLYANAYA, K.V.LUKYANOV

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

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V.K.LUKYANOV, E.V.ZEMLYANAYA, K.V.LUKYANOV

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  1. THE K+-NUCLEUS MICROSCOPIC OPTICALPOTENTIAL AND CALCULATIONS OF THE CORRESPONDING DIFFERENTIAL ELASTIC AND TOTAL REACTION CROSSSECTIONS 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 EnergyAuthority, Cairo, Egypt

  2. On the Kaon interaction with nuclei - weaken K+N interaction p=uud n=udd - strong K-N interaction • Comparison of total cross sections at T ~ 0.2-1.0 GeV • K+N ~ 10 mb NN ~ 50 mb ~ 100 mb • The mean free path in nuclear matter • lK+N ~ 5-6 fm lNN ~ 1-1.5 fm ~ 0.8 fm • Thus a folding potential is available for K+A interaction

  3. Relativization approach for K+ + A scattering • klab > mK+= 0.494 GeV • The semi-relativistic wave equation with U=Uopt+Uc • k – relativistic momentum in c.m. system • – relativistic correction factor • - (non)relativistic reduced mass, M1= 1*m1

  4. 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

  5. The K+N scattering amplitude The K+N scattering amplitude is parameterized as follows For example, in the case of klab=0.8 GeV/c one has K

  6. 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

  7. Calculated microscopic OP (at r=1)

  8. Differential elastic cross sections K++40Ca (0.8 GeV/c) r = 367 mb r(r=1) = 245 mb

  9. Differential elastic cross sections K+ + 12C r(r=1) = 93 mb r = 125 – 129 - 129 mb rexp = 140 – 155 mb

  10. 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

  11. Phys.At.Nucl, 67 (2004) Nucl.Phys. A 717 (2003) Nucl.Phys. A 438 (1985) Effect of density distributions on cross sections r(635) = 125 + 1% mb r(715) = 129 + 1% mb r(800) = 129 + 1% mb

  12. 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

  13. 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

  14. Summary • Microscopic model of OP doesn’t 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 K+N 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 K++A scattering cross sections.

  15. Thank you!

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