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 , Russia; K.M.HANNA Math. and Theor. Phys. Dep., NRC, Atomic Energy Authority, Cairo, Egypt

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

k lab > m K+ = GeV The semi-relativistic wave equation with U=U opt +U c k – relativistic momentum in c.m. system – relativistic correction factor - (non)relativistic reduced mass, M 1 =  1 * m 1 Relativization approach for K + + A scattering

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 F K (0)/Im F K (0) – with F K, the KN amplitude  (q) – unfolded nuclear form factor  *) Phys.At.Nucl. 69 (2006) 240

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

Input values for K C, 40 Ca Relativistic momentum in c.m. system Correlation factors Ingemarsson, 1974 Faldt, Ingemarsson, Mahalanabis, 1992 Goldberger, Watson, 1964 (r1) (r2) (r3) (r4)

Calculated microscopic OP (at  r =1)

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

Differential elastic cross sections K C  r (  r =1) = 93 mb  r = 125 – mb  r exp = 140 – 155 mb

Role of the U 2 /2E corrections in the full OP  r (635) = mb  r (715) = mb  r (800) = mb

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

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  r exp = 155 mb

Effect of (-gr d(Im U)/dr) on cross sections g = 0  r = 125 mb g = 0.07  r = 140 mb  r exp ~ 140 mb g = 0  r = 129 mb g = 0.1  r = 149 mb  r exp ~ 150 mb

Summary zMicroscopic model of OP doesn’t use free parameters zRelativistic effects are very important to get the agreement with the existing experimental data zProblem is still open on the “in-medium” effects on K + N amplitude zModel can be improved by addition the surface terms to optical potential zModel is proved to be a workable one for predictions of the K + +A scattering cross sections.

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