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.LUKYANOVJoint Institute for Nuclear Research, Dubna 141980, Russia;

K.M.HANNAMath. and Theor. Phys. Dep., NRC, Atomic Energy Authority, Cairo, Egypt

On the Kaon interaction with nuclei

suK

suK

p=uud n=udd- weaken K+N interaction

- 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

1

~l

• 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

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 FK(0)/Im FK(0) – with FK , 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 klab=0.8 GeV/c one has

K

Input values for K+ + 12C,40Ca

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++40Ca (0.8 GeV/c)

r = 367 mb

r(r=1) = 245 mb

Differential elastic cross sections K+ + 12C

r(r=1) = 93 mb

r = 125 – 129 - 129 mb

rexp = 140 – 155 mb

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

Effect of density distributions on cross sections

Phys.At.Nucl, 67 (2004)

Nucl.Phys. A 717 (2003)

Nucl.Phys. A 438 (1985)

r(635) = 125 + 1% mb

r(715) = 129 + 1% mb

r(800) = 129 + 1% 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 rexp

= 155 mb

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

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.

Thank you!