Title: THE K NUCLEUS MICROSCOPIC OPTICAL POTENTIAL AND CALCULATIONS OF THE CORRESPONDING DIFFERENTIAL ELAST
1THE 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
2On 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
3Relativization 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
4Microscopic 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
5The KN scattering amplitude
- The KN scattering amplitude is parameterized as
follows - For example, in the case of klab0.8 GeV/c one
has
K
6Input 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
7Calculated microscopic OP (at ?r1)
8Differential elastic cross sections K40Ca (0.8
GeV/c)
?r 367 mb ?r(?r1) 245 mb
9Differential elastic cross sections K 12C
?r(?r1) 93 mb ?r 125 129 - 129 mb ?rexp
140 155 mb
10Role of the U2/2E corrections in the full OP
?r(635) 125 128 mb ?r(715) 129 132
mb ?r(800) 129 131 mb
11Effect of density distributions on cross sections
?r(635) 125 1 mb ?r(715) 129 1
mb ?r(800) 129 1 mb
12The 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
13Effect 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
14Summary
- 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.
15Thank you!