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A MODELING OF THE PION-NUCLEUS MICROSCOPIC OPTICAL POTENTIAL
AT ENERGIES OF 33-RESONANCE AND IN-MEDIUM EFFECT ON THE PION-
NUCLEON AMPLITUDE OF SCATTERING
V.K. Lukyanov, E.V. Zemlyanaya, K.V. Lukyanov,
E.I. Zhabitskaya, M.V. Zhabitsky
Joint Institute for Nuclear Research, Dubna, Russia
E-mail: vlukyanov@jinr.ru
Analysis is performed of differential cross sections of elastic scattering of pions on different
nuclei at energies between 130 and 230 MeV. To this end the pion-nucleus microscopic
optical potential (OP) [1] was constructed using the optical limit of a Glauber theory. Such an
OP is defined by the corresponding target nucleus density distribution function and by the
elementary N-amplitude of scattering. Then the pion-nucleus cross sections were calculated
by numerical solving the corresponding relativistic wave equation [2] with the above OPs.
The three parameters of the N scattering amplitude, total cross section, the ratio of real to
imaginary part of the forward N-amplitude, and the slope parameter, are firstly taken from
existing experimental data on scattering of pions on free nucleons. As the next step these
parameters were fitted to the data on the respective pion-nucleus cross sections [3],[4]. Thus,
comparing the sets of “free” parameters to those obtained from pion-nuclear scattering data,
one can estimate the “in-medium” effect on a pion surrounded by nuclear nucleons. The
special procedure of the freely variation of parameters [5] was developed and applied to get
the fast and effective 2 minimization process. A difference between the best fit values of the
in-medium and free parameters of the N scattering amplitude is discussed. Conclusions on
the mechanism of scattering at the 33-resonance energies are made.
1. V.K. Lukyanov, E.V. Zemlyanaya, K.V. Lukyanov // JINR Preprint P4-2004-115, Dubna,
2004; Phys. At. Nucl., 2006. V.69. No.2. P.240.
2. V.K. Lukyanov, E.V. Zemlyanaya, K.V. Lukyanov, and K.M. Hanna // Phys. At.
Nucl., 2010. V.73. No.8. P.1443.
3. B.M. Preedom et.al. // Nuc.Phys. A, 1979. V.326. P.385-400.
4. P.Gretillat et.al. // Nuc. Phys. A, 1981. V.364. P.270-284.
5. E.I. Zhabitskaya, M.V. Zhabitsky // Springer Lecture Notes in Computer Science, 2012.
V.7125. P.328-333.
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