Eikonal Approximation for K+–Nucleus Elastic Scattering

Year 2022, Volume: 8 Issue: 2, 40 - 48, 31.07.2022

Nagat Elmahdy Haytham Gamal

https://doi.org/10.22399/ijcesen.1079685

Abstract

The elastic scattering of kaons from different targets 6Li, 12C, and 40Ca at energies 635, 715, and 800 MeV have been studied. The equivalent local potential form of Kisslinger optical potential with the eikonal approximation using Wallace expansion up to the 2nd order have been used. The potential depends on the density of the target nuclei, and the scattering amplitude parameters. Satisfactory fits to the elastic scattering experimental data are obtained.

Keywords

Equivalent local potential, Eikonal approximation, Scattering amplitudes parameters

Supporting Institution

Modern Academy

Project Number

6

Thanks

thanks

References

• [1] D. Marlow, P. D. Barnes, N. J. Colella, S. A. Dytman, R. A. Eisenstein, R. Grace, F. Takeutchi, W. R. Wharton, S. Bart, D. Hancock, R. Hackenberg, E. Hungerford, W. Mayes, L. Pinsky, T. Williams, R. Chrien, H. Palevsky, and R. Sutter, “Kaon scattering from C and Ca at 800 MeV/c”. Phys. Rev. C 25, (1982) 2619.
• [2] R.E.Chrien, R.Sawafta, R.J.Peterson, R.A.Michael, and E.V.Hungerford, “Elastic and Inelastic Scattering of K+ from 6Li and 12C”. Nucl. Phys. A 625 (1997) 251.
• [3] L. S. Kisslinger. “Scattering of Mesons by Light Nuclei” Phys. Rev. 98 (1955) 761.
• [4] M. B. Johnson and G. R. Satchler, “ Characteristics of local pion-nucleus potentials that are equivalent to Kisslinger-type potentials” Ann. Phys., NY 248 (1996) 134.
• [5] V. K. Lukyanov, E. V. Zemlyanaya, K. V. Lukyanov, D. N. Kadrev, A. N. Antonov, M. K. Gaidarov, and S. E. Massen, “Calculations of 8He+p Elastic Cross Sections Using Microscopic Optical Potential” Arxiv: 0908.1008 V1 [nucl. th] (2009).
• [6] Moon Hoe Cha, and Yong Joo Kim, “Higher-order corrections to the eikonal phase shifts for heavy-ion elastic collision” Phys. Rev. C 51(1995) 212-216.
• [7] Moon Hoe Cha, and Yong Joo Kim “First-order eikonal approximation for the elastic scattering of 800 MeV/c pions from 12C and 40Ca nuclei” Phys. Rev. C 54 (1996) 429.
• [8] M. B. Johnson “Analytical theory of pion single and double charge exchange in resonance region. I. Geometrical limit” Phys. Rev. C 22 (1980) 192.
• [9] M. B. Johnson and E. R. Siciliano “Isospin dependence of second order pion nucleus optical potential” Phys. Rev. C 27(1983) 730-750.
• [10] A. A. Ebrahim and S. A. E. Khallaf “Elastic and inelastic scattering of K+ from nuclei” Phys. Rev. C 66 (2002) 044614.
• [11] R. Weiss, J. Aclander, J. Alster, M. Barakat, S. Bart, R. E. Chrien, R.A. Krauss, K. Johnston, L Mardor, Y. Mardor, S. May Tal-beck, E. Piasetzky, P. H. Pile, R. Sawafta, H. Seyfarth, R. L. Stearns, R.J. Sutter and A.I. Yavin “Measurement of low energy K+ total cross sections on N=Z nuclei” Phys. Rev. C49 (1994) 2569.
• [12] R. Micheal, M. Barakat, S. Bart, R. E. Chrien, D. J. Ernest, S. Hama, K. H. Hicks, Wendy Hinton, E. V. Hungerford, M. F. Jiang, T. Kishimoto, C. M. Kormanyos, L. J. Kurth, L. Lee, B. Mayes, R. J. Peterson, L. Pinsky, R. Sawafta, R. Sutter, L. Tang, and J. E. Wise “K+ elastic scattering from C and Li-6 at 715-MeV/c” Phys. Lett. B 382 (1996) 29-34.
• [13] R. J. Glauber, High-Energy Collision Theory, edited by W. E. Britten Interscience, New York 1959.
• [14] S. J. Wallace “Eikonal expansion” Ann. of Phys. 78 (1973) 190-257.
• [15] Alex Kover, and Urs Achim Weidemann “Eikonal evolution and gluon radiation” Phys. Rev. D64 (2001) 114002.
• [16] M. Krell and T. E. O. Ericson “Energy levels and wave functions of pionic atoms” Nucl. Phys. B 11 (1969) 521-550.
• [17] Reza Safari “A new pion-nucleus optical potential valid for ∆-resonance region” International Journal of Pure and Applied Mathematics. Vol 29, No. 2 (2006) 141-151.
• [18] S.A.E. Khallaf and A.A. Ebrahim “Analysis of π±-nucleus elastic scattering using a local potential” Phys. Rev. C62 (2000) 024603.
• [19] Ricardo Ignacio AIvaIez del Castillo, Ph.D. Thesis, McGill University Montreal, Canada, 1991.
• [20] R. Alvarez del Castillo and N. B. de Takacsy “Analysis of low energy π+ scattering to second O+ states” Phys. Rev. C 43 (1991) 1389.
• [21] B. M. Preedom, S. H. Dam, C. W. Darden, III, R. D. Edge, D. J. Malbrough, T. Marks, R. L. Burman, M. Hamm, M. A. Moinester, R. P. Redwine, M. A. Yates, F. E. Bertrand, T. P. Cleary, E. E. Gross, N. W. Hill, C. A. Ludemann, M. Blecher, K. Gotow, D. Jenkins, and F. Milder “Positive pion-nucleus elastic scattering at 30 and 50 MeV” Phys. Rev. C 23 (1981) 1134.
• [22] K. G. Boyer, W. J. Braithwaite, W. B. Cottingame, S. J. Greene, L. E. Smith, C. Fred Moore, C. L. Morris, H. A. Thiessen, G. S. Blanpied, G. R. Burleson, J. F. Davis, J. S. McCarthy, R. C. Minehart, and C. A. Goulding “Pion elastic and inelastic scattering from 40,42,44,48Ca and 54Fe” Phys. Rev. C 29 (1984)182.
• [23] M. Y. M. Hassan, Z. Metawei “First and second order corrections to the eikonal phase shifts for the interactions of α-particle with 12c and ca isotopes” Acta Physica Slovaca. Vol. 52 (2002) 23-34.
• [24] A.A. Ebrahim and R.J. Peterson “Parametrization of pion-nucleon phase shifts and effects upon pion-nucleus scattering calculations” Phys. Rev. C 54 (1996) 2499.
• [25] A. A. Ebrahim, Ph.D. Thesis, Assiut University, 1997.
• [26] R. E. Chrien, R. Sawafta,, R. J. Peterson, R. A. Michael, and E. V. Hungerford “Elastic and Inelastic Scattering of K+ from 6Li and 12C” Nucl. Phys. A 625 (1997) 251.
• [27] D. Marlow, P. D. Barnes, N. J. Colella, S. A. Dytman, R. A. Eisenstein, R. Grace, F. Takeutchi, W. R. Wharton, S. Bart, D. Hancock, R. Hackenberg, E. Hungerford, W. Mayes, L. Pinsky, T. Williams, R. Chrein, H. Palevsky, and R. Sutter “Kaon Scattering from C and Ca at 800 MeV/c” Phys. Rev. C 25 (1982) 2619.