Analyses of Low-Energy π--12C Elastic Scattering Data
Author(s)
Zuhair F. Shehadeh*
ABSTRACT
A new updated simple local optical potential is proposed for analyzing low-energy π--12C elastic scattering data at 80 MeV and below. This potential is composed of two real terms and an imaginary term. The nature of the real part of the potential is repulsive at smaller radii and attractive at larger ones. In fact, the height of the repulsive term is found to change linearly with the incident pion kinetic energy. On the other hand, the imaginary part of the potential is attractive, shallow and non-monotonic with a dip at about 1.6 fm. Such a nature of the potential makes it feasible to predict π--12C cross sections at other energies in the energy region considered herein. Coulomb effects are incorporated by following Stricker’s prescription. This study will serve positively in studying both pionic atoms and the role of negative pions in radiotherapy.
A new updated simple local optical potential is proposed for analyzing low-energy π--12C elastic scattering data at 80 MeV and below. This potential is composed of two real terms and an imaginary term. The nature of the real part of the potential is repulsive at smaller radii and attractive at larger ones. In fact, the height of the repulsive term is found to change linearly with the incident pion kinetic energy. On the other hand, the imaginary part of the potential is attractive, shallow and non-monotonic with a dip at about 1.6 fm. Such a nature of the potential makes it feasible to predict π--12C cross sections at other energies in the energy region considered herein. Coulomb effects are incorporated by following Stricker’s prescription. This study will serve positively in studying both pionic atoms and the role of negative pions in radiotherapy.
Cite this paper
Shehadeh, Z. (2014) Analyses of Low-Energy π--12C Elastic Scattering Data. Journal of Modern Physics, 5, 1652-1661. doi: 10.4236/jmp.2014.516165.
Shehadeh, Z. (2014) Analyses of Low-Energy π--12C Elastic Scattering Data. Journal of Modern Physics, 5, 1652-1661. doi: 10.4236/jmp.2014.516165.
References
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http://journals.tubitak.gov.tr/physics/
http://dx.doi.org/10.3906/fiz-1207-5 [19] Shehadeh, Z.F. (2014) Journal of Modern Physics, 5, 341-352.
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http://dx.doi.org/10.1103/PhysRevC.29.581 [24] Edelstein, R.M., Baker, W.F. and Rainwater, J. (1961) Physical Review, 122, 252-261.
http://dx.doi.org/10.1103/PhysRev.122.252 [25] Seth, K.K., Barlow, D., Iverson, S., Kaletka, M., Nann, H., Smith, D., Artuso, A., Burleson, G., Blanpied, G., Daw, G., Burger, W.J., Redwine, R.P., Saghai, B. and Anderson, R. (1990) Physical Review C, 41, 2800-2808.
http://dx.doi.org/10.1103/PhysRevC.41.2800 [26] Burleson, G., Blanpied, G., Gottingame, W., Daw, G., Park, B., Seth, K.K., Barlow, D., Iversen, S., Kaletka, M., Nann, H., Saha, A., Smith, D., Redwine, R.P., Burger, W., Farkhondeh, M., Saghai, B. and Anderson, R. (1994) Physical Review C, 49, 2226-2229.
http://dx.doi.org/10.1103/PhysRevC.49.2226 [27] Hanna, M. (1988) Low Energy Elastic Scattering and the Pionic Atom Anomaly. M.S. Thesis, Department of Physics, University of British Columbia, Vancouver, Canada. [28] Friedman, E. (1983) Physical Review C, 28, 1264-1271.
http://dx.doi.org/10.1103/PhysRevC.28.1264 [29] Friedman, E., Bauer, M., Breitschopf, J., Clement, H., Denz, H., Doroshkevich, E., Erhardt, A., Hofman, G.J., Kritchman, S., Meier, R., Wagner, G.J. and Yaari, G. (2005) Physical Review C, 72, 034609-(1-8). [30] Raju, M.R. (1974) Negative Pion Beams for Radiotherapy. Proceedings of the XIth International Cancer Congress, Report Number(s): LA-UR--74-1530; CONF-741034-2, Florence, Italy, 20 October 1974, 33-62.
[1] Krane, K.S. (1988) Introductory Nuclear Physics. Wiley John & Sons, New York. [2] Ericson, T. and Weise, W. (1988) Pions and Nuclei. Clarendon Press, Oxford. [3] Lee, T.-S.H. and Redwine, R.P. (2002) Annual Review of Nuclear and Particle Science, 52, 23-63.
http://dx.doi.org/10.1146/annurev.nucl.52.050102.090713 [4] Akhter, Md., Sultana, S., Sen Gupta, H. and Petersen, R. (2001) Journal of Physics G: Nuclear and Particle Physics, 27, 755-771.
http://dx.doi.org/10.1088//0954-3899/27/4/302 [5] Begum, L., Haque, S., Nahar, W., Nasmin, R.S. and Rahman, Md.A. (2003) On Pion-Nucleus Scattering, Paper-II. The Abdus Salam International Center for Theoretical Physics, IC/2003/40.
http://www.ictp.trieste.it/~pub_off [6] Satchler, G. (1992) Nuclear Physics A, 540, 533-576. [7] Shehadeh, Z.F., Sabra, M. and Malik, F.B. (2003) Condensed Matter Theories, 18, 339-346. [8] Shalaby, A.S., Hassan, M.Y.M. and El-Goary, M.M.H. (2007) Brazilian Journal of Physics, 37, 388-397.
http://www.redalyc.org/pdf/464/46437309.pdf
http://dx.doi.org/10.1590/S0103-97332007000300009 [9] Leitch, M.J., Burman, R.L., Carlini, R., Dam, S., Sandberg, V., Blecher, M., Gotow, K., Ng, R., Auble, R., Bertrand, F.E., Gross, E.E., Obenshain, F.E., Wu, J., Blanpied, G.S., Preedom, B.M., Ritchie, B.G., Bertozzi, W., Hynes, M.V., Kovash, M.A. and Redwine, R.P. (1984) Physical Review C, 29, 561-568.
http://dx.doi.org/10.1103/PhysRevC.29.561 [10] Blecher, M., Gotow, K., Jenkins, D., Milder, F., Bertrand, F.E., Cleary, T.P., Gross, E.E., Ludemann, C.A., Moinester, M.A., Buman, R.L., Hamm, M., Redwine, R.P., Yates-Williams, M., Dam, S., DardenIII, C.W., Edge, R.D., Malbrough, D.J., Marks, T. and Preedom, P.M. (1979) Physical Review C, 20, 1884-1890.
http://dx.doi.org/10.1103/PhysRevC.20.1884 [11] Shehadeh, Z.F., Alam, M.M. and Malik, F.B. (1999) Physical Review C, 59, 826-831.
http://dx.doi.org/10.1103/PhysRevC.59.826 [12] Stricker, K. (1979) A Study of the Pion-Nucleus Optical Potential. Ph.D. Thesis, Department of Physics, Michigan State University, Michigan. [13] Zemlyanaya, E.V., Lukyanov, K.V., Lukyanov, V.K. and Hanna, K.M. (2004) Calculations of Differential Elastic and Total Reaction Cross Sections of K+-Nucleus Scattering in the Framework of Microscopic Model of Optical Potential. JINR Preprint P4-2004-115, Dubna. [14] Gmitro, M., Kamalov, S. and Mach, R. (1987) Progress of Theoretical Physics, 91, 60-72.
http://ptps.oxfordjournals.org/10.1143/PTPS.91.60
http://dx.doi.org/10.1143/PTPS.91.60 [15] Johnson, R.R., Masterson, T.G., Erdman, K.L., Thomas, A.W. and Landau, R.H. (1978) Nuclear Physics A, 296, 444-460.
http://dx.doi.org/10.1016/0375-9474(78)90084-2 [16] Kerman, A.K., McManus, H. and Thaler, R.M. (1959) Annals of Physics, 8, 551-635.
http://dx.doi.org/10.1016/0003-4916(59)90076-4 [17] Shehadeh, Z.F. (2009) International Journal of Modern Physics E, 18, 1615-1627.
http://dx.doi.org/10.1142/S0218301309012823 [18] Shehadeh, Z.F. (2013) Turkish Journal of Physics, 37, 190-197.
http://journals.tubitak.gov.tr/physics/
http://dx.doi.org/10.3906/fiz-1207-5 [19] Shehadeh, Z.F. (2014) Journal of Modern Physics, 5, 341-352.
http://dx.doi.org/10.4236/jmp.2014.56044 [20] Shehadeh, Z.F. (2013) Journal of the Association of Arab Universities for Basic and Applied Sciences, 14, 32-37.
http://dx.doi.org/10.1016/j.jaubas.2013.03.003 [21] Stricker, K., McManus, H. and Carr, J.A. (1979) Physical Review C, 19, 929-947.
http://dx.doi.org/10.1103/PhysRevC.19.929 [22] Ion, D.B., Ion, M.L.D., Ion-Mihai, R. and Angelescu, T. (2010) Romanian Journal of Physics, 55, 296-308. [23] Dumbrajs, O., FrOhlich, J., Klein, U. and Schlaile, H.G. (1984) Physical Review C, 29, 581-591.
http://dx.doi.org/10.1103/PhysRevC.29.581 [24] Edelstein, R.M., Baker, W.F. and Rainwater, J. (1961) Physical Review, 122, 252-261.
http://dx.doi.org/10.1103/PhysRev.122.252 [25] Seth, K.K., Barlow, D., Iverson, S., Kaletka, M., Nann, H., Smith, D., Artuso, A., Burleson, G., Blanpied, G., Daw, G., Burger, W.J., Redwine, R.P., Saghai, B. and Anderson, R. (1990) Physical Review C, 41, 2800-2808.
http://dx.doi.org/10.1103/PhysRevC.41.2800 [26] Burleson, G., Blanpied, G., Gottingame, W., Daw, G., Park, B., Seth, K.K., Barlow, D., Iversen, S., Kaletka, M., Nann, H., Saha, A., Smith, D., Redwine, R.P., Burger, W., Farkhondeh, M., Saghai, B. and Anderson, R. (1994) Physical Review C, 49, 2226-2229.
http://dx.doi.org/10.1103/PhysRevC.49.2226 [27] Hanna, M. (1988) Low Energy Elastic Scattering and the Pionic Atom Anomaly. M.S. Thesis, Department of Physics, University of British Columbia, Vancouver, Canada. [28] Friedman, E. (1983) Physical Review C, 28, 1264-1271.
http://dx.doi.org/10.1103/PhysRevC.28.1264 [29] Friedman, E., Bauer, M., Breitschopf, J., Clement, H., Denz, H., Doroshkevich, E., Erhardt, A., Hofman, G.J., Kritchman, S., Meier, R., Wagner, G.J. and Yaari, G. (2005) Physical Review C, 72, 034609-(1-8). [30] Raju, M.R. (1974) Negative Pion Beams for Radiotherapy. Proceedings of the XIth International Cancer Congress, Report Number(s): LA-UR--74-1530; CONF-741034-2, Florence, Italy, 20 October 1974, 33-62.