Two Pion versus σ-Meson Exchange Potentials


The two pion exchange potentials are evaluated by carrying out the numerical integrations of three Feynman parameters in the corresponding Feynman diagrams. The two pion exchange potentials give rise to the attractive force which is quite similar to the effective scalar meson with its mass of ms≃4.7mπ and its strength of at T = 0 channel. However, there is a strong isospin dependence of (t1·t2)2 which should be different from the phenomenological σ-meson exchange calculations. Therefore, the medium range attraction of the T = 0 nuclear interaction should be due to the two pion exchange processes, but the T = 1 channel is still an open problem.

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Oshima, S. , Fujita, T. , Kanda, N. and Yoshimi, A. (2015) Two Pion versus σ-Meson Exchange Potentials. Journal of Modern Physics, 6, 927-936. doi: 10.4236/jmp.2015.67097.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Yukawa, H. (1935) Proceedings of the Physico-Mathematical Society of Japan, 17, 48.
[2] Wortman, W.R. (1968) Physical Review Letters, 176, 1762.
[3] Haracz, R.D. and Sharma, R.D. (1968) Physical Review Letters, 176, 2013.
[4] Partovi, M.H. and Lomon, E.L. (1970) Physical Review D, 2, 1999.
[5] Kiang, D., Preston, M.A. and Tip, P. (1968) Physical Review Letters, 170, 907.
[6] Sakurai, J.J. (1967) Advanced Quantum Mechanics. Addison-Wesley, Boston.
[7] Bohr, A. and Mottelson, B.R. (1998) Nuclear Structure. Vol. 1, World Scientific, Singapore City.
[8] Machleidt R., Holinde, K. and Elster, Ch. (1987) Physics Reports, 149, 1-89.
[9] Machleidt, R. (1989) Advances in Nuclear Physics, 19, 189.
[10] Lacombe, M., Loiseau, B., Richard, J.M., Vinh Mau, R., Cote J., Pires, P. and de Tourreil, R. (1980) Physical Review C, 21, 861.
[11] Lacombe, M., Loiseau, B., Richard, J.M., Vinh Mau, R., Cote, J., Pires, P. and de Tourreil, R. (1981) Physics Letters B, 101, 139-140.
[12] Törnqvist, N.A. and Roos, M. (1996) Physical Review Letters, 76, 1575-1578.
[13] Holinde, K. (1981) Physics Reports, 68, 121-188.
[14] Valderrama, M.P. and Ariola, E.R. (2011) Physical Review C, 83, Article ID: 044002.
[15] Particle Data Group, Roos, M., et al. (1970) Physics Letters, B33, 125.
[16] Particle Data Group, Söding, P., Bartels, J., Barbaro-Galtieri, A., Enstrom, J.E., Lasinski, T.A., Rittenberg, A., Rosenfeld, A.H., Trippe, T.G., Barash-Schmidt, N., Bricman, C., Chaloupka, V. and Roos, M. (1972) Physics Letters B, 39, 25- 145.
[17] Trippe, T.G., Barbaro-Galtieri, A., Kelly, R.L., Rittenberg, A., Rosenfeld, A.H., Yost, G.P., et al. (1976) Reviews of Modern Physics, 48, S1-S245.
[18] Gross, F. (1993) Relativistic Quantum Mechanics and Field Theory. John Wiley & Sons, New York.
[19] Bjorken, J.D. and Drell, S.D. (1964) Relativistic Quantum Mechanics. McGraw-Hill Book Company, New York.
[20] Reid, R.V. (1968) Annals of Physics, 50, 411-448.
[21] Nambu, Y. and Jona-Lasinio, G. (1961) Physical Review, 122, 345-358.
[22] Fujita, T. (2011) Symmetry and Its Breaking in Quantum Field Theory. 2nd Edition, Nova Science Publishers, New York.
[23] Fujita, T. and Kanda, N. (2013) Fundamental Problems in Quantum Field Theory. Bentham Publishers, Emirate of Sharjah.
[24] Nishijima, K. (1969) Fields and Particles. W. A. Benjamin, Inc., New York.
[25] Kanda, N., Abe, R., Fujita, T., Kato, H. and Tsuda, K. (2011) T-Matrix of Z0 Decay into Two Photons.

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