Two-pion exchange contribution to the nucleon-nucleon potential
1967; Elsevier BV; Volume: 3; Issue: 3 Linguagem: Inglês
10.1016/0550-3213(67)90080-6
ISSN1873-1562
Autores Tópico(s)Particle accelerators and beam dynamics
ResumoThe low-energy scattering of two nucleons is studied within the framework of dispersion theory, using the Mandelstam representation. Certain ϱ-functions occur in the treatment of this problem and these ϱ-functions are expressed in terms of the helicity amplitudes for the process 2π → NN for any value of the angular momentum J. These ϱ functions are evaluated using the BCL model and using the “realistic” helicity amplitudes for the S- and P-waves for the process 2π → NN, as supplied by Professor Hamilton and his co-workers. Next, going over to the potential approximation, the two-pion contribution to the nucleon-nucleon potential was evaluated. In the nucleon-nucleon potential, as calculated by Cottingham and Vinh Mau, we replace the BCL S- and P-wave model-dependent contributions by the corresponding S- and P-wave contributions calculated using the realistic helicity amplitude data for the process 2π → NN. The nucleon-nucleon potentials so obtained in the various cases, such as the central potential, the spin-orbit potential, etc., are described graphically by curves for both the triplet and singlet states. The various ϱ-functions obtained are also illustrated graphically and a critical discussion of the work is included. In conclusion, we observe that the nucleon-nucleon potential we calculate agrees with that calculated by Cottingham and Vinh Mau and with the Yale curves for the potential, except in special cases where the ω meson is expected to contribute strongly.
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