Soft two-meson-exchange nucleon-nucleon potentials. I. Planar and crossed-box diagrams

Abstract

Pion-meson-exchange nucleon-nucleon potentials are derived for two nucleons in the intermediate states. The mesons we include are (i) pseudoscalar mesons: $\pi ,\eta ,{\eta }^{\prime }$; (ii) vector mesons: $\rho ,\omega ,\varphi$; (iii) scalar mesons: $a_0(980),\epsilon (760),f_0(975)$; and (iv) the $J=0$ contribution from the Pomeron. Strong dynamical pair suppression is assumed, and at the nucleon-nucleon-meson vertices Gaussian form factors are incorporated into the relativistic two-body framework using a dispersion representation for the pion- and meson-exchange amplitudes. The Fourier transformations are performed using factorization techniques for the energy denominators. The potentials are first calculated in the adiabatic approximation to all planar and crossed three-dimensional momentum-space $\pi$-meson diagrams. Next, we calculate the $1/M$ corrections.

Comments: 28 pages RevTeX, 8 postscript figures; revised version as to appear in Phys. Rev. C