The Nucleon-Nucleon Interaction in a Chiral Effective Field Theory

10 1. Introduction
such interactions written down by Ord6iiez et al. [74], [77], [78] are redundant or have coefficients
suppressed by two powers of the inverse nucleon mass, see appendix F. This has no consequences
for the two-nucleon scattering or bound state problem but becomes quite important for systems
with three and more nucleons andjor for two-nucleon problems with external probes.
In chapter 4 we will concentrate on practical applications of the derived potential for studying
bound and scattering states in the two-nucleon system [128]. To that aim we will determine
the ni ne parameters related to the contact interactions by a fit to the np S- and P-waves and
the mixing parameter EI far laboratory energies below 100 MeV. The corresponding partial wave
decomposition of the potential is explained in appendix G. An alternative determination of some
of these constants from the leading effective range parameters is considered as weIl. Other lowenergy
constants are obtained from pion-nucleon scattering. We will discuss numerical results
for phase shifts and show that the predicted partial waves and mixing parameters for higher
energies and higher angular momenta are mostly well described for energies below 300 MeV. We
will also consider various deuteron properties following from our potential. The role of virtual
�-excitations is also discussed.
In the chapter 5 we will consider charge symmetry and charge independence breaking in an effective
field theory approach for the two-nucleon system. We first discuss various terms in the effective
Lagrangian, which lead to isospin violating effects. For that investigation we use the formalism
proposed by Kaplan, Savage and Wise [91] and calculate the nn, np and pp I So phase shifts.
We do not explicitely include virtual photons in this analysis. The charge dependence observed
in the nucleon-nucleon scattering lengths is due to one-pion exchange and one electromagnetic
four-nucleon contact term. This gives a parameter free expression for the charge dependence of
the corresponding effective ranges, which is in agreement with the rat her small and uncertain
empirical determinations. We also compare the low energy phase shifts of the nn and the np
system with data. Finally, we summarize our findings in chapter 6.