Two-particle potential in :λ(φ6-φ4): field theory

The many-particle binding energy in the model :λ(φ6-φ4): in 1 + 1 dimensions is obtained using simple nonrelativistic quantum mechanics. We determine an effective two-particle potential from approximate field-theoretical solutions of the two-particle bound state and use it to obtain the many-particle binding energy. The results agree reasonably well with numerical calculations of the three and four-particle binding energy in the field theory for weak coupling, λ. We also use this nonrelativistic potential to calculate the two-particle scattering amplitude