Composite Particle Representation as an Effective Method for Three-Nucleon Bound States

An effective boson-mapping approach, known as the Composite Particle Represen-tation (CPR), has been further developed to study the existing three-nucleon systems (3He and 3H nuclei). Within the present CPR formalism it is possible to study the cluster effect in the three-nucleon system, with a neutron-proton pair forming deuteron (d) cluster inside 3He or 3H, and building an effective two-body system (such as d + p in 3He or d + n in 3H). The total interaction in the three-nucleon system can then be calculated from a nucleon-nucleon (NN) interaction which reproduces the deuteron binding energy and wave function as a solution of the two-nucleon problem. The use of a harmonic oscillator basis to construct the single-particle wave functions allows us to subtract out the center-of-mass motion explicitly in the present CPR formalism. An exact summation method for the infinite series of the Wigner-Brillouin perturbation expansion has been suggested, which naturally takes into account the deuteron cluster formation or breakup inside the three-nucleon system. The results obtained, using an appropriately chosen effective NN interaction, reproduce the binding energies of 3He and 3H reasonably well and show a significant d clus er component in the total wav