Composite particle representation as an effective method for three-nucleonbound states

An effective boson-mapping approach, known as the Composite Particle Repres entation (CPR), has been further developed to study the existing three-nucl eon systems (He-3 and H-3 nuclei). Within the present CPR formalism it is p ossible to study the cluster effect in the three-nucleon system, with a neu tron-proton pair forming deuteron (d) cluster inside He-3 or H-3, and build ing an effective two-body system (such as d + p in He-3 or d + n in H-3). T h, total interaction in the three-nucleon system can then be calculated fro m 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 functi ons allows us to subtract out the center-of-mass motion explicitly in the p resent CPR formalism. An exact summation method for the infinite series of the Wigner-Brillouin perturbation expansion has been suggested, which natur ally takes into account the deuteron cluster formation or breakup inside th e three-nucleon system. The results obtained, using an appropriately chosen effective NN interaction, reproduce the binding energies of He-3 and H-3 r easonably well and show a significant d cluster component in the total wave function for these nuclei.