Generality of the Uniform-Limit Formalism for Many-Boson Systems in the Weak-Coupling Limit

Ground states of two typical many-boson model systems are studied: (i) a weakly interacting boson system at low density, and (ii) a low-density hard-sphere boson gas in the low-energy limit. For both of these systems it is shown explicitly that the uniform-limit formalism based on the method of correlated basis functions can be used to obtain, in a relatively simple way, exact results for the ground-state energy per particle and other related properties in the weak-coupling limit. In the problem of the hard-sphere boson gas the $T$-matrix method is found to be particularly useful in dealing with the singular interaction potential.