V. H. Smith,, Jr., H. A. Gersch; Theory of Many-Boson Systems: Pair Approximation and the Jastrow Trial Pair Function, Progress of Theoretical Physics, Volume 2
Progress of Theoretical Physics Vol. 20 No. 6 (1958) pp. 785-797 Ground State Energy of Bose Particle System Ryuzo Abe Progress of Theoretical Physics Vol. 27 No. 2 (1962) pp. 342-360 Variational Study of Ground State of a Bose-Einstein Fluid Kazuo Hiroike Progress of Theoretical Physics Vol. 30 No. 4 (1963) pp. 421-434 Cluster Expansions and the Theory of Many-Boson Systems V. H. Smith, Jr. and H. A. Gersch Progress of Theoretical Physics Vol. 41 No. 5 (1969) pp. 1217-1226 An Extension of Jastrow's Method for the Quantum Mechanical Many-Body Problem with Strong Forces. I S. Ali, M. E. Grypeos and L. P. Kok
The method of correlated basis functions is used in the study of the ground-state properties of a one-dimensional system of bosons interacting through a repulsive $\ensuremath{\delta}$-function potential. Ground-state energies are determined numerically for intermediate values of the coupling constant in three steps: (1) a trial form of the radial distribution function generated by the Bijl-Dingle-Jastrow (BDJ) type of wave function is introduced to obtain approximate ground-state energies, (2) the paired-phonon analysis is applied to improve the BDJ description of the ground state, and (3) leading corrections to the improved approximate energies are evaluted from the second-order perturbation energy generated by the three-phonon vertex. The obtained energy values are found to agree closely with the exact results calculated by Lieb and Liniger.