In this contribution, we investigate the structure of short-range correlations in many-body states. We obtain the highly correlated many-body states with an explicitly correlated basis which enables us to get a precise solution of a many-body Schrödinger equation for a realistic interaction. We show two-body density distributions calculated from three- and four-body states to investigate the short-range correlations between nucleon pairs. At distances below 1 fm a universal behavior is found which does not depend on the many-body states. The universality is also seen in the high momentum components of the two-body momentum distributions.
Within the hyperspherical framework, the solution of the time-independent Schr\"odinger equation for a
n-particle system is divided into two steps: the solution of a Schr\"odinger-type equation in the hyperangular degrees of freedom and the solution of a set of coupled Schr\"odinger-type hyperradial equations. The solutions to the former provide effective potentials and coupling matrix elements that enter into the latter set of equations. This paper develops a theoretical framework to determine the effective potentials, as well as the associated coupling matrix elements, for few-body systems with finite angular momentum
L=1 and negative and positive parity $\ensuremath{\Pi}$. The hyperangular channel functions are expanded in terms of explicitly correlated Gaussian basis functions, and relatively compact expressions for the matrix elements are derived. The developed formalism is applicable to any
n; however, for $n\ensuremath{\ge}6$, the computational demands are likely beyond present-day computational capabilities. A number of calculations relevant to cold-atom physics are presented, demonstrating that the developed approach provides a computationally efficient means to solving four-body bound and scattering problems with finite angular momentum on powerful desktop computers. Details regarding the implementation are discussed.
It is generally accepted that with suitable boundary conditions the Lippmann-Schwinger (LS) integral equation is equivalent to the Schr\"odinger equation, even in systems of more than two particles. It also is generally accepted that although in two-particle systems the scattering solutions to the LS equation are uniquely defined by that equation without need for boundary conditions, the same cannot be said of systems containing more than two particles; in such many-particle systems, it is generally agreed, unique scattering solutions to the LS equation are not obtained unless boundary conditions are imposed. However, these assertions have not been verified heretofore in any system of three or more particles, because exact closed-form solutions of the Schr\"odinger or LS equation for such systems are so difficult to achieve. We have examined these questions in a one-dimensional three-body model first discussed by McGuire, wherein three equal-mass particles interact via equal and finite strength attractive \ensuremath{\delta}-function potentials. With this model, the scattering solutions to the Schr\"odinger equation can be written exactly, in closed form. Thereby we are able to demonstrate explicitly that in this model the scattering solutions to the Schr\"odinger equation do satisfy the LS equation; we also demonstrate explicitly that the LS equation's scattering solutions really are nonunique unless boundary conditions are imposed. This latter result strongly suggests that, in three-particle systems at any rate, recent criticisms of the aforementioned generally accepted nonuniqueness thesis are not well taken.