The Schrödinger equation of A nucleons is transformed to new coordinates. Six of them have collective nature and 3A − 9 are single-particle coordinates. The connection is given to the conventional collective model in which five collective coordinates are used. The additional sixth collective coordinate of this paper gives a simple description of monopole vibrations. The new coordinates can also be used in the theory of nuclear reactions: By introducing a symmetrized distance vector for reaction partners, the antisymmetrization procedure is simplified considerably.

The configuration-space approach to the three-particle problem is generalized to the case of four particles. Special coordinates are defined which have simple symmetry properties with respect to the exchange of identical particles. The construction of a suitable orthogonal system is discussed. Some of these functions are given explicitly. It is pointed out that the use of this orthogonal system leads to a considerable simplification for a large number of four-particle problems, namely, the approximate reduction of the Schrödinger equation to a finite system of coupled differential equations for functions that depend on one variable only.

No abstract

No abstract

Abstract. The expansion of the wavefunction for a bound three particle state in the five-dimensional hyperspace of hyperspherical harmonics in some cases suffers bad convergence, especially for weakly bound states. For this reason correlated hyperspherical harmonics are proposed, of which the ordinary hyperspherical harmonics are one special choice. The "best" suited correlated hyperspherical harmonics are chosen from an infinite set of complete orthogonal systems by a Ritz variational calculation.