Zum quantenmechanischen Dreikörperproblem

The three-body problem of quantum mechanics has been treated in appropriate co-ordinates. These are, besides those of the center-of-mass, the distances between the three particles and three Eulerian angles, fixing in space the position of the triangle formed by the particles. The Hamiltonian can be simplified by introducing the usual angular momentum operators of a gyrating rigid body. The solution of the wave equation has been discussed. Factorization into an angular part and a part depending on the particle distances only leads to certain linear combinations of such products. The angular parts have the well-known form of the representation coefficientsD _MK ^L of the three-dimensional rotational group. The parts depending on the distances may be derived from a system of differential equations coupling, in two separate sets, either even or odd values ofK for each given value ofL.     

Zum Drei- und Vierkörperproblem der Kernphysik

The independent pair model has been applied to the nuclear three- and four-body problem. The equations of the model have been solved by a perturbation approach in the case of spin- and charge-independent central two-body forces with hard-core. In lowest order of perturbation theory the nuclear average potential has been approximated by an oscillator potential including an effective mass, the parameters of which were so chosen as to give as nearly a self-consistent potential as possible. For a sqare well two-body interaction the lowest order equations have been solved exactly, the corrections are shown to be small. Some tests for the internal consistency of the approach have been developped and are shown to be well fulfilled by our solutions. According to a proposal byLipkin we succeeded in separating off the energy of the center of mass motion. The results for the binding energy of He⁴(27,9 MeV), the binding energy of H³ (7,1 MeV), the energy difference between H³ and He³ (0,735 MeV) and the RMS-radius of He⁴ (1,75f) are in rather good agreement with experimental results.     

Zum Dreikörperproblem der Kernphysik

For the ground state of the triton a wave function is calculated by a variational procedure assuming pure central forces between the nucleons. A method for computing a first correction term is proposed and applied to get an estimate for the error, which is less than 3 percents. The three-nucleon-correlations and the charge form factor are calculated.     

Anwendung des Paarmodells auf das kernphysikalische Fünfkörperproblem

The nuclear Five-body-problem ist treated as a stationary state on the basis of the Independent Pair Model. Square well potentials with hard core, Serber exchange character and averaged over spin-dependence are used so that the two-particle equations (Bethe-Goldstone-equations) can be solved analytically. The calculated binding energy (?25,98 MeV) is quite close to the weighted mean value of the measuredj=3/2 andj=1/2 resonances of nucleon-α-scattering (?24 Mev). Ther. m. s. radius of the α-core is about 35% greater than in Helium 4 which shows a moderately strong polarization of the α-core by the presence of the p-nucleon. This value is also very close to the radius of the Litium 6-α-core obtained by fitting the experimental charge distribution.