Zur Theorie von Systemen aus drei Teilchen mit Coulombwechselwirkung

Extending the results of a preceding paper the excited vibrational states of the H ₂ ⁺ ion are calculated. To this end we employ an improved Born-Oppenheimer-approximation.     

Funktionalmittelwerte in der statistischen Theorie von quantenmechanischen und klassischen Systemen vieler Teilchen

The grand-canonical partition function of an interacting many-particle-system is represented as a functional integral with Gaussian random variables. The representation can be regarded as a Gaussian average over the partition function of free particles in an external fluctuating potential. The latter partition function is studied by means of diagrammatical techniques. The set of diagrams of a particularly simple structure is summed up by introducing the full scattering amplitude for the scattering in the external potential. The thermodynamicalGibbs' potential proves to be stationary with respect to the true particle density. It is shown that a variational procedure leads directly to an approximation which may be regarded as the renormalized form of the well-known Random-Phase-Approximation (RPA). The main feature of the approximation is thatGibbs' potential is stationary with respect to the two-particle-density correlation function. The classical limit of the renormalized RPA yields the results of the Debye-Hückel theory. In case of an hard-core potential the approximation applies only to the long-range part of the potential. The results are similar to recent developments in the theory of the Ising model and of real gases.     

Zur Theorie des Zerfalls von Kohlenstoff 12 in drei α-Teilchen

A Complete orthogonal system derived in an earlier paper is used to analyze the Dalitzdiagram for the three α-particles in the decay of carbon 12. The hypothesis, that only few of these orthogonal functions will be of importance, is confirmed.     

Lee-Modell mit Coulomb-Wechselwirkung

The Hamiltonian of the Lee model in the sector (1, 0) with an additional N Θ-interaction is diagonalized by means ofGreen's operator (E-H)^?1. In addition to a continuous spectrum of scattering states one gets a discrete spectrum consisting of a groundstate level determined essentially byLee's interaction H₁ and excited states generated by the additional interactionH ₂.     

Zur statistischen Theorie der Entropieproduktion in nicht abgeschlossenen Systemen

On the basis of a statistical theory it is shown that the internally produced entropy is positive definite in a system which is in interaction with another system when the system goes over from an arbitrary statistical state to thermal equilibrium. Thereafter the most general type of change of statistical states is analyzed which are possible for a system in thermal contact with its surroundings. Thermal contact corresponds to a special type of correlation between the system and its surroundings. It leads to the result that the internally produced entropy increases monotonically with time.     

Das Problem der körperfesten Achsen bei Systemen mit gleichen Teilchen

The suitable choice of a body-fixed frame of reference (BFR) is an essential point in the treatment of systems with identical particles. Starting from the fact that there exists a “best” BFR (“specific decoupling”), in which the wave function is a product of an internal and a collective part, we show that the collective term has to be invariant under permutations of the particles. On the other side in symmetrical configurations the BFR has to jump in a well-defined manner under those permutations which are equivalent to spatial rotations. It is shown that for non-symmetrical configurations the BFR must have the same properties. For 3 identical particles it is possible to construct in a purely geometrical way a BFR which has the right behaviour under particle permutations. The Hamiltonian in that BFR is derived and the connection with the “best” BFR is discussed.     

Zur Möglichkeit von Oberflächen-Magnetismus in Systemen mit weitreichender Wechselwirkung

We consider a system, where the magnetic susceptibility of the atoms at the surface is larger than inside the bulk. Assuming a model interaction of exponential form, the mean field equations for the critical temperature can be solved exactly. The consequences for real systems are discussed.