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The undulatory behavior in the velocity dependence of the total elastic cross-section Q( v) for atom-atom-scattering can be calculated by the semiclassical approximation. In a previous paper J numerical values of the classical deflection function, which are necessary to evaluate the amplitude of the extrema in Q( v), were reported for a Kihara-potential as a function of the reduced energy K and the potential parameter α. The present paper gives the correspondent reduced maximum phase shifts η ( K,α), which determine the location of the extrema. The results for the Kihara-potential are compared with similar calculations for a Lennard-Jones-( n, 6)-potential. [ABSTRACT FROM AUTHOR]

The results of the preceding paper are specialized to three-atomic molecules in which the three atoms are allowed only small vibrations about their equilibrium positions. This restriction to the vibrational amplitudes makes a perturbation calculation suitable. A sketch of the zero order approximation has been given in this paper, and it has been shown - at least for a symmetrical molecule of the type AB - how the limiting case of the rigid body may be obtained for which there exist the well-known formulas of Wang. [ABSTRACT FROM AUTHOR]

The present paper determines the spectral functions of the Greens-functions for quasiparticles defined in a previous paper by a variational procedure minimizing the thermodynamic potential Ω( T, V,μ). An approach for generalizing the results to an inhomogeneous model (e.g., a lattice) is proposed. [ABSTRACT FROM AUTHOR]

In previous papers we have introduced a simple model for backbending nuclei which satisfactorily describes the essential experimental features of those nuclei. In this paper we show that the basic assumptions of this model can be deduced by a more microscopic treatment. [ABSTRACT FROM AUTHOR]

Entropy which is produced in the interior of a non-isolated system during a process is quite different from its total change of entropy. In an earlier paper was given an expression for produced entropy in the statistical theory. This expression is associated with a statistical measure, the 'gain of information' (Informationsgewinn). A special application of the general scheme is the statistical derivation of the principle of Le Chatelier and Braun. [ABSTRACT FROM AUTHOR]

In this paper the analysis of gas heating phenomena in wallstabilized electric arcs with axial gas flow derived in an earlier paper is applied to a nitrogen arc at a pressure of one atmosphere. For this reason the behaviour of the inlet length, the perturbation quantities and the integral characteristic values of such an arc is discussed and their parameter dependences are investigated. The results give the best parameter values for getting the highest enthalpy flux and the best efficiency of the arc heater. [ABSTRACT FROM AUTHOR]

The aim of the paper is the development of a complete macroscopic description (generalized Bloch equations) of multipole resonance and relaxation in terms of multipolarisations, which are the expectation values of normalized multipole operators. These operators are constructed with the help of the Wigner-Eckart theorem. Using a relation for their commutators the reversible part of the generalized Bloch equations is derived, the structure of which depends on the spin quantum number I. The irreversible part was treated in an earlier paper (I). [ABSTRACT FROM AUTHOR]

In the present paper we give a fully quantummechanical treatment of the self-sustained oscillation of one mode in solid-state lasers. The total laser system consists of various subsystems: The lasing mode is coupled to the atoms of the active material and to a loss mechanism. It is assumed to be in complete resonance with the homogeneously broadened atomic transition. The pump of the active atoms, which are assumed to have only two levels, is brought about by their interaction with a large system of negative temperature. The active atoms decay not only by induced and spontaneous emission into the lasing mode, but also by spontaneous emission into the continuum of nonlasing modes (and possibly by nonradiative transitions). This process is fully taken into account. The pumping process and the spontaneous emission into the continuum of nonlasing modes are treated as in a preceding paper. There we have shown that the coordinates of these fields can be eliminated in some sense and give rise to a mean dissipative motion of the atoms and to fluctuations. Using the Heisenberg picture we obtain a system of coupled nonlinear equations of motion for the atomic operators and for the creation operator of the oscillating mode. We then eliminate the atomic operators by the iteration procedure of the semiclassical laser theory. This leaves us with a nonlinear differential equation of the van-der-Pol type for the creation operator of the laser mode, which contains the fluctuations of the pumping process, the spontaneous emission into the continuum and the loss mechanism as inhomogeneities of operator character. Such an operator equation has previously been obtained by Haken, who has shown, that in the neighbourhood of the stationary saturated level of oscillation the amplitude is highly stabilized, whereas the phase undergoes an undamped diffusion process. This process takes the phase in the course of time arbitrarily far from any given initial value. We use Haken's method of solution and demonstrate that the correct commutation rules for the oscillating mode [ b( t), b( t)]=1 are preserved for all times. Besides these quantum mechanical properties our solution contains all the well known results of the semiclassical theory. Our main result is the expression for the linewidth, which is caused by phase diffusion. The half width at half maximum power is in circular frequencies given by κ is the half width of the cavity, Γ the half width of the atomic transition (we have assumed κ ≪ Γ), σ the critical inversion per atom, P the energy radiated per sec and $$n_{TH} = \left[ {e^{\frac{{\hbar \omega }}{{kT}}} - 1} \right]^{ - 1}$$ the number of thermal noise quanta. We prove that $$\frac{1}{{2\sigma _k }} = n_{SP}$$ , where n is the number of spontaneous noise quanta in the mode, n is determined in complete analogy to n+1/2. It arises from the spontaneous emission of the active atoms into the laser mode and is for optical frequencies much more important than n+1/2, which stems from the finite temperature of the cavity walls and the vacuum fluctuations of the cavity. Both noise sources, however, enter our formula entirely symmetrical. The two terms containing the cavity fluctuations represent the old Townes formula corrected by a factor 1/2. The spontaneous noise term on the other hand agrees in the limit κ≪ Γ with Haken's expression, if we account for the different description of the pumping process. Before we study the nonlinear oscillation of the mode above threshold, we investigate its behaviour in the linear or amplification region below threshold. The laser line is shown to grow out of a broad background of spontaneous emission noise. [ABSTRACT FROM AUTHOR]

The present paper contains a mathematically exact, fully quantummechanical treatment of dissipation and fluctuations in a two-level system. We consider an atom with only two levels, which is coupled to the radiation field and to a system of negative temperature. As a consequence, the atom decays to the lower level and is pumped to the upper one alternately. Although the methods, which are developed, do not depend on this model, it has been chosen because of its applicability in laser theory. In fact, we will give in a second paper a fully quantummechanical treatment of a laser, using the results given here. We discuss the motion of the atom in terms of its time-dependent 'spin-flip' and occupation number operators, i.e. we use the Heisenberg picture. In such cases usually one writes down the nonlinear coupled system of equations of motion for the field and atomic operators. We, however, start with a transformation of the time evolution operator of the total system using the technique of disentangling, which has been developed by Feynman. Incidentally this transformation allows for a generalization of the Wigner-Weisskopf theory of spontaneous emission, which will be published in a forthcoming paper. For the present purpose it permits us to write down the equations of motion for the atomic operators in terms of a mean motion, which refers to the coupled fields only through relaxation times and equilibrium values of the occupation numbers, and of fluctuating forces, which give the effect of the quantummechanical fluctuations of the fields on the atom. The mean or dissipative motion agrees with that of a 2×2 density matrix, which describes N identical atoms coupled to our fields. The fluctuating forces are given by operators and they are therefore noncommuting. Their properties are discussed in detail. An important result is, that they are not correlated in time. It is shown that they are responsible for the commutation relations of the atomic operators for all times. Such fluctuations do not occur in a density matrix description, because it contains already an averaging over fluctuations. Our results show clearly that dissipation and fluctuations cannot be split in quantum mechanics, because the neglection of the fluctuations would violate the commutation relations. [ABSTRACT FROM AUTHOR]