Scattering of particles with internal degrees of freedom

The scattering of particles with a small number of internal degrees of freedom is considered. Billiard formalism is used to study the scattering of two such structurally complex particles. The main scattering characteristics are found. Various types of scattering modes are revealed. In particular, a mode is detected when the velocity of motion of such particles away from each other is higher than their approach velocity before the collision. The scattering of such particles is shown to occur after a finite number of collisions. A generalized Newton law is proposed for the collision of particles with a small number of degrees of freedom, and the form of the effective coefficient of restitution is found.     

On the coupling of ion cyclotron motion to ion internal degrees of freedom

The possibility of significant coupling between gas-phase ion cyclotron motion and two internal angular momentum terms is explored. The first case, coupling with ion spin, is treated via the relativistic Hamiltonian, and found to produce only relativistic perturbations which are entirely negligible. The second case, coupling with ion rotation, is developed via its equivalence to a Stark effect. Small shifts in the cyclotron resonance frequency, ω_c, and the appearanceof a weak-cyclotron resonance at 2ω_c, are predicted, but these effects are negligible in general. If the cyclotron frequency is near an ion rotational transition, however, a shift of 10⁻⁵ in cyclotron frequency may be observed, and could provide a means of investigating low-frequency rotational transitions of ions.     

Laser cooling of internal degrees of freedom of molecules

Optical pumping techniques using laser fields combined with photo-association of ultracold atoms leads to control of the vibrational and/or rotational population of molecules. In this study, we review the basic concepts and main steps that should be followed, including the excitation schemes and detection techniques used to achieve ro-vibrational cooling of Cs₂ molecules. We also discuss the extension of this technique to other molecules. In addition, we present a theoretical model used to support the experiment. These simulations can be widely used for the preparation of various experiments because they allow the optimization of several important experimental parameters.     

Semiclassical description of scattering with internal degrees of freedom

The scattering of systems with internal degrees of freedom is studied in the semi-classical approximation. It is found that a special set of states, named coherent internal states, are specially relevant for the semi-classical treatment. A classical trajectory is defined for each coherent internal state. The semi-classical expressions obtained satisfy the superposition principle and are valid for arbitrary coupling strength.     

A disordered ising model with internal degrees of freedom

A solvable Ising-system withnn-interactions as a basic system is considered. This system is assumed to undergo a phase transition so that the thermal quantityq=Σ _i> ₀ ² /N, which is not necessarily the order parameter of the basic system, is different from zero (q≠0) forT _c. The whole system consists of the basis {S _i} and an equal number of additional spins η _i which are coupled linearly with the basic spinsS _i through an exchange constantJ _i which is distributed at random. The pairs of spinsS _i ?η _i can be interpreted as clusters with an internal degree of freedom. The specific heat Δc and the susceptibility Δ_χ of the internal degree of freedom can be separated exactly and show typical spin glass properties: the specific heat Δc is an analytic function over the whole temperature range and the susceptibility Δ_χ shows a cusp at the transition temperatureT _c of the basic system.     

A disordered ising model with internal degrees of freedom

A solvable Ising-system withnn-interactions as a basic system is considered. This system is assumed to undergo a phase transition so that the thermal quantityq= _i> ₀ ² /N, which is not necessarily the order parameter of the basic system, is different from zero (q0) forT _c. The whole system consists of the basis {S _i} and an equal number of additional spins _i which are coupled linearly with the basic spinsS _i through an exchange constantJ _i which is distributed at random. The pairs of spinsS _i – _i can be interpreted as clusters with an internal degree of freedom. The specific heat c and the susceptibility of the internal degree of freedom can be separated exactly and show typical spin glass properties: the specific heat c is an analytic function over the whole temperature range and the susceptibility shows a cusp at the transition temperatureT _c of the basic system.     

On dielectric and magnetic relaxation phenomena and vectorial internal degrees of freedom in thermodynamics

It has been shown by the author in a previous paper that thermodynamic vectorial internal degrees of freedom which influence the polarization or the magnetization of a medium may give rise to dielectric or magnetic relaxation phenomena. Snoek's equation for magnetic relaxation phenomena was derived and it was shown that Debye's theory for dielectric after-effects in polar liquids is a special case of the developed theory. In this paper it is shown that if Z is some vectorial internal degree of freedom which influences the polarization a new internal degree of freedom bip^(int) may be defined which is a function of biZ, which may replace biZ as vectorial internal degree of freedom and which is a part of the total specific polarization. Furthermore, p^(int) may be introduced in such a way that the remaining part of the polarization, p^(el) (defined by $\text{p}{}^{\mathrm{<mtext>(</mtext><mtext>el</mtext><mtext>)</mtext>}}\text{=}\text{p}\text{?}\text{p}{}^{\mathrm{<mtext>int</mtext><mtext>)</mtext>}}$, where p is the total polarization per unit of mass), has the property that it vanishes for all values of p^(int) if the medium is in a state where the electric field E and the mechanical elastic stresses vanish and the temperature of the medium equals some reference temperature. If the equations of state are linearized the latter result implies for an isotropic medium $\text{E}\text{=ρa}{}^{\mathrm{(0,0)}}{}_{\mathrm{(bdp)}}\text{p}{}^{\mathrm{<mtext>(</mtext><mtext>el</mtext><mtext>)</mtext>}}$, where ρ is the mass density and a^(0,0)_(P) a constant. On the other hand p^(int) satifies a relaxation equation. It is seen that the use of p^(int) as an internal degree of freedom is of great advantage. This is connected with the fact that p^(int) is a measurable quantity in contradistinction to an arbitrary “hidden” vectorial internal degree of freedom. Analogous results may be obtained for magnetic after-effects.     

On pionic degrees of freedom in atomic nuclei

The possibility of explicit pionic degrees of freedom in atomic nuclei and their association with pionic reactions involving fragment emission is discussed. Although no present direct evidence for such degrees of freedom is available they could be searched for in doorway states — other than the anticipated N¹ doorway — in the excitation function in the pion-induced partial reaction cross sections. Such a search is underway. A framework is discussed in terms of which such new pion doorways might be described.     

Influence of internal degrees of freedom on the structure of one-dimensional systems

Summary The influence of internal degrees of freedom on the behaviour of one-dimensional systems is discussed. For systems with half-filled bands the coupling to internalviz. lattice coordinates decides whether Peierls distortion is caused by intramonomer coordinates or by a lattice coordinate. Thereby the various intramonomer degrees of freedom act cooperatively. We show that there is a small regime of parameters where both kinds of distortion exist simultaneously. For increasing temperature we find that distortions can also move from the lattice coordinate to the intramonomer coordinate.     

Inelastic scattering of phonons by quadrupole defects with internal degrees of freedom

We solve the quantum mechanical problem of the inelastic scattering of phonons by a quadrupole defect in a crystal lattice for the case of solid parahydrogen whose matrix contains pair complexes of H₂ orthomolecules. By employing the pseudospin approximation for the operator of the energy of quadrupole-quadrupole interaction of the molecules in an orthopair we derive an effective Hamiltonian that describes the interaction of phonons with a pair quadrupole orthodefect in the lattice. We set up the scattering matrix and calculate the effective phonon relaxation time τ(ω, T) as a function of the frequency ω and the crystal temperature T. We also find that a pair quadrupole defect, which has a complicated system of levels, can be replaced by an effective two-level system with temperature-dependent parameters. The fact that a pair quadrupole orthocluster has internal degrees of freedom results in a resonant scattering peak near a certain critical temperature T ₀. Our estimates for H₂ yield T ₀≃ 6–7 K. Finally, we discuss the contribution of this mechanism to the low-temperature thermal conductivity of solid hydrogen. Zh. éksp. Teor. Fiz. 114, 555–569 (August 1998)     

The three-nucleon bound state with mesonic and internal nucleonic degrees of freedom

Conclusion Even the simplest properties of the three-nucleon bound state, i.e. binding energy and e.m. properties, cannot be described satisfactorily within the classic picture of the nucleus. The classic format of microscopic nuclear structure needs corrections. Some effects on the three-nucleon bound state arising from the revival of mesonic and internal nucleonic degrees of freedom have been discussed. The effects are by and large beneficial.The three-nucleon system should be of vital interest for nuclear physics. Calculations of comparable quality for heavier nuclei are still out of reach. Nevertheless, the problems of the classic nucleus as seen in the three-nucleon bound state appear quite characteristic also for heavier nuclei. It therefore appears tempting to simulate the almost exact results of the three-nucleon system in a simplified perturbation-theoretical form and to carry the discussed corrections over to heavier nuclei in the same approximation. In this way the three-nucleon system might not only have philosophical importance for nuclear structure, it might even be of practical usefulness.The work discussed in sections 2 and 3 has been done in collaboration with W. Bentz, K. Dreissigacker, S. Furui, Ch. Hajduk and W. Strueve. It is supported in part by funds of the Deutsche Forschungsgemeinschaft (DFG) contract Sa 247/3. Computations were done at Regionales Rechenzentrum für Niedersachsen in Hannover.Work supported by funds of the Deutsche Forschungsgemeinschaft (DFG) contract Sa 247/3.Invited talk at the symposium Mesons and Light Nuclei, Liblice, Czechoslovakia, June 1981.     

Energy characteristics of oscillatory systems with internal (Hidden) degrees of freedom

The general formulas are derived for calculating the kinetic and potential energies and other energy characteristics of linear oscillatory systems, a portion of the degrees of freedom of which are internal, i.e., inaccessible for direct measurements and/or excluded from consideration. The energy characteristics are expressed by means of parameters pertaining only to the part of accessible (or selected for consideration) degrees of freedom. The formulas are derived based on the use of certain novel properties of the so-called Shur matrix complement. The obtained formulas are applicable for calculating the energy characteristics of the elements of acoustic metamaterials by means of their effective inertial-elastic parameters. The main focus is the case of negative values of these parameters. Proceeding from the nonnegativity of the kinetic and potential energies of mechanical structures, limitations on the character of the frequency dependences of the effective parameters are formulated.     

On the interaction of collective degrees of freedom in nuclei

The structure of the interaction of giant dipole and giant quadrupole oscillations with nuclear surface vibrations is established. The various coupling parameters are calculated in the hydrodynamic model. The significance of the interaction terms is discussed.