Physica最新文献

In the earlier paper with this title it was concluded that the anomaly in the constant-volume heat capacity near the critical point arises from the density fluctuations, which originate from the increase in the compressibility. The specific heat depends upon the correlation length ξ, and factors influencing the effective value of ξ are considered in greater detail in the present paper. The density fluctuations have a feedback effect on the compressibility and the energy fluctuations arising from the specific-heat anomaly produce a feedback on the specific heat itself. It is shown that these feedback effects are relatively small. In considering the feedback on the compressibility we used the relationship which expresses the self-limitation of the fluctuations on account of the change of compressibility with density along the critical isotherm (previously we had considered other isotherms at the critical density). This allows a new derivation of one of the known exponent scaling relations.

The structure factor $\text{S(}\text{q}\text{) = (1/n)〈ϱqϱ−q〈}$ of an electron gas is investigated by a diagrammatic analysis of perturbation theory. By generalizing the theoretical treatment in a previous paper, it is shown that S(q) has the following exact dominant asymptotic form for large q (q ⪢ p_F; p_F, the Fermi momentum): $\text{S(}\text{q}\text{)= 1 −}\text{4}\text{3}\text{(αr}{}_{\mathrm{s}}\text{/π) (p}{}^4{}_{\mathrm{<mtext>F</mtext>}}\text{/q}{}^4\text{) g}\textcolor{red}{}\text{(0) +hellip;}$, where g (0) is th e exact value of the spin-up-spin-down pair correlation function at the origin. It is therein clarified that “electron-electron” ladder interactions which are included in the Goldstone energy diagrams as a part, play an essential role in determining the above coefficient of the order q⁻⁴ of S(q).

Sound-absorption measurements have been made in mixtures of CD₄ with He, Ne, Ar and Xe to investigate the effect of the noble gases on the rotational relaxation of CD₄. The measurements were carried out in the pressure range of 100 to 150 torr, at 308 K and a frequency of 3 MHz. The relaxation times and rotational collision numbers obtained show the same tendency as was found in CH₄—noble-gas mixtures. The collision numbers Z_rot, defined as the ratio of the rotational relaxation time and the mean time between two elastic collisions, increase with increasing mass of the noble gas. We found the following numbers: Z_rot (CD₄CD₄) = 10.0 ± 0.3, Z_rot (CD₄He) = 2.6±0.7, Z_rot (CD₄Ne) = 4.1±0.6, Z_rot (CD₄Ar) = 7.3±0.6, Z_rot (CD₄Xe) = 14±3.

A comparison between these experimental results and theoretical predictions by the rough-sphere model is given.

The direct-summation procedure of Bartis and Oppenheim is generalized for correlation- function expressions which contain N-particle dynamic fluxes of both momentum and spatial coordinates. The generalized procedure is used to evaluate the coefficient of thermal conductivity for moderately dense gases. A general expansion of the transport coefficient is formulated for all orders in the density while explicit expressions are given to first order in the density.

A nonperturbational theory for nonlinear response of externally driven systems is presented. A set of integral equations for the response of observables, which are slow variables of the system and form a commutator algebra, is derived. This set of integral equations reduces to a tractable form, if some nonlinear memory effects are negligible. The kernels depend only on the linear relaxation functions and the driving field. As an example of the theory the paramagnetic saturation problem is discussed. In a simple way the modified Bloch equations follow as a special result.

Expressions are obtained using the Distorted-Wave Born Approximation (DWBA) for a number of kinetic-theory collision cross sections. In particular, DWBA results are given for the (production) collision integrals that couple angular-momentum directional polarizations with the hydrodynamic fluxes. These integrals as well as the full relaxation rate (kinetic-theory collision) matrix of angular-momentum polarizations involve energetically inelastic collisions. Except for this energy inelasticity, the DWBA results can be written as a product of an internal-state dependent factor and a translational factor. The simplest approximation is to ignore the dependence of the translational factor on energy inelasticity, or if the integral vanishes if that is done, to include the energy inelasticity to first order. Such a procedure yields an explicit estimate of the complete dependence of the collision integrals on internal-state quantum numbers. A crude approximation for the translational factors is also investigated. This amounts to assuming that the transition operator depends (translationally) only on the momentum transfer. Some relations between relaxation and production collision integrals then follow. Throughout this work, reduced matrix elements (in the sense of the 3-dimensional rotation group) are stressed, so that the results are applicable to any molecular species and most results are valid for any form of intermolecular potential.

The sixth and eighth frequency moments of the dynamical structure factor for a classical liquid are examined in some recent approximate models. These are compared with their exact expressions. Using the approximate models, the moments are calculated for liquid argon and the results are compared with those obtained from the molecular-dynamics data.

In order to study the thermal vibrational relaxation of CO₂, the gas is given a perturbation such that the bending mode, b, and the symmetric-stretching mode, s, remain in equilibrium with each other while the asymmetric stretching mode, a, undergoes a different evolution. Two relaxation times, τ_VT and τ_VV, occur in the collisional exchanges of energy: respectively, that of vibration-translation (V-T) between the set bs and the degrees of translation-rotation; and that of vibration-vibration (V-V) between a and bs. A third parameter, $\text{G}$, characterizes the ratio of energies, gained by bs and lost by a, during the V-V exchange. τ_VT can be obtained from thermodynamic experiments and τ_VV by a fluorescence technique. The spectrophone method used here allows the simultaneous determination of τ_VT, τ_VV and $\text{G}$; one can therefore determine the quantum levels concerned in the exchanges and compute the corresponding transition probabilities.

It is pointed out that the stochastic theory of spin relaxation is mathematically identical with the theory of stochastic linear differential equations. Three treatments of spin relaxation and three from stochastic differential equations are brought into correspondence. Furthermore, a double projector is used to derive an exact integro-differential equation for spin—lattice relaxation.