Bayesian analysis of the physical-measurement process is formulated with respect to the physical quantity being subject to the master equation. Here nonlinear dynamics of the measurement system and its own fluctuations are taken into account with the use of a nonlinear Langevin equation. The coupled nonlinear equations of the most probable path and of the variance of the fluctuations around the path are derived with the results of the measurement taken into account. The theory is applied to the measurement in which the field is detected with the use of a cavity resonator or laser amplifier. The minimum uncertainty in the estimate of the most probable path of the field is determined as a function of the variance of the fluctuations of the measurement system itself.

We present here the phase diagram of a binary system of dipolar molecules in which five distinct smectic-$A$ regions are put in evidence both by calorimetric and x-ray investigations, four of these smectic-$A$ areas are contiguous and thus several $S_A-S_A$ transition lines and two triple $S_A$ points are present, and the fifth phase is only connected to the nematic phase. From x-ray measurements we are able to describe the molecular and the dipolar array of each of these five phases.

A new semiclassical expansion for quantum mechanics is developed. The high-energy asymptotic expansion for the coordinate-space matrix elements of the $N$-body Green's function is derived. The asymptotic series is characterized by its coefficient functions, $P_n$. It is shown that the coefficient of the $n$th term in the expansion, $P_n$, satisfies a simple recursion relation. The functions, $P_n$, turn out to be polynomials in Planck's constant $h$ of order $2(n-1\mathrm{})\mathrm{}$. In terms of the interaction, the $P_n$ are also polynomials of the potential and its derivatives. If all the $P_n$ are truncated to some common power $M$ in $h$, one generates a natural $M$th order semiclassical approximation to the Green's function. This semiclassical expansion is given a physical interpretation which is particularly simple in terms of state density. By relating the asymptotic series to the Born series, a closed form for the functions $P_n$ is derived.

The critical behavior of simple single-component fluids near the liquid-vapor critical point (and of other systems in the same universality class) is examined via an asymmetric spin Hamiltonian in Landau-Ginzburg-Wilson form. The leading important odd terms to be added to an Ising-type system are a five-spin interaction $\int \varphi {}_{}{}^5{}_{}{}^{}\mathrm{}\left(x\right)\mathrm{}$ and a nonlocal cubic interaction $-\int \varphi {}_{}{}^2{}_{}{}^{}\nabla _{}^2{}_{}{}^{}\varphi$. These two operators can be combined into two different eigenoperators with distinct physical interpretations. One combination can be shown to be exactly equivalent to the mixing of field variables (e.g., chemical potential and temperature) in the temperaturelike variable of an Ising or Ising-type system. This mixing has been used phenomenologically, found in certain models, and justified on general geometric grounds. This is the first proof that all asymmetric models, assuming universality and barring accidents, will have such mixing; this implies the universal occurrence of a $t^{1-a}$ fluid diameter. The second combination is treated by renormalization-group methods and its contributions to the Helmholtz free energy, magnetic equation of state, and correlation length are calculated to $O\left({\epsilon }^2\right), \epsilon \equiv 4-d$. There are several novel features of this interaction which persist to all orders in perturbation theory. In addition to the expected renormalized $M^5$ contribution to the free energy, there are also terms linear in $h$ (the magnetic field) and $M$ which could be described as nonanalytic fluctuation-induced shifts in the order parameter and field. These might appear experimentally as apparent shifts in the background terms for $h$ and $M$.

The Hartree-Fock wave functions of Weiss for the lithium isoelectronic sequence through $Z=10\mathrm{}$ are used to calculate the generalized oscillator strengths (GOS) and total cross sections for excitation in length and velocity formulations of the Born approximation for all possible transitions between the initial state $n=2\mathrm{}$ to the final state $N=3\mathrm{}$. The present results for the total cross sections are compared with the available theoretical Coulomb-Born calculations and experimental data. The existence of regularities and systematic trends in the GOS and cross sections along the isoelectronic sequence are qualitatively discussed.

A calculation of the ground-state hyperfine splitting in muonic ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is given. It is based on a perturbative approach that was applied to the analogous calculation in muonic ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The result for the hyperfine splitting is $\Delta \nu =4164.9\mathrm{}\pm 3.0$ MHz. A semiempirical value for this splitting, based on the measured splitting in muonic ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, is $\Delta \nu =4166.5\mathrm{}\pm 0.4$ MHz.

Local approximations for the exchange interaction between valence and core electrons are much improved if one parameter is adjusted so that the lowest state of each symmetry has the correct ionization energy. Two nonadjustable local potentials, previously found successful at representing exchange effects, were modified by treating the ionization potential of the core as an adjustable parameter. Values of average radii and one-electron energies in Rb and Ag for the two resulting approximations are compared with frozen-core relativistic Hartree-Fock results as well as with values from an adjustable exchange potential suggested previously by the authors. All computations include core-polarization effects and are also otherwise identical except for their treatments of exchange. By allowing the one-parameter adjustment, we were able to reduce rms errors in the energies by a factor of about 25, and those in average radii by a factor of about 9.

We have attempted to use the ${}_{}{}^1{}_{}{}^{}\mathrm{H}({}_{}{}^{19}{}_{}{}^{}\mathrm{F},\alpha \gamma ){}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ resonance reaction at a ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ energy of 16.44 MeV to investigate the influence of projectile inner-shell vacancies on stopping power ($\frac{\mathrm{dE}}{\mathrm{dx}}$). Our results indicate that it is not necessary to consider the near-surface-depth dependence of $\frac{\mathrm{dE}}{\mathrm{dx}}$ in determining H profiles with this resonant nuclear reaction.

The nematic-isotropic transition temperature was measured by means of an optical technique as a function of applied magnetic field for the material octyl-cyanobiphenyl. The results represent the first unambiguous demonstration of the magnetic field term in the thermodynamic equation for a liquid-crystal phase transition.

In a recent paper, Bambini and Berman [A. Bambini and P. R. Berman, Phys. Rev. A 23, 2496 (1981)] presented analytic solutions to a certain family of coherent-coupling pulses for a two-level system. They show, for nonresonant temporally asymmetric members of the class, that there are no solutions corresponding to vanishing transition probabilities. In this Comment, we examine the problem in greater generality and demonstrate that this property is the norm for asymmetric pulses, and that a vanishing transition probability is possible only if severely overdetermined conditions are satisfied.

It is shown that an ensemble introduced to allow for variation in the number of species of particles is merely a derivative version of the grand canonical ensemble.

The argument advanced by Farquhar purporting that the author's recently introduced great ensemble (which generalizes the usual grand ensemble to allow for uncertain speciation of particles) is only a derivative of the grand ensemble, is shown not to hold upon a more precise explication of the great ensemble, in particular, a clarification of a misleading example I had mentioned. The great ensemble then remains a novel ensemble, not obtainable from any grand ensemble, for describing systems with appreciable but uncertain speciation.

Schenzle, Wong, and Brewer have recently proposed a theorem [Phys. Rev. A 22, 635 (1980)] which states that the coherent transient signals produced in an optically thin gaseous sample of atoms are limited to a certain time interval after the excitation process which produces them. We comment on the range of validity of this theorem.

The limits of validity of our previous theorem on coherent transients are discussed with reference to a recent comment.

We consider some general properties of the orientational order in a fluid, such as a smectic-$C$ liquid crystal, which has a plane of symmetry and whose molecules have a twofold symmetry axis (at least in a statistical sense). In particular, it is shown that such a fluid has only eight independent orientational order parameters, associated with symmetric, second-rank orientational tensors, and not nine as assumed in the recent NMR work by Photinos, Bos, Doane, and Neubert. The failure to recognize this may be responsible for the fact that two of the order parameters reported by these authors are clearly inconsistent with each other.

A rigorous description of the NMR data in the smectic-$C$ phase in terms of eight order parameters that are given in the preceding Comment by A. Wulf is not possible and does not include all of the information the experiment provides. Furthermore, the failure of two order parameters to satisfy a functional inequality is not due to excessive or redundant order parameters as implied in the Comment, but to a lack of precise values for conformational coefficients. The segmental order parameters directly measured in the NMR experiment and their relationship to global molecular order is discussed here more completely.

Angular distributions of photoelectrons from the $\mathrm{Xe}4d$ subshell, and $N_{4,5}\mathrm{OO}$ Auger electrons, have been measured using synchrotron radiation. The $4d$ asymmetry parameter exhibits strong oscillations with energy, in agreement with several theoretical calculations. The Auger electrons show large asymmetries due to alignment of ${\mathrm{Xe}}^{+}$ by photoionization.

Charge-density excitations of a simple ionic liquid exhibit an anomalous decrease of their spectral linewidth with increasing wave number. We explain this phenomenon on the basis of charge-current decay processes. We show that it is not sufficient to identify the frequency-integrated current-decay rate as a decreasing function of wave number. Notably, the frequency dependence of this rate, which is governed by mode-decay processes, plays a crucial role.

It is demonstrated that the initial decay of the number-fluctuation autocorrelation from Brownian particles is not exponential with $\frac{\mathrm{Dt}}{l^2}$, where $l$ is the dimension of the sampling volume with sharp boundaries, $t$ is the correlation time, and $D$ is the particle diffusivity. Experimental results show that the initial rate of change of the measured correlation function is consistent with the theoretical expression for diffusing particles particles of radii between 30 Å and 1 μm.

We report the first calculation of the photodetachment cross section for the metastable, $1s2s2p{}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$ state of ${\mathrm{He}}^{-}$. Extensive configuration-interaction wave functions and the Stieltjes-moment-theory technique were used to determine the total cross section from threshold to 3.0 eV. The $1s2p^2{}_{}{}^4{}_{}{}^{}P_{}^e{}_{}{}^{}$ state of ${\mathrm{He}}^{-}$ gives rise to a very large (∼ 24 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$) and narrow peak 10 meV above the $2^3{P}^o$ threshold.