A one-dimensional quantum gas with δ-function interaction is known to be integrable for any finite number of particles. We show that in the thermodynamic limit invariants of motion are destroyed in conjunction with a class of singular density matrices that appear commonly in both equilibrium and nonequilibrium statistical mechanics. The system becomes nonintegrable, due to Poincaré resonances. However, the eigenvalue problem of the Liouville–von Neumann operator $L_H$ may be solved in an extended functional space that contains the singular density matrices. We may in this way describe the approach to equilibrium. This is a simple example of the Liouville space extension of quantum mechanics, due to Prigogine and his co-workers. The fundamental quantity in this formulation is the probability (and not the wave function). We obtain indeed an irreducible complex spectral representation of $L_H.$ Irreducible means that the eigenstates of $L_H$ cannot be implemented by wave functions, and complex means that the eigenvalues are complex numbers, whose imaginary parts determine relaxation times of the system. The dynamical evolution is described by a semigroup. Due to dissipative effects the real part of the eigenvalues is no more a difference of energy levels, as is the case in standard quantum mechanics.

Vacuum polarization screening corrections to the ground-state energy of two-electron ions are calcualated in the range $Z=20\mathrm{}-100.$ The calculations are carried out for a finite nucleus charge distribution.

Ab initio calculations of $E1\mathrm{}$ transition amplitudes from low-lying odd-parity levels ${}^9{G}_J$ $(J=0\mathrm{}–4)$ and ${}^9{F}_J$ $\mathrm{}(J=1,2\mathrm{})\mathrm{}$ levels to the even-parity states ${}^7{F}_J$ $(J=0\mathrm{}–5),$ ${}^9{H}_J$ $(J=1\mathrm{}–5),$ and ${}^9{D}_J$ $\mathrm{}(J=2,3\mathrm{})\mathrm{}$ were performed using the configuration-interaction method. Using the results obtained for these $E1\mathrm{}$ amplitudes, the oscillator strengths and probabilities of the corresponding transitions were calculated. The estimates of the lifetimes of the odd-parity states are also presented.

The theory of sub-Doppler spectra of molecules subjected to rotational and translational relaxation in the supersonic jet is developed in a weak collision approximation. The broad background of unknown origin (“the pedestal”) emerging beneath the resolved spectrum is attributed to a biline structure of all hyperfine components whose broad lines overlap. Such a composite structure is shown to appear neither at stationary nor at nonstationary saturation regimes, but only in the case of nearly collisionless molecular transit through the laser beam of finite width. The theory accounting for a single collision during transit explains the rise of the pedestal at shorter distances from the nozzle and higher backing pressure.

An ab initio potential for the interaction of the neutral helium atom with antiprotons and protons is calculated using the Born-Oppenheimer approximation. Using this potential, the annihilation cross section for antiprotons in the energy range 0.01 $\mu$eV to 1 eV is calculated.

We investigate hierarchical representation of three-electron radial excitations, relying on the replacement of a sequence of ordered individual electron radial coordinates by a hierarchical sequence of hyperspherical radial variables. In the spirit of the hyperspherical method we argue that the latter variables allow adiabatic quasiseparability of the three-electron wave function. We examine this by approximately evaluating hyperspherical adiabatic potential curves and channel functions for the Li${(s}^3)$ configuration. The hierarchical representation permits one to display manifold aspects of the triply excited states with a pair of radial quantum numbers.

We have experimentally studied the nonradiative transport of excitation in a dense $[N$=(0.3-2.5)×${10}^{17}{\mathrm{cm}}^{\mathrm{-}3}]$ potassium vapor. We show that in such a high-density vapor the diffusive nonradiative transport of excitation via “hopping” of excitation in dipole-dipole collisions between excited- and ground-state atoms is dominant over the radiative transport through photons. The nonradiative transport mechanism becomes visible in the fluorescence-excitation spectrum signal as a sharp dip close to the resonance frequency. The appearance of the dip, its shape, width, and density dependence can all be explained in terms of a simple diffusion model for the nonradiative transport. This yields values for the diffusion coefficient and the resonance-exchange rate coefficient.

Radiative corrections using third-order perturbation theory are considered in a theoretical calculation of the Zeeman effect. The corrections have been calculated for the states $2{}^{3}P$ of helium, and found to be of the same order as other radiative corrections calculated by Anthony and Sebastian [Phys. Rev. A 48, 3792 (1993)].

Complete five-body dynamical calculations of antiproton $\left(\overline{p}\right)$ capture by the hydrogen molecule $\left({\mathrm{H}}_2\right)$ have been carried out using a generalization of the Kirschbaum-Wilets method (belonging to a class of quasiclassical methods sometimes called fermion molecular dynamics). The differences between capture by ${\mathrm{H}}_2$ and the H atom are found to be dramatic. The effects due to the two-center structure, rotational motions, and vibrational motions are distinguished. Of particular importance, the vibrational degree of freedom enables the molecule to capture antiprotons having lab energies above 100 eV, whereas atomic capture cuts off sharply above the ionization threshold of 27 eV (in the lab system). Antiproton capture by the atom is calculated by the same method as well as by the classical-trajectory Monte Carlo method, which is applicable only to the atom. The initial quantum numbers (assigned quasiclassically) of the $\overline{p}p$ formed are found to be shifted to significantly smaller values for the molecular target; the $n$ distribution is also narrower for the molecular target as compared with the atomic target.

The equation of motion method is used to express the external potential in terms of the first- and second-order interacting density matrices (DMs) for a molecule. By also introducing noninteracting DMs built from the Kohn-Sham (KS) reference system orbitals, the exchange-correlation potential is derived. Applying the perturbation theory of Görling and Levy [Phys. Rev. B 47, 13 105 (1993)], this potential is separated into the exchange-only potential and various orders of the correlation terms. Each potential term can be determined self-consistently from a specific equation written in terms of both occupied and excited KS orbitals and differences of orbital energies, plus potential terms of lower orders. Naturally, the determination of these orbitals and energies requires a self-consistent solution of KS equations. Explicit expressions for calculation of the exchange potential and the leading term of the correlation potential are obtained and discussed. An approximate exchange potential written directly in terms of noninteracting DMs is also proposed.

The properties of the ground state of the muonic Helium atom $e\mu {\hspace{0.5em}}^4{\mathrm{He}}^{2+}$ have been calculated nonvariationally. The correlation function hyperspherical harmonic method utilizing a nonlinear parametrization of the correlation function has been used. Up to $N=561\mathrm{}$ coupled second-order differential equations were taken into account. Although all parametrizations of the correlation function accelerate the convergence with respect to linear parametrizations by several orders of magnitude, an especially fast converging parametrization was found. All parametrizations make the observables converge to the same values in the limit of large $N$. The lowest-order hyperfine splitting obtained, 4454.206(3) MHz, has error margins smaller than the differences in the literature. One variational value is 0.023 MHz lower and another 0.013 MHz higher, after the adjustment for the different masses used. The expectation value of the distance between the electron and the muon also differs slightly from that in the literature, while the energy obtained was below the variational values.

We calculate the decay rates due to spontaneous emission for electronic states described by Trojan wave packets. The spontaneous decay rate for a typical Trojan state $\mathrm{}(n=60\mathrm{})\mathrm{}$ is six orders of magnitude smaller than the ionization rate and it is about one order of magnitude smaller than the rate for the corresponding ordinary circular Rydberg state.

We present an accurate and flexible method for the numerical simulation of the evolution of electronic wave packets in alkali atoms. As a testing ground for our approach, we calculate the dynamics of Stark wave packets in cesium for different electric-field strengths. An agreement with recent experimental results is demonstrated, and especially the influence of the electric-field strength and the core scattering on the recurrence spectra is reproduced accurately.

Doubly excited ${}^1{S}^e$ and ${}^1{D}^e$ Feshbach resonances of ${\mathrm{H}}^{\mathrm{-}}$ lying below the $\mathrm{H}\mathrm{}(N=3\mathrm{})\mathrm{}$ threshold under the influences of external electric and magnetic fields in parallel directions are investigated theoretically using a method of complex-coordinate rotation. Products of Slater-type orbitals are used to represent the two-electron wave functions, with $l_{\max }=9\mathrm{}$ being employed for the individual electron. Block matrices with up to $L_{\max }=5\mathrm{}$ including ${}^1{S}^e,$ ${}^1{P}^o,$ ${}^1{D}^e,$ ${}^1{F}^o,$ ${}^1{G}^e,$ and ${}^1{H}^o$ states are used. Convergence behavior for the resonance parameters (resonance energy and width) is examined by using different values of $L_{\max }.$ Results for the combined electric and magnetic field effects on the $M_L=0\mathrm{}$ components of the ${}^1{S}^e\mathrm{}\left(1\right)\mathrm{}$ and ${}^1{D}^e\mathrm{}\left(1\right)\mathrm{}$ Feshbach resonances are reported.

Quantum calculations have been carried out on the vibrational and rotational excitation processes for CO molecules in collision with positron projectiles below the threshold of Ps formation ${(E}_{\mathrm{coll}}<~7\mathrm{}\mathrm{eV}).\mathrm{}$ The coupled equations have been solved for the vibrationally inelastic process in the body-fixed frame of reference, and Born-type corrections for the divergent behavior of the angular distributions due to the permanent molecular dipole have been applied. Detailed comparisons are made between the partial (rotational and/or vibrational) integral and differential cross sections and earlier available calculations and measurements.

The results of our exact partial-wave triply differential electron-atom bremsstrahlung calculations are compared with those of simpler theories. This triply differential cross section is expected to provide a more sensitive test of the adequacy of theoretical descriptions of the process than the doubly differential cross section, not observing the scattered electron. Our method is an extension and reformulation of the relativistic partial-wave and multipole decomposition method of Tseng and Pratt, which was only used to calculate the doubly differential cross section. We compare our calculations to those using the Bethe-Heitler equation (first Born approximation including form factors) and to calculations using the formalism of Elwert and Haug (which utilize approximate Coulomb wave functions and form factors). We examine silver and heavier elements, where the validity of the simpler theories is in question. For such elements we find no significant region of agreement with the Bethe-Heitler theory. We find some agreement with the theory of Elwert and Haug at small momentum transfers, improving with increasing energy. We find poor agreement of our results with the Elwert-Haug results for large momentum transfers. The differences from simpler theories are indeed much greater in the triply differential cross section than in the double differential cross section.

We present a measurement of the partial and differential photoionization cross sections for production of the fine-structure states of Cl${}^{+\hspace{0.5em}3}{P}_J$ in the region of the ${3p}^{41}\mathrm{Dnl}\hspace{0.5em}\mathrm{}(l=0,2\mathrm{})\mathrm{}$ autoionizing resonances. All series of resonances show distinctive behavior for the $J=2\mathrm{}$ to $J=1\mathrm{}$ cross-section ratio. The angular distribution parameter $\beta$ was also measured for the two principal ionic states $\mathrm{}(J=1,2\mathrm{})\mathrm{}$. The behavior of $\beta$ is very similar for both $J=1,2\mathrm{}$ channels, except at the $\mathrm{LS}$-forbidden ${\mathrm{nd}}^{2}S$ resonance series, where the $J=2\mathrm{}$ channel shows a pronounced dip that indicates an important contribution from the parity-unfavored $\epsilon d$ photoelectron waves. The widths of the ${4d}^{2}S$, ${6s}^{2}D$, and ${7s}^{2}D$ resonances were measured and the results are compared with available theoretical calculations.

Calculations on the Auger decay of CO after the $\mathrm{C}1s\to 2{\pi }^{*}$ excitation have been performed utilizing a multichannel Schwinger approach. The bound orbitals used to expand the multichannel configuration-interaction wave functions of the ion state were the natural orbitals of a single excitation and double excitation configuration-interaction (CI) calculation on the $\mathrm{C}{1s}^{-1}$ core-hole state of CO. Fixed-nuclei photoionization cross sections were then obtained with target states represented by complete active space CI wave functions. An analysis of the resulting cross sections using Fano’s spectral line profile and the lifetime vibrational interference theory has lead to photoabsorption profiles in good agreement with experimental measurements. Additionally, we have found good agreement with experimental data for the resulting photoelectron and photoemission spectra.

We employ the four-body continuum distorted-wave (CDW-4B) method to compute the total cross sections for the single electron-capture process ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{e}{(1s}^2)\to \mathrm{H}\mathrm{}(1s)+{\mathrm{He}}^{+}\mathrm{}(1s)\mathrm{}$ at incident energies ranging from 20 to 20 000 keV. The purpose of the present work is twofold: (i) to verify whether the CDW-4B approximation for one-electron transfer is as successful as for double charge exchange in fast proton-helium collisions and (ii) to search for evidence of dynamic electron correlation effects as a function of increased projectile energy. The validity of our findings is critically assessed in comparisons with the available experimental data in the quoted impact energy range.

Free positrons from electron-positron pairs produced by 33-TeV ${\mathrm{Pb}}^{82+}$ ions in Coulomb collisions with targets of carbon $\left[\right(\mathrm{CH}{)}_x],$ aluminum, palladium, and gold have been measured to determine cross sections and momentum distributions. Upper limits have been established for contributions from multiple pair formation. Comparison with similar data taken for 6.4-TeV ${\mathrm{S}}^{16+}$ ions shows that cross sections scale as the product of the squares of the projectile and target nuclear charges. Positron momentum distributions for ${\mathrm{S}}^{16+}$ and ${\mathrm{Pb}}^{82+}$ ions on all targets are observed to be similar, but indicate a tendency for higher-energy positron emission for the ${\mathrm{Pb}}^{82+}$ projectiles.