Equilibrium thermodynamic properties of binary hard-sphere mixtures from integral equation theory

We present an equilibrium thermodynamic properties of binary hard-sphere mixtures from integral equation approach combined with the Percus-Yevick (PY) and the Martynov-Sarkisov (MS) approximations. We use the virial, the compressibility and the Boubl\'{i}k-Mansoori-Carnahan-Starling-Leland (BMCSL) equations of state in the PY approximation, while the virial equation of state is only employed in the MS approximation. We employ a closed-form expression for evaluating the excess chemical potential. The excess Helmholtz free energy is obtained using the Euler relation of thermodynamics. For a number of binary sets of the mixtures we compare our findings for thermodynamic properties with previously obtained results in the literature. Generally, the findings from the MS approximation show better agreement with the results than those from the PY approximation.Comment: 10 pages, 6 figure

Pressure consistency for binary hard-sphere mixtures from an integral equation approach

The site-site Ornstein-Zernike equation combined with the Verlet-modified bridge function has been applied to the binary hard sphere mixtures and pressure consistency has been tested. An equation of state has been computed for the case where a packing fraction is $\eta = 0.49$, diameter ratios are $\sigma_{2}/\sigma_{1} = 0.3$ and $0.6$, and the mole fractions are $x_{1} = 0.125, 0.5, 0.75$, and $1$. An excess chemical potential for each component has been obtained as well. Our findings for thermodynamic properties are in good agreement with available data in literature.Comment: 9 page

Calculation of the entropy for hard-sphere from integral equation method

The Ornstein-Zernike integral equation method has been employed for a single-component hard sphere fluid in terms of the Percus-Yevick (PY) and Martynov-Sarkisov (MS) approximations. Virial equation of state has been computed in both approximations. An excess chemical potential has been calculated with an analytical expression based on correlation functions, and the entropy has been computed with a thermodynamic relation. Calculations have been carried out for a reduced densities of 0.1 to 0.9. It has been shown that the MS approximation gives better values than those from the PY approximation, especially for high densities and presents a reasonable comparison with available data in the literature.Comment: 7 page

A method for accurate electron-atom resonances: The complex-scaled multiconfigurational spin-tensor electron propagator method for the ^2P\, \mbox{Be}^{-} shape resonance problem

We propose and develop the complex scaled multiconfigurational spin-tensor electron propagator (CMCSTEP) technique for theoretical determination of resonance parameters with electron-atom/molecule systems including open-shell and highly correlated atoms and molecules. The multiconfigurational spin-tensor electron propagator method (MCSTEP) developed and implemented by Yeager his coworkers in real space gives very accurate and reliable ionization potentials and attachment energies. The CMCSTEP method uses a complex scaled multiconfigurational self-consistent field (CMCSCF) state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. CMCSCF was developed and applied successfully to resonance problems earlier. We apply the CMCSTEP method to get ^2 P\,\mbox{Be}^{-} shape resonance parameters using $14s11p5d$, $14s14p2d$, and $14s14p5d$ basis sets with a $2s2p3d$\,CAS. The obtained value of the resonance parameters are compared to previous results. This is the first time CMCSTEP has been developed and used for a resonance problem. It will be among the most accurate and reliable techniques. Vertical ionization potentials and attachment energies in real space are typically within $\pm 0.2\,eV$ or better of excellent experiments and full configuration interaction calculations with a good basis set. We expect the same sort of agreement in complex space.Comment: 13 pages, 3 figue

Numerical solution to the time-dependent Gross-Pitaevskii equation

We solve the time-dependent Gross-Pitaevskii equation modeling the dynamics of the Bose-Einstein condensate trapped in one-dimensional and two-dimensional harmonic potentials using the split-step technique combined with a pseudospectral representation. We apply this method to the simulation of condensate breathing when an inter-particle interaction in the system is not too strong.Comment: 11 pages, 8 figure

Editorial

No abstract in Englis

Ionization of the Hydrogen Molecular Ion by Strong Infrared Laser Fields

The ionization of simple molecular targets, such as molecular hydrogen, or even the molecular hydrogen ion (\mbox{H}^{+}_{2}) by strong laser fields has become the focus of experimental research in the past few decades. On the theoretical side the problem presents two challenges: on the one hand one has to solve the problem numerically even in the one-electron case (\mbox{H}^{+}_{2}), since no analytic closed-form solution is possible; on the other hand there is the many-electron problem (\mbox{H}_{2} and other diatomic molecules, such as \mbox{N}_{2}, \mbox{O}_{2}, etc.), which currently is at the limit of computational feasibility (\mbox{H}_{2}), or exceeds it for molecules with more than two electrons. In this thesis the single-electron problem of the hydrogen molecular ion in intense continuous-wave laser fields is addressed. The focus is on ionization rates of the molecule as a function of internuclear separation within the framework that the motion of the nuclei can be neglected (Born-Oppenheimer approximation). First, the problem of the DC limit is considered, i.e., a strong static electric field is applied along the internuclear axis. The field ionization rate is calculated by solving a stationary non-hermitean Schr\"odinger equation in a suitable coordinate system (prolate spheroidal coordinates). Some previously obtained values from the literature are reproduced; for larger internuclear separations improved values are obtained. For the more interesting case of an infrared (continuous-wave) laser field Floquet theory is applied to transform the time-dependent Schr\"odinger equation for the electronic motion into a non-hermitean coupled-channel stationary problem. Ionization rates are found as a function of laser frequency ($\omega$), and the low-frequency limit is pursued to understand how one can establish a connection to the DC limit. Results are obtained for the two lowest electronic states, which are named the {\it gerade} and {\it ungerade} (or even and odd) ground states in the field-free limit. From the calculated results it is observed that the ionization rates peak at certain internuclear separations, such that a dissociating \mbox{H}^{+}_{2} molecule will be preferentially field ionized. In addition, the thesis reports on calculations of so-called high harmonic generation - a process where photo-electrons acquire energy from the laser field, are deflected back by the linearly polarized laser and recombine under the emission of photons with energies that correspond to odd-integer multiples of the laser photon energy

Observation of ηc→ωω\eta_c\to\omega\omega in J/ψ→γωωJ/\psi\to\gamma\omega\omega

Using a sample of $(1310.6\pm7.0)\times10^6$ $J/\psi$ events recorded with the BESIII detector at the symmetric electron positron collider BEPCII, we report the observation of the decay of the $(1^1 S_0)$ charmonium state $\eta_c$ into a pair of $\omega$ mesons in the process $J/\psi\to\gamma\omega\omega$. The branching fraction is measured for the first time to be $\mathcal{B}(\eta_c\to\omega\omega)= (2.88\pm0.10\pm0.46\pm0.68)\times10^{-3}$, where the first uncertainty is statistical, the second systematic and the third is from the uncertainty of $\mathcal{B}(J/\psi\to\gamma\eta_c)$. The mass and width of the $\eta_c$ are determined as $M=(2985.9\pm0.7\pm2.1)\,$MeV/$c^2$ and $\Gamma=(33.8\pm1.6\pm4.1)\,$MeV.Comment: 13 pages, 6 figure

Observation and study of the decay J/ψ→ϕηη′J/\psi\rightarrow\phi\eta\eta'

We report the observation and study of the decay $J/\psi\rightarrow\phi\eta\eta'$ using $1.3\times{10^9}$ $J/\psi$ events collected with the BESIII detector. Its branching fraction, including all possible intermediate states, is measured to be $(2.32\pm0.06\pm0.16)\times{10^{-4}}$. We also report evidence for a structure, denoted as $X$, in the $\phi\eta'$ mass spectrum in the $2.0-2.1$ GeV/$c^2$ region. Using two decay modes of the $\eta'$ meson ($\gamma\pi^+\pi^-$ and $\eta\pi^+\pi^-$), a simultaneous fit to the $\phi\eta'$ mass spectra is performed. Assuming the quantum numbers of the $X$ to be $J^P = 1^-$, its significance is found to be 4.4$\sigma$, with a mass and width of $(2002.1 \pm 27.5 \pm 21.4)$ MeV/$c^2$ and $(129 \pm 17 \pm 9)$ MeV, respectively, and a product branching fraction $\mathcal{B}(J/\psi\rightarrow\eta{}X)\times{}\mathcal{B}(X\rightarrow\phi\eta')=(9.8 \pm 1.2 \pm 1.7)\times10^{-5}$. Alternatively, assuming $J^P = 1^+$, the significance is 3.8$\sigma$, with a mass and width of $(2062.8 \pm 13.1 \pm 7.2)$ MeV/$c^2$ and $(177 \pm 36 \pm 35)$ MeV, respectively, and a product branching fraction $\mathcal{B}(J/\psi\rightarrow\eta{}X)\times{}\mathcal{B}(X\rightarrow\phi\eta')=(9.6 \pm 1.4 \pm 2.0)\times10^{-5}$. The angular distribution of $J/\psi\rightarrow\eta{}X$ is studied and the two $J^P$ assumptions of the $X$ cannot be clearly distinguished due to the limited statistics. In all measurements the first uncertainties are statistical and the second systematic.Comment: 10 pages, 6 figures and 4 table