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The Wigner distribution function for a quantum system with an infinitely deep square-well potential is obtained analytically and presented by plotting the Wigner distribution functions on the quantum phase space. The cross-matrix elements of the expectation values of some classical quantities are also obtained. The case of the symmetrical square-well potential is studied briefly.

Creation and existence of order are of philosophical significance and practical utility. This paper spells clear, succinct, yet comprehensive directives for order creation, existence and total destruction, in the form of nine exclusive directives established from the broken symmetry in the inter-convertibility of order and disorder stated by the Entropy Principle and the Law of Maximum Entropy Production. They form the guiding principles for order creation, stable existence and total destruction, at all scales. A representative mathematical model of order within disorder portrays these directives and spells the sustainability criterion for order existence. Since order is possibly stable only in chaotic systems, some of these directives have a probabilistic tone.

Energy levels and radiative rates for transitions among the lowest 24 fine-structure levels belonging to the 1s²nl (n ≤ 5) configurations of Li-like O VI have been calculated using the fully relativistic GRASP code. Additionally, collision strengths for transitions among these levels have been computed over a wide energy range below 63 Ry, using the Dirac Atomic R-matrix Code. Resonances have been resolved in a fine energy mesh in order to calculate the effective collision strengths. Results for radiative rates, collision strengths, and effective collision strengths are presented for all transitions. Comparisons with other available results are made, and the accuracy of the present data is assessed. Energy levels are expected to be accurate to within 1%, while other parameters are probably accurate to better than 20%.

A large scale configuration-interaction (CI) calculation is performed of excitation energies for 109 fine-structure levels belonging to the configurations (1s²2s²2p⁶)3s²3p(²P^o), 3s3p²(²S, ²P, ²D, ⁴P), 3s² 3d(²D), 3p³(⁴S^o, ²P^o, ²D^o), 3s3p(³P^o) 3d(²P^o, ²D^o, ²F^o, ⁴P^o, ⁴D^o, ⁴F^o), 3s3p(¹P^o)3d(²P^o, ²D^o, ²F^o), 3p²(¹S)3d(²D), 3p²(¹D)3d(²S, ²P, ²D), 3p²(³P)3d(²P, ²D, ⁴P), 3s3d²(²S, ²P, ²D, ⁴P), 3p3d²(¹S)(²P^o), 3p3d²(¹D)(²P^o, ²D^o, ²F^o), 3p3d²(¹G)(²F^o), 3p3d²(³P)(²P^o, ²D^o, ⁴S^o, ⁴P^o, ⁴D^o), 3p3d²(³F)(²D^o, ²F^o, ⁴D^o, ⁴F^o), 3s²4s(²S), 3s²4p(²P^o), 3s²4d(²D), 3s²4f(²F^o), 3s3p(³P^o)4s(²P^o, ⁴P^o), and 3s3p(¹P^o)4s(²P^o) of Al-like Titanium, using the CIV3 computer code of Hibbert. The states are represented by very extensive CI wave functions. The relativistic effects in intermediate coupling are incorporated by means of the Breit–Pauli Hamiltonian, which consists of the non-relativistic term plus the one-body mass correction, Darwin term, and spin-orbit, spin-other-orbit, and spin-spin operators. The errors, which often occur with sophisticated ab initio atomic structure calculations, are reduced to a manageable magnitude by adjusting the diagonal elements of the Hamiltonian matrices. Our calculated excitation energies, including their ordering, are in excellent agreement with the available experimental results. We predict new data for several levels where no other theoretical and experimental results are available. The mixing among several fine-structure levels is found to be very strong, with most of the strongly mixed levels belonging to the (1s²2s²2p⁶)3p²3d and 3p3d² configurations. The enormous mixing among several fine-structure levels makes it very difficult to identify them correctly. Perhaps, that may be the reason for the lack of experimental results for these levels. We believe that our extensive calculated values can guide experimentalists identify the fine-structure levels. From our radiative decay rates, we have calculated radiative lifetimes of the high angular momentum and high spin levels 3s3p3d(⁴F_J). The large difference in the lifetime of the 3s3p3d(⁴F^o_1.5) level obtained from our two calculations (ab initio & adjusted energies) is explained. We conclude by recommending remeasurements of the energy levels of the 3s3p3d(⁴F^o_1.5) in Ti X and Fe XIV to reduce the current large experimental uncertainties.

A method alternative to the density matrix formalism is applied to derive a general expression for the radiative decay probability following the photoionization of polarized atoms in two-step approximation. The graphical technique of the angular momentum theory is used for the integration over angular and spin variables. The general expression joining both steps of photoionization and fluorescence contains the possibility to investigate the polarization of all particles in the initial and final states and the angular distributions as well as angular correlations of photoelectrons and radiation. A simple way to get the expressions for special cases of the angular distribution and polarization of fluorescence radiation in the photoionization of randomly orientated and polarized atoms is given as an example of the practical application of the general formula.

In this work, a classical mechanics study of the autoionization process induced by ion impact is performed. The electron distribution in momentum space is obtained and compared with the results of the continuum distorted wave quantum theory. Typical structures arising in quantum and classical treatments are identified and compared. Oscillatory profiles for the autoionization spectrum are obtained within the present classical picture, in contrast with existing models which attach them to a purely quantum behavior.

Relativistic Configuration Interaction results are obtained for the lowest 9 J = 0 even parity and the lowest 30 J = 1 odd parity levels of Mo V. Some of the levels (e.g. 4p⁵4d³) are new to this work, and several of the others (e.g. 5s², 5p², 4d6d and 5s5p ¹P₁) are repositioned. Average errors for the remaining energy differences are 229 cm^-1 (J = 0) and 368 cm^-1 (J = 1). All 360 electric dipole f-values connecting these levels have been obtained, and the average gauge agreement for the 88 transitions with f > 0.01 is 3.1%.

The properties of dust-Alfvén waves in self-gravitating partially ionized astrophysical dusty magnetoplasmas are investigated. Accounting for the self-gravitational and inter-particle collisional effects in a hydrodynamic model of multi-species collisional plasmas, we derive a dispersion relation which exhibits a linear coupling between the modified Alfvén waves and Jeans modes. The influence of the electron density depletion on the growth rate of gravitationally unstable coupled Alfvén-Jeans modes is numerically investigated.

The implosion dynamics and fusion parameters of a high density θ-pinch plasma driven by a multicascade liner Z-pinch is investigated. The imploding multicascade liner Z-pinch plasma traps an axial magnetic field, compressing it to several megagauss in an extremely short time. The fast changing magnetic flux then induces an azimuthal θ-current on the fiber surface, with a rise time an order of magnitude smaller than the applied Z-pinch current. Numerical simulation shows that for optimum choice of shell thickness of the multicascade liner system, high-densities and temperatures can be realized for fibers seeded with some high-Z impurities. At peak compression the fuel densities of the order of 10²⁶/cm³ and temperature about 10 keV can be achieved on a time scale of the order of 0.5 ns, yielding the Lawson criterion parameter nτ ≥ 10¹⁴ s/cm³ for DT-plasma.