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The hydrogenic system, confined in an off-centre oscillator potential, is separable in terms of elliptic coordinates. Its general properties are analysed and energies are obtained for some states, for some values of displacement and potential strength. A model wave function is developed and used to obtain the energies and polarizabilities for the ground state. PACS Nos.: 03.65.Ge, 73.21.La, 78.67.Hc

A simple description of the spectrum of confined hydrogen atom is obtained in terms of an scheme involving interpolation between the expressions for large and small values of the confining radius. Satisfactory agreement is shown to exist between the eigen energies thus calculated and exact values. The scheme is extended for helium and lithium. With the simulation of interaction between the electrons by a screened nuclear charge, some energy levels are deduced for the confined helium and lithium.PACS Nos.: 03.65.Ge, 73.21.La, 78.67.Hc

A hydrogen atom in a high-density plasma is simulated by a model in which the hydrogen atom is confined in an impenetrable spherical box, with the atom at the centre. For the proton–electron interaction the Debye–Huckel potential is used. Variational wave functions are proposed for the 1s and 2p states. Energies calculated from these for different values of the radius of box (r0) are shown to be in good agreement with the exact values. The variational wave functions are further employed to calculate the absorption oscillator strength for the 1s [Formula: see text] 2p transition and the dipole polarizability for different values of r0. PACS Nos.: 03.65.Ge, 32.70.Os, 31.70.Dk, 52.20.–j

The effect of high pressure on a hydrogen atom has frequently been simulated by enclosing the atom in an impenetrable spherical box. It is shown that for such a confined hydrogen atom placed at the centre of a spherical box a simple scaling relation exists between the energy and the radius of the confining box for 1s, 2p, 3d, and 4f levels, and another similar relation exists for 2s, 3p, and 4d levels.

The energies of ten excited states of screened two-dimensional excitons in a semiconducting quantum-well structure are calculated as a function of the screening parameter qs by the WKB method. The screening of the Coulomb interaction between the electron-hole pair by the free carriers present is taken into account by using the screened potential obtained by Stern and Howard (1967). The energies of the excited states are found to decrease with increasing values of the screening parameter qs in all cases. Further the levels become unbound at finite values of the screening parameter. Critical screening parameters are estimated for the ten states. PACS Nos.: 73.21Fg, 78.67De, 71.35-y, 71.35Cc Resume : Nous presentons un calcul WKB pour les energies de dix etats excites d'excitons blindes (ecran) en 2-D dans un puits quantique de semi-conducteur, en fonction du parametre d'ecran qs. L'interaction de Coulomb avec ecran entre les paires electron-trou par les porteurs de charges libres est decrit par le potentiel avec ecran de Stern et Howard (1967). Dans tous les cas, nous trouvons que les energies d'excitation decroissent lorsqu'augmente le parametre qs. De plus, les etats excites cessent d'etre lies pour des valeurs finies de qs. Nous donnons les valeurs critiques du parametre qs pour les dix etats. (Traduit par la Redaction)

In certain endohedral systems a metallic ion is trapped inside C 60 such that the energy minimum corresponds to an off-centre position of the ion. A simple analytical function is proposed to represent the potential–energy curve for such systems. The applicability of this function to potential energy curves of endohedral Na + and Li + ions in C 60 is demonstrated and it is then used to calculate the structure of spectra for the two systems.

Two parametric relations are proposed for calculating the level energies of an electron bound in a screened Coulomb potential in a plasma. The first relation is between the energies of levels which have the same l quantum number. The second relation is able to represent the bound-state energies for 1s, 2p, 3d...levels as a function of the screening parameter to a good degree of accuracy. These two relations taken together can give the energies of any level up to and including n = 8, and estimated energies for n = 9 and 10 for any value of ne and Te. These are relevant for at least three topics in plasma physics. The application of these relations for the calculation of the partition function of plasmas is discussed.

A hydrogen atom confined in a spherical box with impenetrable surface is investigated. The critical cage radius , at which a state is no longer bound is calculated for levels up to and including n = 10. Regularities present in these radii are pointed out. An empirical equation is proposed between and n for a fixed . The total number of bound states is also studied as a function of .

Wavefunctions are proposed for the 1s, 2p and 3d states of the compressed hydrogen atom at high pressures. It is shown that these wavefunctions give highly accurate energies in the positive energy region.

We present a systematic perturbative method for calculating the binding energies of ro-vibrational quantum states for a finite depth potential. Using an asymptotic expansion in powers of 1/η, where η is the dimensionless physical depth parameter, explicit calculations are performed. Our analytic results lead to highly convergent series for the binding energies, and numerical results for realistic potentials such as Morse and Lennard-Jones potentials are found to be in excellent agreement with the exact ones.

Computations of energy levels, expectation values of various powers of internuclear separation, and Franck–Condon factors for molecular potentials have been carried out within the framework of shifted large‐N technique. In contrast to other perturbative as well as semiclassical calculations, we obtain compact analytic expressions for these quantities. For illustration, our predicted results for perturbed Kratzer potential are compared with those derived by numerical integration. The method gives quite accurate results for a wide range of rovibrational quantum numbers. Further possible applications, in particular, to Morse oscillators are finally discussed.

The conditions for the existence of an ion-acoustic double layer in a plasma with warm ions and two distinct groups of hot electrons have been studied using the Sagdeev potential method. A comparison is made with the published results of Bharuthram and Shukla for cold ions and a two-temperature electron population. Numerical studies have been made to find out the effect of a finite ion temperature on the Mach number of the double layers.

A simple asymptotically correct model potential is considered for the valence electron in an alkali atom. Superposed with the confining infinite barrier potential, this potential yields the energies of various states and the dipole polarizability of the ground state of the confined alkali atom. Superposed with the fullerene shell potential, this potential yields the energies of the alkali atom inside a fullerene cage. Numerical results are presented for Li, Na, K, Rb, and Cs under such confinements. PACS Nos.: 03.65.Ge, 73.21.La, 78.67.Hc

The Inglis-Teller relation, generalized for a hydrogen-like or alkali-like ion with an arbitrary core charge, is used to estimate the electron density in the emission-line region of Wolf-Rayet stars. It is found that the electron density in the region which gives rise to Heii emission lines is ≃4×1014 cm−3.

The Drickamer–Franck–Slichter model for the effects of high pressure on electronic spectra is reformulated by incorporating the Kratzer–Fues potential to allow for anharmonicity. The configuration‐coordinate parameters for the ground and excited states are shown to be readily derivable from the experimental data. The proposed model is applied to six cases for which experimental data are available.

Energy levels of neutral atoms have been re-examined by applying the method of shifted large-N expansion (whereN is the number of spatial dimensions) to the model Yukawa potential with a modified screening parameter. The predicted shell binding energies are found to be quite accurate over the entire range of the atomic number Z up to 84 and compare very well with those obtained within the framework of hypervirial-Pade scheme. It is observed that the large-N technique which is hitherto used in different contexts may also be applied to other areas of atomic physics.

The ground-state energy of the helium atom in a plasma is calculated by the variational method with the static screened Coulomb potential as the interparticle potential. This is used to calculate the ionization energy of the helium atom as a function of the screening parameter. The critical value of the screening parameter at which the ionization energy becomes zero is also estimated.

A variational solution of the Thomas-Fermi differential equation is obtained. The proposed solution is used to calculate the total ionization energy of atoms, and also the repulsive interaction energy between rare-gas atoms. It is shown that the results obtained by the proposed function are better than those obtained from Csavinszky's function for medium and high atomic number elements.

The recently developed shifted 1/N expansion technique, where N is the number of spatial dimensions, is applied to the study of the energy levels of the hydrogen atom in presence of intense laser radiation. The analytic expressions for the energy eigenvalues En,l yield very accurate results for a wide range of n,l and the intensity-dependent truncation parameter lambda appearing in the effective laser-dressed binding potential. It is found that the level ordering satisfies En,l>En,l' for l

A numerical method is used to calculate the vibrational energy eigenvalues for the Lennard-Jones 8-6 potential. Values are given for the excimers NaAr, NaKr, NaXe, KNe, KAr, KKr, and KZe. Systematics of the eigenvalues are studied for three values of β, where β is a dimensionless parameter which is a measure of the strength of the interatomic potential. Birge-Sponer plots are made and it is shown that a plot of β 1 2 ΔG v+ 1 2 versus v′ β 1 2 , where v′ is the quantum number of the upper level, yields a “universal” curve which is almost independentt of β.

Fresh calculations of the X-ray screening constantsσ2 forLIILIII,MIIMIII andMIVMV have been made. It has been found thatσ2 is not absolutely constant for differentZ. Some regular variations inσ2 with electronic shell structure have been noted.

For nuclei withZ ≥ 84 andN ≥ 128, it has been shown that (Q - 0.625Z) is a smooth function of the mass numberA, whereQ is the α-disintegration energy. This has been utilized to develop two equations forQ. Results by these two equations are compared with those given by Roger’s equation.

The effective ion–ion interaction for sodium is calculated from a fundamental basis, using a one-orthogonalized plane wave (OPW) bare electron – ion matrix element, and the Geldart and Taylor electron gas screening function. Particular attention is paid to the form of the interaction for asymptotically large ion–ion separation, and it is shown that this interaction varies approximately as the fifth power of the ion–ion separation in the region in which the amplitude of the potential is appreciable. The elastic constants, cohesive energy, and the specific heats of body-centered cubic (b.c.c.) and close-packed sodium are shown to be in excellent agreement with experiment. The equilibrium and stability of the model sodium lattice described by the proposed potential are discussed, and it is concluded that the potential can be used tentatively in a fundamental calculation of atomic properties of defects.

A two-parameter wavefunction for the 1s sigma ground state of H2+ is proposed and is shown to give good results for the energy over a wide interval of the internuclear separation. Comparison is made with results obtained from several other wavefunctions.

Hall mobility and other transport properties of electromas in a completely ionized gas were investigated when a magnetic field is applied, taking into account electron-electron scattering. Results are presented for different mean ionic charges. (auth)

A new asymptotic approximation for the average lifetime of hydrogenic levels is developed and is shown to be much better than the one suggested by Bethe and Salpeter.

The effect of using denser charge distributions in theoretical calculations of the energy of x rays emitted during 2p--1s transitions in mu mesons is examined. The denser distributions seem to largely resolve discrepancies between earlier experimental and theoretical results. (D.C.W.)

The variation of drift and Hall mobilities of electrons in a fully ionized gas with magnetic field was investigated. (auth)

A geometric-mean type of variation function has been examined for the 1sσ state of HeH2+ and has been found to give very good results for the energy.