Calculation of the lowest 1 S resonance state of the H− anion by the stabilization method

By the example of the lowest resonance state of the H^? system, two versions of the stabilization method are considered: with introduction of an external potential into the Hamiltonian and with enlargement of the single-particle function basis. A comparison of the results suggests the possibility of applying these methods to calculating the resonance parameters in many-electron systems.     

Doubly-Excited States of Two-Electron Systems in Lorentzian Astrophysical Plasmas

The nonthermal effects on the doubly-excited resonance states of two-electron positive ions are investigated in Lorentzian astrophysical plasma environments using highly correlated Hylleraas-type wave functions in the framework of the stabilization method. Resonance parameters (resonance position and width) for Li⁺,  Be²⁺ and B³⁺ are reported for the first time as functions of the spectral index and plasma parameter.     

Doubly Excited <Superscript>1,3</Superscript><Emphasis Type="Italic">P</Emphasis><Superscript>e</Superscript> Resonance States of the Positronium Negative Ion with Coulomb and Screened Coulomb Potentials

We have investigated the doubly excited ^1,3 P ^e resonance states of positronium negative ion with Coulomb and screened Coulomb potentials using highly accurate correlated exponential wavefunctions. For Coulomb interaction, the stabilization and the complex-rotation methods are employed to extract resonance parameters (resonance positions and widths). We have obtained two ¹ P ^e resonances and three ³ P ^e resonances below the n = 3 Ps threshold. In addition to Feshbach resonances lying below n = 3 Ps threshold, we have calculated one ³ P ^e shape resonances lying above the Ps (n = 2) threshold. For screened Coulomb (Yukawa) interaction, we employ the stabilization method to extract resonance parameters as functions screening parameter. The resonance energies and widths for ^1,3 P ^e resonance states of Ps⁻ below the n = 3 Ps threshold for different screening parameters ranging from infinity (Coulomb case) to small values are reported, along with the Ps(3S) and Ps(3P) threshold energies. The screened Coulomb results for the ^1,3 P ^e resonance states are reported for the first time in the literature.     

The ground state and doubly-excited <Superscript>1,3</Superscript>P° states of hot-dense plasma-embedded Li<Superscript>+</Superscript> ions

We have investigated the ground state and the doubly excited ^1,3P^○ resonance states of plasma-embedded Li⁺ ion. The plasma effect is taken care of by using a screened Coulomb potential obtained from the Debye model. A correlated wave function has been used to represent the correlation effect between the charged particles. The ground state of Li⁺ in plasmas for different screening parameters has been estimated in the framework of Rayleigh-Ritz variational principle. In addition, a total of 18 resonances (9 each for ¹P^○ and ³P^○ states) below the n=2 Li⁺ thresholds has been estimated by calculating the density of states using the stabilization method. For each spin state, this includes four members in the 2snp₊ (2≤n ≤5) series, three members in the 2snp_- (3≤n ≤5) series, and two members in the 2pnd (n=3, 4) series. The resonance energies and widths for various Debye parameters ranging from infinity to a small value for these ^1,3P^○ resonance states along with the ground state energies of Li⁺ and the Li²⁺ (1S), Li²⁺ (2S) threshold energies are reported. Furthermore, the wavelengths for the photo-absorption of lithium ion from its ground state to such ¹P^○ resonance states for different Debye lengths are also reported.     

Semimicroscopic description of basic modes of relaxation of the Gamow-Teller resonance

Semimicroscopic approach based on the continuum version of the random-phase approximation and on a phenomenological method for taking into account the fragmentation effect is used to describe quantitatively basic relaxation parameters of the Gamow-Teller resonance in magic and nearmagic nuclei. For the ²⁰⁸Bi nucleus, the results obtained by calculating the resonance parameters in question are compared with respective experimental data.     

Doubly-Excited 1,3 P o States of H− Interacting with Screened Coulomb (Yukawa) Potentials

We have investigated the doubly excited 2s2p ³ P ^o and 2s3p ¹ P ^o resonance states of H⁻ embedded in a model plasma environment. Plasma effects are taken care of by using a screened Coulomb (Yukawa-type) potential. Correlated wave functions are used to represent the correlation effect between the charged particles. The density of resonance states has been calculated using the stabilization method. The calculated resonance energies and widths for various screening parameters are reported.     

Calculation of the Lowest <Superscript>2</Superscript><Emphasis Type="Italic">S</Emphasis> Resonance State of He<Superscript>−</Superscript> by a Stabilization Method

The parameters of the lowest ²S resonance state of the He^? system were calculated using the Coulomb potential stabilization method. It was found that the errors of the resonance energy and width have the same character as that in the earlier studied two-electron systems H^?, He, and Li⁺. It was shown that the errors can be minimized using a single-electron basis sets, which provides the best reproduction of the low-lying states of the helium atom.     

Approximation of photonuclear interaction cross-sections

Photonuclear interaction cross-sections from the GEANT4 database are approximated for all nuclei and all energies (from the hadron production threshold to about 40 TeV). The approximation methods in the giant-dipole resonance region, nucleon resonance region, and high-energy region are improved with respect to existing approximations. As an application of the approximation for photonuclear cross-sections, an improved method of calculating electronuclear cross-sections is developed. The interaction cross-section of virtual photons with nuclei at high Q² are approximated and a simple algorithm for describing the electronuclear reactions, including high-Q² scattering, is proposed. Received: 22 February 2002 / Accepted: 6 May 2002     

<Emphasis Type="Italic">D</Emphasis>-Wave Resonances in Three-Body System Ps<Superscript>−</Superscript> with Pure Coulomb and Screened Coulomb (Yukawa) Potentials

We have investigated the doubly excited ¹ D ^e resonance states of Ps⁻ interacting with pure Coulomb and screened Coulomb (Yukawa) potentials employing highly correlated wavefunctions. For pure Coulomb interaction, in the framework of stabilization method and complex coordinate rotation method we have obtained two resonances below the n = 2 threshold of the Ps atom. For screened Coulomb interaction, we employ the stabilization method to extract resonance parameters. Resonance energies and widths for the ¹ D ^e resonance states of Ps⁻ for different screening parameter ranging from infinity (pure Coulomb case) to a small value are also reported.     

The <Superscript>1,3</Superscript>D<Superscript>○</Superscript> resonance states of positronium negative ion using exponential correlated wave functions

The doubly excited ^1,3D^○ resonance states of Ps^- associated with N=3, N=4 and N=5 Ps thresholds have been investigated using highly accurate correlated wave functions with exponents generated by a quasirandom process. Resonance parameters (both resonance positions and widths) are extracted in the framework of the stabilization method and the complex coordinate rotation method. In addition to many Feshbach resonances below the various Ps thresholds, we have identified two ¹ D^○ shape resonances with one each lying above the N=3 and N=4 thresholds, respectively, and two ³ D^○ shape resonances with one each lying above the N=3 and N=5 thresholds, respectively. The ¹ D^○ shape resonance associated with N=3 Ps threshold and some other Feshbach resonances are reported for the first time in the literature.     

Manifestation of exchange effects in heavy-ion interactions

Three different approaches to taking into account exchange effects in heavy-ion collisions are studied. Within the first of them, the lowest eigenstates of the Hamiltonian are treated as forbidden states. In the second approach, the eigenstates of the normalization kernel of the resonating-group model that correspond to zero eigenvalues are treated as forbidden states. The third approach takes additionally into account semiforbidden states. The ¹⁶O + ¹⁶O system is considered. A hybrid approach that combines the methods of discrete and continuous mathematics is developed for calculating the widths of narrow resonance states. The resonance width calculated within the approach that takes into account semiforbidden states proves to be sharply different from the widths obtained within traditional approaches.     

Complex-scaling treatment for high-lying doubly excited resonances for screened Coulomb helium atom

This work presents an investigation on the doubly excited ¹S ^e autoionizing states of screened helium atom lying below the n = 4 threshold of the He⁺ ion. The potential generated in this system is represented by a Yukawa type potential. We have employed complex-coordinate rotation method, as it is a powerful scheme to study high lying resonances. Hylleraas type wave function is used to consider the correlation effect between all the charged particles. Our resonance parameters for the resonances lying below the He⁺ (n = 2) threshold agree well with those of the existing calculations by using the stabilization method. Resonances associated with higher thresholds are new calculations. All the present results are well converged with basis length N = 444.     

Magnetic Resonance and Optical Spectroscopy of Yb<Superscript>3+</Superscript> in CsCaF<Subscript>3</Subscript> Single Crystal: an Analysis of Distortions of the Crystal Lattice near Yb<Superscript>3+</Superscript>

A trigonal Yb³⁺ paramagnetic center in the CsCaF₃ single crystal was studied by magnetic resonance and optical spectroscopy methods. The structural model of the complex and the empirical energy level scheme were established. The transferred hyperfine interaction parameters and the crystal field ones were determined. The crystal field parameters were used to analyze the lattice distortions in the vicinity of Yb³⁺ using the superposition model.     

Resonance absorption band model

A model is derived for the resonance absorption of molecular bands composed of Lorentzian lines that is suitable for calculating fluorescence from irradiated air. The model is based on an explicit functional form derived for the resonance absorption of a single Lorentzian line which properly accounts for the possibility of unequal emission and absorption line widths. A procedure for rapid numerical computation of this function is given. This function yields a model for the resonance absorption of molecular bands composed of either overlapping or separated lines. A significant savings in computation time is obtained by using the model in place of exact expressions for resonance absorption. Examples are given for the resonance absorption of the N₂⁺ First Negative band system.     

Autoionization states of the positronium negative ion in exponential cosine-screened Coulomb potentials

The 2s^2 1S^e2s^2~^1{\rm S}^e autoionization resonance states of the positronium negative ion (Ps^-) in exponential cosine-screened Coulomb potentials (ECSCP) are investigated using stabilization method. Highly correlated wave functions for Ps^- are used to take into account the correlation effect of the charged particles. Results for resonance energies and widths are reported for the screening parameter in the range 0.0-0.07 (in a₀ ^-1), to the best our knowledge, for the first time in the literature.     

Bound states and resonance states of the plasma-embedded tdμ and ddμ molecular ions

We have investigated the bound states and resonance states of plasma-embedded tdμ and ddμ molecular ions using accurate correlated basis functions. The plasma effect has been taken care of by considering the Debye shielding approach of plasma modeling which admits a variety of plasma conditions. The density of resonance states are calculated using the stabilization method. The ground and excited states energies, and the S-wave resonance energies of tdμ and ddμ molecular ions immersed in plasmas are reported for various shielding parameters, along with the 1S and 2S threshold energies of the tμ and dμ atoms.     

The effect of doping three Al and N atoms on the chemical shielding tensor parameters of the boron phosphide nanotubes: A DFT study

In this work, an armchair model of the (4,4) boron phosphide nanotubes (BPNTs) with a 1-nm length and consisting of 32 B and 32 P atoms is considered to study the influence of doping three atoms of aluminum in sites of boron (B_3AlPNTs) and three atoms of nitrogen in sites of phosphors (BP_3NNTs) on the electrostatic structure properties. The mouths of nanotubes are capped by hydrogen atoms in order to saturate the dangling bonds of the boundaries and to decrease the calculation time. The structures of BPNTs, B_3AlPNTs and BP_3NNTs are optimized by performing the level of density functional theory (DFT) using 6-31G^? basis set. The optimized structures are used for calculating the chemical shielding (CS) tensors and nuclear magnetic resonance parameters such as isotropic chemical shielding (CS^I) and anisotropic chemical shielding (CS^A). The results reveal that in both models of B_3AlPNTs and BP_3NNTs by doping N atoms the chemical shielding parameters of P and B atoms, which are directly connected to the Al and N atoms decreased and the other sites significantly changed.     

Determination of the Position of the Impurity Yb3+ ion in the CsCaF3 crystals

CsCaF₃ crystals doped with Yb³⁺ ions have been studied using the electron paramagnetic resonance and optical spectroscopy methods. Several types of paramagnetic Yb³⁺ centers were found, among which a paramagnetic center in the unusual position was established. The parameters of the corresponding spin Hamiltonians and schemes of the energy levels of the observed centers were determined.     

Intense interactions of molecules with a short-wavelength electromagnetic radiation field: II. Resonance scattering of radiation and fluorescence

Within the framework of the nonadiabatic approach developed in the preceding paper, the resonance scattering, resonance Raman scattering, and resonance fluorescence are studied in detail for diatomic and triatomic molecules, and polyatomic symmetric and antisymmetric top molecules, which interact with the field of short-wavelength radiation with a wavelength λ ≥ Å and an intensity up to 10¹⁴ W/cm². The coherent excitations of high-lying Rydberg and autoionizing states are taken into account. Analytical expressions for calculating the tensors and cross sections of the above processes are derived.     

Coherent population trapping resonance on the <Superscript>87</Superscript>Rb D<Subscript>1</Subscript> line in the field of circularly polarized counterpropagating waves

The study of the previously proposed method for improving the parameters of the coherent population trapping resonance on the ⁸⁷Rb D₁ line using two counterpropagating bichromatic fields with orthogonal circular polarizations is continued. The method consists in elimination of trap states existing in the conventional σ⁺ measurement scheme and limiting the resonance amplitude. The resonance parameters are studied in a wide range of pump radiation intensities and in various configurations implementing the σ⁺-σ^? scheme.