An alternative solution of diatomic molecules

The spectrum of r ^?1 and r ^?2 type potentials of diatomic molecules in radial Schrödinger equation are calculated by using the formalism of asymptotic iteration method. The alternative method is used to solve eigenvalues and eigenfunctions of Mie potential, Kratzer-Fues potential, Coulomb potential, and Pseudoharmonic potential by determining the α, β, γ and σ parameters.     

Inclusion of the Δ resonance in the optical potential between two nuclei and its application to medium energy12C-12C scattering

An energy dependent complex optical potential between two nuclei is calculated from the potential energy density for two colliding nuclear matters generated by solving the Bethe-Goldstone equation in whichNΔ and ΔΔ channels are explicitly coupled to theNN channel. By adding the contributions from the third and fourth order ring diagrams and the relativistic correction to the calculated potential energy density, the saturation property of a nuclear matter is reasonably well reproduced. This is used together with the kinetic energy density to calculate the optical potential for the¹²C+¹²C system in the energy density formalism with the local density approximation. The surface correction term and the symmetry energy term in the energy density functional are determined to reproduce the observed binding energy and the rms radius of¹²C. Using this potential, the differential cross sections for elastic¹²C-¹²C scattering atE _lab=1440 and 2400 MeV are calculated and compared with recent experimental data.     

Accurate ab initio-based DMBE potential energy surface for HLi2(X 2A′) via scaling of the external correlation

A globally accurate potential energy surface is reported for the electronic ground-state HLi₂ by fitting ab initio energies to double many-body expansion formalism. The total 3726 ab initio energies used to map the HLi₂ potential energy surface are calculated using the multi-reference configuration interaction method, with their dynamical correlation being semiempirically corrected by the double many-body expansion-scaled external correlation method. The current potential energy surface generates an excellent fit of the ab initio energies, showing a small root-mean squared derivation of 0.636 ? kcal ? mol^-1. The topographical features of the HLi₂ potential energy surface are examined in detail, which concludes that the H + Li₂(X ? ¹ Σ _g ) → Li + LiH(X ? ¹ Σ) reaction is essentially barrierless and the exothermicity is calculated to be 33.668 ? kcal ? mol^-1, thus corroborates the available experimental and theoretical results.     

Constrained variational calculations of closed shell nuclei with the reid potential

Lowest-order constrained variational calculations with harmonic oscillator wave functions are carried out for ⁴He, ¹⁶O, and ⁴⁰Ca nuclei with the Reid potential. The results obtained with this simple method are in very close agreement with those obtained by renormalized Brueckner-Hartree-Fock theory with orthogonalized plane wave intermediate states. The A-dependence of the difference between the experimental and calculated binding energies for A = 2, 3, 4, 16, 40 and ∞ can be explained by a three-body cluster term coming either from a wrong off-energy-shell behavior of the Reid potential or a three-body force. The calculated radii of ¹⁶O and ⁴⁰Ca are ≈ 10% too small, indicating that the Reid potential may not be very realistic.     

Generator-coordinate study of 3He+3He elastic scattering with a semirealistic nucleon-nucleon potential

The elastic scattering of ³He by ³He is studied in the framework of the generator coordinate method, using a new semirealistic nucleon-nucleon potential. All components of this potential have a soft core in the sense that they can be used in calculations where short-range correlations between nucleons are not taken into account. With this potential, a good agreement between calculated and measured cross sections and polarizations is obtained. The tensor component of the potential is found to be essential to explain the J-dependence of the empirical phase shifts, although the calculated polarizations are insensitive to the strength of the tensor potential.     

Interaction potentials of Hg* + He at moderate interatomic separations and the radiative decay of the Hg(63 P 2) metastable state in collisions with He atoms

By using the modified method of the Fermi pseudopotential and the effective Hamiltonian method, a multiconfiguration calculation of the potential curves is performed for the Hg(6^{1, 3} P _J ) + He and Hg(7^{1, 3} S _J ) + He interactions in the region of interatomic separations R≥5a ₀. In this calculation, the interactions of different excited configurations and the spin-orbit coupling of singlet and triplet states were taken into account. The Hg⁺ + He ion-atom interaction potential was obtained by the nonempirical configuration interaction method MRD-CI with the use of the relativistic effective core potential (RECP) for the Hg atom. Based on the calculated potential curves and the transition dipole moments, the process of radiative decay of the Hg(6³ P ₂) metastable state in collisions with He atoms is considered and the temperature dependence of the rate constant is calculated.     

Analytical Formulation for ϕ 4 Field Potential Dynamics

An analytical model for adding a space-dependent potential to the ? ⁴ field equation of motion is presented, by constructing a collective coordinate system for the solitary solutions of this model. The interaction of ? ⁴ solitons with a delta function potential barrier and also delta function potential well is investigated. Most of the characters of interaction are derived analytically while they are calculated by other models numerically. We will find that the behaviour of a solitary solution is like a point particle which is moved under the influence of a complicated effective potential. The effective potential is a function of the field initial conditions and also of parameters of the added potential.     

Microscopic calculation of the surface absorption in the optical potential

We calculated the contributions of the two-particle one-hole (2p-1h) and the one-particle two-hole (1p-1h) excitations to the imaginary partW(E, R) of then-⁴⁰Ca optical potential. The bound single particle states and energies of the⁴⁰Ca nucleus are calculated quantum mechanically by solving the Schrödinger equation with a Woods-Saxon potential. For the excited states in the continuum we use the Thomas-Fermi approximation. Different forms of contact residual interactions have been tested. A combination of aδ-force and a smeared SDI can fit the phenomenologicalW(E, R).     

The effective potential and the bound states for a class of two dimensional gauge theories

The effective potential is calculated for a two dimensionalU(N) gauge theory with scalar quarks to leading order in the 1/N expansion. If there is noφ ⁴ interaction present, the potential is unbounded from below. If theφ ⁴ interaction is present, the potential is bounded from below and there is an unbroken and a spontaneously broken symmetry phase. The bound state spectrum of the unbroken phase is very similar to that of anU(N) gauge theory without theφ ⁴ term.     

Two-loop corrections to the potential of a pointlike charge in a superstrong magnetic field

The potential of the pointlike charge in a superstrong homogeneous magnetic field B ? m _e ² /e ³ ≈ 6 × 10¹⁵ G is considered. It is well known that Coulomb potential is significantly modified by taking into account vacuum polarization (calculated in one loop approximation). We consider electron selfenergy and correction to the vertex function at one loop, and show that these diagrams are not enhanced by magnetic field like eB.We calculate two-loop corrections to the vacuum polarization and find that these contributions are small.     

Effective theory of NN interactions in a separable representation

We consider the effective field theory of the NN system in a separable representation. The pionic part of the effective potential is included nonperturbatively and approximated by a separable potential. The use of a separable representation allows for the explicit solution of the Lippmann-Schwinger equation and a consistent renormalization procedure. The phase shifts in the ¹ S ₀ channel are calculated to subleading order.     

Quantum-statistical mechanics of a system of charged particles at high temperatures

If a quantum-mechanical potential is introduced the calculation of the quantummechanical binary distribution function for a system with Coulomb interaction is reduced to the well-known mathematical formalism of classical statistical mechanics in the case ofnλ³?1 (λ being the thermal wavelength). The two-particle quantummechanical potential is determined by the two-particle Slater sum. In this paper we calculated the two-particle Slater sum using an expansion according toe ² and the resolvent formalism. From the binary distribution function the correlation energy and the free energy as well were determined up to ordere ⁶. Symmetry effects were taken into account.     

Photoassociation spectroscopy of collisional pairs of mercury atoms: Determination of parameters of molecular terms

The photoassociation spectrum of an equilibrium vapor of mercury atoms in the range of 34960–37250 cm^?1 is recorded with the help of a tunable laser in observations of laser-induced fluorescence. The Franck-Condon fstructure, i.e., periodic variations in absorption intensity against a continuous background, is observed. The structure makes it possible to determine spectroscopic parameters of the upper attractive potential and the lower repulsive potential including that with a van der Waals well. The absorption spectrum of collisional pairs of mercury atoms is calculated using the Numerov-Cooley procedure for integrating the Schrödinger equation. Potential curves of the upper and lower states Hg₂(D1_u) and Hg₂(X0 _g ⁺ ) are determined by comparing the calculated spectra with the experimental one.     

Evaluated Integral Cross Sections of the <Superscript>3</Superscript>H(<Emphasis Type="Italic">t</Emphasis>,2<Emphasis Type="Italic">n</Emphasis>)<Superscript>4</Superscript>He Reaction in the Low-Energy Region Obtained with Regard to Electron Screening

procedure is considered for analyzing ³H(t,2n)⁴He reaction proceeding in a gas environment with regard to electron screening [1–4]. Results from such an analysis are presented. An electron screening potential of 121 eV is obtained. The magnitude of this potential is three times higher than the one given in [5]. Starting with a 100 eV energy of particle interaction the cross sections of ³H(t,2n)⁴He reaction are calculated using the above potential. The reaction rates are calculated using the evaluated cross sections in the lowenergy region. Enhancement factors for cross sections and reaction rates are defined.     

Ab initio SCF-Cl studies on the large amplitude bending motion of the water molecule: Rigid,semirigid, and nonrigid bender models for the Hamiltonian

Self-Consistent Field (SCF) and Configuration Interaction (CI) studies are performed on the bending mode of the water molecule using a double zeta plus polarization basis set. The ab initio points are fitted to a three-parameter double minimum potential consisting of a quadratic plus Lorentzian terms. The vibration-rotation energies are then evaluated using the large amplitude Hamiltonian developed by P. R. Bunker and co-workers at various levels of approximations. It is found that the calculated frequencies improve significantly as one proceeds from approximate H_b⁰⁰(ρ) to rigid bender H_b⁰(ρ) [P. R. Bunker and J. M. R. Stone, J. Mol. Spectrosc.41, 310–332 (1972)] to semirigid bender H_b⁰(r, ρ) [P. R. Bunker and P. M. Landsberg, J. Mol. Spectrosc.67, 374–385 (1977)] Hamiltonian. With H_b⁰(r, ρ), the ab initio calculated bending frequency ν₂ differs from the observed value (1595 cm^?1) by 30 cm^?1 and the barrier height is 12 229 cm^?1. It is also shown that ν₂ and its first four overtones are better calculated by 45–98 cm^?1 when the ab initio potential is used directly instead of the three-parameter analytic potential fitted to ab initio data. Finally, rotation bending energy levels are calculated for v₂ ≤ 3 and J ≤ 10 on the basis of a nonrigid bender Hamiltonian of A. R. Hoy and P. R. Bunker [J. Mol. Spectrosc.74, 1–8 (1979)], using the ab initio quadratic force field of P. Hennig, W. P. Kraemer, G. H. F. Diercksen, and G. Strey, [Theor. Chim. Acta47, 233–248 (1978)]. These results show that the accuracy of calculated force constants and frequencies is critically dependent not only on the size of the basis set but also on the number and spacing of the ab initio points used to derive the force field.     

Influence of strongly coupled inelastic excitations on the optical potential for12C+12C

The contributions of some of the strongly coupled collective excitations in¹²C+¹²C to the heavy ion optical potential have been explicitly obtained by calculating the exact Green's function for this problem. The resulting nonlocal heavy ion potential and the trivially equivalent local potential are calculated and theirJ- andE-dependence are discussed. It is shown that the strong direct excitations contribute significantly to the absorptive part of the heavy ion potential in the surface region.     

α8Be cluster model for the 0 2 + resonance in the 12C nucleus

The 0 ₂ ⁺ resonance in the ¹²C nucleus is treated on the basis of the α+⁸Be two-cluster model. An equation for the function describing the relative motion of the clusters is derived by using the s-wave differential Faddeev equations for the 3α system and by relying on the simplest version of the resonating-group method. A phenomenological potential is taken to simulate the pair αα interaction. A three-body potential binding three alpha particles together gives rise to a resonance in two-cluster α+⁸Be scattering. The calculated resonance features and the calculated parameters of the wave function of the system are compared with the results obtained by other authors.     

Collision of Rydberg atom A** with atom B in the ground electronic state. Optical potential

A method for calculating the complex optical potential of slowly colliding Rydberg atom A^** and neutral atom B in the ground electronic state is suggested. The method is based on the asymptotic approach and the theory of multichannel quantum defects, which uses the formalism of renormalized Lippmann-Schwinger equations. The potential is introduced as the 〈q|V _opt|q〉 matrix element of the optical interaction operator, for which the integral equation is derived, and is calculated in the basis set of free particle wave functions |q〉. Fairly simple equations for the shift and broadening of the ionic term are obtained, and the principal characteristics of these equations are analyzed. By way of illustration, the optical potential of the Na^**(nl)+B systems, where B is a rare gas atom, is calculated.     

On the nuclear interaction potential in the reactions with heavy ions

The interaction potential of heavy ions⁴He,⁶Li,¹²C and¹⁶O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of⁶Li from¹²C at laboratory energy of lithium ionsT _L =90.0 MeV. Reasonable agreement with experiment is obtained.