Accurate calculation of the scattering length for the cooling of hydrogen atoms by lithium atoms

An improved ab initio calculation has been performed for the potential for the LiH a ³Σ⁺ state, using two very large basis sets. The Basis Set Superposition Error (BSSE) correction has been determined for both basis sets and the non-Born-Oppenheimer correction estimated to be negligible. The best potential is approximately 10% deeper than the previous estimate. Vibrational energies and scattering lengths have been calculated for ^6,7LiH(D) with both potentials, with and without the BSSE correction, and also with an estimated potential expected to bracket the true potential. The ⁷LiH scattering length is estimated to be (45 ± 4)a₀ and hence the low-energy cross-section in the best a ³Σ⁺ potential is about half that calculated previously. Enhanced cooling by ⁷Li of trapped H atoms remains feasible. Received 30 April 2001     

Constructing effective nucleon-nucleon interaction on the basis of the Idaho potential

An effective nucleon-nucleon interaction at an energy of 200 MeV is constructed for the Idaho nucleon-nucleon potential obtained on the basis of the theory of spontaneous chiral-symmetry breaking. This interaction approximates the nonlocal t matrix obtained for free nucleon-nucleon scattering from a solution to the Lippmann-Schwinger equation for the Idaho potential. The exact and approximated t matrices for the Paris potential, Idaho potential, and the von Geramb Hamburg potential are compared. The effective potential obtained in the way outlined above is used to calculate the inelastic scattering of 200-MeV polarized protons that is accompanied by the excitation of the 2⁺ level at 4.44 MeV and the 1⁺ level at 15.11 MeV in the ¹²C nucleus and the 6^? level at 14.1 MeV in the ²⁸Si nucleus. The results are compared with the results of the calculations on the basis of the Paris potential.     

On the reconstruction of an optical potential on the basis of experimental data in the WKB approximation

The inverse scattering problem at a fixed energy for a complex-valued potential is solved in the WKB approximation. The method is used to reconstruct the optical potential for elastic ¹⁶O + ¹⁶O scattering at E _lab = 350 MeV. The stability of the solution against small changes in the scattering matrix is studied.     

Nuclear transparency due to the pauli exclusion principle and the study of densities in the nuclear interior

24.5 MeV proton elastic scattering data for ³²S, ¹¹⁸Sn and ²⁰⁸Pb are analyzed in the framework of an optical-model potential. This potential is calculated by a folding procedure using interactions corrected for Pauli effects and Fermi motion. Neutron densities are extracted in a model-independent fashion. The sensitivity of low-energy proton scattering to the density in the nuclear interior due to the long mean free path is established.     

The Triton from the Reid93 Potential in the UPA

The unitary pole approximation (UPA) provides an effective means to construct a rank one separable potential for calculations in which one requires a simple representation of the deuteron and/or triton ground-state wave function. By construction the deuteron wave function and the ¹S₀ anti-bound state wave function of the original potential are reproduced. We report results for the corresponding triton ground state. We choose to utilize the realistic Reid93 potential for this purpose. The Reid93 potential, generated by the Nijmegen group, is a Reid-like, partial-wave local potential that produces a χ² representation of the nucleon–nucleon (NN) scattering data that is as precise as an NN partial-wave analysis. Results for properties of ²H and ³H from the UPA are compared with those for the original potential. To further illustrate the precision of the method, results for properties of the deuteron and triton from the UPA are also compared with those for the original Reid68 potential.     

The Reid93 Potential Triton in the Unitary Pole Approximation

The Reid93 potential provides a representation of the nucleon–nucleon (NN) scattering data that rivals that of a partial wave analysis. We present here a unitary pole approximation (UPA) for this contemporary NN potential that provides a rank one separable potential for which the wave function of the deuteron (³S₁-³D₁) and singlet anti-bound (¹S₀) state are exactly those of the original potential. Our motivation is to use this UPA potential to investigate the sensitivity of the electric dipole moment for the deuteron and ³H and ³He to the ground state nuclear wave function. We compare the Reid93 results with those for the original Reid (Reid68) potential to illustrate the accuracy of the bound state properties.     

The temperature dependence of the Hi optical potential

Within a realistic effective nucleon-nucleon interaction, derived from the Reid soft-core potential at zero temperature, the dependence on temperature of the heavy ion optical potential is investigated for the systems ⁴⁰Ca + ⁴⁰Ca and ²⁰⁸Pb + ²⁰⁸Pb. The hot nuclear densities are generated using the Thomas-Fermi model at a finite temperature. It is found that both the real and the imaginary parts of the optical potential become more attractive and extend to large distances when the temperature increases. The barrier heights are lowered and shifted outwards.     

A consistent derivation of the real and imaginary parts of the heavy ion potential below and above the Coulomb barrier

In a model including approximately a large set of non-elastic channels, the real and imaginary potentials are consistently derived. The “anomaly” of the real potential which sharply increases in the vicinity of the Coulomb barrier where the imaginary potential is strongly reduced is studied in ¹⁶O + ⁴⁰Ca and ¹⁶O + ²⁰⁸Pb systems. The results on the imaginary potential are discussed and compared to our previous calculation.     

Energy spectrum of the A + + e complex in a quantum dot in the adiabatic approximation

The energy states of an A ⁺ + e complex in a quantum dot described within the hard-wall potential model are considered using the zero-range potential method in the adiabatic approximation. These complexes can be formed under nonequilibrium conditions (for example, under photoexcitation). A relationship describing the dependence of the binding energy of a hole located at a neutral acceptor on the parameters of the zero-range potential of the system and the quantum state of the electron is obtained analytically. It is demonstrated that, in quantum dots of small radius, the binding energy of a hole in the A ⁺ + e complex can be considerably higher than the ground-state energy of the A ⁺ stationary center.     

Relationship of the Williams-Poulios and Manning-Rosen Potential Energy Models for Diatomic Molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved form of the Williams-Poulios potential energy model. It is found that the negative Williams-Poulios potential model is equivalent to the Manning-Rosen potential model for diatomic molecules. We observe that the Manning-Rosen potential is superior to the Morse potential in reproducing the interaction potential energy curves for the \({{a}^{3} \Sigma_{{\rm u}}^{+}}\) state of the ⁶Li₂ molecule and the \({{X}^{1} \sum^{+}}\) state of the SiF⁺ molecule.     

Theoretical investigations of the SH and LiS cations

Reliable theoretical data on spectroscopy and spin-orbit matrix elements are computed for the lowest electronic states of SH⁺ and LiS⁺ ions. Accurate spectroscopic predictions for their excited electronic states are given. For SH⁺, polarization minima at large internuclear distances are located in addition to the strongly bound electronic states already known. For LiS⁺, our calculations confirm that the electronic ground state of this ion is of ³Σ⁻ species and reveal the existence of a ¹Δ state presenting a potential well as deep as the potential of the ground state. Moreover, the LiS⁺ electronic excited states potential energy curves possess shallow potential minima in the molecular region and at long-internuclear distances. Generally, these shallow minima may be populated during low energy collisions between the corresponding atomic fragments. Finally, spin-orbit calculations have allowed giving accurate determinations of the spin-orbit splittings for these cations and elucidation of the predissociation mechanisms of SH⁺ leading to the formation of the S⁺ and H species in their electronic ground states. Accordingly, long-lived SH⁺ ions can be found in the X³Σ⁻, a¹Δ and b¹Σ⁺ electronic states and the rovibrational levels of LiS⁺ in its electronically excited and ground states should be weakly perturbed.     

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.     

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.     

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.     

Damping of the giant dipole resonance in hot,strongly rotating nuclei

The isovector dipole density-density response of hot rotating nuclei is calculated applying a cranked deformed Nilsson potential together with a separable dipole-dipole residual interaction. The transformation of the response function from the internal rotating coordinate frame to the laboratory frame is discussed and illustrated by classical results for a charged particle moving in a harmonic-oscillator potential. Calculations for ¹⁰⁸Sn, ¹⁵²Dy and ¹⁹⁶Pb are presented. For ¹⁰⁸Sn at high excitation energy thermal fluctuations of the shape gives rise to a rather structureless strength function with a considerable width. For ¹⁵²Dy and ¹⁹⁶Pb superdeformed minima of the potential surface are predicted. The coupling of the giant dipole resonance to the shape degrees of freedom of superdeformed nuclei can split the vibration by ≈ 10 MeV, the lowest peak being expected at an excitation energy of ≈ 7–8 MeV and carrying ≈ 30% of the energy-weighted sum rule.     

Real part of the optical potential for composite particles

The optical potential for a composite particle is most simply approximated by the sum of the optical potentials of the constituent nucleons. Restricting ourselves to the real parts of the potentials we use this model as a first approximation in a calculation of the potentials for d, ³He, α and ¹²C. We add corrections for (i) the energy dependence of the nucleon potentials, (ii) three-body terms, (iii) the Pauli principle. All corrections can be important and that for the Pauli principle can be very large. We obtain a good explanation of the following phenomena: (a) the deuteron potential is nearly the sum of the neutron and proton potentials, (b) the potential for ³He is about 20 % less than the sum of the potentials of the nucleons in the ³He projectile, (c) the volume integral of the potential for ³He falls at both high and low energies in the energy range 20–100 MeV, (d) shallow potentials with large radii are found for low energy (30 MeV) scattering of α-particles, (e) deeper potentials are found for higher energy α-particle scattering. We predict shallow potentials for ¹²C scattering from light targets but deeper potentials for heavier targets.