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.     

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     

Calculation of the imaginary part of the heavy ion potential

The paper contains a numerical evaluation of the expressions for the absorptive potential in heavy ion reactions given earlier. With a standard folding expression for the real part of the ion-ion potential general good agreement is found with experimental data for the angular distributions of elastic and inelastic scattering. Special interest is attached to the case of ¹⁶O + ²⁸Si where the calculated imaginary potential is very small at low bombarding energies.     

Dynamical calculation of the mass fragmentation in the collision238U-238U

The fragmentation of the nuclear system²³⁸U-²³⁸U is studied by treating the fragmentation coordinate quantum mechanically. The time dependent Schrödinger equation, the Hamiltonian of which is calculated from the microscopic asymmetric two center shell model, is solved by the finite difference method. In order to study the fragmentation mechanism, model calculations have been carried out, by assuming the collective fragmentation potential as an oscillator potential which is adjusted to the realistic potential. Effects arising from the dynamical treatment of the fragmentation coordinate are found to be important in the collision of²³⁸U on²³⁸U. The dependence of the fragmentation on the incident energy is discussed.     

Mechanism of charging of the pyrite/aqueous interface as deduced from the surface potential measurements

Surface potential of pyrite in an aqueous environment was measured by means of a single crystal pyrite electrode. The effect of the activity of S²⁻ and Fe²⁺ ions as well as of pH, was examined. The results show that S²⁻ and Fe²⁺ ions are the dominant potential determining ions. These ions are bound to surface sites with the extent depending on their activity in the bulk of the solution. Adsorption affinity of S²⁻ ions is significantly higher than that of Fe²⁺ ions so that in most cases the pyrite surface is negatively charged. The results were explained on the basis of the surface complexation model. It was found that the surface potential depends also on pH.     

First determination of isotopically invariant parameters of the negative ion—Hydrogen sulfide anion (SH)

The first isotopically invariant Dunham analysis of a negative ion (the hydrogen sulfide anion SH⁻) that uses all available infrared and sub-millimeter wave experimental data on ³²SH⁻, ³³SH⁻, ³⁴SH⁻, and ³²SD⁻ yields accurate information on Born-Oppenheimer breakdown parameters. The potential constants of expansion of the potential function up to the sixth order were calculated. Differences between the construction of the potential function based on the Morse potential and that on the base of the power series expansion are shown.     

On the total binding energy of spherical nuclei

The total binding energy of nuclei is determined by means of many-body field theory. The problem is then reduced to finding the energy-dependent average potential (mass operator) and solving the single-particle equations of motion. Such a potential can be established phenomenologically by using data on low excitations and reactions knocking out nucleons from deep “hole” levels. Calculations of the total binding energy of the nuclei ¹⁶O, ⁴⁰Ca and ⁵⁸Ni with this potential are in satisfactory agreement with experiment.     

Calculation of the Coulomb potential between spherical-deformed and deformed-deformed nuclei using the Monte Carlo method

The Coulomb potential between spherical-deformed and deformed-deformed nuclei has been calculated using the Monte Carlo simulation. The results obtained for the Coulomb potential in the ¹⁶O$ + $²³⁸U and ²⁷Al$ + $⁷⁰Ge reactions are in good agreement with those obtained using the double-folding method. The simulation technique employed here has the ability of calculating the Coulomb potential taking into account the finite diffuseness parameter, all the possible deformation degrees of freedom, and different orientations of the symmetry axes of the target and the projectile nuclei with respect to each other. The accuracy of this simulation technique is high and the computer time taken to do these calculations is much less than those of the double-folding method.     

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.     

An Approximation for the Density Matrix in Calculations of the Mean-Field Potential of the Interaction of Nuclei

An approximation has been proposed for the nucleus single-particle density matrix in calculating the exchange component of the mean-field potential in the double-folding model. The method is based on the pseudo-oscillator representation of the density matrix and makes it possible to separate single-particle and internucleon variables, which greatly simplifies and accelerates the process of calculating the mean-field potential. Test calculations based on examples of alpha-particle interactions with ¹²C, ¹⁶O, and ⁴⁰Ca nuclei have shown the adequacy of the proposed approximation.     

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.     

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.     

Microscopic calculation of the repulsive core in the elastic nucleon-nucleon scattering

The resonating group method is used to study the effective potential between two nucleons, due to the confining potential between quarks taken together with the Pauli principle for quarks. The potential used has harmonic form, unitary spin factor λ(1)·λ(2), and both ordinary and spin-spin components. Its parameters are determined by appeal to experimental data, and phase shifts are calculated for the¹ S ₀ and³ S ₁ states of the nuncleon-nucleon (NN) system. The results indicate that the repulsive core in theNN potential may arise from quark antisymmetrization required if nucleons are composed of quarks.     

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.     

Dynamical calculation of the mass fragmentation in the collision238U-238U

The fragmentation of the nuclear system²³⁸U-²³⁸U is studied by treating the fragmentation coordinate quantum mechanically. The time dependent Schrödinger equation, the Hamiltonian of which is calculated from the microscopic asymmetric two center shell model, is solved by the finite difference method.In order to study the fragmentation mechanism, model calculations have been carried out, by assuming the collective fragmentation potential as an oscillator potential which is adjusted to the realistic potential. Effects arising from the dynamical treatment of the fragmentation coordinate are found to be important in the collision of²³⁸U on²³⁸U. The dependence of the fragmentation on the incident energy is discussed.     

Hyperdeformed states in the third minimum of the fission potential

The fission probability and the angular distribution of the associated fission fragments have been measured for the²³⁵U(d, pf)²³⁶U reaction slightly above the top of the inner fission barrier with the aim of disclosing new hyperdeformed states lying in the third minimum of the fission potential. The results are analyzed together with the data obtained from the literature for²³⁴U. The experimental resonances are interpreted as being rotational bands with rotational parameters of ?/2Θ=1.6±0.6 and 1.8±0,8 keV for²³⁴U and²³⁶U, respectively. TheK=1, 2 and 4 values of the resonances suggest that these rotational bands are built on some higher-lying excited states in the third minimum of the potential well.     

Diffusion transport of negative ions through the interface between cryogenic liquids

A theory of electron bubble transport through the interface between cryogenic liquids is developed based on a new approach to calculating the potential of interaction of a bubble with the interface. The theory is in good agreement with experiments on the electric-field dependence of the potential barrier near the interface between liquid ⁴He, ³He, and vacuum, as well as at the interface between ³He and ⁴He saturated solutions. It is found that the interaction potential dependence on the distance between the electron bubble and the interface is isotopically invariant to three versions of such an interface. The dependence of the lifetime of negative ions in ⁴He and ³He on the temperature and electric field has been determined using the Kramers theory.     

Description of proton-calcium scattering using the α-particle model

The theoretical proton-⁴⁰Ca optical potential is constructed based on theα-particle model of the nucleus. With this potential, the differential cross section, analysing power and the spin rotation function for 200 MeV proton-⁴⁰Ca elastic scattering are calculated. The results are in good agreement with the experimental data.     

Influence of the atomic polarization potential on the tunneling rates of electrons between atoms and surfaces

The tunneling rate of electrons between a Li⁻ ion and a surface is studied using the coupled angular mode method and the complex scaling method. The comparison of the two sets of results obtained with various representations of the e⁻Li interaction and their analysis shows that the e⁻Li polarization potential plays an important role in determining the tunneling rates. This effect is attributed to a lowering of the potential barrier between the atom and the surface.     

Analytical Solutions of the Kratzer-Fues Potential in an Arbitrary Number of Dimensions

No Heading Some aspects of the N dimensional Kratzer-Fues potential are discussed, which is an extension of the combined Coulomb-like potential with inverse quadratic potential in N dimensions. The analytical solutions obtained (eigenfunctions and eigenvalues) are dimensionally dependent, so also, the solutions depend on the value of the coefficient of the inverse quadratic term. The expectation values for < r^–2 >, < r^–1 > and the virial theorem for this potential are obtained and the values are also dimensions and parameter dependent.