Equivalent Local Potential Research Articles

Comparison of the microscopic potential with the optical potential in the alpha +16O system.

The $\ensuremath{\alpha}$+$^{16}\mathrm{O}$ resonating-group-method calculation which fits well the spectroscopic data of the $^{20}\mathrm{Ne}$ levels is shown to fit well also the scattering cross section up to high energy. The equivalent local potential derived from the resonating-group method is found to be very similar to the optical potential of Michel et al. Thus it is concluded that a significant part of the energy dependence of the real part of the $\ensuremath{\alpha}$+$^{16}\mathrm{O}$ optical potential is due to the internucleus antisymmetrization.

Quantal equivalent local potentials from resonating group method n+ alpha nonlocal interactions.

A quantal method to construct equivalent local potentials for the resonating group method nonlocal kernels is presented. The method requires two linearly independent solutions of the resonating group method integrodifferential equation. This Wronskian equivalent local potential is generally smooth, well behaved at all energies and partial waves, and is free of singularities. Therefore it can be used for interpreting purposes where the semiclassical method of Horiuchi either fails (low energies, small size of nuclei, comparable ranges of nonlocality and nucleus, etc.) or is multivalued. The necessity and importance of renormalization of the wave functions are discussed. The kernel need not be renormalized. Results are given for an n+\ensuremath{\alpha} system and the l, E, r, and parity dependence of the system is investigated.

Microscopic Analysis of Inelastic Coupling Potential Based on the Coupled Channel Resonating Group Method. I: --Formulation and Study of 6Li- System--

Microscopic coupling potentials obtained by the coupled channel resonating group.method are studied by converting them into the equivalent local coupling potentials. The method to get the equivalent coupling potentials proposed before is extended so as to be applicable to the coupled radial equation. The method is applied to the 6Li-a system, which shows that our method is reliable in the application to the realistic case. The obtained equivalent coupling potentials show the large effect of antisymmetrization between projectile and target nuclei. The energy and the parity dependence of them are also prominent.

Inelastic excitation and the nucleon optical potential

We study nucleon elastic scattering from targets of 40Ca and 208Pb in the presence of inelastic excitation to a fairly realistic set of levels. We suggest a method of averaging over the l-dependence of the trivially equivalent local potentials so as to obtain smooth, surface-peaked potentials which yield cross sections in good agreement with exact results in the forward hemisphere. Only slightly poorer agreement is obtained with potentials from simple, analytical formulae derived from the plane wave approximation. We also briefly compare approximate and exact inelastic cross sections.

Comparison of several equivalent local potentials for microscopic nonlocal Nα potentials

The phase shifts obtained in the Perey-Saxon, Horiuchi and Peierls-Vinh Mau approximations for the microscopic nonlocal Nα interaction of Lassaut and Vinh Mau have been compared at 10 and 20 MeV to the exact results, without the customary approximation of Perey and Buck, which neglects part of the angular dependence of the nonlocality and is inadequate. We have also compared the equivalent local potentials with the corresponding local wave functions and damping factors to their exact wronskian counterparts and obtained the corresponding nonlocal wave functions as a product of the approximate local wave function and the damping factor in all cases. The results show that of all the approximations the Peierls-Vinh Mau approximation is the most accurate one for s-waves and that the Perey-Saxon approximation is inadequate for Nα scattering. The accuracy of all the approximations is dependent on the degree of repulsiveness of the effective nuclear force. For the exact wronskian equivalent local potential and damping factor however, we reproduce the exact nonlocal wave function to high accuracy in all cases, confirming the accuracy of our numerical methods. The implications for nuclear reactions where the off-shell behaviour of the Nα interaction is important are discussed.

One-Dimensional Model of Nucleus-Nucleus Collision with Zero-Range Force: Exact Scattering Amplitude and Equivalent Local Potential

One-Dimensional Model of Nucleus-Nucleus Collision with Zero-Range Force: Exact Scattering Amplitude and Equivalent Local Potential

Equivalent local potentials from nonlocal separable ones.

A method is presented for the explicit construction of a family of equivalent local potentials from a given nonlocal separable potential. This procedure can be also applied in the case when a Coulomb potential is added to the separable short range interaction.

Equivalent local potential for the fish bone optical potential by inversion of its phase shifts

By inversion of the fish bone optical model phase shifts for α -16O scattering we confirm the presence of a Pauli barrier in the surface region of the corresponding equivalent local potential. In the interior the potential depth increases with decreasing energy, in agreement with the semiclassical results of Horiuchi. The advantages of the inversion method for the determination of equivalent local potentials are discussed.

Equivalent local potentials for nucleon-alpha scattering.

Quantum mechanical inversion is used to obtain l-independent phase equivalent local potentials to microscopic nucleon-alpha potentials of Lassaut and Vinh Mau between ${E}_{\mathrm{lab}=15}$ and 25 MeV. These potentials are compared with the corresponding local potentials obtained in the Perey-Saxon approximation.

A Semi-Classical Treatment of the Coupled Channel Equation with Non-Local Interaction. IV: Higher Order Corrections to the Equivalent Local Potentials

We investigate the higher order corrections to the equivalent local potentials of the non· local potentials in the coupled channel equation which are obtained in previous papers. We also examine the choice of the local momentum around which we expand the Wigner transform of the non· local coupling potential in getting the equivalent local potential.

A Semi-Classical Treatment of the Coupled Channel Equation with Non-Local Interaction. II: Equivalent Local Potentials to Be Used in the Coupled Channel Treatment

A Semi-Classical Treatment of the Coupled Channel Equation with Non-Local Interaction. II: Equivalent Local Potentials to Be Used in the Coupled Channel Treatment

Short-range part of the NN interaction: Lowest-order relativistic corrections to equivalent local potentials from quark exchange kernels

The full Breit hamiltonian, including the Darwin term and relativistic kinetic-energy correction, has been used to construct resonating group kernels in analytic form for the six-quark NN system. The nonlocal kernels have been converted to equivalent local potentials using the WKB approximation based on their Wigner transforms. The equivalent local potentials have been confirmed to be rather insensitive to a choice of parameters and to be fairly accurate by comparing with the phase shifts and the wave functions obtained with the RGM equation. The results indicate the importance of the Darwin term. The term leads to a large reduction of the strong repulsive cores given by the color magnetic interaction and makes the resulting potentials less repulsive than those which neglect this term. The relative importance of the various components in the Breit interaction and of the quark-gluon exchange diagrams is made clear.

Polarization potentials in heavy-ion scattering

A polarization potential is defined in terms of the Feshbach projection operator formalism to represent the effect upon the elastic channel of the coupling to non-elastic channels in heavy-ion scattering. The polarization potential represents coupling to specific surface degrees of freedom of the particular reaction considered and it is contrasted to the complementary global approaches for the volume potential such as the folding model and the proximity potential. The coupled channels method is used both as a source of exact model solutions for comparison with the various approximate potential forms and also as a numerical means of constructing trivially equivalent local potentials. The imaginary Coulomb polarization potential is due in lowest order to quadrupole coupling to the lowest collective 2 + state of a nucleus. It is considered in detail since it provides the insight of closed analytical forms in various approximations. Multistep coupling to higher states, energy loss and off-energy shell effects are also considered analytically. The real Coulomb polarization potential due to the virtual excitation of multipole giant resonances, and the polarization potential arising from relativistic corrections, are investigated in detail. Polarization potential components due to nuclear coupling are investigated numerically. Analytical cross section approaches are contrasted with the polarization potential approach and with coupled channels.

Local potentials equivalent to matrix effective potentials fore-He scattering at 200 and 400 eV

We have obtained equivalent local potentials (ELP's) to matrix effective potentials for e-He scattering at 200 and 400 eV by means of semiclassical WKB inversion of the phase shifts. The absorptive parts of these ELP's are compared with current models for absorption potentials.

Mean free path and the absorptive potential of a Σ particle in nuclear matter

It is shown that a proper treatment of the momentum dependence of the real part of the Σ optical potential in nuclear matter leads to a significant increase in the calculated Σ mean free path, and to a corresponding decrease in the depth of the imaginary part of an equivalent local optical potential of Σ in nuclear matter.

Equivalent Local Potentials and Perey Factors for Various Kinds of Relative Wave Functions of RGM. II: Quantitative Investigation of the Foundation of the Orthogonality Condition Model

Equivalent Local Potentials and Perey Factors for Various Kinds of Relative Wave Functions of RGM. II: Quantitative Investigation of the Foundation of the Orthogonality Condition Model

Nonlocal potentials and their exact and approximate local and velocity-dependent equivalents

We show that good approximations to the exact equivalent local potential (ELP) and damping factor of a nonlocal Perey-Buck potential can be calculated in the partial wave WKB approximation of Horiuchi. The exact ELP and damping factor are obtained by means of a method previously given by one of us. We also confirm that an approximate ELP proposed by Bauhoff et al. is of comparable accuracy as the Horiuchi approximation. Thesel-dependent ELP's exhibit reduced attraction in the interior and provide a test for higher order WKB approximations. We subsequently obtain an equivalent velocity dependent potential (EVDP) which is even exactly wave function equivalent to the original nonlocal potential. This almost local potential, unlike the trivial equivalent local potential, is smooth and well-behaved and is therefore particularly useful in nuclear reactions where the off-shell behaviour of the potential is important.

Short-range part of the NN interaction: Effects of changes in six-quark spatial symmetry

A study of nonrelativistic resonating group method quark exchange kernels shows that even large changes in the relative (6) and (42) space symmetry of the six-quark system do not make significant changes in the extreme short range parts of the NN interaction. The repulsive core heights of equivalent local potentials derived by the Wentzel-Kramers-Brillouin approximation from the Wigner transform of the quark exchange kernels are changed by only approx.20% under a large change in the relative (6) and (42) space symmetry of the antisymmetrized internal six-quark resonating group method wave function.

Some applications of the Gel'fand–Levitan inverse method in atomic and molecular physics

AbstractThe Gel'fand–Levitan theory is applied to obtain the exact potential function for an atomic or a molecular system when the solution of the Schrödinger equation with a reference potential which is close to the actual potential is known. With this method one can construct bound state equivalent local potentials, or potentials which, for large quantum numbers, have spectra similar to that of the reference potential. In one‐dimensional problems the resulting potentials are not generally symmetric about the origin, even if one starts with symmetric reference potentials. This lack of symmetry is due to the presence of additional terms in the Hamiltonian which are of purely quantal origin, and therefore in any semiclassical treatment become negligible. This observation leads one to investigate the relationship between the spectrum of a given system and the symmetry of the underlying Hamiltonian. Examples are given to show that the dynamical symmetries usually associated with the spectral properties do not necessarily follow from the Gel'fand–Levitan inverse theory, but can be imposed as constraints on the solution. Additional constraints on the form of the two‐body wave function also arise from the observable transition rates for atom–molecule collisions and for the interaction of the charged particles in the system with an external electromagnetic field.

Nonlocal and local equivalent microscopic optical potentials

Medium energy elastic proton scattering is analyzed with a microscopically generated nonlocal nucleon nucleus optical model. A through discussion is presented on the transition from a nonlocal potential to phase equivalent local potentials. These local potentials reveal a strong repulsive $l$-dependent core which is beyond phenomenological potential models. This core leads to a damping of the diffraction pattern at medium angles and a backward rise of the cross section. These features have been observed experimentally. The formalism is applied to scattering from $^{12}\mathrm{C}$ and $^{40}\mathrm{Ca}$ at low and medium energies and compared to experimental data.NUCLEAR REACTIONS Microscopic optical potential; $^{12}\mathrm{C}(p, p)$, $E=40, 180, 200$ MeV; $^{40}\mathrm{Ca}(p, p)$, $E=160, 180$ MeV; comparison with experimental data.