Local Potential Model Research Articles

Test of local model potentials for positron scattering from rare gases.

We report calculations of differential and integral cross sections for positron (${\mathit{e}}^{+}$) scattering from He, Ne, Ar, Kr, and Xe rare gases. An optical-potential approach is employed in which the repulsive Coulombic interaction is calculated exactly at the Hartree-Fock level and the attractive polarization and correlation effects are included via a model potential determined from the use of a local density-functional theory (DFT). These model calculations are further compared with the results from two other local potentials, one based on determining the short-range correlation energy, ${\mathit{E}}_{\mathrm{C}}$, for a positron in an homogeneous electron gas and the other from the correlation-polarization potential of an electron interacting with a free-electron gas. We found that the present DFT-based, correlation-polarization treatment is fairly simple to implement computationally and appears to be the most accurate of all the models examined here. Our results are in fact compared with recent measurements of differential and integral cross sections for positron scattering with rare gases and are found to be remarkably close to both sets of experiments.

Riemann zeros and a fractal potential.

The nontrivial Riemann zeroes are reproduced using a one-dimensional local-potential model. A close look at the potential suggests that it has a fractal structure of dimension d=1.5.

Measurements of polarized-neutron-polarized-proton scattering: Implications for the triton binding energy.

Measurements have been made of \ensuremath{\Delta}${\mathrm{\ensuremath{\sigma}}}_{\mathit{T}}$ for polarized neutrons incident on a polarized-proton target from 3.65 to 11.60 MeV. In the energy range near 10 MeV, \ensuremath{\Delta}${\mathrm{\ensuremath{\sigma}}}_{\mathit{T}}$ is very sensitive to the nucleon-nucleon tensor interaction. Comparison of the data to potential-model predictions indicate that the tensor interaction is weak, resulting in values of the $^{3}$${\mathit{S}}_{1}$${\mathrm{\ensuremath{-}}}^{3}$${\mathit{D}}_{1}$ mixing parameter ${\mathrm{\ensuremath{\epsilon}}}_{1}$ which are smaller than predicted by any nucleon-nucleon potential model. A smaller tensor force will bring the predictions of local potential models for the triton binding energy into closer agreement with the experimental value.

Electron scattering with H2S and PH3 molecules

Calculated total, differential and momentum transfer cross sections are reported for the vibrationally elastic scattering of electrons from H2S and PH3 molecules in the range of energy 0.1–50 eV. The scattering process is approximated by two incoherent scatterings caused, separately, by a central field and a long-range electric dipole interaction. The central field is calculated with a spherical approximate molecular wave function, in which the exchange interaction is treated in two ways: (i) exactly within the accuracy of the molecular wave function; (ii) approximately by a local model potential. The scattering by the central field is calculated with partial wave expansion technique, while the scattering by the electric dipole potential is calculated by using the first Born approximation for a rotating dipole model with experimental values of the dipole moments of H2S and PH3. The total cross sections are approximated by the incoherent sum of the cross section due to the central potential and the cross section of 00→10 rotational transition caused by the electric dipole potential. The effects of the polarization interaction are also tested. The contribution of small-angle scattering to the integral cross section is analyzed for these weakly polar molecules with some quantitative comparison.

Spectroscopic factors for alpha -cluster wave functions in 44Ti observed via the (6Li,d) reaction.

Using the theoretical \ensuremath{\alpha}-cluster wave functions, \ensuremath{\alpha}-spectroscopic factors for the members of the parity doublet ${\mathit{K}}^{\mathrm{\ensuremath{\pi}}}$=${0}^{+}$ and ${0}^{\mathrm{\ensuremath{-}}}$bands in $^{44}\mathrm{Ti}$ have been deduced by the finite-range distorted wave Born approximation analyses of the ${(}^{6}$Li,d) reaction on $^{40}\mathrm{Ca}$. Form factors for $^{44}\mathrm{Ti}$ were calculated with a local potential model which describes \ensuremath{\alpha}-elastic scattering from $^{40}\mathrm{Ca}$ and the resonating group method, respectively. The resulting spectroscopic factors for \ensuremath{\alpha}-cluster states in $^{44}\mathrm{Ti}$ are greater than 0.1, which supports an \ensuremath{\alpha}-cluster model for $^{44}\mathrm{Ti}$.

Local potential model for pion-nucleus scattering and [formula omitted] excitation ratios

Local potentials of Woods-Saxon shape are introduced to describe the elastic scattering of pions from the nuclei 40,48Ca, 58Ni, 90Zr, 118Sn and 208Pb at energies in the 100–300 MeV range. Good fits to the measurements are easily obtained and potential ambiguities are discussed. The optical potentials are then applied, using the deformed-potential prescription and independent information on B(E2) and B(E3) values, to inelastic scattering exciting the lowest 2 + and 3 − collective states of these nuclei, as well as the giant quadrupole resonances. This procedure is parallel to that used in the analysis of scattering data for other hadrons. Sufficiently good agreement with experimental data is obtained to establish the validity of this approach for pions also. Remaining discrepancies are similar to those found when using a more microscopic and nonlocal approach. In particular, our semi-empirical method does not change the apparently anomalous M n M p ratios for the giant resonances deduced from comparisons of π + and π − scattering. These discrepancies are discussed in detail, and in relation to results obtained using other hadronic probes. We suggest that they arise from uncertainties in the data rather than in deficiencies in our understanding of the scattering.

Recent energy dependent phaseshift analysis and deuteron interaction models

The unusual low energy behaviour of the experimental mixing parameter epsilon 1 of the recent energy dependent phaseshift analysis has been reproduced by five simple local deuteron potential models. For a fixed very low energy, the relation between the quadrupole moment Q and epsilon 1 of standard potential models is a typical straight line which does not pass through the experimental point ( epsilon 1exp, Qexp) reported in this very low energy region. Correlations between Q and epsilon 1 are not found in the range of energies for which epsilon 1 has a pathological behaviour. The disagreement between the shape of the low energy behaviour of epsilon 1 of the data published in 1969, 1977 and 1983 disappears when the data are expressed in the RS-K-AR experimental mixing parameter Delta 12, of Ross and Shaw (1960), Kermode (1967) and Arndt and Roper (1970).

Coupled-reaction-channel calculation of a model n-d scattering problem above the breakup threshold.

An s-wave local potential model of n-d scattering at collision energies above the breakup threshold is solved using a pseudochannel extension of the coupled-reaction-channel method. Results obtained for both quartet and doublet scattering agree within a few percent with the benchmark solutions of Friar et al., Phys. Rev. C 42, 1838 (1990), for the same model.

Electrical resistivity of the alkaline earth metals Ca, Sr and Ba in the 50–300K temperature region

The computed values of the temperature dependent electrical resistivity is presented for the alkaline earth metals Ca, Sr and Ba. Numerical values of the mean free paths obtained using a finite mean free path approach is also reported. The structure factor has been evaluated using experimental values for the phonon spectra while local model potentials were used for the form factors. Our numerical results compare favourably with experiments.

Low-order perturbation theory for shake-up cross sections in atomic photoionization in a local-potential model.

Cross sections for the process in which photoionization of an atom is accompanied by excitation of an electron from an occupied orbital to an unoccupied orbital are calculated in lowest order in perturbation theory. The calculation is carried out in a local-effective-potential model for the atom that permits the summation over the intermediate states by using the Green's function for ordinary differential equations. It is assumed that the coupling scheme for the final ionic state is that the two holes couple to a state of definite ${L}_{12}$ and ${S}_{12}$ that then combines with the particle state to give a state of definite L and S. Expressions for the total cross section and asymmetry parameter are given for closed-shell atoms. Calculated results for Ne photoionization are compared with experimental results.

Analytical screened form factor obtained from Bachelet, Hamann and Schluter pseudopotential I

Model-(Pseudo)potential method has proven to be an interesting technique for calculating electronic properties in the framework of Ziman [1] formula for pure liquid metals and Faber-Ziman [2] expression for liquid alloys. First principle model-potentials are non local and their parameters are energy dependent. In the alloy one must take into account an energy dependent effective mass, a depletion hole and the Fermi energy core shift which is not known for alloys. More, the thermopower includes explicitely an energy dependent contribution. The first principle model-(pseudo)potential of BACHELET, HAMANN and SCHLUTER ( B.H.S.) [3] is energy independent and avoids the necessity of making these corrections. {itWe have used this potential to calculate analytically the corresponding form factor which is given in this paper (this paper : paper I). The resistivity and the thermopower of pure germanium and gallium and of the germanium-gallium alloy has been measured and calculated by using the FABER-ZIMAN [2] formalism. Both hard sphere and experimental structure factors have been used (when available). The agreement between experimental and calculated properties can be considered as good and confirms that the B.H.S. [3] model-potential is adequate for describing liquid alloys electronic properties. The discussion is made in paper II [4]. The transferability of B.H.S. potential allows us to use it for alloys and to compute the alloy effective interatomic potential. The results are compared with those obtained from the local screened non local ANIMALU model potential ( S.M.P.) and with pure metal results. These results are discussed in paper III [5].

Interatomic potentials of alloys obtained from non local model potentials III

The pseudopotential theory has been used to compute the interatomic potential in pure metals and in liquid alloys. The results obtained with the non local ANIMALU ( S.M.P.) model potential (local screening) [1] are compared to those computed with the analytical form factor that we calculated in I [2] from the non local energy independent BACHELET, HAMANN and SCHLUTER ( B.H.S.) [3] model (pseudo) potential.

Alpha-cluster spectroscopy in 40Ca and in the sd-shell closure region.

The low-energy {sup 36}Ar({alpha},{alpha}) elastic scattering data of Gaul {ital et} {ital al}. are analyzed within the frame of the optical model, using energy-independent Woods-Saxon squared or model-independent geometries for the real part of the potential. The optical-model scattering amplitude is decomposed into its barrier and internal wave components to understand the rapid and complicated evolution of the angular distributions with incident energy. The properties of the low-energy bound and quasibound states supported by this potential are compared with those of the states of the deformed 4p-4h rotational band in {sup 40}Ca, built on the {ital J}{sup {pi}}=0{sup +}, {ital E}{sub {ital x}}=3.35 MeV state. The possibility of extending this local potential model approach to neighboring nuclei near the {ital sd}-shell closure is discussed. A negative-parity band of states with appreciable {alpha}-cluster character, starting around the {alpha}-particle threshold, is expected to be systematically present in this mass region.

The quadrupole moment of the deuteron and local potential models

It was believed that the value of the quadrupole moment of the deuteron Q is too large to be fitted by realistic local potential models. Two simple local potential models for the deuteron with large Q are considered.

Solution of the two-nucleons Schrödinger equation with nonlocal tensor potential in the 3S 1- 3D 1 state

The program NPSD calculates the scattering parameters and deuteron properties for a neutron-proton system in the 3S 1- 3D 1 state when the potential model consists of a local part having cnetral, spin-orbit and tensor components, plus a nonlocal separable tensor contribution of the form γ g( r) g( r′) S 12. The numerical method for solving the radial Schrödinger equation (which in this case, is a pair of coupled integro-differential equations) is given. NPSD can be used with γ = 0 for any standard local potential model, provided that a subsidiary routine is rewritten.

Simulation of ionic transition-metal crystals: The cluster model and the cluster-lattice interaction in the light of the theory of electronic separability.

The cluster model often applied to the study of transition-metal ions in ionic crystals is rigorously formulated in the framework of the theory of electronic separability (TES). This theory shows that the cluster-lattice coupling appearing in the effective cluster Hamiltonian should include two separate operators: (1) the lattice effective potential containing nuclear attraction, Coulomb, and exchange terms, and (2) a lattice projection operator enforcing the cluster-lattice orthogonality required by the Pauli principle. The analysis of the TES equations also suggests a hierarchy of lattice models for dealing with the cluster-lattice interaction in an approximate way. Using a Hartree-Fock-Roothaan description for the intracluster interactions, three of these models are investigated and illustrated by means of several examples. First, the familiar point-charge model is deduced from the TES equations. The main conceptual and practical deficiencies of this model are discussed. Then, a TES-consistent lattice model in which the cluster-lattice exchange interactions are approximated by Slater X\ensuremath{\alpha} formula is presented. It is shown that this scheme, named the PX\ensuremath{\alpha} model, does not suffer from most limitations of the point-charge approximation and gives a coherent and reasonable description of the equilibrium geometry of the (${\mathrm{CrF}}_{6}$${)}^{4\mathrm{\ensuremath{-}}}$ unit in ${\mathrm{KCrF}}_{3}$. Finally, the model potential (MP) lattice model is presented and discussed. In this model the lattice ions are described by accurate local model potentials without resorting to the X\ensuremath{\alpha} approximation. The MP scheme gives satisfactory equilibrium geometries and relative stabilization energies for V, Cr, and Mn impurities in ${\mathrm{KMgF}}_{3}$.

Numerical study of zeno and anti-zeno effects in a local potential model

The effect of perturbation of a barrier on the passage of a wave packet is studied as an example of a perturbed unstable system. It is found that with a small periodic perturbation, significant modification of the effective lifetime occurs. The decay may be retarded (Zeno effect) or enhanced according to the relative phase of the perturbation and arrival time of the packet.

Potential description of the positive- and negative-energy properties of the alpha + 40Ca system and alpha -cluster structure of 44Ti.

The \ensuremath{\alpha}-cluster structure of the $^{44}\mathrm{Ti}$ nucleus is investigated within a local potential model description, starting from the unique optical potential which describes elastic $^{40}\mathrm{Ca}$(\ensuremath{\alpha},\ensuremath{\alpha}) scattering on broad angular and energy ranges, and which has recently been shown to describe the broad oscillations seen in the low energy fusion excitation function as well. It is found that the various \ensuremath{\alpha}-cluster states group into quasirotational bands whose properties are not dissimilar to those of the well-understood $^{20}\mathrm{Ne}$ nucleus. The lowest lying band is composed of states of even parity with moderate cluster character at low spin; it agrees within a few MeV's in absolute energy with the $^{44}\mathrm{Ti}$ experimental ground state band, and the experimental intraband quadrupole transition probabilities are reproduced with good accuracy. The potential supports an excited positive parity band with strong cluster character, starting a few MeV's above the \ensuremath{\alpha}${+\mathrm{}}^{40}$Ca threshold; the states of this band with spins ranging from 6 to 12 are responsible for the oscillations observed in the fusion excitation function. It supports, in addition, a negative parity band starting just above the threshold and composed of narrow states with intermediate cluster character; the latter has up to now no experimentally known counterpart. The states of higher lying bands are very broad and overlapping but they play an important role in enhancing the $^{40}\mathrm{Ca}$(\ensuremath{\alpha},\ensuremath{\alpha}) backward angle cross section. Our results are discussed in terms of the available experimental evidence and of the various, often conflicting theoretical interpretations which have been put forward to describe the $^{44}\mathrm{Ti}$ \ensuremath{\alpha}-cluster spectroscopy.

Unified study of lead: Energy-dependent pseudopotential calculation

A Unified study of lattice-mechanical properties of lead using energy-dependent pseudopotential is carried out. Energy dependence in pseudopotential is considered through the effective mass approximation; the pseudopotential model chosen is the local Heine-Abarenkov model potential. Properties studied include cohesive energy, equilibrium lattice parameter, second-order elastic constants, pressure derivative of second-order elastic constants, equation of state (atT=0 K), phonon-dispersion and effective two-body interaction. The results show fairly good agreement with experiment especially with a modified Heine-Abarenkov potential.

Non-Locality Effects of the Model Potential on the One-Component Plasma Structure Factor

Abstract We demonstrate that non-locality of the model potential plays a dominant role in the determination of the structure factor of alkali metals in the OCP model. Shaw's non local model potential combined with an analytic form of the direct correlation function in the Baus and Hansen scheme is found accurate to determine the structure factor of alkali metals up to the first peak. on leave from Kanpur University India. low-q behaviour they are displayed in last column to compare with bare OCP reference system in Baus and Hansen scheme.