Flat-bottom Potential Research Articles

Calculation of kaon electromagnetic form factor

The kaon meson electromagnetic form factor is calculated in the framework of coupled Schwinger-Dyson and Bethe-Salpeter formulation in simplified impulse approximation (dressed vertex) with modified flat-bottom potential, which is a combination of the flat-bottom potential taking into consideration the infrared and ultraviolet asymptotic behaviours of the effective quark-gluon coupling. All the numerical results give a good fit to experimental values.

Calculation of the π Meson Electromagnetic Form Factor

The modified flat-bottom potential (MFBP) is given by the combination ofthe flat-bottom potential with considerations for the infrared andultraviolet asymptotic behaviour of the effective quark-gluon coupling.The π meson electromagnetic form factor is calculated in theframework of the coupled Schwinger-Dyson equation and the Bethe-Salpeterequation in the simplified impulse approximation (dressed vertex)with the MFBP. All our numerical results give a good fit toexperimental values.

Nonlocal quark vacuum condensate

The nonlocal quark condensate is calculated with the Flat-Bottom Potential in rain-bow Schwinger–Dyson equation. The numerical result is compatible with other theoretical results.

X-ray and neutron diffraction study of benzoylacetone in the temperature range 8-300 K: comparison with other cis-enol molecules.

The crystal structure of benzoylacetone (1-phenyl-1,3-butanedione, C(10)H(10)O(2); P2(1)/c, Z = 4) has been determined at 300, 160 (both Mo Kalpha X-ray diffraction, XRD), 20 (lambda = 1.012 Å neutron diffraction, ND) and 8 K (Ag Kalpha XRD), to which should be added earlier structure determinations at 300 (Mo Kalpha XRD and ND, lambda = 0.983 Å) and 143 K (Mo Kalpha XRD). Cell dimensions have been measured over the temperature range 8-300 K; a first- or second-order phase change does not occur within this range. The atomic displacement parameters have been analyzed using the thermal motion analysis program THMA11. The most marked change in the molecular structure is in the disposition of the methyl group, which has a librational amplitude of approximately 20 degrees at 20 K and is rotationally disordered at 300 K. The lengths of the two C-O bonds in the cis-enol ring do not differ significantly, nor do those of the two C-C bonds, nor do these lengths change between 8 and 300 K. An ND difference synthesis (20 K) shows a single enol hydrogen trough (rather than two half H atoms), approximately centered between the O atoms; analogous results were obtained by XRD (8 K). It is inferred that the enol hydrogen is in a broad, flat-bottomed single-minimum potential well between the O atoms, with a libration amplitude of approximately 0.30 Å at 8 K. These results suggest that at 8 K the cis-enol ring in benzoylacetone has quasi-aromatic character, in agreement with the results of high-level ab initio calculations made for benzoylacetone [Schiøtt et al. (1998). J. Am. Chem. Soc. 120, 12117-12124]. Application [in a related paper by Madsen et al. (1998). J. Am. Chem. Soc. 120, 10040-10045] of multipolar analysis and topological methods to the charge density obtained from the combined lowest temperature X-ray and neutron data provides evidence for an intramolecular hydrogen bond with partly electrostatic and partly covalent character, and large p-delocalization in the cis-enol ring. This is in good agreement with what is expected from the observed bond lengths. Analysis of the total available (through the Cambridge Structural Database, CSD) population of cis-enol ring geometries confirms earlier reports of correlation between the degree of bond localization in the pairs of C-C and C-O bonds, but does not show the dependence of bond localization on d(O.O) that was reported earlier for a more restricted sample. It is suggested that the only reliable method of determining whether the enol hydrogen is found in a single or double potential well is by low-temperature X-ray or (preferably) neutron diffraction.

Calculation of the Electromagnetic Form Factor of the Kaon

The wavefunctions of the bound state of the charged kaon are obtained from the Bethe-Salpeter equation with the phenomenological vector-vector-type flat-bottom potential. The physical space-like electromagnetic form factor of the charged kaon is calculated. The results calculated give a good fit to the experimental values.

Calculations of some properties of the kaon

The wave functions of the bound state of the charged kaon are obtained from Bethe-Salpeter equation with the phenomenological vector-vector-type flat-bottom potential. The physical spacelike electromagnetic form factor of the charged kaon is calculated from the wave functions. The radius of the kaon is given from the electromagnetic form factor. The decay constant f K of the kaon is estimated by the relationship between the decay constant and the normalization factor derived from the axial-vector Ward identity. All calculated results give a good fit to the experimental values.

Calculations on some properties of the pion in the framework of Schwinger - Dyson and Bethe - Salpeter equations

The flat-bottom potential is modified according to some physical considerations for the infrared and ultraviolet asymptotic behaviour of the effective quark - gluon coupling. The propagator functions and mass function for the quark, and the Bethe - Salpeter wavefunctions, mass, electromagnetic form factor, radius and decay constant for the pion are calculated numerically in the framework of the Schwinger - Dyson equation in the rainbow approximation and the Bethe - Salpeter equation in the ladder approximation with the modified flat-bottom potential. All results agree with other theories and experimental results, respectively.

Calculations of the Decay Constant and Radius of the Pion

We calculated the decay constant and radius of the pion in the framework of the Bethe-Salpeter equation with the vector-vector-type flat-bottom potential. The calculated results, fπ = 102 MeV and ⟨rπ2⟩½ = 0.632 fm, are close to experimental values of fπ = 93 MeV and ⟨rπ2⟩½ = 0.663±0.023 fm.

Molecular conformation and potentials for out-of-plane ring vibrations in the S and S1 electronic states of 1,4-benzodioxan from supersonic-jet fluorescence and high-resolution absorption measurements

In a study of the 281 nm S1–S0 electronic spectrum of 1,4-benzodioxan, the high-resolution vapor absorption spectrum, the fluorescence excitation spectrum in a supersonic jet, and the dispersed single-vibronic-level fluorescence spectra for excitation into several different S1 levels have been measured. Four out-of-plane ring vibrations have been characterized in each electronic state, and it is shown that the partially saturated six-membered ring is rigidly nonplanar with a twisted C2 conformation. The twisting vibration is nearly harmonic and the barrier to planarity is high in both electronic states; however, there is some lowering of the barrier upon excitation. There is strong Duschinsky mixing in S1 between two of the out-of-plane ring bending modes, one of which is quite anharmonic with a flat-bottomed potential.

Phenomenological model for 0(-) mesons.

With the use of the spinor-spinor Bethe-Salpeter equation, a phenomenological vector-vector-type flat-bottom hadronic potential is assumed which is fully relativistic covariant. The ${0}^{\ensuremath{-}}$ meson wave functions in momentum space have been obtained. Then, the physical spacelike electromagnetic form factor of the ${0}^{\ensuremath{-}}$ meson is calculated directly from the Euclidean space ${0}^{\ensuremath{-}}$ meson wave functions. Numerical results show that the theoretical calculation gives a good fit to the experimental results by appropriately choosing the parameters in the phenomenological flat-bottom potential.

Quantum interference and Landau level broadening in narrow GaAs-AlGaAs channels

High 2D electron mobility narrow Hall bars, 0.8 mu m wide by 30 mu m long, were fabricated in which, after photoexcitation, the scattering mean free path was up to 4.5 mu m long at 1.3 K. The low field negative magnetoresistance arises from quantum interference (weak localization) with the flux cancellation mechanism absent, even though the mean free path is much greater than the width. The Landau levels are significantly broadened, implying that a flat-bottomed model potential is inappropriate in this particular case. It is suggested that the potential fluctuations giving rise to the broadening are responsible for the absence of the flux cancellation, and when small angle scattering contributes to the elastic mean free path. The value of this length compared with the width is no longer a sufficient criterion for the determination of the nature of the magnetoresistance.

Methyl and vinyl torsional potentials in cis- and trans-3-methylstyrene from supersonic jet fluorescence spectra

Part of the fluorescence excitation spectrum and several single vibronic level dispersed fluorescence spectra of the cis and trans rotamers of 3-methylstyrene in a supersonic jet have been obtained. Both rotamers show overlapping progressions involving methyl and vinyl torsional vibrations in S0 and involving just the methyl torsion in S1. The resulting torsional levels have been fitted to a ½ΣnVn(1 – cos nϕ) potential with V″1= 8.9 cm–1, V″2= 1212 cm–1 and V″4=–302 cm–1 for the vinyl torsion in S0. Both rotamers are very similar in energy with the cis rotamer probably being the more stable, and, although they are planar, both of them show, like styrene, a very flat-bottomed potential. The methyl torsional levels have been fitted with V″3= 45 cm–1 in S0, V′3= 165 cm–1 and V′6=–13 cm–1 in S1 of the cis rotamer, and V″3= 52 cm–1 and V″6= 19 cm–1 in S0, V′3= 79 cm–1 and V′6= 5 cm–1 in S1 of the trans rotamer.

Vinyl torsional potential function of 4-fluorostyrene in the S0 electronic state from electronic absorption and supersonic jet fluorescence spectroscopy

Analysis of sequence and cross-sequence bands in the gas phase absorption spectrum together with supersonic jet single vibronic level fluorescence spectra of 4-fluorostyrene, with excitation in the 0 0 0 and 41 0 142 0 1 bands, has given the v 42 = 0–6 term values for the C(1)-C(α) torsional uration is planar but the potential, like that of 4-methylstyrene, is not so flat-bottomed as that of V(θ) cm −1 = 1 2 [(950 ± 60)(1 − cos 2θ) − (229 ± 30)(1 − cos 4θ)] . The torsional barrier height is, like that of 4-methylstyrene, about 10% lower than that in styrene. The large, negative value of V 4 results in a very flat-bottomed potential. The equilibrium configuration is planar but the potential, like that of 4-methylstyrene, is not so flat-bottomed as that of styrene.

Nucleon-nucleon interaction with a flat bottom linear confinement potential in the Quark model

Nucleon-nucleon interaction is studied in the non-relativistic quark model with a flat bottom linear confinement potential. The results are consistent with the calculated ones from the lattice quantum chromodynamics. The quark-quark interaction also consists of those caused by the one gluon exchange and the one pion exchange. The phenomenological sigma meson exchange between two nucleons is also included to fit the S-wave N-N scattering data. The calculated NN channel S-wave phase shifts show that the flat bottom linear confinement potential can provide part of the medium range attraction.

A PHENOMENOLOGICAL MODEL FOR 0- MESON (Ⅱ)——THE ELECTROMAGNETIC FORM FACTOR

The physical space-like electromagnetic form factor has been calculated directly from the Euclidean 0- meson wave functions solved for the flat bottom potential in the Euclidean space. Numerical results show that the theoretical calculation may be in accordance with experiment by appropriately choosing the parameters.

Anharmonic Debye-Waller factors and the study of structural phase transitions

Analytical expressions are obtained for the Debye-Waller factors of highly anharmonic double-minimum and flat-bottomed one-particle potential which differ only in the presence or absence of a potential barrier at the mid-point. A lack of sensitivity in the Debye-Waller factors to the presence of the potential barrier is demonstrated for potentials with parameters modelling the hydrogen atom in the KH2PO4-type ferroelectrics at room temperature. The analysis indicates that a series of measurements with decreasing temperature may be necessary for a double minimum in the potential to be resolvable for these systems. The Debye-Waller factors investigated here show an anomalous temperature dependence in certain regions of reciprocal space, where they produce constant or even increasing integrated intensities of Bragg diffraction peaks with increase in temperature. Comparisons are made with the Debye-Waller factors for a disorder model, based on a one-particle probability density constructed from two displaced Gaussian distributions. This model is unable to reproduce the anomalous temperature dependence predicted by the anharmonic potentials.

Infrared problems in the presence of instantons

In theories without an intrinsic mass scale, the semiclassical approximation may yield erroneous results. A concrete example is provided by a flat-bottom potential in one dimension. This massless model is discussed in detail and compared to a model which has a mass scale. Both models have finite-action instantons. Nevertheless only in the massive case does instanton physics lead to the correct results. Since quantum chromodynamics is a massless theory, infrared divergences may occur while quantizing it around the instanton; this possibility is discussed.