Four-parameter Fit Research Articles

Far-infrared reflectivity of GeSe2

The far-infrared reflectivity of single-crystal GeSe2 has been measured with polarized light when E//a and E//b. Using Kramers-Kronig analysis and four-parameter semi-quantum model fits of the reflectivity data, the infrared-active TO and LO modes (phonon frequencies) and damping factors have been determined. Five reststrahlen peaks were observed for the case E//a but only one for E//b. The ratio of intralayer to interlayer force constants are discussed and appeared to be between 18 and 30.

Impulse Approximation and Multiple-Scattering Series forπ+d↔ppat High Energy

A new model for ${\ensuremath{\pi}}^{+}d\ensuremath{\leftrightarrow}pp$ at high energy, based on the impulse approximation, is formulated. It is observed that the shape of the differential cross section for this process is qualitatively consistent with the deuteron momentum-space density, implying that nuclear structure plays a dominant role in determining the momentum-transfer distribution. Despite the drastically nondiffractive nature of the reaction, a multiple-scattering-like series can be formulated from the Lippmann-Schwinger equation and evaluated by the linearized-propagator method. The resulting amplitude yields a good four-parameter fit to $pp\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}d$ data at 3.74, 10.0, 14.2, 21.1, and 24.0 GeV/c. Arguments against some aspects of the Reggeistic interpretation of this process are also presented.

Elastic Scattering ofO16byTi48,Ca40,Al27,C12,Li7, andLi6

A number of isotopically enriched light targets were bombarded with ${\mathrm{O}}^{16}$ ions of 36- to 48- MeV energy (lab), and ten elastic angular distributions were measured. All cross sections show strongly destructive interference of nuclear and Coulomb scattering at angles above 30 to 60\ifmmode^\circ\else\textdegree\fi{} c.m., and fall orders of magnitude below the Coulomb cross section. The data were fitted reasonably well with conventional optical-model calculations, and $〈{\ensuremath{\chi}}^{2}〉$ values between 0.5 and 5.2 could be obtained for all targets. Typically, four-parameter fits were adequate. For the heavier targets the parameter sets are not unique, but were found to have continuous well-depth---geometry ambiguities, which were investigated in some detail. A procedure to produce in situ clean targets of highly reactive elements is described.

Stellar Reaction Rates for ^{28}Si

Stellar rates for the reactions ^(27)Al(p,-y)^(28)Si and ^(24)Mg(ɑ,-y)^(28)Si have been calculated from new cross- section data for these reactions. The contributions to the interaction rates, (σv)_(py) and (σv)_(ay), and to the corresponding photodisintegration rates, λ_(yp) and λ_(ya), from the excited states of ^(27)Al, ^(24)Mg, and ^(28)Si are discussed. The calculated interaction rates, N_A(σv), are listed for temperatures from 0.1 X 10^9o to 5.0 X 10^9° K; two- and four-parameter fits are given for N_A(σv) as a function of temperature.

Exchange-Degenerate Regge Trajectories and Meson-Nucleon Charge-Exchange Scattering

Based on exchange degeneracy and $\mathrm{SU}(3)$ symmetry, a Regge-pole model fitting the differential cross sections for pion-nucleon and kaon-nucleon charge exchange and $\ensuremath{\eta}$ production as well as polarization in ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ is given. Besides the $\ensuremath{\rho}\ensuremath{-}{A}_{2}$ trajectory, a conspiring and exchange-degenerate ${\ensuremath{\rho}}^{\ensuremath{'}}\ensuremath{-}{{A}_{2}}^{\ensuremath{'}}$ trajectory with the same slope as $\ensuremath{\rho}\ensuremath{-}{A}_{2}$ but with an intercept near zero is taken into account. The residues are assumed to have $\frac{1}{\ensuremath{\Gamma}(\ensuremath{\alpha})}$ behavior. A four-parameter fit gives good agreement with the experimental data.

π−pCharge-Exchange Differential Cross Section and Polarization in a Regge-Pole Model

Regge-pole fits to ${\ensuremath{\pi}}^{\ensuremath{-}}p$ charge-exchange differential-cross-section and polarization data have been given at moderately high energies and over a wide range of momentum transfers. Besides the $\ensuremath{\rho}$ trajectory, whose slope and intercept are determined by exchange degeneracy, a conspiring ${\ensuremath{\rho}}^{\ensuremath{'}}$ trajectory of the same slope but intercept near zero has been taken into account. In the spirit of the Veneziano formula, the residues are assumed to be of the form $\frac{\mathrm{const}}{\ensuremath{\Gamma}(\ensuremath{\alpha})}$. A four-parameter fit gives good agreement with the experimental data.

Study of theΛ−NSystem in Low-EnergyΛ−pElastic Scattering

The present paper is based on 378 $\ensuremath{\Lambda}\ensuremath{-}p$ elastic scattering events in the incident-momentum region 120-320 $\frac{\mathrm{MeV}}{c}$. Differential and total cross sections have been measured in several momentum intervals and found to be consistent with predominantly $S$-wave scattering. No significant indication for the existence of a low-energy $\ensuremath{\Lambda}\ensuremath{-}p$ resonance has been found. Using the effective-range approximation, the four scattering parameters ${a}_{s}$, ${a}_{t}$, ${r}_{s}$, and ${r}_{t}$ were evaluated with and without further assumptions on the $\ensuremath{\Lambda}\ensuremath{-}p$ interaction properties. Best values obtained from the four-parameter fit were ${a}_{s}=\ensuremath{-}1.8$, ${a}_{t}=\ensuremath{-}1.6$, ${r}_{s}=2.8$, and ${r}_{t}=3.3$ F. A likelihood-function mapping procedure is used to describe the large and strongly correlated errors of these values.

Fitting of Electromagnetic Nucleon Form Factors in a Vector-Dominance Model

By using the Lagrangian theory of vector dominance of Kroll, Lee, and Zumino, a four-parameter fit to the experimental data for the electromagnetic nucleon form factors for spacelike four-momentum transfer squared (${q}^{2}$) is obtained. The isovector, hypercharge, and baryon-number parts of the nucleon-vector-meson vertices are assumed to have phenomenologically ${(1+\frac{{q}^{2}}{{{\ensuremath{\Lambda}}_{I}}^{2}})}^{\ensuremath{-}1}$, ${(1+\frac{{q}^{2}}{{{\ensuremath{\Lambda}}_{Y}}^{2}})}^{\ensuremath{-}1}$, and ${(1+\frac{{q}^{2}}{{{\ensuremath{\Lambda}}_{N}}^{2}})}^{\ensuremath{-}1}$ momentum dependence. The slope of ${{G}_{E}}^{n}$ at ${q}^{2}=0$ is set equal to the Krohn-Ringo value of 0.457 ${(\frac{\mathrm{BeV}}{c})}^{\ensuremath{-}2}\ifmmode\pm\else\textpm\fi{}5%$. The result of the fitting is satisfactory for both large and small ${q}^{2}$.

Rare-Earth-Iron Exchange Interaction in the Garnets. II. Exchange Potential for Ytterbium

To determine the magnitude of the anisotropy of the ytterbium-iron (Yb-Fe) exchange interaction we have evaluated the exchange splittings of the lowest $^{2}F_{\frac{5}{2}}$ and $^{2}F_{\frac{7}{2}}$ doublets of ytterbium (${\mathrm{Yb}}^{3+}$) in ytterbium iron garnet (YbIG). By using the wave functions of ${\mathrm{Yb}}^{3+}$ in yttrium gallium garnet (those for YbIG are not known) we are able to express these splittings in terms of ten parameters which characterize the anisotropy of the exchange interaction. As there are only six experimental splittings it is necessary to reduce the number of unknowns by assuming: (1) that the rare-earth-iron (RE-Fe) exchange interaction takes place through the neighboring eight oxygen ions, and (2) (somewhat more uncertainly) that the rare-earth-oxygen (RE-O) exchange interaction is axial about the RE-O axis. This leads us to express the exchange splittings in two sets of four exchange constants. We find a good four-parameter fit of the experimental exchange splittings by adopting essentially zero values for the rare-earth-ferric ion exchange interactions that take place through the four nearest oxygen ions. This result corroborates qualitative conjectures on the RE-Fe exchange based on superexchange bonding angles. The validity of the extrapolation of the anisotropy of the Yb-Fe exchange interaction to other rare earths is discussed.

Resonance Model forΣ+−K+Production

A model for the process ${\ensuremath{\pi}}^{+}+p\ensuremath{\rightarrow}{\ensuremath{\Sigma}}^{+}+{K}^{+}$ is proposed, consisting of hyperon- and ${K}^{*}$-exchange diagrams as well as the ${p}_{\frac{3}{2}}$ resonance, and a resonance of 1940 MeV, assumed to be ${f}_{\frac{7}{2}}$. The resulting four-parameter fit is compared with the cross-section, angular distribution, and polarization data at beam momenta from 1.04 to 1.76 BeV/c.