Real Form Factor Research Articles

Factor de forma para la Tectona grandis L.F, empresa MLR-Forestal, Siuna, Costa Caribe Norte de Nicaragua

Esta investigación se realizó en la empresa MLR-Forestal de Nicaragua, en la comunidad Waspado, municipio de Siuna, Región Autónoma Costa Caribe Norte. Fue un estudio predictivo, transversal y prospectivo, orientado en la determinación del factor de forma de la Tectona grandis L.F. La muestra equivale a 255 árboles distribuido en 51 parcelas circulares de 1000 metros cuadrados en tres fincas (Waspado con un total de 86.28 ha, Danli con 58.87 y Mutiwas con 52.85) para un total de 198 ha, dentro de cada parcela fueron seleccionados 5 árboles, entre dominantes, codominantes y suprimidos. Se obtuvieron los factores de forma por finca de 0.54 para Waspado, 0.57 para Mutiwas y 0.53 para Danli y un factor de forma promedio general para las tres fincas de 0.55. El cual di ere del factor de forma nacional para las latifoliadas 0.70. Los datos permitieron construir una tabla para estimaciones de volúmenes en plantaciones de TECA. Al encontrar el factor de forma real de la Tectona grandis L.F obtuvimos las siguientes diferencias con relación al porcentaje de error según el factor de forma estipulado por el Instituto Nacional Forestal (INAFOR) y con el modelo matemático encontrado (porcentaje de error según el factor de forma encontrado (-5.84 %), el estipulado por el INAFOR es de (19.83 %) y modelo matemático (-11.30 %), los valores negativos hacen una subestimación de volumen real y los positivos hacen una sobreestimación de volumen.

Models and form factors for stand volume estimation in natural forest ecosystems: a case study of Katarniaghat Wildlife Sanctuary (KGWS), Bahraich District, India

In view of the difficulties in stand volume estimation in natural forests, we derived real form factors and models for volume estimation in these types of forest ecosystems, using Katarniaghat Wildlife Sanctuary as a case study. Tree growth data were obtained for all trees (dbh >10 cm) in 4 plots (25 × 25 m) randomly located in each of three strata selected in the forest. The form factor calculated for the stand was 0.42 and a range of 0.42–0.57 was estimated for selected species (density >10). The parameters of model variables were consistent with general growth trends of trees and each was statistically significant. There was no significant difference (p>0.05) between the observed and predicted volumes for all models and there was very high correlation between observed and predicted volumes. The output of the performance statistics and the logical signs of the regression coefficients of the models demonstrated that they are useful for volume estimation with minimal error. Plotting the biases with respect to considerable regressor variables showed no meaningful and evident trend of bias values along with the independent variables. This showed that the models did not violate regression assumptions and there were no heteroscedacity or multiculnarity problems. We recommend use of the form factors and models in this ecosystem and in similar ones for stand and tree volume estimation.

Measurement of real and imaginary form factors of silver atom using a high resolution HPGe detector

The real and imaginary form factors of silver atom have been determined by using EDXRF method. The K x-ray photons in the energy range from 8.62 keV to 52.18 keV are generated by sending 59.56 keV gamma photons from <formula>^{241}</formula>Am radioactive source on various targets. These K x-ray photons are transmitted through silver foils of suitable thickness. The incident and transmitted K x-ray photon intensities have been measured with a high resolution HPGe detector which is coupled to 16K MCA. The photoelectric cross sections at different K x-ray energies have been determined by measuring the intensities of the incident and transmitted x-ray photons. From these photoelectric cross section values, the imaginary form factors and the real form factors have been determined at various photon energies. Measured imaginary and real form factor values have been compared with theoretical values predicted by XCOM [23] and FFAST [24].

Neutron analysing powers and a low-energy optical model analysis

Neutron elastic scattering analysing powers have been measured at 3 MeV incident energy for natW, natHg, natTl, natPb, 209Bi and 238U. Differential cross sections have also been measured for natHg, natTl, natPb and 208Bi. A local, phenomenological, spherical optical model analysis of these data is performed with comparison made between pure Woods-Saxon real form factors and those having surface-peaked components. The latter have been predicted in dispersion integral calculations. The effects of introducing an imaginary spin-orbit potential component are also tested. For natW and 238U a deformed phenomenological optical potential is used in coupled-channels calculations. Coupled-channels effects are also investigated for 208Pb, assuming it to be a harmonic vibrator. Microscopic calculations of real and imaginary potentials are made using the methods of Brieva and Rook, (1977,8), and Jeukenne et al. (1977). Calculation of the spin-orbit interaction is less sophisticated with an energy- and density-independent form used. At 3 MeV compound elastic scattering must be accounted for in all nuclei presently studied. This has been calculated using a recent formulation of the statistical model.

Large-angle 6Li + 28Si elastic and inelastic scattering at 27 and 34 MeV

Elastic and inelastic scattering data extending to θ c.m ≈ 175° are reported for 6Li + 28Si at 27 and 34 MeV. Optical model analyses of the elastic data were made using a variety of real potential forms. The large-angle data cannot be fitted with a Woods-Saxon real potential, but are well described by Woods-Saxon squared, double-folded or Fourier-Bessel potentials. The real potential is the same at both energies, but the imaginary potential is weaker at 27 MeV. The inelastic data were analyzed using the DWBA and coupled channels techniques with folded real form factors and deformed Woods-Saxon imaginary potentials, with the deformations taken from electron scattering. The 2 + state was fitted well at both energies with the DWBA, while the prediction decreased too rapidly at large angles for the 4 + state. The large-angle 4 + data were better described when two-step excitations were included in the coupled-channels calculations. The forward-angle 2 + data are sensitive to the interference between Coulomb and nuclear scattering and show that the nuclear and Coulomb deformation parameters β 2 are equal for this transition.

Microscopic theory of the imaginary inelastic transition form factor

A microscopic formulation of the nucleon-nucleus imaginary inelastic form factor using particle-hole intermediate states gives a result which is roughly the real form factor times a function consisting of intermediate particle- and hole-scattering terms. These terms have opposite signs, allowing the possibility of a radial dependence for the form factor similar to the collective model. Numerical results for 30 MeV /sup 40/Ca(n,n')/sup 40/Ca(3/sup -/,3.73 MeV) scattering are compared with the collective model.

The (p, n) reaction to the isobaric analogue state of high-Z elements at 25.8 MeV

Angular distributions have been measured for the (p, n) reaction to the isobaric analogue state of the targets 197 Au, 206 Pb, 207 Pb, 208 Pb, 209 Bi, and 232 Th at a proton energy of 25.8 MeV. Results of distorted wave Born approximation calculations indicated that angular distributions were predicted well by both real and complex form factors, although there was less sensitivity to an imaginary surface term than found in previous studies for lower- Z elements. An isospin correction to parameters for proton elastic scattering as determined from (p, n) quasi-elastic scattering was used to predict neutron elastic scattering in an application of the isospin model due to Lane. Although the isospin correction appeared necessary, it was not sufficient to provide adequate agreement with neutron elastic scattering data. A microscopic interpretation of the form factor provided a model in which angular distributions could be predicted well by a real form factor involving only two free parameters. This model was also used to determine the ratio of the rms radii of the neutron matter distribution to the proton matter distribution in 208 Pb and gave the result 〈r n 2 〉 1 2 /〈r p 2 〉 1 2 = 1.07±0.02 .

The role of the imaginary form factor in the microscopic description of (p, p′) scattering from nuclei with one closed shell

The inelastic scattering of protons from the lowest 2+ and 3− levels in 40Ca, Ni, Sn and N = 50 isotopes is analyzed for different incident proton energies. The addition of a collective imaginary term to the microscopic real form factor very much improves the agreement between the calculated and experimental cross section angular distributions. The variation with energy of the relative contributions of the ΔT = 1 and gDT = 0 isospin parts of the transitions is discussed.

Study of the Reactionν+n→μ−+p

166 events of the reaction $\ensuremath{\nu}+n\ensuremath{\rightarrow}{\ensuremath{\mu}}^{\ensuremath{-}}+p$ at an average neutrino energy of \ensuremath{\sim} 0.7 GeV have been observed in the Argonne National Laboratory 12-ft deuterium bubble chamber. The results are well described by the conventional current-current weak-interaction theory with three real form factors ${{F}_{V}}^{1}$, ${{F}_{V}}^{2}$, and ${F}_{A}$. Using electron-nucleon scattering results to fix the vector mass ${M}_{V}$ at 0.84 GeV, and assuming a dipole form for ${F}_{A}$, we obtain the value 0.95 \ifmmode\pm\else\textpm\fi{} 0.12 GeV for the axial-vector mass ${M}_{A}$.

The role of the imaginary part in the microscopic description of (p, p′) scattering

A (p, p′) scattering experiment at E p = 40 MeV was performed on the targets 92Mo and 116, 120, 124Sn. The addition of a simple collective imaginary from factor to the microscopic real form factor provides an important improvement in the agreement between calculated and experimental cross sections for the lowest 2 + and 3 − states. Results concerning the ΔT = 1 and ΔT = 0 contributions to the transitions are discussed.

Optical-model analysis of the 208Pb(p, n) 208Bi (IAS) reaction

The isobaric analog of the 208pb ground state was populated in the 208Pb(p, n) 208Bi(IAS) reaction. The proton (p̃) decay of the IAS was used to obtain the IAS neutron angular distributions at proton bombarding energies of 24.8, 30.5 and 38.6 MeV by detecting the neutrons in coincidence with the p̃. DWBA analyses were performed for these data along with the data obtained at 50 MeV by the Rutherford Laboratory using a macroscopic interaction. Both complex and real form factors were found which adequately reproduce the data. These macroscopic form factors have rms radii more than 1 fm larger than the rms radius for the folded microscopic interaction. A possible interpretation for a complex form factor is presented.

Muon pair production in strong interactions

The general analysis ofμ+μ− (or e+e−) pair production from any unpolarized initial state of strongly interacting particles is given to lowest order in the electromagnetic interaction. The process is completely described by five real form factors that are simply related to the density matrix elements for the production of a virtual photon which then decays into the pair. The angular distribution of theμ+μ− pairs in their center of momentum and their polarizations are computed in terms of the form factors. By measuring the angular distribution and polarizations of the pair one can determine all five form factors and thereby investigate the structure of the production process. Finally, some peripheral-meson-exchange models of the process are considered.

Determination of the Nucleon's Isotopic Spectral Functions

We employ the method of exact inversion, discussed in an earlier paper, to determine the nucleon's isotopic spectral functions from their corresponding real form factors. Specific analytic expressions, as suggested by previous pole fits, are used for the real form factors and these give spectral functions that have all the required analytic properties. The constraint that the electric and magnetic form factors are equal at the threshold for proton-antiproton annihilation into an electron-positron pair is used throughout. We find that the complex proton's form factors are zero at the annihilation threshold and using this observation we compare our results with the predictions of the internal symmetry theories.