Empirical Cross Research Articles

RNAV到着機の横方向経路逸脱量の推定

For effective aircraft operation, Civil Aviation Bureau promotes route restructuring for utilizing Area Navigation (RNAV) operation by means of making an RNAV roadmap. RNAV is a method of navigation which permits aircraft operation on any desired flight path within the coverage of station-referenced navigation aids or within the limits of the capability of self-contained aids, or a combination of these. Estimating optimal route spacing between parallel arrival routes is required. It's necessary to estimate lateral overlap probability, which is one of the most important parameters of collision risk model, for estimating the risk of the given route spacing. For estimating the lateral overlap probability, a distribution of cross track deviations was estimated using the radar data of Kagoshima Airport, flight plan data and flight strips. The results obtained are as follows. (1) The standard deviation of the observed cross track deviations of 2,298 flights is 0.077 NM. (2) The ninety five percent containment interval of the deviations is [-0.13 NM, 0.17 NM]. (3) The best fitted model for the empirical cross track deviations is the mixed model of two Normal (Gaussian) distributions. The fitted parameters are α=0.117, σ_1=0.0673 NM and σ_2=0.129 NM.

L-subshell and total M-shell X-ray production cross sections of Ta, W, Pt, Au, Pb and Bi by 0.7–2.4 MeV protons

The L-subshell and total M-shell X-ray production cross sections of Ta, W, Pt, Au, Pb and Bi have been measured by protons of energy between 0.7 and 2.4MeV. The obtained results for X-ray production cross sections have been compared with the existing experimental data, prediction of the ECPSSR theory and also with fitted empirical cross sections of Strivay and Weber.

Semi-empirical and empirical L X-ray production cross sections for elements with 50 ⩽ Z ⩽ 92 for protons of 0.5–3.0 MeV

We present in this contribution, semi-empirical production cross sections of the main X-ray lines Lα, Lβ and Lγ for elements from Sn to U and for protons with energies varying from 0.5 to 3.0 MeV. The theoretical X-ray production cross sections are firstly calculated from the theoretical ionization cross sections of the L i ( i = 1, 2, 3) subshell within the ECPSSR theory. The semi-empirical Lα, Lβ and Lγ cross sections are then deduced by fitting the available experimental data normalized to their corresponding theoretical values and give the better representation of the experimental data in some cases. On the other hand, the experimental data are directly fitted to deduce the empirical L X-ray production cross sections. A comparison is made between the semi-empirical cross sections, the empirical cross sections reported in this work and the empirical ones reported by Reis and Jesus [M.A. Reis, A.P. Jesus, Atom. Data Nucl. Data Tables 63 (1996) 1] and those of Strivay and Weber [Strivay, G. Weber, Nucl. Instr. and Meth. B 190 (2002) 112].

Reaction cross section described by a black sphere approximation of nuclei

We identify a length scale that simultaneously accounts for the observed proton-nucleus reaction cross section and diffraction peak in the proton elastic differential cross section. This scale is the nuclear radius, $a$, deduced from proton elastic scattering data of incident energies higher than $\sim800$ MeV, by assuming that the target nucleus is a ``black'' sphere. The values of $a$ are determined so as to reproduce the angle of the first diffraction maximum in the scattering data for stable nuclei. We find that the absorption cross section, $\pi a^2$, agrees with the empirical total reaction cross section for C, Sn, and Pb to within error bars. This agreement persists in the case of the interaction cross section measured for a carbon target. We also find that $\sqrt{3/5}a$ systematically deviates from the empirically deduced values of the root-mean-square matter radius for nuclei having mass less than about 50, while it almost completely agrees with the deduced values for $A\gtrsim50$. This tendency suggests a significant change of the nuclear matter distribution from a rectangular one for $A\lesssim50$, which is consistent with the behavior of the empirical charge distribution.

Iterative Joint Channel Decoding of Correlated Sources Employing Serially Concatenated Convolutional Codes

This correspondence looks at the problem of joint decoding of serially concatenated convolutional codes (SCCCs) used for channel coding of multiple correlated sources. We assume a simple model whereby two correlated sources transmit SCCC encoded data to a single destination receiver. We do not assume the existence of, nor do we use channel side information at the receiver. In particular, we present a novel iterative joint channel decoding algorithm for correlated sources by using the empirical cross-correlation measurements at successive decoding iterations to provide extrinsic information to the outer codes of the SCCC configuration. Two levels of soft metric iterative decoding are used at the receiver: 1) iterative maximum a posteriori probability (MAP) decoding is used for efficient decoding of individual SCCC codes (local iterations) and 2) iterative extrinsic information feedback generated from the estimates of the empirical cross correlation in partial decoding steps is used to pass soft information to the outer decoders of the global joint SCCC decoder (global iterations). We provide analytical results followed by simulation studies confirming the robustness of the cross-correlation estimates to channel-induced errors, justifying the use of such estimates in iterative decoding. Experimental results suggest that relatively few global iterations (two to five) during which multiple local iterations are conducted are sufficient to reap significant gains using this approach specially when the sources are highly correlated.

L1, L2 and L3 subshell ionization cross sections for elements with 71 ⩽ Z ⩽ 80 for protons of 0.5 to 3.0 MeV

We present in this contribution theoretical predictions of the L i (i = 1, 2, 3) subshells ionization cross sections within the ECPSSR theory for elements with atomic number 71 ⩽ Z ⩽ 80 for protons with energy of 0.5 to 3.0 MeV. These predictions are compared to the experimental data reported by Orlic et al. [At. Data Nucl. Data Tables 56 (1994) 159] and by Sokhi and Crumpton [At. Data Nucl. Data Tables 30 (1984) 49] by plotting the ratio S = σ exp/ σ ECPSSR as a function of the reduced velocity parameter for each individual subshell L1, L2 and L3. By fitting separately the ratio S, we deduced reference ionization cross sections for each Li subshell. On the other hand, we report empirical ionization cross sections and make a comparison between the reference cross sections, the empirical cross sections reported in this paper and those reported by Sow et al. [Nucl. Instr. and Meth. B 75 (1993) 58] and by Orlic et al. [Int. J. PIXE 4 (4) (1994) 217]

Model dependence in the photoproduction of kaons from protons and deuterons

The reactions $\ensuremath{\gamma}p\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}$ and $\ensuremath{\gamma}d\ensuremath{\rightarrow}{K}^{+}\ensuremath{\Lambda}n$ have been investigated over the energy range from ${E}_{\ensuremath{\gamma}}=1.0\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}{E}_{\ensuremath{\gamma}}=1.8\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$ in a tree-level effective Lagrangian model that incorporates most of the well-established resonances of spins $\frac{1}{2}$ and $\frac{3}{2}$ below $1.9\phantom{\rule{0.3em}{0ex}}\mathrm{GeV}$. Several sets of values for the resonance couplings are generated by fitting empirical cross section curves for the proton reaction at three different energies. Results obtained with a number of these fits are then presented for the cross sections and several single polarization observables for both reactions. The deuteron reaction is treated within the impulse approximation with final state interactions incorporated by means of a nonrelativistic overlap integral in momentum space. We explore the dependences of the calculated quantities on several facets of the model, including the particular resonance fit employed, the treatment of the spin $\frac{3}{2}$ resonance propagator, the prescription used for the resonance widths, and for the deuteron reaction, the final state interaction and deuteron wave function employed. We find that for neither reaction are the cross sections very sensitive to any of the model details. The polarization observables, on the other hand, are quite sensitive to certain model details, particularly to the resonance model employed and to the prescription used for the resonance widths. In general the polarization observables in the proton reaction are more sensitive to model details than the polarization observables in the deuteron reaction. The calculated deuteron observables are not strongly dependent on either the final state interaction or the deuteron wave function employed.

Rescattering contributions to the photoproduction of kaons from the deuteron

A model is developed for the reaction $\ensuremath{\gamma}+d\ensuremath{\rightarrow}{K}^{+}+\ensuremath{\Lambda}+n$ that includes both impulse and rescattering contributions. Most of the well-established resonances of spins $\frac{1}{2}$ and $\frac{3}{2}$ below $1.9\phantom{\rule{0.3em}{0ex}}\text{GeV}$ are incorporated in the model. Initial estimates for the relevant coupling strengths are extracted from empirical information and SU(3) symmetry relations. For certain resonances, these initial estimates are modified to bring the cross sections calculated for certain elementary processes related to the rescattering terms in rough qualitative agreement with the empirical cross sections for these processes. For the ${N}^{*}$ and $\ensuremath{\Delta}$ resonances included in the model, off-shell width extrapolations are obtained by treating the energy and momentum dependence of each decay channel separately. Since the main intent of the study is to ascertain the importance of the rescattering terms in the reaction amplitudes, no attempt has been made to include final state correlations. To represent the initial state, a nonrelativistic deuteron wave function is employed. Results are presented for the differential cross section in the deuteron rest frame at fixed kaon energy and angle. The results indicate that rescattering contributions to the photoproduction of kaons from the deuteron may be significant over a wide kinematical range.

Cavity Ringdown Spectroscopy of the à − X̃ Electronic Transition of the CH3C(O)O2Radical

Cavity ringdown spectra of the near-IR Ã2A‘ − X̃2A‘ ‘ electronic transition of the acetyl peroxy radical and its perdeutero analogue are reported. The electronic origin for the CH3C(O)O2 is observed at 5582.5(5) cm-1. Extensive ab initio calculations have been carried out to predict frequencies and help assign the electronic origin, observed vibrational hot bands, and several à state vibrational frequencies. An empirical absorption cross section for the origin of the Ã2A‘ − X̃2A‘ ‘ transition is estimated at σCH3C(O)O2 = (1±0.5) × 10-19 cm2.

A stochastic Monte Carlo approach to modelling real star cluster evolution -- III. Direct integration of three- and four-body interactions

Spherically symmetric equal mass star clusters containing a large amount of primordial binaries are studied using a hybrid method, consisting of a gas dynamical model for single stars and a Monte Carlo treatment for relaxation of binaries and the setup of close resonant and fly-by encounters of single stars with binaries and binaries with each other (three- and four-body encounters). What differs from our previous work is that each encounter is being integrated using a highly accurate direct few-body integrator which uses regularized variables. Hence we can study the systematic evolution of individual binary orbital parameters (eccentricity, semi-major axis) and differential and total cross sections for hardening, dissolution or merging of binaries (minimum distance) from a sampling of several ten thousands of scattering events as they occur in real cluster evolution including mass segregation of binaries, gravothermal collapse and reexpansion, binary burning phase and ultimately gravothermal oscillations. For the first time we are able to present empirical cross sections for eccentricity variation of binaries in close three- and four-body encounters. It is found that a large fraction of three-body and four-body encounters results in merging. Previous cross sections obtained by Spitzer and Gao for strong encounters can be reproduced, while for weak encounters non-standard processes like formation of hierarchical triples occur.

A comparative analysis of a-C:H by infrared spectroscopy and mass selected thermal effusion

A comparative analysis of quantitative infrared absorption spectra and mass selected thermal effusion transients measured for a large number of hydrogenated amorphous carbon (a-C:H) films is presented in order to establish reliable IR absorption cross sections for the different hydrogen bonding configurations in the material. The structural character of the material and the hydrogen concentration were varied over a wide range from soft and wide band gap polymerlike a-C:H, via so-called diamondlike carbon, to the tetrahedral form of a-C:H deposited from a plasma beam source. The results show that the IR absorption cross sections from molecular hydrocarbons can well be transferred to the solid state as long as the material is of polymeric character, but that this procedure fails as soon as the material converts into a three-dimensional cross-linked and mechanically hard structure. For the latter material an empirical average IR absorption cross section for the C–H stretch band can nevertheless be determined from a comparison between hydrogen effusion and IR spectra.

CASINO: A new monte carlo code in C language for electron beam interactions—part II: Tabulated values of the mott cross section

AbstractThis paper presents routines to compute the Mott cross section used in the CASINO program (Monte CArlo SImulation of electroN trajectory in sOlid). The routines used tabulated values of the Mott cross section computed in the work of Czyzewski et al. (1990). The cross section is available over the range 0.02 to 30 keV and for the first 94 elements of the Periodic Table. The routines are written in C language and use a binary file to interpolate the cross section. The first routine computes the total Mott cross sections; the second calculates the polar angle of collision. Backscattered coefficients computed using different cross section are compared for C, Al, Ag, and Au. The Rutherford (1911) cross section and the available empirical equations (Browning et al. 1994, Gauvin and Drouin 1993) are compared to tabulated values of Mott. Also, the energy distribution of backscattered electrons is shown for Al and Au at 10 keV. Finally, the relative computation times for the different Mott cross sections are compared. It was found that tabulated Mott cross sections are more accurate and faster than any empirical Mott cross sections. The tabulated Mott cross sections are even faster than simple Rutherford cross sections.

Low‐energy electron/atom elastic scattering cross sections from 0.1–30 keV

AbstractEmpirical forms for electron/atom scattering cross sections predict backscattering factors that compare well with those calculated using tabulated Mott data from 0.1 to 30 keV. The form of the empirical total cross section is similar to the screened Rutherford cross section. The fit to the tabulated differential Mott cross sections is decomposed into two parts, one part being of the same mathematical form as the screened Rutherford cross section (σR), and the second part being an isotropic distribution (σI). The ratio of the total cross sections (σR/σI) between the screened Rutherford part of the differential scattering cross section and the isotropic part of the distribution is fitted to give the same ratio of forward to backscattered currents as the tabulated Mott differential cross sections. The three equations, one for the total elastic cross section and two describing the differential cross section—one for the Rutherford screening parameter and one for the ratio σR/σI—give backscattering results covering all the major trends with energy and atomic number compared with the backscattering coefficients calculated using tabulated Mott cross sections. However, agreement with experiment is poor for some well‐researched examples such as Au. Monte Carlo calculations using the empirical cross sections show that surface effects may be critical in interpreting experimental results.

Transitional Dynamics in Two-Sector Models of Endogenous Growth

The steady state and transitional dynamics of two-sector models of endogenous growth are analyzed in this paper. We describe necessary conditions for endogenous growth. The conditions allow us to reduce the dynamics of the solution to a system with one state-like and two control-like variables. We analyze the determinants of the long run growth rate. We use the Time-Elimination Method to analyze the transitional dynamics of the models. We find that there are transitions in real time if the point-in-time production possibility frontier is strictly concave which occurs for example if the two production functions are different or if there are decreasing point-in-time returns in any of the sectors. We also show that if the models have a transition in real time the models are globally saddle path stable. We find that the wealth or consumption smoothing effect tends to dominate the substitution or real wage effect so that the transition from relatively low levels of physical capital is carried over through high work effort rather than high savings. We develop some empirical implications. We show that the models predict conditional convergence in that in a cross section the growth rate is predicted to be negatively related to initial income but only after some measure of human capital is held constant. Thus the models are consistent with existing empirical cross country evidence. (authors)

Fitted Empirical Reference Cross Sections for K-Shell Ionization by Alpha Particles

On the basis of our collection of experimental x-ray and Auger production cross-section data for H and He ions, we present a table of best-fitted cross sections for K-shell vacancy production (direct ionization plus electron capture) by 4He ions on all elements from 6C to 92U. Experimental values are first convened (if necessary) to vacancy production cross sections using fluorescence yields with an approximate correction for the effect of multiple ionization. These values are then normalized, i.e., divided, by an improved version (due to Benka et al.) of the ECPSSR theory by Brandt and Lapicki, to which a correction for electron capture by the projectile (following Lapicki and McDaniel) has been added. Since we have found empirically that the normalized cross sections (which describe the deviation of theory from experiment), at a certain scaled projectile speed, depend only on the ratio of projectile and target atomic numbers, we can use the data for both He and H ions as input. The normalized values are averaged, fitted by a polynomial, and multiplied by theory to produce best reference cross sections. Discrepant data sets are rejected using a statistical criterion which compares the deviations found to the errors stated in the original publications. The error assigned to the cross section consists of a calculated random contribution and an estimated systematic contribution that describes the limitations of the method. A list of the experimental input data (for 1H, 2H, 3He, and 4He projectiles) and a table showing the consistency or inconsistency of these data are also given.

Reaction p-barp--> Lambda -bar Lambda in the meson-exchange picture.

A study of the strangeness production process {ital {bar p}p}{r arrow}{bar {Lambda}}{Lambda} at threshold and intermediate energies has been performed doing a full coupled-channel ({ital {bar p}p},{bar {Lambda}}{Lambda}) calculation. The elastic part of the {ital {bar p}p} and {bar {Lambda}}{Lambda} interactions has been derived from a one-boson-exchange version of the Bonn {ital NN} potential and a corresponding extension to the hyperon-nucleon case whereas the annihilation part is taken into account by introducing suitable optical potentials. The transition interaction between {ital {bar p}p} and {bar {Lambda}}{Lambda} is based on {ital K}- and {ital K}{sup *}-meson exchange. A reasonably good description of empirical cross sections as well as polarization data is achieved. It is demonstrated that the results are quite sensitive even to short-range modifications of the channel interactions. We also compare our model with other approaches and suggest a new experiment which would be able to check the very different predictions of the meson-exchange and constituent quark model, respectively.

Measurements of K-shell ionization cross sections of35Br,37Rb,39Y using low energy protons

K-shell ionization cross section measurements are reported for35Br,37Rb and39Y targets caused by protons over 300–400 keV energy range in 20 keV increment. The K-shell ionization cross sections (σkl) at different energies were deduced from the Kα and Kβ X-ray production cross sections which were obtained from X-ray yields of the Kα and Kβ transitions. The experimental values are compared with the calculated values of ECPSSR theory and empirical reference cross sections. The resultant K-shell ionization cross sections are found to be in reasonable agreement with the ECPSSR theory. The Kα/Kβ intensity ratios are also presented and compared with other experimental values and also with the theoretical one-hole values given by Scofield.

Empirical cross sections for K X-ray emission by proton bombardment

Empirical proton-induced K X-ray emission cross sections are presented for all elements from 4Be up to 92U in a wide energy range. These values are obtained by fitting almost all the experimental data available from the literature in terms of weighted orthonormal polynomials. Original data are carefully screened to ascertain their precision and accuracy. Methods are discussed for removing statistical bias both on a local and a global basis. Final estimates are precise and accurate and have noticeably smaller errors than any single measurement. The present results are compared to empirical and analytical cross-section formulae.

K-shell ionization cross sections for Si, P, K, Ca, Zn, and Ga by protons and carbon ions in the energy range 1-6.4 MeV.

Absolute K-shell ionization cross sections have been measured for thin targets of Si, P, S, K, Ca, Zn, and Ga using carbon ions between 1.0 and 6.4 MeV and protons of 1 and 2 MeV. The dependence of x-ray production cross sections on target thickness was determined. The experimental results are compared to the semiclassical approximation [Laegsgaard, Andersen, and Lund in 3 Proceedings of the Tenth International Conference on the Physics of Electron and Atomic Collisions, Paris, 1977, edited by G. Watel (North-Holland, Amsterdam 1977)], to the theory for direct Coulomb ionization of the 1s\ensuremath{\sigma} molecular orbital [Montenegro and Sigaud, J. Phys. B. 18, 299 (1985)], to the perturbed stationary-state approximation with energy-loss, Coulomb, and relativistic corrections (ECPSSR) [Brandt and Lapicki, Phys. Rev. A 23, 1717 (1981)], and to the modification of the ECPSSR approximation (MECPSSR) [Benka, Geretschl\"ager, and Paul, J. Phys. (Paris) Suppl. 12, C9-251 (1987)]. The results for carbon ions are also compared to the statistical molecular orbital theory of inner-shell ionization for symmetric or nearly symmetric atomic collisions [Mittelman and Wilets, Phys. Rev. 154, 12 (1967)].The proton results agree with empirical reference cross sections [Paul, Nucl. Instrum. Methods 169, 249 (1980)]. Also, MECPSSR and ECPSSR provide best overall agreement for protons. For carbon ions the MECPSSR theory predicts the experimental data best. For the lightest targets, however, the MECPSSR underestimates the measured ionization cross sections appreciably for scaled velocities 0.4\ensuremath{\le}\ensuremath{\xi}\ensuremath{\le}0.8. We found that in this \ensuremath{\xi} range Pauli excitation via interacting level crossing contributes strongly to the measured ionization cross section. The sum of Mittelman-Wilets predictions and MECPSSR predictions then reproduces the measured cross sections satisfactorily. This result indicates that the direct Coulomb ionization of atomic orbitals, the Pauli excitation, and the direct Coulomb ionization again, but now of molecular orbitals, are the significant K-shell ionization mechanisms for carbon ions (atomic number ${Z}_{1}$=6) on targets (atomic number ${Z}_{2}$) with ${Z}_{1}$/${Z}_{2}$\ensuremath{\sim}0.4, for high ion velocities, intermediate velocities, and the lowest velocities, respectively.

A test of theoretical K-shell ionization cross sections for protons

Various sophisticated theories (relativistic plane wave Born approximation (RPWBA), semi-classical approximation (SCA), coupled-channels codes) are tested by comparison to our recent extended list of empirical K-shell ionization cross sections for protons. Differences between the theories are outlined. Surprisingly, the elaborate coupled-channels codes appear low compared to experiment, especially for light targets. Possible reasons for this are discussed. The RPWBA calculations describe the data better in a large projectile velocity range, in spite of the fact that binding and Coulomb effects are only treated as corrections. The SCA calculations by Hansteen et al. appear closer to the data than those by Trautmann; this is surprising since both codes should give identical results. Systematic comparisons are still severely hampered by the fact that most published cross sections describe different targets or different energies.