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Journal articles on the topic 'Born approximations'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Wei, Jia, Zengxi Ge, Mianshui Rong, and Zhenning Ba. "Preconditioned Splitting Series Approximation for 2D Rough Surface Scattering." Bulletin of the Seismological Society of America 110, no. 3 (2020): 1149–61. http://dx.doi.org/10.1785/0120190309.

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ABSTRACT Scattering sensitivity of waves to surface roughness has been widely observed in many fields. Some series approximations for rough surface scattering, such as the general Born, the splitting, and the preconditioned splitting series, are presented for a numerical description of rough surface scattering by multiscale surfaces. In fact, the splitting series approximation is a specific form of the preconditioned splitting series. Numerical tests with several benchmark models are compared with the full-waveform numerical solution and the general Born series approximation to investigate the range of validity of the splitting and the preconditioned splitting series approximations. The splitting and the preconditioned splitting series approximations to multiscale surfaces are not subject to the strict limit applied to the general Born series approximation. Each order of the splitting series represents an increase of multiple scatterings between surface points. Therefore, higher-order splitting series approximation accounts for stronger surface scattering. A suitable preconditioned splitting and the splitting series approximations improve the general Born series approximation for the convergence of high-incident angle scattering, and, therefore, become realistic methods for multiscale surfaces with infinite gradients and extremely large surface heights. This series approximation mathematically provides a unified framework for rough surface scattering, which contains Born or Rytov series approximation as specific cases.

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2

Friar, J. L., and G. L. Payne. "Configuration-Space-Faddeev Born Approximations." Few-Body Systems 33, no. 4 (2003): 233–40. http://dx.doi.org/10.1007/s00601-003-0016-0.

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3

Zaidi, H. R. "Green's function equations of motion for driven two-level atoms." Canadian Journal of Physics 63, no. 3 (1985): 314–26. http://dx.doi.org/10.1139/p85-049.

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Using a diagram technique, equations of motion for N coherently driven two-level atoms are obtained from Green's functions. The longitudinal (Coulomb) dipole–dipole interaction is neglected. Three approximations (Born approximation, extended Born approximation, and screened interaction approximation) are considered. The existing theories are shown to be equivalent to the extended Born approximation. For a small sample, the equations of motion exhibit S conservation in this case. The screened interaction model predicts a different behaviour; in particular, S-breaking terms appear in the equations of motion for a small sample.

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4

Yang, Kai, and Jianfeng Zhang. "Comparison between Born and Kirchhoff operators for least-squares reverse time migration and the constraint of the propagation of the background wavefield." GEOPHYSICS 84, no. 5 (2019): R725—R739. http://dx.doi.org/10.1190/geo2018-0438.1.

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The Born approximation and the Kirchhoff approximation are two frameworks that are extensively used in solving seismic migration/inversion problems. Both approximations assume a linear relationship between the primary reflected/scattered data to the corresponding physical model. However, different approximations result in different behaviors. For least-squares reverse time migration (LSRTM), most of the algorithms are constructed based on Born approximation. We have constructed a pair of Kirchhoff modeling and migration operators based on the Born modeling operator and the connection between the perturbation model and the reflectivity model, and then we compared the different performances between Born and Kirchhoff operators for LSRTM. Numerical examples on Marmousi model and SEAM 2D salt model indicate that LSRTM with Kirchhoff operators is a better alternative to that with Born operators for imaging complex structures. To reduce the computational cost, we also investigate a strategy by restricting the propagation of the background wavefield to a stopping time rather than the maximum recording time. And this stopping time can be chosen as half of the maximum recording time. This computational strategy can be used in LSRTM procedures of predicting the primary reflected data, calculating the step length, and computing the gradient. Theoretical analyses and numerical experiments are given to justify this computational strategy for LSRTM.

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5

Rajan, Subramaniam D., and George V. Frisk. "A comparison between the Born and Rytov approximations for the inverse backscattering problem." GEOPHYSICS 54, no. 7 (1989): 864–71. http://dx.doi.org/10.1190/1.1442715.

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We compare the Born and Rytov approximations in solving the inverse acoustic backscattering problem, i.e., determining medium properties from reflections. For the one‐dimensional problem, we show that the Rytov approximation is generally better than the Born approximation in predicting sound speed changes, while both methods have the same error in determining the positions of reflectors. This is shown analytically for simple models and numerically for more general models. The performance of the Rytov approximation is degraded when low‐velocity regions are present in the medium being probed. The accuracy of the inversion depends on the manner in which the sound speed perturbation is linearized. The location of the receiver affects the accuracy of the inversion, and, in the case of the Rytov approximation, best results are obtained when the receiver is at the interface between the known and unknown regions. Furthermore, the Rytov method is less sensitive to the choice of reference sound speed used in the inversion than is the Born approximation.

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6

Lo, Tien‐when, M. Nafi Toksöz, Shao‐hui Xu, and Ru‐Shan Wu. "Ultrasonic laboratory tests of geophysical tomographic reconstruction." GEOPHYSICS 53, no. 7 (1988): 947–56. http://dx.doi.org/10.1190/1.1442531.

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In this study, we test geophysical ray tomography and geophysical diffraction tomography by scaled model ultrasonics experiments. First, we compare the performance of these two methods under limited view‐angle conditions. Second, we compare the adaptabilities of these two methods to objects of various sizes and acoustic properties. Finally, for diffraction tomography, we compare the Born and Rytov approximations based on the induced image distortion by using these two approximation methods. Our experimental results indicate the following: (1) When the scattered field can be obtained, geophysical diffraction tomography is in general superior to ray tomography because diffraction tomography is less sensitive to the limited view‐angle problem and can image small objects of size comparable to a wavelength. (2) The advantage of using ray tomography is that reconstruction can be done using the first arrivals only, the most easily measurable quantity; and there is no restriction on the properties of the object being imaged. (3) For geophysical diffraction tomography, the Rytov approximation is valid over a wider frequency range than the Born approximation in the cross‐borehole experiment. In the VSP and the surface reflection tomography experiments, no substantial difference between the Born and Rytov approximations is observed.

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7

Moy, G., J. Hope, and C. Savage. "Born and Markov approximations for atom lasers." Physical Review A 59, no. 1 (1999): 667–75. http://dx.doi.org/10.1103/physreva.59.667.

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8

McCarthy, IE. "The Electron - Atom Ionisation Problem." Australian Journal of Physics 49, no. 2 (1996): 219. http://dx.doi.org/10.1071/ph960219.

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Methods of calculating electron–atom ionisation as a three-body problem with Coulomb boundary conditions are considered. In the absence of a fully-valid computational method for a time-independent experiment the approximation is made that the incident electron experiences a screened potential. Approximations involving a final state that obeys the three-body Coulomb boundary condition are compared with the distorted-wave Born approximation and the convergent close-coupling method.

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9

Beylkin, G., and M. L. Oristaglio. "Distorted-wave born and distorted-wave rytov approximations." Optics Communications 53, no. 4 (1985): 213–16. http://dx.doi.org/10.1016/0030-4018(85)90157-9.

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10

Birch, A. C., and A. G. Kosovichev. "Towards a Wave Theory Interpretation of Time-Distance Helioseismology Data." Symposium - International Astronomical Union 203 (2001): 180–82. http://dx.doi.org/10.1017/s0074180900219025.

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Time-distance helioseismology, which measures the time for acoustic waves to travel between points on the solar surface, has been used to study small-scale three-dimensional features in the sun, for example active regions, as well as large-scale features, such as meridional flow, that are not accessible by standard global helioseismology. Traditionally, travel times have been interpreted using geometrical ray theory, which is not always a good approximation. In order to develop a wave interpretation of time-distance data we employ the first Born approximation, which takes into account finite-wavelength effects and is expected to provide more accurate inversion results. In the Born approximation, in contrast with ray theory, travel times are sensitive to perturbations to sound speed which are located off the ray path. In an example calculation of travel time perturbations due to sound speed perturbations that are functions only of depth, we see that that the Born and ray approximations agree when applied to perturbations with large spatial scale and that the ray approximation fails when applied to perturbations with small spatial scale.

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11

Babak, O. V., Yu A. Berezhnoy, and V. P. Mikhailyuk. "Born Approximation for Polarization Observables at the Scattering of Protons by 40Ca Nuclei." Ukrainian Journal of Physics 65, no. 5 (2020): 369. http://dx.doi.org/10.15407/ujpe65.5.369.

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A development of the optical model for the description of the hadron-nucleus scattering is proposed. When describing the behavior of polarization observables for the elastic proton scattering on 40Ca nuclei in the energy interval from 200 to 800 MeV, the Born approximation is used. Analytical expressions for the scattering amplitudes, as well as for the differential cross-sections and polarization observables, are obtained. The comparison of the scattering observables calculated in the 1st and 2nd Born approximations is made. It is shown that the observables calculated in this approach are in a reasonable agreement with the available experimental data.

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12

McCarthy, IE. "Distorted-wave Born and Impulse Approximations for Electron-Atom Ionisation." Australian Journal of Physics 48, no. 1 (1995): 1. http://dx.doi.org/10.1071/ph950001.

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The distorted-wave Born and impulse approximations set the standard for the calculation of the ionisation of atoms by electrons. The approximations are derived from formal scattering theory. Their computational forms are given and a program for their numerical calculation is described. Input and output data are given for a trial run.

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13

Angermeier, William A., and Thomas G. White. "An Investigation into the Approximations Used in Wave Packet Molecular Dynamics for the Study of Warm Dense Matter." Plasma 4, no. 2 (2021): 294–308. http://dx.doi.org/10.3390/plasma4020020.

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Wave packet molecular dynamics (WPMD) has recently received a lot of attention as a computationally fast tool with which to study dynamical processes in warm dense matter beyond the Born–Oppenheimer approximation. These techniques, typically, employ many approximations to achieve computational efficiency while implementing semi-empirical scaling parameters to retain accuracy. We investigated three of the main approximations ubiquitous to WPMD: a restricted basis set, approximations to exchange, and the lack of correlation. We examined each of these approximations in regard to atomic and molecular hydrogen in addition to a dense hydrogen plasma. We found that the biggest improvement to WPMD comes from combining a two-Gaussian basis with a semi-empirical correction based on the valence-bond wave function. A single parameter scales this correction to match experimental pressures of dense hydrogen. Ultimately, we found that semi-empirical scaling parameters are necessary to correct for the main approximations in WPMD. However, reducing the scaling parameters for more ab-initio terms gives more accurate results and displays the underlying physics more readily.

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14

Baliyan, K. S., and M. K. Srivastava. "Triple differential cross sections for the ionization of helium by intermediate-energy electrons." Canadian Journal of Physics 66, no. 1 (1988): 82–85. http://dx.doi.org/10.1139/p88-011.

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The recent triple differential cross-section data of Jung for the ionization of helium in the coplanar asymmetric geometry at 250 eV incident electron energy is analyzed within the framework of the second Born (B2) and modified Glauber (MG) approximations. At this energy B2 and MG results, although better than those obtained by using the first Born and Glauber approximations, do not lead to a satisfactory description of the experimental data in all the kinematic situations considered here.

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15

Kim, M., and C. Bustamante. "Differential polarization imaging. IV. Images in higher Born approximations." Biophysical Journal 59, no. 6 (1991): 1171–82. http://dx.doi.org/10.1016/s0006-3495(91)82333-5.

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16

Lee, D. A., and G. T. Warhola. "Time‐domain first‐Born approximations to backscattering from cylinders." Journal of the Acoustical Society of America 79, no. 3 (1986): 681–90. http://dx.doi.org/10.1121/1.393458.

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17

Kirkinis, Eleftherios. "Renormalization group interpretation of the Born and Rytov approximations." Journal of the Optical Society of America A 25, no. 10 (2008): 2499. http://dx.doi.org/10.1364/josaa.25.002499.

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18

Lasaygues, Philippe, Loic Le Marrec, and Thierry Scotti. "2D‐ultrasonic tomography using first‐order Born and canonical approximations." Journal of the Acoustical Society of America 123, no. 5 (2008): 3275. http://dx.doi.org/10.1121/1.2933617.

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19

Makridakis, Charalambos, and Endre Süli. "Finite Element Analysis of Cauchy–Born Approximations to Atomistic Models." Archive for Rational Mechanics and Analysis 207, no. 3 (2012): 813–43. http://dx.doi.org/10.1007/s00205-012-0582-8.

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20

Stelbovics, AT, and T. Winata. "A Study of L2 Approximations in Atomic Scattering." Australian Journal of Physics 43, no. 5 (1990): 485. http://dx.doi.org/10.1071/ph900485.

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The approximation of Coulomb continuum functions by an L 2 basis is studied using a Laguerre� function basis which can be extended to completeness. Also studied is the convergence rate of L2 approximations to Born matrix elements for electron impact ionisation as a function of basis�set size. This important class of matrix elements occurs in pseudo�state close-coupling calculations, accounting for scattering to the three�body continuum. Convergence rates in both cases are derived analytically and confirmed numerically. We find that the rate of pointwise convergence of L2 expansions to the continuum function is slow, and of conditional type; however, it is proven that the corresponding ionisation matrix elements converge geometrically, Our result agrees with the behaviour observed in pseudo�state calculations.

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21

Thierry, Philippe, Stéphane Operto, and Gilles Lambaré. "Fast 2-D ray+Born migration/inversion in complex media." GEOPHYSICS 64, no. 1 (1999): 162–81. http://dx.doi.org/10.1190/1.1444513.

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In this paper, we evaluate the capacity of a fast 2-D ray+Born migration/inversion algorithm to recover the true amplitude of the model parameters in 2-D complex media. The method is based on a quasi‐Newtonian linearized inversion of the scattered wavefield. Asymptotic Green’s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method. The model is described by velocity perturbations associated with diffractor points. Both the first traveltime and the strongest arrivals can be inverted. The algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm. Both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2-D Marmousi example. Comparison between logs extracted from the exact Marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations are recovered accurately in the regions of the model where the ray field is single valued. In the presence of caustics, neither the first traveltime nor the most energetic arrival inversion allow for a full recovery of the amplitudes although the latter improves the results. We conclude that all the arrivals associated with multipathing through transmission caustics must be taken into account if the true amplitude of the perturbations is to be found. Only 22 minutes of CPU time is required to migrate the full 2-D Marmousi data set on a Sun SPARC 20 workstation. The amplitude loss induced by the numerical approximations on the first traveltime and the most energetic migrated images are evaluated quantitatively and do not exceed 8% of the energy of the image computed without numerical approximation. Computational evaluation shows that extension to a 3-D ray+Born migration/inversion algorithm is realistic.

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22

Mayo, R., S. Rolston, and T. J. Morgan. "Born and impact-parameter cross sections for the process H(1s) + H(1s) → H(2s) + H(1s)." Canadian Journal of Physics 66, no. 7 (1988): 645–48. http://dx.doi.org/10.1139/p88-107.

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We report the results of a series of calculations of the cross section for the excitation of a neutral hydrogen atom to the 2s level, due to the collision of two neutral ground-state hydrogen atoms within the energy range 1–100 keV. Cross sections are presented for the first-Born approximation and for the straight-line impact-parameter method employing velocity truncation approximations. Electron exchange terms have been included in all calculations. Reported impact-parameter calculations are the best results of a series of calculations studying the inclusion, in the equation of motion, of terms that are zero- and first-order in the internuclear velocity. These results are compared with first- and second-order Born calculations neglecting exchange, recent infinite-order impact-parameter calculations, and experimental data.

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23

Younger, S. M. "Convergence of the Born and Coulomb-Born approximations for the electron-impact excitation of positive ions." Physical Review A 36, no. 11 (1987): 5432–34. http://dx.doi.org/10.1103/physreva.36.5432.

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24

Datta, S. K., D. S. F. Crothers, and R. McCarroll. "The relation between the Coulomb-Born and the boundary-corrected first-order Born approximations for electron capture." Journal of Physics B: Atomic, Molecular and Optical Physics 23, no. 3 (1990): 479–93. http://dx.doi.org/10.1088/0953-4075/23/3/017.

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25

Hudson, Thomas, and Christoph Ortner. "On the stability of Bravais lattices and their Cauchy–Born approximations." ESAIM: Mathematical Modelling and Numerical Analysis 46, no. 1 (2011): 81–110. http://dx.doi.org/10.1051/m2an/2011014.

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26

Schafbuch, P. J., R. B. Thompson, and F. J. Rizzo. "Elastic scatterer interaction via generalized Born series and far‐field approximations." Journal of the Acoustical Society of America 93, no. 1 (1993): 295–307. http://dx.doi.org/10.1121/1.405664.

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27

Stenius, P., and A. Imamoglu. "Stochastic wavefunction methods beyond the Born - Markov and rotating-wave approximations." Quantum and Semiclassical Optics: Journal of the European Optical Society Part B 8, no. 1 (1996): 283–95. http://dx.doi.org/10.1088/1355-5111/8/1/021.

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28

Marks, Daniel L. "A family of approximations spanning the Born and Rytov scattering series." Optics Express 14, no. 19 (2006): 8837. http://dx.doi.org/10.1364/oe.14.008837.

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29

Montenegro, E. C., and T. J. M. Zouros. "Relationship between the Born and impulse approximations for the antiscreening process." Physical Review A 50, no. 4 (1994): 3186–91. http://dx.doi.org/10.1103/physreva.50.3186.

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30

Fedotov, Aleksey, Alexander Vakhrushev, Olesya Severyukhina, et al. "Theoretical Basis of Quantum-Mechanical Modeling of Functional Nanostructures." Symmetry 13, no. 5 (2021): 883. http://dx.doi.org/10.3390/sym13050883.

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The paper presents an analytical review of theoretical methods for modeling functional nanostructures. The main evolutionary changes in the approaches of quantum-mechanical modeling are described. The foundations of the first-principal theory are considered, including the stationery and time-dependent Schrödinger equations, wave functions, the form of writing energy operators, and the principles of solving equations. The idea and specifics of describing the motion and interaction of nuclei and electrons in the framework of the theory of the electron density functional are presented. Common approximations and approaches in the methods of quantum mechanics are presented, including the Born–Oppenheimer approximation, the Hartree–Fock approximation, the Thomas–Fermi theory, the Hohenberg–Kohn theorems, and the Kohn–Sham formalism. Various options for describing the exchange–correlation energy in the theory of the electron density functional are considered, such as the local density approximation, generalized and meta-generalized gradient approximations, and hybridization of the generalized gradient method. The development of methods of quantum mechanics to quantum molecular dynamics or the dynamics of Car–Parrinello is shown. The basic idea of combining classical molecular modeling with calculations of the electronic structure, which is reflected in the potentials of the embedded atom, is described.

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31

de Gosson, Maurice. "Short-Time Propagators and the Born–Jordan Quantization Rule." Entropy 20, no. 11 (2018): 869. http://dx.doi.org/10.3390/e20110869.

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We have shown in previous work that the equivalence of the Heisenberg and Schrödinger pictures of quantum mechanics requires the use of the Born and Jordan quantization rules. In the present work we give further evidence that the Born–Jordan rule is the correct quantization scheme for quantum mechanics. For this purpose we use correct short-time approximations to the action functional, initially due to Makri and Miller, and show that these lead to the desired quantization of the classical Hamiltonian.

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32

Tajik, Daniel, Aaron D. Pitcher, and Natalia K. Nikolova. "COMPARATIVE STUDY OF THE RYTOV AND BORN APPROXIMATIONS IN QUANTITATIVE MICROWAVE HOLOGRAPHY." Progress In Electromagnetics Research B 79 (2017): 1–19. http://dx.doi.org/10.2528/pierb17081003.

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33

Das, T. K., H. T. Coelho, and V. P. Brito. "Comparison of Born-Oppenheimer and hyperspherical adiabatic approximations in the trinucleon problem." Physical Review C 48, no. 5 (1993): 2201–7. http://dx.doi.org/10.1103/physrevc.48.2201.

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34

Aslangul, C., N. Pottier, and D. Saint-James. "Spin-boson systems: equivalence between the dilute-blip and the Born approximations." Journal de Physique 47, no. 10 (1986): 1657–61. http://dx.doi.org/10.1051/jphys:0198600470100165700.

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35

Habashy, Tarek M., Ross W. Groom, and Brian R. Spies. "Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering." Journal of Geophysical Research: Solid Earth 98, B2 (1993): 1759–75. http://dx.doi.org/10.1029/92jb02324.

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36

Birch, A. C., A. G. Kosovichev, G. H. Price, and R. B. Schlottmann. "The Accuracy of the Born and Ray Approximations in Time-Distance Helioseismology." Astrophysical Journal 561, no. 2 (2001): L229—L232. http://dx.doi.org/10.1086/324766.

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37

Gureyev, Timur E., Timothy J. Davis, Andrew Pogany, Sheridan C. Mayo, and Stephen W. Wilkins. "Optical phase retrieval by use of first Born- and Rytov-type approximations." Applied Optics 43, no. 12 (2004): 2418. http://dx.doi.org/10.1364/ao.43.002418.

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38

Sun, Chang-Pu, and Mo-Lin Ge. "Generalizing Born-Oppenheimer approximations and observable effects of an induced gauge field." Physical Review D 41, no. 4 (1990): 1349–52. http://dx.doi.org/10.1103/physrevd.41.1349.

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39

Skarsoulis, Emmanuel, George Piperakis, and George Makrakis. "Tangent linear and second‐order models from the Born and Rytov approximations." Journal of the Acoustical Society of America 119, no. 5 (2006): 3248. http://dx.doi.org/10.1121/1.4786052.

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40

Blackledge, J. M., and K. I. Hopcraft. "Equivalence of the born and rytov approximations for back-scattered scalar fields." Physics Letters A 118, no. 8 (1986): 367–70. http://dx.doi.org/10.1016/0375-9601(86)90261-6.

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41

Wenzel, F., and D. Menges. "A comparison between Born inversion and frequency‐wavenumber migration." GEOPHYSICS 54, no. 8 (1989): 1006–11. http://dx.doi.org/10.1190/1.1442725.

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Employing appropriate high‐frequency approximations, we find that frequency‐wavenumber migration of spherically corrected data coincides with Born inversion for the reflectivity function. We consider zero‐offset seismic data in a 2.5-dimensional medium that consists of a homogeneous reference velocity with embedded reflectors. For marine data, where the pressure is measured, migration and inversion are identical. For land data, where vertical particle velocity is measured, modifications are required in order to match inversion and migration. The modifications become important only if dips larger than 30°are to be migrated.

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42

ZETTILI, NOUREDINE, and ABDELKRIM BOUKAHIL. "THE NUCLEAR BORN–OPPENHEIMER METHOD APPLIED TO NUCLEAR COLLECTIVE MOTION." International Journal of Modern Physics E 11, no. 03 (2002): 231–48. http://dx.doi.org/10.1142/s0218301302000818.

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We deal with the application of the nuclear Born–Oppenheimer (NBO) method to the study of nuclear collective motion. In particular, we look at the description of nuclear rotations and vibrations. The collective operators are specified within the NBO method only to the extent of identifying the type of collective degrees of freedom we intend to describe; the operators are then determined from the dynamics of the system. To separate the collective degrees of freedom into rotational and vibrational terms, we transform the collective tensor operator from the lab fixed frame of reference to the frame defined by the principal axes of the system; this transformation diagonalizes the tensor operator. We derive a general expression for the NBO mean energy and show that it contains internal, collective and coupling terms. Then, we specify the approximations that need to be made in order to establish a connection between Bohr's collective model and the NBO method. We show that Bohr's collective Hamiltonian can be recovered from the NBO Hamiltonian only after adopting some rather crude approximations. In addition, we try to understand, in light of the NBO approach, why Bohr's collective model gives the wrong inertial parameters. We show that this is due to two major reasons: the ad hoc selection of the collective degrees of freedom within the context of Bohr's collective model and the unwarranted neglect of several important terms from the Hamiltonian.

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43

T Whelan, Colm, HRJ Walters, J. Hansen, and RM Dreizler. "High Energy Electron Impact Ionisation of H(1s) in Coplanar Asymmetric Geometry." Australian Journal of Physics 44, no. 1 (1991): 39. http://dx.doi.org/10.1071/ph910039.

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Various effective charge approximations are explored for the high energy electron impact ionisation of H(ls) in coplanar asymmetric geometry, using a first order perturbative model. Our results are compared with other more sophisticated calculations and with experiment. It is found that effective charge prescriptions satisfying the requirement that, in the limit of zero ejection energy, the escaping electron sees the full nuclear charge while the scattered electron is totally screened, are unsuccessful. In contrast it is found that the Coulomb projected Born exchange approximation, where both electrons see the full nuclear charge, gives much better results. In general it reproduces the position and magnitude of the binary peak fairly well, although it is not so successful in the description of the recoil.

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44

Devaney, Anthony J. "Generalized Projection-Slice Theorem for Fan Beam Diffraction Tomography." Ultrasonic Imaging 7, no. 3 (1985): 264–75. http://dx.doi.org/10.1177/016173468500700306.

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A generalized projection-slice theorem is derived for transmission fan beam diffraction tomography within the Born or Rytov approximations. The development is based on the use of the so-called paraxial approximation which requires that the object being probed subtend a small angle relative to the source point and to the measurement plane. Within this approximation it is shown that the transmitted field measured over a plane surface located on the opposite side of the object from the insonifying point source determines the three-dimensional spatial Fourier transform of the object profile over the surface of an ellipsoid of revolution in Fourier space. In the special case where the point source is in the far field of the object the semiaxes of the ellipsoid become equal and the surface degenerates to a sphere and the result reduces to the usual projection-slice theorem of plane beam diffraction tomography.

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45

Bertuccelli, D., and H. O. Di Rocco. "Linewidths of singly charged, noble gas ions from Born and Born-Robb approximations: dependence with atomic parameters and electron density." Physica Scripta 47, no. 6 (1993): 747–50. http://dx.doi.org/10.1088/0031-8949/47/6/010.

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McCarthy, I. E. "Range of validity of distorted wave Born and impulse approximations for (e, 2e)." Zeitschrift f�r Physik D Atoms, Molecules and Clusters 23, no. 4 (1992): 287–93. http://dx.doi.org/10.1007/bf01429249.

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Kolyshkin, A. A., and R. Vaillancourt. "Comparing the layer and Born approximations with experimental data in eddy-current testing." IEEE Transactions on Magnetics 34, no. 2 (1998): 524–26. http://dx.doi.org/10.1109/20.661484.

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Birch, A. C., and G. Felder. "Accuracy of the Born and Ray Approximations for Time‐Distance Helioseismology of Flows." Astrophysical Journal 616, no. 2 (2004): 1261–64. http://dx.doi.org/10.1086/424961.

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Beydoun, Wafik B., and Albert Tarantola. "First Born and Rytov approximations: Modeling and inversion conditions in a canonical example." Journal of the Acoustical Society of America 83, no. 3 (1988): 1045–55. http://dx.doi.org/10.1121/1.396537.

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Hounkonnou, Mahouton Norbert, Michel Sana, Olamba Kalonda, and Xavier Chapuisat. "All-particle Hamiltonians for polyatomic molecules. II. Born—Oppenheimer and other adiabatic approximations." Chemical Physics Letters 197, no. 6 (1992): 635–42. http://dx.doi.org/10.1016/0009-2614(92)85827-w.

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