John H. Hubbell

Atomic form factors, incoherent scattering functions, and photon scattering cross sections

Tabulations are presented of the atomic form factor, F (α,Z), and the incoherent scattering function, S (x,Z), for values of x (=sin ϑ/2)/λ) from 0.005 A−1 to 109 A−1, for all elements A=1 to 100. These tables are constructed from available state‐of‐the‐art theoretical data, including the Pirenne formulas for Z=1, configuration‐into action results by Brown using Brown‐Fontana and Weiss correlated wavefunctions for Z=2 to 6 non‐relativistic Hartree‐Fock results by Cromer for Z=7 to 100 and a relativistic K‐shell analytic expression for F (x,Z) by Bethe Levinger for x≳10 A−1 for all elements Z=2 to 100. These tabulated values are graphically compared with available photon scattering angular distribution measurements. Tables of coherent (Rayleigh) and incoherent (Compton) total scattering cross sections obtained by numerical integration over combinations of F2(x,Z) with the Thomson formula and S (x,Z) with the Klum‐Nishina Formual, respectively, are presented for all elements Z=1 to 100, for photon energies ...

Relativistic Atomic Form Factors and Photon Coherent Scattering Cross Sections

Tabulations are presented of relativistic Hartree‐Fock atomic form factors F (x,Z), for values of x (=sin(ϑ/2)/λ from 0.01 to 109 A−1, for all elements Z=1 to 100. For Z=1, F (x,Z) is given by the exact expression of Pirenne. For Z=2 to 98, x=0.01 to 2.0 A−1, the tabulated values are those of Cromer and Waber given in the International Tables for X−Ray Crystallography (Vol. IV, 1974), based in part on the work of Doyle and Turner. For Z=21 to 92, x=2.2 to 6.0 A−1, the present tables are based on the values of Doyle and Turner and additional values (Z=44,60,68, and 74) as given by O/verbo/. For Z=3 to 20.x=2.2 to 45 A−1, Z=21 to 92,x=62 to 45 A−1 the tables are interpolated from values given for 36 elements by O/verbo/, extended to x=109 A−1 using O/verbo/’s corrections to the Bethe‐Levinger K‐shell expression. The remainder of the table is filled in by interpolation and extrapolation, guided for high x‐values by the Bethe‐Levinger result. Tables of relativistic coherent (Rayleigh) scattering cross section...

A Review, Bibliography, and Tabulation of K, L, and Higher Atomic Shell X‐Ray Fluorescence Yields

The K, L, and higher atomic shell x‐ray fluorescence yield measured data, covering the period 1978 to 1993, following the major previous compilations by Bambynek et al. (1972) and Krause (1979), are reviewed. An annotated bibliography of x‐ray fluorescence yield measurements, analyses, fits and tables 1978–1993 is presented. Comparisons of the fluorescence yields ωk, ωL, and ωM, based on measurements, and on theoretical models, are presented. Values of ωK, ωL, and ωM, fitted to standard empirical parametric formulations, are presented. In addition, selected well‐characterized measured ωK, ωL, and ωM results restricted to the period 1978–1993 are listed. These selected measured values are fitted by least squares to polynomials in Z of the form ∑nanZn and compared with theoretical and with earlier fitted values. A section on application of fluorescence yield data to computations of x‐ray energy‐absorption coefficients is included.

Pair, Triplet, and Total Atomic Cross Sections (and Mass Attenuation Coefficients) for 1 MeV-100 GeV Photons in Elements Z=1 to 100,

Tables of photon cross sections and mass attenuation coefficients for all elements Z=1 to 100 are given for photo energies in the range 1 MeV to 100 GeV. The pair and triplet production cross sections take into account recent theoretical work, including atomic form factor and incoherent scattering function data, as well as extensive new total attenuation coefficient measurements at Mainz. Cross section values for the atomic photoeffect and coherent and incoherent (Compton) scattering are explicitly listed and are included in the total cross sections (excluding photonuclear) and mass attenuation coefficients.

Small‐Angle Rayleigh Scattering of Photons at High Energies: Tabulations of Relativistic HFS Modified Atomic Form Factors

Tabulations are presented of relativistic Hartree–Fock–Slater modified atomic form factors from x=0 to 100 A−1 for all elements from Z=1 to Z=100. These modified form factors represent the atomic Rayleigh scattering amplitudes with good accuracy at energies well above the K‐shell binding energies and small momentum transfers and therefore should be used instead of the normal relativistic atomic form factors in the MeV energy range.

Review and history of photon cross section calculations

Photon (x-ray, gamma-ray, bremsstrahlung) mass attenuation coefficients, mu/rho, are among the most widely used physical parameters employed in medical diagnostic and therapy computations, as well as in diverse applications in other fields such as nuclear power plant shielding, health physics and industrial irradiation and monitoring, and in x-ray crystallography. This review traces the evolution of this data base from its empirical beginnings totally derived from measurements beginning in 1907 by Barkla and Sadler and continuing up through the 1935 Allen compilation (published virtually unchanged in all editions up through 1971-1972 of the Chemical Rubber Handbook), to the 1949 semi-empirical compilation of Victoreen, as our theoretical understanding of the constituent Compton scattering, photoabsorption and pair production interactions of photons with atoms became more quantitative. The 1950s saw the advent of completely theoretical (guided by available measured data) systematic compilations such as in the works of Davisson and Evans, and by White-Grodstein under the direction of Fano, using mostly theory developed in the 1930s (pre-World War II) by Sauter, Bethe, Heitler and others. Post-World War II new theoretical activity, and the introduction of the electronic automatic computer, led to the more extensive and more accurate compilations in the 1960s and 1970s by Storm and Israel, and by Berger and Hubbell. Todays mu/rho compilations by Cullen et al, by Seltzer, Berger and Hubbell, and by others, collectively spanning the ten decades of photon energy from 10 eV to 100 GeV, for all elements Z= 1 to 100, draw heavily on the 1970s shell-by-shell photoabsorption computations of Scofield, the 1960s coherent and incoherent scattering computations of Cromer et al, and the 1980 computations of electron-positron pair and triplet computations of Hubbell, Gimm and Øverbø, these names being representative of the vast legions of other researchers whose work fed into these computations.

Polarization effects on multiple scattering gamma transport

Abstract The scattering of X-rays and γ-rays are events that have strong dependencies on the polarization of the incident and scattered photons. Because of this, scattering problems that can be solved without explicit reference to the state of polarization of the incident and scattered radiation are exceptional. This article reviews available information on polarization effects arising when photons in the X-ray and γ-ray regime undergo photoelectric effect, coherent (Rayleigh) scattering and incoherent (Compton) scattering by atomic electrons. In addition to descriptions and discussion of these effects, we study the backscattering of γ-rays from an infinite thickness target excited with a plane slant monodirectional and monochromatic source, using the Boltzmann transport theory and the mathematical representation of polarization introduced by Stokes. Results from this model, for both unpolarized and polarized γ-ray sources, are compared with computations performed neglecting or averaging polarization effects, showing the limitations of such approximations.

Production of Li subshell and M shell vacancies following inner-shell vacancy production

Abstract The probabilities for transfer of vacancies from the K shell to an L i Subshell ( η KL i ) and to the M shell (η KM ), and from the L i Subshell to the M shell ( η L i M ) are evaluated for elements with atomic numbers 18 ≤ Z ≤ 96 using the theoretical radiative transition rates of Scofield [Phys. Rev. A 9 (1974) 1041; At. Data Nucl. Data Tables 14 (1974) 121] and radiationless transition rates tabulated by Chen et al. [At Data Nucl. Data Tables 24 (1979) 13; Phys. Rev. A 21 (1980) 442]. The calculated vacancy transfer probabilities are least-squares fitted to polynomials to obtain analytical relations that represent these probabilities as a function of atomic number.

Further results on generalized elliptic-type integrals

Simple direct proofs of some recent results by Kalla, Conde, and Hubbell for a generalized elliptic type integral [Appl. Anal., 22 (1986), pp. 273-287] are presented. Furthermore, a new single term asymptotic approximation for this function is derived, which is superior to the two term approximation given by these authors

Exact series solution to the Epstein-Hubbell generalized elliptic type integral using complex variable residue theory

In this paper, complex variable residue theory is used to arrive at an exact infinite series solution to the Epstein-Hubbell integral. This method of solution is different from those used to derive previous solutions to the Epstein-Hubbell integral, but produces exactly equivalent results. Several sets of numerical data are included that verify the results. Additional information on the improvement of convergence will be forthcoming at a later date.