Calculation of photionization cross-sections and dynamic polarizabilities using square integrable basis sets and correlated wave functions

The quantal theory of the continuous photo-electric absorption of radiation is briefly summarized, pàrticular attention being given to the alternative formulae available and to the accuracy to be expected in practical calculations. Detailed calculations are described for the photo-ionization cross-section of neon, a system for which it is understood that experimental data should be available in the near future. The calculation is made using Hartree-Fock wave functions and the two formulae of the dipole length and the dipole velocity. The corresponding cross-sections are found to be 5.8 and 4.4 x 10- 18 cm 2 . at the spectral head and to rise slowly with increasing frequency until a broad maximum is reached for an energy of the ejected electron of about 11 eV. A comparison is made with previous calculations on the elements from boron to neon ; the general trend of the results is discussed and improved estimates for boron and fluorine are given (10 x 10 -18 cm 2 . for boron and 4.3 x 10- 18 cm 2 . for fluorine at the spectral head).

Download Full-text

Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields

International Journal of Modern Physics A ◽

10.1142/s0217751x2150086x ◽

2021 ◽

pp. 2150086

Author(s):

V. P. Neznamov ◽

V. E. Shemarulin

Keyword(s):

Cross Sections ◽

Magnetic Moment ◽

Anomalous Magnetic Moment ◽

Quantum Electrodynamics ◽

Lamb Shift ◽

Wave Functions ◽

Self Energy ◽

Fermion Fields ◽

Spinor Wave

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED. Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particles and antiparticles have the opposite signs.

Download Full-text

Direct Photodisintegration of 9Be in the Low and Sub-Giant Resonance Energy Region

Zeitschrift für Naturforschung A ◽

10.1515/zna-1969-0803 ◽

1969 ◽

Vol 24 (8) ◽

pp. 1188-1195

Author(s):

Terje Aurdal

Keyword(s):

Cross Sections ◽

Giant Resonance ◽

Resonance Energy ◽

Wave Functions ◽

Nuclear Model ◽

Final States ◽

Core State ◽

Radial Wave ◽

Total Cross Sections ◽

Reaction Channels

Abstract Photodisintegration cross sections for the reaction 9Be(γ,n) 8Be with photonenergies varied from threshold to about 17 MeV are calculated. As nuclear model is assumed a single particle shell model where the valence neutron outside the 8Be core is feeling a spherical field. The core state is assumed to be a mixture of the ground (0+) and the first excited (2+) state of the 8Be nucleus. The total cross sections are splitted up according to the different contributing reaction channels. The radial wave functions in initial as well as final states are of the Saxon-Woods type.

Download Full-text

Gamow–Teller strength functions from scattering experiments

Canadian Journal of Physics ◽

10.1139/p87-100 ◽

1987 ◽

Vol 65 (6) ◽

pp. 691-698 ◽

Cited By ~ 8

Author(s):

O. Häusser

Keyword(s):

Shell Model ◽

Cross Sections ◽

Mean Field ◽

Wave Functions ◽

Structure Information ◽

Model Wave ◽

Spin Flip ◽

Strength Functions ◽

Gamow Teller ◽

Good Agreement

We present here recent [Formula: see text] results from TRIUMF that are relevant to the determination of spin-flip isovector strength functions in nuclei. Distortion factors needed for the extraction of nuclear-structure information have been deduced from cross sections and analyzing powers in elastic scattering for several energies and targets. Nonrelativistic optical potentials obtained by folding effective nucleon (N)–nucleus interactions with nuclear densities are found to overpredict both elastic and reaction cross sections, whereas Dirac calculations that include Pauli blocking are in good agreement with the data. Spin observables (Snn and Ay) for the quasi-elastic region in 54Fe[Formula: see text] at 290 MeV provide some evidence for the reduction of the effective proton mass predicted in relativistic mean-field theories as a consequence of the attractive scalar field in the nuclear medium. The energy dependence of the effective N–nucleus interaction at small momentum transfers has been investigated using isoscalar and isovector 1+ states in 28Si as probe states. We find that the cross sections for the isovector transitions are in good agreement with predictions for the dominant Vστ part of the Franey–Love interaction. Gamow–Teller (GT) strength functions have been obtained in 24Mg and 54Fe from measurements of both cross sections and spin–flip probabilities Snn. The spin-flip cross sections σSnn are particularly useful in heavier nuclei to discriminate against a continuous background of ΔS = 0 excitations. In the (s, d) shell where full shell-model wave functions are available, the GT quenching factors [Formula: see text] are in good agreement with those from recent (p, n) and (n, p) experiments. We show that a state-by-state comparison of (p, p′) and (e, e′) results has the potential of identifying pionic current contributions in (e, e′). The GT quenching factors in 54Fe are smaller than in the (s, d) shell probably because of severely truncated shell-model wave functions, particularly those of the nuclear ground state.

Download Full-text

On the quenching of Gamow–Teller strength

Canadian Journal of Physics ◽

10.1139/p87-081 ◽

1987 ◽

Vol 65 (6) ◽

pp. 574-577 ◽

Cited By ~ 10

Author(s):

J. Rapaport

Keyword(s):

Cross Sections ◽

Wave Functions ◽

Light Nuclei ◽

Final States ◽

Excitation Energies ◽

Intermediate Energies ◽

Quenching Factor ◽

Configuration Mixing ◽

Gamow Teller ◽

Model Strength

The (p, n) reaction at intermediate energies has been used to measure differential cross sections in light nuclei to final states characterized with a ΔJπ = 1+ transfer (Gamow–Teller (GT) states). Experimental ft values for allowed beta-decay transitions in these nuclei are used to normalize the strength of the GT transitions in units of B(GT). This experimental GT strength is compared with predicted shell–model strength. For p-shell nuclei, the calculated excitation energies of the GT strength using Cohen and Kurath wave functions are in general agreement with the empirical GT distribution. Up to an excitation energy of about 20 MeV, the total experimental and calculated GT strengths are used to obtain the quenching factor, QF = Σ B(GT)exp/Σ B(GT)theor. It is found that QF decreases as the shell gets filled-up. The lowest value seems to occur for single-hole nuclei. This decrease may be explained by configuration mixing not specifically included in the calculations.

Download Full-text

HADRON PRODUCTION IN NEUTRINO–NUCLEON INTERACTIONS AT HIGH ENERGIES

International Journal of Modern Physics A ◽

10.1142/s0217751x03013557 ◽

2003 ◽

Vol 18 (04) ◽

pp. 673-683

Author(s):

M. T. HUSSEIN ◽

N. M. HASSAN ◽

W. ELHARBI

Keyword(s):

Cross Sections ◽

Particle Production ◽

High Energy ◽

Neutrino Energy ◽

Wave Functions ◽

Variation Method ◽

Hypothetical Model ◽

High Energies ◽

Color Field

The multi-particle productions in neutrino–nucleon collisions at high energy are investigated through the analysis of the data of the experiment CERN-WA-025 at neutrino energy less than 260 GeV and the experiments FNAL-616 and FNAL-701 at energy range 120–250 GeV. The general features of these experiments are used as base to build a hypothetical model that views the reaction through a Feynman diagram of two vertices. The first of which concerns the weak interaction between the neutrino and the quark constituents of the nucleon. At the second vertex, a strong color field is assumed to play the role of particle production, which depend on the momentum transferred from the first vertex. The wave functions of the nucleon constituent quarks are determined using the variation method and relevant boundary conditions are applied to calculate the deep inelastic cross sections of the virtual diagram.

Download Full-text

Stueckelberg-Landau-Zener-(SLZ)-Modell für atomare Stoßprozesse / Stueckelberg-Landau-Zener-(SLZ) Model for Atomic Scattering Processes

Zeitschrift für Naturforschung A ◽

10.1515/zna-1973-1011 ◽

1973 ◽

Vol 28 (10) ◽

pp. 1642-1653

Author(s):

G.-P. Raabe

Keyword(s):

Cross Sections ◽

Differential Cross ◽

Wave Functions ◽

Differential Cross Sections ◽

Rare Gases ◽

Radial Wave ◽

Atomic Scattering ◽

The Cross

Scattering processes of atoms, molecules and ions with two crossing electronic potentials may be treated in the Stueckelberg-Landau-Zener-(SLZ) model. In this paper the WKB-solutions for the radial wave functions, given by Stueckelberg are used to calculate differential cross sections. The effects on the cross sections are explained in a semiclassical picture, following the procedures of Ford and Wheeler, and Berry. In the scattering of H+ by rare gases, some effects in the elastic cross sections are observed which can be explained by the influence of the potential of the chargeexchanged particles, using the SLZ-model. The structure in the elastic cross sections for H2+-Kr can be explained as a rainbow structure with superimposed Stueckelberg oscillations.

Download Full-text

Intensities in Complex Spectra of Highly Ionized Atoms

International Astronomical Union Colloquium ◽

10.1017/s0252921100085262 ◽

1984 ◽

Vol 86 ◽

pp. 44-44

Author(s):

M. Klapisch ◽

A. Bar-Shalom ◽

A. Cohen

Keyword(s):

Cross Sections ◽

Wave Functions ◽

Coupling Scheme ◽

Distorted Wave ◽

Intermediate Coupling ◽

Potential Wave ◽

Excitation Cross Sections ◽

Collisional Radiative Model ◽

Radiative Model ◽

Efficient Program

We describe a package of programs for the implementation of the collisional-radiative model to complex configurations. The number of levels taken into account may be several hundreds. The heart of the package is a very efficient program for excitation cross sections in the Distorted Wave framework, using the Relativistic Parametric Potential wave functions. The basic jj coupling scheme actually simplified the computations, enabling a useful factorization into radial and angular parts. Intermediate coupling and configuration interactions are accounted for. We computed ratios of intensities of 3d9 − 3d84s (E2) to 3d9 −3d84p (El) transitions as functions of ne and Te in Xe XXVIII and other Co-like spectra. The atomic model involves all the levels of configurations (3p6)3d9; −3d84s, −3d84p, −3d84d, −3d84f, and (3p5) −3d10, −3d94p. (275 levels) and all the transitions between them. Results compare very well with experimental spectra from TFR.

Download Full-text