Born Cross Sections for the Excitation of Helium by Fast Protons

1972 ◽  
Vol 50 (19) ◽  
pp. 2253-2256 ◽  
Author(s):  
S. P. Ojha ◽  
P. Tiwari ◽  
D. K. Rai
Keyword(s):  
Cross Sections ◽  
Ground State ◽  
Born Approximation ◽  
Wave Functions ◽  
Final States ◽  
Interaction Type ◽  
Hartree Fock ◽  
Approximate Wave ◽  
Fast Protons ◽  
Accurate Wave

Cross sections for excitation of helium by proton impact have been calculated in the Born approximation. Transitions from the ground state to the n1P(n = 2 and 3) states have been considered. Highly accurate wave functions of the Hartree–Fock and configuration-interaction type have been used to represent the ground state. Approximate wave functions due to Messmer have been employed for the final states. The results are compared with other calculations and with experiments.

Inelastic Scattering of High Energy Electrons by Helium

1973 ◽  
Vol 51 (3) ◽  
pp. 311-315 ◽  
Author(s):  
S. P. Ojha ◽  
P. Tiwari ◽  
D. K. Rai
Keyword(s):  
Ground State ◽  
High Energy ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Final States ◽  
Interaction Type ◽  
Hartree Fock ◽  
High Energy Electrons ◽  
Approximate Wave ◽  
Accurate Wave

Generalized oscillator strengths and the cross section for excitation of helium by electron impact have been calculated in the Born approximation. Transitions from the ground state to the n1P (n = 2 and 3) states have been considered. Highly accurate wave functions of the Hartree–Fock and "configuration–interaction" type have been used to represent the ground state. Approximate wave functions due to Messmer have been employed for the final states. The results are compared with other calculations and with experiment.

The partial wave theory of electron-hydrogen atom collisions

1957 ◽  
Vol 53 (3) ◽  
pp. 654-662 ◽  
Author(s):  
I. C. Percival ◽  
M. J. Seaton
Keyword(s):  
Hydrogen Atom ◽  
Partial Wave ◽  
Cross Sections ◽  
Wave Theory ◽  
Wave Functions ◽  
Scattered Electron ◽  
Hartree Fock ◽  
Angular Momenta ◽  
Continuous State ◽  
Approximate Wave

ABSTRACTThe paper is concerned with the solution of the algebraic problems arising in the partial wave treatment of electron-hydrogen atom collisions. Explicitly antisymmetrized wave functions are used throughout. The boundary conditions are written in S-matrix notation and expressions for total and differential cross-sections obtained. The algebraic coefficients fλ and gλ occurring in the continuous state Hartree-Fock equations are expressed in terms of Racah coefficients, and tabulated as functions of the total angular momentum for atomic s, p and d electrons and all angular momenta of the scattered electron. Expressions are given for the calculation of first-order corrections to the results obtained using approximate wave functions.

Electron capture by fast protons and α-particles in hydrogen

1963 ◽  
Vol 272 (1351) ◽  
pp. 542-556 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Wave Functions ◽  
Final States ◽  
Resonance Case ◽  
Ion Energies ◽  
The Cross ◽  
Proper Allowance ◽  
Fast Protons ◽  
Α Particles

Cross-sections are calculated for the accidental resonance reaction, He 2+ + H(ls) -> He + (2s or 2p) + H + , and the non-resonance reaction, H + + H (ls)-> H(2s or 2p) + H + by means of the method due to Bates in which account is taken of the non-orthogonality of the wave functions describing the initial and final states. Proper allowance is made for the effects of distortion and of momentum transfer. The calculations are carried out for incident ion energies in the range 25 to 800 keV. In the accidental resonance case, the cross-section is small at low velocities of relative motion, and tends rapidly towards zero as the velocity is decreased in accordance with the prediction of Bates & Lynn. In all processes investigated the effect of distortion is considerable. Using the results of McCarroll & McElroy and of McCarroll for capture into the ground states of He + and H, the cross-sections for capture into all states are estimated. Comparisons are made with the experimental data of Fite, Smith & Stebbings for the incident alpha particle case and with that of Fite, Stebbings, Hummer & Brackman for the incident proton case. The highest energy for which cross-sections are measured in either case is however only 40 keV.

A comparison of theory and experiment for photo-ionization cross-sections I. Neon and the elements from boron to neon

1951 ◽  
Vol 208 (1094) ◽  
pp. 408-418 ◽  
Keyword(s):  
Cross Sections ◽  
General Trend ◽  
Wave Functions ◽  
Ionization Cross ◽  
Hartree Fock ◽  
Quantal Theory ◽  
Ionization Cross Sections ◽  
Photo Ionization ◽  
Near Future ◽  
Dipole Length

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).

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

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.

scholarly journals On the quenching of Gamow–Teller strength

1987 ◽  
Vol 65 (6) ◽  
pp. 574-577 ◽  
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.

Hartree–Fock calculation for the electronic structure of H+3 using numerically optimized orbitals

2001 ◽  
Vol 79 (2-3) ◽  
pp. 673-679
Author(s):  
J D Talman
Keyword(s):  
Electronic Structure ◽  
Ground State ◽  
Equilateral Triangle ◽  
Wave Functions ◽  
Equilibrium Geometry ◽  
Molecular Ion ◽  
Interatomic Spacing ◽  
Hartree Fock ◽  
Gaussian Orbitals

The Hartree–Fock wave functions for the ground state of the H2 molecule and the H+3 molecular ion are computed using radial orbitals that are numerically optimized. It is shown that these orbitals yield results comparable in accuracy to those obtained using much larger bases of Gaussian orbitals. As in previous calculations, the equilibrium geometry for H+3 is found to be that of an equilateral triangle, with an interatomic spacing of 1.64a0. PACS No.: 13.15+q

Excited states of positronium in positron–hydrogen charge exchange

1978 ◽  
Vol 56 (5) ◽  
pp. 565-570 ◽  
Author(s):  
V. S. Kulhar ◽  
C. S. Shastry
Keyword(s):  
Excited States ◽  
Charge Exchange ◽  
Cross Sections ◽  
Ground State ◽  
Born Approximation ◽  
Energy Region ◽  
Hydrogen Charge ◽  
Positronium Formation ◽  
State Approximation ◽  
Higher Excited States

The two state approximation method for the study of the rearrangement collisions is applied to the process of positronium formation in excited states for positron–hydrogen charge exchange collisions. Differential and integrated cross sections are computed for positronium formation in 2S, 2P, and 3S excited states. The results obtained in the energy region 2 to 10 Ry are compared with positronium formation cross sections in ground state. Total positronium formation cross sections including the contributions of capture into all the higher excited states of positronium are also computed in the first Born approximation and the two state approximation in the energy region considered.

Electronic wave functions II. A calculation for the ground state of the beryllium atom

1950 ◽  
Vol 201 (1064) ◽  
pp. 125-137 ◽  
Keyword(s):  
Wave Function ◽  
Variational Method ◽  
Ground State ◽  
Accurate Result ◽  
Energy Criterion ◽  
Wave Functions ◽  
Exponential Functions ◽  
Approximate Wave Function ◽  
Electronic Wave Functions ◽  
Approximate Wave

An approximate wave function expressed in terms of exponential functions, spherical harmonics, etc., with numerical coefficients has been calculated for the ground state of the beryllium atom . Judged by the energy criterion this gives a more accurate result than the Hartree result which was the best previously known. This has been calculated as a trial of a fresh method of calculating atomic wave functions. A linear combination of Slater determinants is treated by the variational method. The results suggest that this will provide a more powerful and convenient method than has previously been available for atoms with more than two electrons.

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