HARTREE–FOCK WAVE FUNCTIONS FOR EXCITED STATES: III. DIPOLE TRANSITIONS IN THREE-ELECTRON SYSTEMS

1967 ◽  
Vol 45 (5) ◽  
pp. 1661-1673 ◽  
Author(s):  
Maurice Cohen ◽  
Paul S. Kelly
Keyword(s):  
Excited States ◽  
Wave Functions ◽  
Electron Systems ◽  
Matrix Elements ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
Transition Matrix Elements ◽  
Simplified Procedure ◽  
Good Agreement ◽  
Dipole Length

Hartree–Fock wave functions for a number of S, P, and D states of the lithium isoelectronic sequence have been calculated, using a simplified procedure described in an earlier paper. Transition matrix elements for all permitted dipole transitions between these states have been computed using both the dipole length and the dipole velocity formulations. The results are in good agreement with earlier calculations.

HARTREE–FOCK WAVE FUNCTIONS FOR EXCITED STATES: IV. OSCILLATOR STRENGTHS IN THE HELIUM ISOELECTRONIC SEQUENCE

1967 ◽  
Vol 45 (6) ◽  
pp. 2079-2090 ◽  
Author(s):  
Maurice Cohen ◽  
Paul S. Kelly
Keyword(s):  
Matrix Element ◽  
Excited States ◽  
Transition Matrix ◽  
Transition Matrix Element ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
Good Agreement

Orbital wave functions for a number of singlet and triplet S, P, and D states of the helium sequence through C+4 have been calculated using an approximation described earlier. The wave functions have been employed to calculate the oscillator strengths for all allowed dipole transitions between these states, using both the length and velocity forms of the transition matrix element. Our results are in good agreement with the most accurate values available.

Systematic Trends in Atomic Oscillator Strengths: The Helium Isoelectronic Sequence

1972 ◽  
Vol 50 (12) ◽  
pp. 1363-1369 ◽  
Author(s):  
M. Cohen ◽  
R. P. McEachran
Keyword(s):  
Electric Dipole ◽  
Nuclear Charge ◽  
Principal Quantum Number ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Isoelectronic Sequence ◽  
Dipole Oscillator ◽  
Good Agreement ◽  
Comparison Data ◽  
Dipole Length

Electric dipole oscillator strengths (f values) have been calculated for a large number of singlet and triplet S–P, P–D, and D–F transitions in the helium isoelectronic sequence through O+6. The analytical orbital wave functions employed were of frozen-core type, and generally produce very good agreement between length and velocity values of the calculated oscillator strengths. A conspicuous exception occurs in many cases where the principal quantum number remains unchanged in the transition, and the more reliable dipole length values have been adopted for such transitions. The smooth variation of the calculated f values as functions of the inverse of the nuclear charge Z provided a sensitive check on the accuracy of the computations and indicated a considerable number of P–D transitions where the velocity values seemed the more reliable. Wherever comparison data are available, our calculated oscillator strengths are in excellent agreement with the most accurate values; in other cases, the absolute uncertainty in the f values should in no case exceed 5%.

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).

scholarly journals Studying the x- ray atomic Scattering form Factor and Nuclear Magnetic Shielding Constant for Be atom in its Excited state (1s2 2s 3s) and the Be - like ions

2015 ◽  
Vol 12 (1) ◽  
pp. 204-209
Author(s):  
Baghdad Science Journal
Keyword(s):  
Form Factor ◽  
Excited State ◽  
Computer Software ◽  
Wave Functions ◽  
Magnetic Shielding ◽  
Electron Systems ◽  
X Ray ◽  
Hartree Fock ◽  
Atomic Scattering ◽  
Nuclear Magnetic

The division partitioning technique has been used to analyze the four electron systems into six-pairs electronic wave functions for ( for the Beryllium atom in its excited state (1s2 2s 3s ) and like ions ( B+1 ,C+2 ) using Hartree-Fock wave functions . The aim of this work is to study atomic scattering form factor f(s) for and nuclear magnetic shielding constant. The results are obtained numerically by using the computer software (Mathcad).

Microscopic description of the fusion excitation function of 32,36S+90,94,96Zr

2020 ◽  
Vol 29 (07) ◽  
pp. 2050046
Author(s):  
M. Rashdan ◽  
T. A. Abdel-Karim
Keyword(s):  
Excitation Function ◽  
Excited States ◽  
Density Functional ◽  
Neutron Density ◽  
Energy Density Functional ◽  
Hartree Fock ◽  
Density Distributions ◽  
Text Interaction ◽  
Good Agreement

The fusion excitation function for the systems [Formula: see text]S+[Formula: see text]Zr is investigated using a microscopic internuclear potential derived from Skyrme energy density functional. The inputs in this approach are the proton and neutron density distributions of the interacting nuclei, which are derived from Skyrme–Hartree–Fock calculations. The SkM[Formula: see text] interaction is used in the calculation of the nuclear densities as well as the internuclear potential. The coupling to low lying inelastic excited states of target and projectile is considered. The role of the neutron transfer is discussed, where it is considered through the CCFULL model calculation. A good agreement with the experimental data is obtained without adjustable parameters.

Inelastic electric and magnetic electron scattering form factors of 24Mg nucleus: Role of g factors

2017 ◽  
Vol 26 (05) ◽  
pp. 1750032 ◽  
Author(s):  
Anwer A. Al-Sammarraie ◽  
M. L. Inche Ibrahim ◽  
Muna Ahmed Saeed ◽  
Fadhil I. Sharrad ◽  
Hasan Abu Kassim
Keyword(s):  
Experimental Data ◽  
Electron Scattering ◽  
Form Factors ◽  
Wave Functions ◽  
Matrix Elements ◽  
Model Hamiltonian ◽  
Transverse Electron ◽  
Magnetic Electron ◽  
Good Agreement

The electric and magnetic transitions in the [Formula: see text]Mg nucleus are studied based on the calculations of the longitudinal and the transverse electron scattering form factors. The universal sd-shell model Hamiltonian (USDA) is used for calculations. The wave functions of radial single-particle matrix elements are calculated using the Skyrme potential. For the longitudinal form factors, a good agreement is obtained between the calculations and the experimental data. For the transverse form factors, the effective [Formula: see text] factors are made as adjustable parameters in order to describe the experimental data.

scholarly journals Nuclear transition matrix elements for neutrinoless double-β decay within mechanisms involving light Majorana neutrino mass and right-handed current

2019 ◽  
Vol 28 (01n02) ◽  
pp. 1950001
Author(s):  
Yash Kaur Singh ◽  
R. Chandra ◽  
K. Chaturvedi ◽  
Tripti Avasthi ◽  
P. K. Rath ◽  
...  
Keyword(s):  
Neutrino Mass ◽  
Transition Matrix ◽  
Weak Coupling ◽  
Majorana Neutrino ◽  
Nuclear Transition ◽  
Matrix Elements ◽  
Β Decay ◽  
Hartree Fock ◽  
Transition Matrix Elements ◽  
Majorana Neutrino Mass

Employing the projected-Hartree-Fock-Bogoliubov (PHFB) model in conjunction with four different parametrizations of pairing plus multipolar effective two-body interaction and three different parametrizations of Jastrow short-range correlations, nuclear transition matrix elements for the neutrinoless double-[Formula: see text] decay of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] isotopes are calculated within mechanisms involving light Majorana neutrino mass and right-handed current. Statistically, model specific uncertainties in sets of twelve nuclear transition matrix elements are estimated by calculating the averages along with the standard deviations. For the considered nuclei, the most stringent extracted on-axis limits on the effective light Majorana neutrino mass [Formula: see text], the effective weak coupling of right-handed leptonic current with right-handed hadronic current [Formula: see text], and the effective weak coupling of right-handed leptonic current with left-handed hadronic current [Formula: see text] from the observed limit on half-life [Formula: see text] of [Formula: see text] isotope are [Formula: see text][Formula: see text]eV, [Formula: see text] and [Formula: see text], respectively.

Electric Quadrupole Transitions in Na I, Mg II and Al III

1972 ◽  
Vol 50 (11) ◽  
pp. 1169-1174 ◽  
Author(s):  
C. E. Tull ◽  
M. Jackson ◽  
R. P. McEachran ◽  
M. Cohen
Keyword(s):  
Electric Quadrupole ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Hartree Fock ◽  
Good Agreement

Theoretical multiplet strengths for electric quadrupole transitions between 2S, 2P0, 2D, and 2F0 levels of Na I, Mg II, and Al III have been calculated using Hartree–Fock wave functions of frozen-core type. The resulting 2S–2D oscillator strengths for Na I are in good agreement with calculations by Bogaard and Orr, Boyle and Murray, and Warner; however, for Mg II there is a discrepancy of a factor of 2 between our results and those of Warner.

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