scholarly journals Study of the Inter-Particle Expectation Values for Inter and Outer Shell

2014 ◽  
Vol 11 (2) ◽  
pp. 527-530
Author(s):  
Baghdad Science Journal
Keyword(s):  
Atomic Number ◽  
Wave Functions ◽  
Outer Shell ◽  
Expectation Values ◽  
Hartree Fock

In this research the Inter-Particle Expectation Values have been studied for atomics Helium (He) and Beryllium (Be) also for He-like ions, Be-like ions (Li-1, B+1? Li+1, Be+2, B+3) by using Hartree-Fock wave functions, We compared the results to some ions which have the same atomic number from each group with atomic number, We compared the results with published calculations to the last studied .

Lifetimes for singly ionized nitrogen

2014 ◽  
Vol 92 (1) ◽  
pp. 82-85 ◽  
Author(s):  
Murat Yıldız ◽  
Yasin Gökçe
Keyword(s):  
Model Theory ◽  
Potential Model ◽  
Wave Functions ◽  
Quantum Defect ◽  
Orbital Theory ◽  
Expectation Values ◽  
Hartree Fock ◽  
First Time ◽  
Bound Electron

The lifetimes of some excited levels for singly ionized nitrogen are calculated by using the weakest bound electron potential model theory and quantum defect orbital theory. We determined expectation values of radii using numerical nonrelativistic Hartree–Fock wave functions. The necessary energy values have been taken from NIST. The present results have been compared with previous calculations and experiments. Most of the lifetime results are presented for the first time in the present work. For N II, because there are few lifetime results available in the literature, the present study compared to existing investigations, provides detailed results for the lifetimes of several of the excited 2s22pns, 2s22pnp, and 2s22pd → 2s22p2 where, n = 3–6 for the ns series, n = 3–5 for the nd series and n = 3–4 for the np series.

"VECTAL" REPRESENTATION OF THE WAVE FUNCTION AND ITS PHYSICAL MEANING

1967 ◽  
Vol 45 (11) ◽  
pp. 3667-3676
Author(s):  
C. S. Lin
Keyword(s):  
Wave Function ◽  
Wave Functions ◽  
Electron Wave Function ◽  
Electron Wave ◽  
Expectation Values ◽  
Expectation Value ◽  
Hartree Fock ◽  
The One ◽  
The Relationship ◽  
Determinantal Form

A new form of one-electron wave function, "vectal," is introduced. It is shown that an arbitrary CI geminal and a certain class of many-electron wave functions can be represented in a single-determinantal form in terms of the vectal. Eigenvalue equations for the vectal, similar to that of the Hartree–Fock theory, are derived and the vectal representation is shown to enable a formal interpretation of the CI theory in the Hartree–Fock manner. The eigenvalue, vectal energy, is interpreted as the negative of an ionization potential, in Koop-man's sense, of the system described by the CI wave function. It is also shown that the expectation value of any one-electron operator, [Formula: see text], where Ψ is the CI wave function, is expressible in terms of the expectation values of the same operator with respect to the vectals. The vectals are interpreted as the one-electron wave function in the CI space.A possible application of the vectal representation is briefly described, and the relationship between the vectal representation and the "scalar representation" is discussed.

Theoretical calculations of transition probabilities for individual and multiplet lines between some excited levels of atomic potassium

2008 ◽  
Vol 86 (3) ◽  
pp. 487-494 ◽  
Author(s):  
Gültekin Çelik ◽  
Şule Ateş
Keyword(s):  
Excited States ◽  
Potential Model ◽  
Transition Probabilities ◽  
Theoretical Calculations ◽  
Wave Functions ◽  
Expectation Values ◽  
Data Bases ◽  
Hartree Fock ◽  
Coulomb Approximation ◽  
Bound Electron

The transition probabilities for individual and multiplet lines between some excited levels of atomic potassium are calculated using weakest bound electron potential model theory (WBEPMT). The numerical nonrelativistic Hartree–Fock wave functions for the expectation values of radii in all excited states, unlike the Numerical Coulomb Approximation method traditionally used for WBEPMT and experimental ionization energies, have been employed to determine the parameters. The results obtained during this work agree very well with the accepted values taken from National Institute Standards and Technology. Moreover, some transition probabilities not existing on the data bases for highly excited levels in atomic potassium have been obtained using this method. PACS No.: 32.70.Cs

Non-relativistic Hartree–Fock scattering factors for the actinides and their positive ions

1978 ◽  
Vol 56 (1) ◽  
pp. 1-2
Author(s):  
Robert Benesch ◽  
K. M. S. Saxena
Keyword(s):  
Wave Functions ◽  
Expectation Values ◽  
X Ray ◽  
Hartree Fock ◽  
Positive Ions ◽  
X Ray Scattering ◽  
Ray Scattering

Coherent X-ray scattering factors F(μ) for the neutral actinides (Z = 89 through Z = 102) and for various configurations of their positive ions have been computed from non-relativistic Hartree–Fock wave functions. The expectation values [Formula: see text] are also reported for the 119 systems considered in the present study.

scholarly journals Energy Calculation for Excited Lithium Atom in Position Space

2015 ◽  
Vol 12 (4) ◽  
pp. 808-813
Author(s):  
Baghdad Science Journal
Keyword(s):  
Excited State ◽  
Ground State ◽  
Lithium Atom ◽  
Wave Functions ◽  
Energy Calculation ◽  
Expectation Values ◽  
Position Space ◽  
Hartree Fock ◽  
Energy Expectation ◽  
Partitioning Technique

The energy expectation values for Li and Li-like ions ( , and ) have been calculated and examined within the ground state and the excited state in position space. The partitioning technique of Hartree-Fock (H-F) has been used for existing wave functions.

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