The radial density function and expectation values for ions

1978 ◽  
Vol 56 (6) ◽  
pp. 780-780 ◽  
Author(s):  
Russell J. Boyd
Keyword(s):  
Density Function ◽  
Radial Density ◽  
Expectation Values ◽  
Hartree Fock

Analytical expansions for the radial density function D(r) and expectation values of rn, −2 ≤ n ≤ 5, as calculated within the Hartree–Fock approximation, are reported for a large number of ions of the first 54 elements.

The radial density function for the neutral atoms from helium to xenon

1977 ◽  
Vol 55 (5) ◽  
pp. 452-455 ◽  
Author(s):  
Russell J. Boyd
Keyword(s):  
Density Distribution ◽  
Density Function ◽  
Radial Density ◽  
Neutral Atoms ◽  
Expectation Values ◽  
Hartree Fock

Analytical expansions for the radial density D(r), as calculated within the Hartree–Fock approximation, are reported for the neutral atoms from helium to xenon. As part of a brief discussion of one-electron properties which may be calculated from D(r) or the related density distribution ρ(r), expectation values for rn, n = −2, −1, 1, 2, 3, 4, and 5 are presented.

scholarly journals Evaluation of the one electron expectation values for different wave function of Be atom

2007 ◽  
Vol 4 (3) ◽  
pp. 393-396
Author(s):  
Baghdad Science Journal
Keyword(s):  
Wave Function ◽  
Slater Determinant ◽  
Open Shell ◽  
Expectation Values ◽  
Electronic Density ◽  
Expectation Value ◽  
Hartree Fock ◽  
Shell System ◽  
Electronic Wave Function ◽  
The One

The aim of this work is to evaluate the one- electron expectation value from the radial electronic density function D(r1) for different wave function for the 2S state of Be atom . The wave function used were published in 1960,1974and 1993, respectavily. Using Hartree-Fock wave function as a Slater determinant has used the partitioning technique for the analysis open shell system of Be (1s22s2) state, the analyze Be atom for six-pairs electronic wave function , tow of these are for intra-shells (K,L) and the rest for inter-shells(KL) . The results are obtained numerically by using computer programs (Mathcad).

scholarly journals Calculation of Radial Density Distribution Function for main orbital of Carbon atom and Carbon like ions

2014 ◽  
Vol 11 (4) ◽  
pp. 1455-1458
Author(s):  
Baghdad Science Journal
Keyword(s):  
Distribution Function ◽  
Carbon Atom ◽  
Density Distribution ◽  
Computer Software ◽  
Negative Ion ◽  
Radial Density ◽  
Density Distribution Function ◽  
Hartree Fock ◽  
Radial Density Distribution ◽  
Nitrogen Ion

Radial density distribution function of one particle D(r1) was calculated for main orbital of carbon atom and carbon like ions (N+ and B- ) by using the Partitioning technique .The results presented for K and L shells for the Carbon atom and negative ion of Boron and positive ion for nitrogen ion . We observed that as atomic number increases the probability of existence of electrons near the nucleus increases and the maximum of the location r1 decreases. In this research the Hartree-fock wavefunctions have been computed using Mathcad computer software .

Perturbation treatment of the Hartree–Fock equations for the ground states of the boron-like ions

1969 ◽  
Vol 47 (7) ◽  
pp. 699-705 ◽  
Author(s):  
C. S. Sharma ◽  
R. G. Wilson
Keyword(s):  
Ground State ◽  
Atomic System ◽  
Ground States ◽  
Great Accuracy ◽  
Second Order ◽  
Expectation Values ◽  
Third Order ◽  
First Order ◽  
Hartree Fock ◽  
The Third

The first-order Hartree–Fock and unrestricted Hartree–Fock equations for the ground state of a five electron atomic system are solved exactly. The solutions are used to evaluate the corresponding second-order energies exactly and the third-order energies with great accuracy. The first-order terms in the expectation values of 1/r, r, r2, and δ(r) are also calculated.

On the Ground State of H-

1981 ◽  
Vol 36 (7) ◽  
pp. 782
Author(s):  
Uday Vanu Das Gupta ◽  
Subal Chandra Saha ◽  
Sankar Sengupta
Keyword(s):  
Oscillator Strength ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Expectation Values ◽  
Hartree Fock ◽  
Present Procedure

Abstract A simple and effective method is described to calculate the ground state energy of H~ starting with the Hartree Fock wavefunction. The expectation values of the opera­ tors 〈r1 • r2〉, 〈r1n + r2n〉 and 〈p1 • p2〉 can be estimated easily with the present procedure. Oscillator strength sums S(k) for k= -1,0, 1 are also evaluated.

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.

scholarly journals Expectation Values of the Neutral Chromium Radius

Atoms ◽  
2018 ◽  
Vol 6 (3) ◽  
pp. 51
Author(s):  
Nafeesah Abdul Rahim Yaqub ◽  
Rabia Qindeel ◽  
Norah Alonizan ◽  
Nabil Ben Nessib
Keyword(s):  
Atomic Data ◽  
Expectation Values ◽  
Laboratory Plasma ◽  
Thomas Fermi ◽  
Hartree Fock ◽  
Relativistic Approximation ◽  
Relativistic Corrections ◽  
Plasma Applications

Neutral Chromium (Cr I) is an important element in many laboratory plasma applications. In this work, expectation values of the radius for Cr I are calculated. These atomic data are calculated with three different atomic codes: Cowan code using the Hartree–Fock Relativistic approximation, SUPERSTRUCTURE and AUTOSTRUCTURE codes using scaled Thomas–Fermi–Dirac–Amaldi potential. Relativistic corrections are introduced according to the Breit–Pauli approach. The 3 d 5 4 s , 3 d 4 4 s 2 , 3 d 5 4 d , 3 d 5 4 p and 3 d 4 4 s 4 p configurations are included to obtain the expectation values of radius of Cr I and compared with available data. The novelty of our work is to obtain new values of < 1 r > , < r > , and < r 2 > for the configuration of 4 p and 4 d and the values of < r 3 > for all orbitals configurations considered in this work.

scholarly journals Calculation of Radial Electron-Electron Distribution function and Expectation Values for Li-Atom in Excited States 1s 2p, 1s 3p and 1s 3d

2015 ◽  
Vol 12 (3) ◽  
pp. 591-596
Author(s):  
Baghdad Science Journal
Keyword(s):  
Distribution Function ◽  
Radial Distribution Function ◽  
Excited States ◽  
Radial Distribution ◽  
Electron Correlation ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Expectation Values ◽  
Hartree Fock

The electron correlation for inter-shells (1s 2p), (1s 3p) and (1s 3d) was described by the inter-particle radial distribution function f(r12). It was evaluated for Li-atom in the different excited states (1s2 2p), (1s2 3p) and (1s2 3d) using Hartree-Fock approximation (HF). The inter particle expectation values for these shells were also evaluated. The calculations were performed using Mathcad 14 program.

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