scholarly journals Hartree–Fock critical nuclear charge in two-electron atoms

2021 ◽  
Vol 154 (11) ◽  
pp. 111103
Author(s):  
Hugh G. A. Burton
Keyword(s):  
Nuclear Charge ◽  
Hartree Fock

scholarly journals Atomic X-ray Transition Probabilities: A Comparison of the Dipole Length, Velocity and Acceleration Forms

1984 ◽  
Vol 37 (1) ◽  
pp. 45 ◽  
Author(s):  
HM Quiney ◽  
FP Larkins
Keyword(s):  
Transition Probabilities ◽  
Nuclear Charge ◽  
Principal Quantum Number ◽  
Dipole Transition ◽  
Final States ◽  
X Ray ◽  
Hartree Fock ◽  
Isoelectronic Series ◽  
Rydberg Electron ◽  
Dipole Length

The length, velocity and acceleration forms of the dipole transition operator are examined in calculations of diagram and satellite X-ray emission probabilities in the Ne + to Ar 9 + isoelectronic series. All calculations are within the relaxed nonrelativistic Hartree-Fock framework, using separately optimized numerical wavefunctions for the initial and final electronic states. Divergence between the alternative forms of the transition moment, as the principal quantum 'number of the Rydberg electron and nuclear charge are increased, is discussed in the context of electron correlation differences between the initial and final states.

The Calculations for Determination of the Age of Supernova Remnants and Galaxy Clusters by Measurements of Hyperfine Splitting in Highly ionized Atoms with Unstable Nuclei

1988 ◽  
Vol 102 ◽  
pp. 127
Author(s):  
I.M. Band ◽  
M.A. Listengarten ◽  
M.B. Trzhaskovskaya
Keyword(s):  
Galaxy Clusters ◽  
Supernova Remnants ◽  
Nuclear Charge ◽  
Magnetic Moments ◽  
Energy Levels ◽  
Hartree Fock ◽  
Hot Gas ◽  
Unstable Nuclei ◽  
Vacuum Polarisation

The possibility of using the transitions between HFS components of atoms with nonstable nuclei in the spectra of hot gas in the supernova remnants and galaxy clusters for obtaining the information on the age of the objects was mentioned in /l/ without calculations. Here we present the numerical results for some ionized atoms obtained by relastivistic Hartree-Fock-Dirac method. Fermi distribution of nuclear charge density, vacuum polarisation, electron anomalous magnetic moment and reduced mass were taken into account. The HFS energy levels can be written aswhere A=A’(μ/J). HFS constants A’ in millielectronvolts for H- Li- and Na-like ions of unstable isotops with well known magnetic moments with Z < 53 are given in the table (abundance rapidly decreases with increasing of Z). For the s-electrons, wavelength λ = (hcJ)/(Aμ(J+(1/2))); J is the nuclear spin, hc= 1,23985.10−4eV.cm T1/2is the halflife.

An expansion method for calculating atomic properties. IX. The dipole polarizabilities of the lithium sequence*

1966 ◽  
Vol 293 (1434) ◽  
pp. 365-377 ◽  
Keyword(s):  
Nuclear Charge ◽  
Expansion Method ◽  
Zero Order ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
Atomic Properties ◽  
Dipole Polarizabilities

A theory is developed for expanding the dipole polarizabilities and shielding factors of an atom or ion in inverse powers of the nuclear charge Z in cases where the field links degenerate zero order configurations. Results for all members of the lithium isoelectronic sequence are presented both within the Hartree-Fock approximation and in a more accurate formulation, and are found to be in agreement with earlier work.

scholarly journals Analysis of correlation and ionization from pair distributions in many-electron systems

2021 ◽  
Vol 136 (7) ◽  
Author(s):  
S. López-Rosa ◽  
J. C. Angulo ◽  
A. L. Martín ◽  
J. Antolín
Keyword(s):  
Periodic Table ◽  
Nuclear Charge ◽  
Arbitrary System ◽  
Electron Systems ◽  
Atomic Systems ◽  
Hartree Fock ◽  
Pair Density ◽  
Singly Charged ◽  
Jensen Shannon Divergence ◽  
Charged Ions

AbstractJensen–Shannon divergence is used to quantify the discrepancy between the Hartree–Fock pair density and the product of its marginals for different N-electron systems, enclosing neutral atoms (with nuclear charge $$Z=N$$ Z = N ) and singly-charged ions ($$N = Z \pm 1$$ N = Z ± 1 ). This divergence measure is applied to determine the interelectronic correlation in atomic systems. A thorough study was carried out, by considering (i) both position and momentum conjugated spaces, and (ii) systems with a nuclear charge as far as $$Z = 103$$ Z = 103 . The correlation among electrons was measured by comparing, for an arbitrary system, the double-variable electron-pair density with the product of the respective one-particle densities. A detailed analysis throughout the Periodic Table highlights the relevance not only of weightiness for the systems considered, but also of their shell structure. Besides, comparative computations between two-electron densities of different atomic systems (neutrals, cations, anions) quantify their dissimilarities, patently governed by shell-filling patterns throughout the Periodic Table.

An expansion method for calculating atomic properties X. 1 s 2 1 S -1 snp 1 P transitions of the helium sequence

1967 ◽  
Vol 301 (1466) ◽  
pp. 253-260 ◽  
Keyword(s):  
Cross Sections ◽  
Nuclear Charge ◽  
Expansion Method ◽  
Probable Error ◽  
Oscillator Strengths ◽  
Matrix Elements ◽  
Isoelectronic Sequence ◽  
First Order ◽  
Hartree Fock ◽  
Atomic Properties

The electric dipole matrix elements connecting the 1 s 2 1 S and 1 snp 1 P states of the helium isoelectronic sequence are calculated exactly to first order in inverse powers of the nuclear charge Z and the differences from the Hartree-Fock approximation are shown to correspond to virtual transitions of the 1 s electrons. Comparison of the oscillator strengths predicted by a screening approximation with more accurate values reveals a regular variation in the error contained in the screening approximation, the correction of which allows the prediction of oscillator strengths and probabilities of 1 s 2 1 S – 1 snp 1 P transitions for all values of n and all values of Z within a probable error of 2% (table 5). Values of the photoionization cross-sections at the spectral heads are also presented.

NEW CALCULATION FOR SOME GROUND STATE FEATURES OF 40Ca, 48Ca32S AND 39K NUCLEI

2010 ◽  
Vol 19 (02) ◽  
pp. 291-298 ◽  
Author(s):  
H. AYTEKIN ◽  
R. BALDIK ◽  
E. TEL ◽  
A. AYDIN
Keyword(s):  
Ground State ◽  
Nuclear Charge ◽  
Mean Field ◽  
Binding Energies ◽  
Charge Radii ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Density Distributions ◽  
Total Binding ◽  
Experimental Values

Some ground states features of 32 S , 39 K , 40 Ca and 48 Ca nuclei are investigated using the Hartree–Fock method with the Skyrme SKM * and SLy4 forces calculated in two different code implementations. The calculated total binding energies per particle and root mean square (rms) nuclear charge radii using the Skyrme–Hartree–Fock (SHF) + BCS method are compared with relativistic mean-field (RMF) theory and experimental values. The obtained charge density distributions from these code implementations are compared with the experimental data. Pairing effects are also included in calculations for the same nuclei. Variations of the total binding energies per particle and rms nuclear charge radii were investigated as the last shell nucleons were carried to the upper shell.

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