Stopping power and range calculations in human tissues by using the Hartree-Fock-Roothaan wave functions

2017 ◽  
Vol 140 ◽  
pp. 43-50 ◽  
Author(s):  
Metin Usta ◽  
Mustafa Çağatay Tufan
2018 ◽  
Vol 96 (12) ◽  
pp. 1338-1348
Author(s):  
Zeynep Yüksel ◽  
M. Çağatay Tufan

The stopping power and range for electrons in matter are the most important parameters in predicting the consequences of the electrons interacting with matter. In this work, we used our previously developed method to calculate these parameters. In our calculation method, the main parameter is the velocity-dependent electronic charge density of the target, which we obtained by using Roothaan–Hartree–Fock (RHF) wave functions. For range calculations, we used the continuous slowdown approach (CSDA), which neglects the energy-loss fluctuations so the incident particle loses its energy in a medium continuously at a rate equal to the total stopping power. The stopping power and CSDA range values have been calculated for electrons incident on brain, breast, and eye tissues. Obtained results have been compared with the available data.


Equations which determine the optimum form of paired-electron orbitals are derived. It is shown that for large nuclear separations these equations become the Hartree-Fock equa­tions for appropriate valence states of the separated atoms. An electrostatic interpretation of chemical bonding is developed using optimum paired-electron orbital functions. For these wave functions this simple procedure yields results identical with those obtained by the conventional method of calculation based on the Hamiltonian integral. Numerical computations by the electrostatic method are also discussed.


1986 ◽  
Vol 41 (1-2) ◽  
pp. 37-46 ◽  
Author(s):  
K. D. Sen ◽  
P. C. Schmidt ◽  
Alarich Weiss

The Sternheimer shielding-antishielding functions ß(r) and γ(r) are reported for all the fourteen lanthanide atoms at the uncoupled Hartree-Fock level of theory. Each atom is considered in two valence state configurations, 4fn 5d0 and 4 fn-1 5d1, and the nonrelativistic HF wave functions have been used. The 5d1 configuration leads to a smaller net antishielding than the 4fn configuration by ~ 6-12% in the series. The electron-electron self consistency effects are found to be less than 5% in the series. The importance of the calculated antishielding functions in the antishielding theory of electric field gradients in noncubic metals is discussed.


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).


2015 ◽  
Vol 12 (1) ◽  
pp. 204-209
Author(s):  
Baghdad Science Journal

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).


1969 ◽  
Vol 47 (13) ◽  
pp. 1331-1336 ◽  
Author(s):  
R. A. Moore ◽  
S. H. Vosko

The dependence of the Fermi surface electron wave functions in Na and K on (i) an L-dependent effective local cellular potential constructed to simulate Hartree-Fock theory and (ii) the inclusion of the Hartree field due to the conduction electrons in the cellular potential is investigated. All calculations are performed using the Wigner–Seitz spherical cellular approximation and the Schrödinger equation is solved by the Kohn variational method. It is found that to ensure a value of the Fermi surface electron density at the nucleus accurate to ~5%, it is necessary to use the L-dependent potential along with the Hartree field due to a realistic conduction electron density.


1961 ◽  
Author(s):  
R. E. WATSON ◽  
A. J. FREEMAN
Keyword(s):  

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