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Register a new userUse of Combined Hartree-Fock-Roothaan Theory in Evaluation of Lowest States of K [Ar]4s^0 3d^1 and Cr+ [Ar]4s^0 3d^5 Isoelectronic Series Over Noninteger n-Slater Type Orbitals
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By the use of integer and noninteger n-Slater Type Orbitals in combined Hartree-Fock-Roothaan method, self consistent field calculations of orbital and lowest states energies have been performed for the isoelectronic series of open shell systems K [Ar]4s^0 3d^1 2(D) (Z=19-30) and Cr+ [Ar] 4s^0 3d^5 6(S) (Z=24-30). The results of calculations for the orbital and total energies obtained from the use of minimal basis sets of integer- and noninteger n-Slater Type Orbitals are given in tables. The results are compared with the extended-basis Hartree-Fock computations. The orbital and total energies are in good agreement with those presented in the literature. The results are accurately and considerably can be useful in the application of non-relativistic and relativistic combined Hartree-Fock-Roothaan approach for heavy atomic systems.
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Three-center nuclear attraction integrals with Slater type orbitals (STOs) appearing in the Hartree-Fock-Roothaan (HFR) equations for molecules are evaluated using one-range addition theorems of STOs obtained from the use of complete orthonormal sets of -exponential type orbitals (-ETOs), where . These integrals are investigated for the determination of the best with respect to the convergence and accuracy of series expansion relations. It is shown that the best values are obtained for . The convergence of three-center nuclear attraction integrals with respect to the indices for is presented. The final results are expressed through the overlap integrals of STOs containing . The hermitian properties of three-center nuclear attraction integrals are also investigated. The algorithm described in this work is valid for the arbitrary values of, and quantum numbers, screening constants and location of orbitals. The convergence and accuracy of series are tested by calculating concrete cases. It should be noted that the theory of three-center nuclear attraction integrals presented in this work is the extension of method described in our previous paper for to the case of (I.I. Guseinov, N. Seckin Gorgun and N. Zaim, Chin. Phys. B 19 (2010) 043101-1-043101-5).
By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two- and four-component spinor wave functions, and Slater spinor orbitals useful in the quantum-mechanical description of the spin- 1/2 particles by the quasirelativistic and Diracs relativistic equations are established in position, momentum and four-dimensional spaces. These function sets are expressed through the corresponding nonrelativistic orbitals. The analytical formulas for overlap integrals over four-component relativistic Slater spinor orbitals with the same screening constants in position space are also derived. The relations obtained in this study can be useful in the study of different problems arising in the quasirelativistic and relativistic quantum mechanics when the position, momentum and four dimensional spaces are employed.
By the use of complete orthonormal sets of nonrelativistic scalar orbitals introduced by the author in previous papers the new complete orthonormal basis sets for two-and four-component spinor wave functions, and Slater spinor orbitals useful in the quantum-mechanical description of the spin - 1/2 particles by the quasirelativistic and relativistic equations are established in position, momentum and four-dimensional spaces. These function sets are expressed through the corresponding nonrelativistic orbitals. The analytical formulas for overlap integrals over four component relativistic Slater spinor orbitals with the same screening constants in position space are also derived. The relations obtained in this study can be useful in the study of different problems arising in the quasirelativistic and relativistic quantum mechanics when the position, momentum and four dimensional spaces are employed.
The positron-neutrino correlation in the $0^+ to 0^+ beta$ decay of $^{32}$Ar was measured at ISOLDE by analyzing the effect of lepton recoil on the shape of the narrow proton group following the superallowed decay. Our result is consistent with the Standard Model prediction. For vanishing Fierz interference we find $a=0.9989 pm 0.0052 pm 0.0036$, which yields improved constraints on scalar weak interactions.
Recent experiments have reported measurements of rainbow scattering features in the angular distributions of hyperthermal Ar colliding with LiF(001) [Kondo et al., J. Chem. Phys. 122, 244713 (2005)]. A semiclassical theory of atom-surface collisions recently developed by the authors that includes multiphonon energy transfers is used to explain the temperature dependence of the measured scattered angular distribution spectra.
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