Accurate Hylleraas-like functions for the He atom with correct cusp conditions

K V RODRIGUEZ; G GASANEO

JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL PHYSICS

Año: 2005 vol. 38 p. 259 - 267

0953-4075

In this letter, a set of ground state wavefunctions for the He atom is given. The functions are constructed in terms of exponential and power series as similar as possible to the Hylleraas functions of Chandrasekhar and Herzberg (1955 Phys. Rev. 98 1050). The accuracy of the calculated energies is found to be about 10−4 au and all the cusp conditions at the Coulomb singularities are satisfied. The nine-parameter functions proposed here are found to have better local energy than those given by the 6 and 14 terms Hylleraas functions of Chandrasekhar. The mean value of various functions evaluated with the different proposals shows their good quality. These properties highly qualify the function to be used as an alternative to the Chandrasekhar functions in collisional problems. The whole set of functions given here can be considered as an alternative to the proposals of Chandrasekhar (1955 Phys. Rev. 98 1050), Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). are satisfied. The nine-parameter functions proposed here are found to have better local energy than those given by the 6 and 14 terms Hylleraas functions of Chandrasekhar. The mean value of various functions evaluated with the different proposals shows their good quality. These properties highly qualify the function to be used as an alternative to the Chandrasekhar functions in collisional problems. The whole set of functions given here can be considered as an alternative to the proposals of Chandrasekhar (1955 Phys. Rev. 98 1050), Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). to be about 10−4 au and all the cusp conditions at the Coulomb singularities are satisfied. The nine-parameter functions proposed here are found to have better local energy than those given by the 6 and 14 terms Hylleraas functions of Chandrasekhar. The mean value of various functions evaluated with the different proposals shows their good quality. These properties highly qualify the function to be used as an alternative to the Chandrasekhar functions in collisional problems. The whole set of functions given here can be considered as an alternative to the proposals of Chandrasekhar (1955 Phys. Rev. 98 1050), Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). are satisfied. The nine-parameter functions proposed here are found to have better local energy than those given by the 6 and 14 terms Hylleraas functions of Chandrasekhar. The mean value of various functions evaluated with the different proposals shows their good quality. These properties highly qualify the function to be used as an alternative to the Chandrasekhar functions in collisional problems. The whole set of functions given here can be considered as an alternative to the proposals of Chandrasekhar (1955 Phys. Rev. 98 1050), Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). Phys. Rev. 98 1050). The accuracy of the calculated energies is found to be about 10−4 au and all the cusp conditions at the Coulomb singularities are satisfied. The nine-parameter functions proposed here are found to have better local energy than those given by the 6 and 14 terms Hylleraas functions of Chandrasekhar. The mean value of various functions evaluated with the different proposals shows their good quality. These properties highly qualify the function to be used as an alternative to the Chandrasekhar functions in collisional problems. The whole set of functions given here can be considered as an alternative to the proposals of Chandrasekhar (1955 Phys. Rev. 98 1050), Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). are satisfied. The nine-parameter functions proposed here are found to have better local energy than those given by the 6 and 14 terms Hylleraas functions of Chandrasekhar. The mean value of various functions evaluated with the different proposals shows their good quality. These properties highly qualify the function to be used as an alternative to the Chandrasekhar functions in collisional problems. The whole set of functions given here can be considered as an alternative to the proposals of Chandrasekhar (1955 Phys. Rev. 98 1050), Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). −4 au and all the cusp conditions at the Coulomb singularities are satisfied. The nine-parameter functions proposed here are found to have better local energy than those given by the 6 and 14 terms Hylleraas functions of Chandrasekhar. The mean value of various functions evaluated with the different proposals shows their good quality. These properties highly qualify the function to be used as an alternative to the Chandrasekhar functions in collisional problems. The whole set of functions given here can be considered as an alternative to the proposals of Chandrasekhar (1955 Phys. Rev. 98 1050), Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). Phys. Rev. 98 1050), Bonham and Kohl (1966 J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47). B: At. Mol. Opt. Phys. 30 L47). J. Chem. Phys. 45 2471) and Le Sech (1997 J. Phys. B: At. Mol. Opt. Phys. 30 L47).30 L47).