Shifted Tietz–Wei oscillator for simulating the atomic interaction in diatomic molecules

doi:10.1007/s40094-015-0173-9

Shifted Tietz–Wei oscillator for simulating the atomic interaction in diatomic molecules

Authors

Abstract

AbstractThe shifted Tietz–Wei (sTW) oscillator is as good as traditional Morse potential in simulating the atomic interaction in diatomic molecules. By using the Pekeris-type approximation, to deal with the centrifugal term, we obtain the bound-state solutions of the radial Schrödinger equation with this typical molecular model via the exact quantization rule (EQR). The energy spectrum for a set of diatomic molecules (NOa4Πidocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${ m NO} left( a^4Pi _i ight) $$end{document}, NOB2Πrdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${ m NO} left( B^2Pi _r ight) $$end{document}, NOL′2ϕdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${ m NO} left( L’^2phi ight) $$end{document}, NOb4Σ-documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${ m NO} left( b^4Sigma ^{-} ight) $$end{document}, IClX1Σg+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${ m ICl}left( X^1Sigma _g^{+} ight) $$end{document}, IClA3Π1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${ m ICl}left( A^3Pi _1 ight) $$end{document} and IClA′3Π2documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$${ m ICl}left( A’^3Pi _2 ight) $$end{document} for arbitrary values of ndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$n$$end{document} and ℓdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} egin{document}$$ell $$end{document} quantum numbers are obtained. For the sake of completeness, we study the corresponding wavefunctions using the formula method.