| الملخص: | The exponentially correlated Hylleraas–configuration interaction method (E-Hy-CI) is a generalization of the Hylleraas–configuration interaction method (Hy-CI) in which the single <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></semantics></math></inline-formula> of an Hy-CI wave function is generalized to a form of the generic type <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>r</mi><mrow><mi>i</mi><mi>j</mi></mrow><msub><mi>ν</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></msubsup><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>ω</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><msub><mi>r</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></mrow></msup></mrow></semantics></math></inline-formula>. This work continues the exploration, begun in the first two papers in this series (on the helium atom and on ground and excited <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="normal">S</mi></semantics></math></inline-formula> states of Li II), of whether wave functions containing both linear and exponential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub></semantics></math></inline-formula> factors converge more rapidly than either one alone. In the present study, we examined not only 1<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>s</mi><mn>2</mn></msup></semantics></math></inline-formula> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>1</mn></msup><mi mathvariant="normal">S</mi></mrow></semantics></math></inline-formula> states but 1<i>s</i>2<i>p</i> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>1</mn></msup><mi mathvariant="normal">P</mi></mrow></semantics></math></inline-formula> states for the He I, Li II, Be III, C V and O VII members of the He isoelectronic sequence as well. All <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>1</mn></msup><mi mathvariant="normal">P</mi></mrow></semantics></math></inline-formula> energies except He I are better than previous results. The wave functions obtained were used to calculate oscillator strengths, including upper and lower bounds, for the He-sequence lowest (resonance) <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>1</mn></msup><mi mathvariant="normal">S</mi><mo>→</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>1</mn></msup><mi mathvariant="normal">P</mi></mrow></semantics></math></inline-formula> transition. Interpolation techniques were used to make a graphical study of the oscillator strength behavior along the isoelectronic sequence. Comparisons were made with previous experimental and theoretical results. The results of this study are oscillator strengths for the 1<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>s</mi><mn>2</mn></msup></semantics></math></inline-formula> <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mrow></mrow><mn>1</mn></msup><mi mathvariant="normal">S</mi><mo>→</mo></mrow></semantics></math></inline-formula> 1<i>s</i>2<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><msup><mspace width="4pt"></mspace><mn>1</mn></msup><mi mathvariant="normal">P</mi></mrow></semantics></math></inline-formula> He isoelectronic sequence with rigorous non-relativistic quantum mechanical upper and lower bounds of (0.001–0.003)% and probable precision ≤ 0.0000003, and were obtained by extending the previously developed E-Hy-CI formalism to include the calculation of transition moments (oscillator strengths).
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