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- W2019622923 startingPage "2306" @default.
- W2019622923 abstract "We study the finite transformation of the O(2,1) group associated with hydrogenic radial functions, and with its aid we evaluate atomic integrals $ensuremath{int}{0}^{ensuremath{infty}}{R}_{mathrm{ml}}({a}_{m}r){R}_{nl}({a}_{n}r){r}^{ensuremath{-}1}{e}^{ensuremath{-}ikr}{r}^{2}mathrm{dr},$ $mathrm{Re}(ik+frac{1}{2}{a}_{m}+frac{1}{2}{a}_{n})>0,$ $ensuremath{int}{0}^{ensuremath{infty}}{[{R}_{nl}({a}_{n}r)]}^{2}{r}^{ensuremath{-}1}sin(mathrm{kr}){r}^{2}mathrm{dr},$ $ensuremath{int}{0}^{ensuremath{infty}}{[{R}_{nl}({a}_{n}r)]}^{2}{r}^{ensuremath{-}1}cos(mathrm{kr}){r}^{2}mathrm{dr},$ $ensuremath{int}{0}^{ensuremath{infty}}{R}_{mathrm{ml}}({a}_{m}r){R}_{nl}({a}_{n}r){r}^{2}mathrm{dr},$ $ensuremath{int}{0}^{ensuremath{infty}}{R}_{mathrm{ml}}({a}_{m}r)T{R}_{nl}({a}_{n}r){r}^{2}mathrm{dr},$ where the functions ${R}_{nl}({a}_{n}r)$ are the hydrogenic radial functions, and the operator $T$ represents the kinetic energy. The scale ${a}_{m}$ for each function can be chosen arbitrarily. Using some of these results, we obtain the two-particle radial integrals $ensuremath{int}{0}^{ensuremath{infty}}{[{R}_{n{l}_{1}}(a{r}_{1})]}^{2}{({r}_{1}{r}_{2})}^{ensuremath{-}1}ensuremath{delta}({r}_{1}ensuremath{-}{r}_{2}){[{R}_{n{l}_{2}}(a{r}_{2})]}^{2}{r}_{1}^{2}{r}_{2}^{2}d{r}_{1}d{r}_{2},$ $ensuremath{int}{0}^{ensuremath{infty}}{[{R}_{n{l}_{1}}(a{r}_{1})]}^{2}{({r}_{>})}^{ensuremath{-}1}{[{R}_{n{l}_{2}}(a{r}_{2})]}^{2}{r}_{1}^{2}{r}_{2}^{2}d{r}_{1}d{r}_{2}.$" @default.
- W2019622923 created "2016-06-24" @default.
- W2019622923 creator A5015180736 @default.
- W2019622923 date "1974-06-01" @default.
- W2019622923 modified "2023-09-24" @default.
- W2019622923 title "Atomic radial integrals and a use of O(2, 1) transformation" @default.
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- W2019622923 doi "https://doi.org/10.1103/physreva.9.2306" @default.
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