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<p>We investigate the multipole polarizabilities of negatively charged helium-like ions interacting with exponential-cosine-screened Coulomb potentials using correlated exponential wave functions. The dynamic dipole and quadrupole polarizabilities of negatively charged helium-like ions <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="601_2025_1980_Article_IEq1.gif" Format="GIF" Height="8" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{\mathrm {\infty }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mi>∞</mi> </mmultiscripts> </math></EquationSource> </InlineEquation>H<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="601_2025_1980_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{\mathrm {-}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>-</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="601_2025_1980_Article_IEq3.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{\textrm{1}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mtext>1</mtext> </mmultiscripts> </math></EquationSource> </InlineEquation>H<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="601_2025_1980_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{\mathrm {-}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>-</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>, D<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="601_2025_1980_Article_IEq5.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{\mathrm {-}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>-</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>, T<InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="601_2025_1980_Article_IEq6.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{\mathrm {-}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>-</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>, Mu<InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="601_2025_1980_Article_IEq7.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{\mathrm {-}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>-</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>, Pi<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="601_2025_1980_Article_IEq8.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{\mathrm {- }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mo>-</mo> </mmultiscripts> </math></EquationSource> </InlineEquation>are presented as functions of screening parameter. The static dipole and quadrupole polarizabilities, and the ground state energies are presented in terms of nuclear mass and screening parameter.</p>

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Polarizabilities of Negatively Charged Helium-Like Ions with Exponential-Cosine-Screened Coulomb Potentials

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Yu-Qi Yang,
  • Zishi Jiang,
  • Bing-Kuan Lyu,
  • Sabyasachi Kar

摘要

We investigate the multipole polarizabilities of negatively charged helium-like ions interacting with exponential-cosine-screened Coulomb potentials using correlated exponential wave functions. The dynamic dipole and quadrupole polarizabilities of negatively charged helium-like ions \(^{\mathrm {\infty }}\) ∞ H \(^{\mathrm {-}}\) - , \(^{\textrm{1}}\) 1 H \(^{\mathrm {-}}\) - , D \(^{\mathrm {-}}\) - , T \(^{\mathrm {-}}\) - , Mu \(^{\mathrm {-}}\) - , Pi \(^{\mathrm {- }}\) - are presented as functions of screening parameter. The static dipole and quadrupole polarizabilities, and the ground state energies are presented in terms of nuclear mass and screening parameter.