<p>Nuclear excitation by electron capture (NEEC) in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(^{229}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>229</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Th offers a potentially controllable route for manipulating nuclear-state populations. In this study, a systematic NEEC analysis is carried out for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(^{229}\text {Th}^{q+}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>229</mn> </mmultiscripts> <msup> <mtext>Th</mtext> <mrow> <mi>q</mi> <mo>+</mo> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> over the charge-state range <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(q=1^+\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>=</mo> <msup> <mn>1</mn> <mo>+</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>–<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(90^+\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>90</mn> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation>, explicitly resolving the roles of the electronic quantum numbers (<i>n</i>,&#xa0;<i>l</i>,&#xa0;<i>j</i>) and of the key observables resonance energy <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(E_\text {r}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>r</mtext> </msub> </math></EquationSource> </InlineEquation>, peak cross section <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>, resonance strength <i>S</i>, and total resonance width <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\Gamma _{\text {NEEC}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="normal">Γ</mi> <mtext>NEEC</mtext> </msub> </math></EquationSource> </InlineEquation>. Particular attention is paid to charge-state control of the isomeric state (IS, 8.36 eV) and the second-excited state (SE, 29.19 keV). The calculations reveal pronounced charge-state-dependent behavior. For the IS, the valid capture channels migrate toward higher <i>n</i> with increasing <i>q</i>, and the dominant principal quantum number follows <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(n \approx 1.241q + 3.178\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≈</mo> <mn>1.241</mn> <mi>q</mi> <mo>+</mo> <mn>3.178</mn> </mrow> </math></EquationSource> </InlineEquation> within the present model; meanwhile, Coulomb-enhanced electron–nucleus coupling partly compensates for the loss of available channels, keeping the total resonance strength nearly charge-state independent. For the SE, the excitation energy exceeds the binding energies of almost all relevant orbitals, so channel screening is weak and the total resonance strength increases monotonically with <i>q</i>. These results clarify how the ionic charge-state reshapes NEEC in <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(^{229}\text {Th}^{q+}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>229</mn> </mmultiscripts> <msup> <mtext>Th</mtext> <mrow> <mi>q</mi> <mo>+</mo> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> and provide a quantitative reference for future experiments, especially those aiming to populate the IS indirectly through the SE.</p>

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Charge-state regulation of nuclear excitation by electron capture in \(^{229}\)Th ions

  • Yang-Yang Xu,
  • Qiong Xiao,
  • Jun-Hao Cheng,
  • Wen-Yu Zhang,
  • Tong-Pu Yu

摘要

Nuclear excitation by electron capture (NEEC) in \(^{229}\) 229 Th offers a potentially controllable route for manipulating nuclear-state populations. In this study, a systematic NEEC analysis is carried out for \(^{229}\text {Th}^{q+}\) 229 Th q + over the charge-state range \(q=1^+\) q = 1 + \(90^+\) 90 + , explicitly resolving the roles of the electronic quantum numbers (nlj) and of the key observables resonance energy \(E_\text {r}\) E r , peak cross section \(\sigma \) σ , resonance strength S, and total resonance width \(\Gamma _{\text {NEEC}}\) Γ NEEC . Particular attention is paid to charge-state control of the isomeric state (IS, 8.36 eV) and the second-excited state (SE, 29.19 keV). The calculations reveal pronounced charge-state-dependent behavior. For the IS, the valid capture channels migrate toward higher n with increasing q, and the dominant principal quantum number follows \(n \approx 1.241q + 3.178\) n 1.241 q + 3.178 within the present model; meanwhile, Coulomb-enhanced electron–nucleus coupling partly compensates for the loss of available channels, keeping the total resonance strength nearly charge-state independent. For the SE, the excitation energy exceeds the binding energies of almost all relevant orbitals, so channel screening is weak and the total resonance strength increases monotonically with q. These results clarify how the ionic charge-state reshapes NEEC in \(^{229}\text {Th}^{q+}\) 229 Th q + and provide a quantitative reference for future experiments, especially those aiming to populate the IS indirectly through the SE.