<p>High multipole electromagnetic transitions are rare in nature. The highest-multipole transition observed in atomic nuclei is the electric hexacontatetrapole <i>E</i>6 transition from the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1812_Article_IEq1.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="100" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_{1/2}=2.54(2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>T</mi> <mrow> <mn>1</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mn>2.54</mn> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-min <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1812_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="85" /> </InlineMediaObject> <EquationSource Format="TEX">\(J^\pi =19/2^-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>J</mi> <mi>π</mi> </msup> <mo>=</mo> <mn>19</mn> <mo stretchy="false">/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> isomer to the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1812_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(7/2^-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>7</mn> <mo stretchy="false">/</mo> <msup> <mn>2</mn> <mo>-</mo> </msup> </mrow> </math></EquationSource> </InlineEquation> ground state in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1812_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{53}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>53</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Fe with an angular momentum change of six units. In the present work, we performed ab initio calculations for this unique case by employing chiral effective field theory (EFT) forces. The in-medium similarity renormalization group is used to derive the valence-space effective Hamiltonian and multipolar transition operators. Bare nucleon charges were used in all the multipolar transition rate calculations, providing good agreement with the experimental data. The valence space takes the full <i>fp</i> shell. In <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1812_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{53}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>53</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Fe, the low-lying states were dominated by the <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1812_Article_IEq6.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="35" /> </InlineMediaObject> <EquationSource Format="TEX">\(0f_{7/2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <msub> <mi>f</mi> <mrow> <mn>7</mn> <mo stretchy="false">/</mo> <mn>2</mn> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation> component. Two different versions of the chiral EFT two- plus three-nucleon interaction were used to test the dependence on the interaction used. We also tested the convergence of the transition rate calculations against the harmonic oscillator parameter <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1812_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(\hbar \Omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ħ</mi> <mi mathvariant="normal">Ω</mi> </mrow> </math></EquationSource> </InlineEquation> and basis truncations <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1812_Article_IEq8.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(e_{\text {max}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>e</mi> <mtext>max</mtext> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41365_2025_1812_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(E_{\text {3max}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mtext>3max</mtext> </msub> </math></EquationSource> </InlineEquation> for two- and three-nucleon forces, respectively.</p>

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Ab initio calculations of the highest-multipole electromagnetic transition ever observed in nuclei

  • Si-Qin Fan,
  • Qi Yuan,
  • Fu-Rong Xu,
  • Philip Malzard Walker

摘要

High multipole electromagnetic transitions are rare in nature. The highest-multipole transition observed in atomic nuclei is the electric hexacontatetrapole E6 transition from the \(T_{1/2}=2.54(2)\) T 1 / 2 = 2.54 ( 2 ) -min \(J^\pi =19/2^-\) J π = 19 / 2 - isomer to the \(7/2^-\) 7 / 2 - ground state in \(^{53}\) 53 Fe with an angular momentum change of six units. In the present work, we performed ab initio calculations for this unique case by employing chiral effective field theory (EFT) forces. The in-medium similarity renormalization group is used to derive the valence-space effective Hamiltonian and multipolar transition operators. Bare nucleon charges were used in all the multipolar transition rate calculations, providing good agreement with the experimental data. The valence space takes the full fp shell. In \(^{53}\) 53 Fe, the low-lying states were dominated by the \(0f_{7/2}\) 0 f 7 / 2 component. Two different versions of the chiral EFT two- plus three-nucleon interaction were used to test the dependence on the interaction used. We also tested the convergence of the transition rate calculations against the harmonic oscillator parameter \(\hbar \Omega \) ħ Ω and basis truncations \(e_{\text {max}}\) e max and \(E_{\text {3max}}\) E 3max for two- and three-nucleon forces, respectively.