<p>In this work, we study the <i>E</i>1 decay processes, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$^3P_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> <msub> <mi>P</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\rightarrow $</EquationSource> <EquationSource Format="MATHML"><math> <mo stretchy="false">→</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$^3S_1\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> <msub> <mi>S</mi> <mn>1</mn> </msub> <mi>γ</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$^3S_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> <msub> <mi>S</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\rightarrow $</EquationSource> <EquationSource Format="MATHML"><math> <mo stretchy="false">→</mo> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$^3P_1\gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> <msub> <mi>P</mi> <mn>1</mn> </msub> <mi>γ</mi> </mrow> </math></EquationSource> </InlineEquation>, in the framework of Bethe–Salpeter equation and calculate their decay widths. We have used algebraic forms of the Salpeter wave functions obtained through the analytic solutions of the mass spectral equations for the ground and excited states of <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$^3S_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> <msub> <mi>S</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$^3P_1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mmultiscripts> <mrow /> <mrow /> <mn>3</mn> </mmultiscripts> <msub> <mi>P</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation> equal mass charmonia in approximate harmonic oscillator basis to do analytic calculations of their decay widths. These decay widths have been compared with data and other models.</p>

Radiative E1 transitions between $^3P_1$ and $^3S_1$ charmonium states

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发表日期：

2025年12月11日

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Vaishali Guleria,
Eshete Gebrehana,
Shashank Bhatnagar

摘要

In this work, we study the E1 decay processes, $^3P_1$ $^{3} P_{1}$ $\rightarrow $ $\to$ $^3S_1\gamma $ $^{3} S_{1} γ$ and $^3S_1$ $^{3} S_{1}$ $\rightarrow $ $\to$ $^3P_1\gamma $ $^{3} P_{1} γ$ , in the framework of Bethe–Salpeter equation and calculate their decay widths. We have used algebraic forms of the Salpeter wave functions obtained through the analytic solutions of the mass spectral equations for the ground and excited states of $^3S_1$ $^{3} S_{1}$ and $^3P_1$ $^{3} P_{1}$ equal mass charmonia in approximate harmonic oscillator basis to do analytic calculations of their decay widths. These decay widths have been compared with data and other models.

Radiative E1 transitions between \(^3P_1\) and \(^3S_1\) charmonium states

摘要