<p>Proton radioactivity, a rare quantum tunneling decay mode occurring in nuclei beyond the proton drip line, provides a sensitive probe of nuclear structure through its dependence on proton-decay energy, angular momentum, deformation, and spectroscopic overlaps. The present work aims to investigate the influence of nuclear structure effects such as shell closures, deformation, and pairing correlations on proton emission half-lives, and to provide reliable predictions for nuclei beyond current experimental limits using gradient boosting regressors as a supportive tool. The dataset includes all known proton emitters with measured proton-decay energies (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Q_{\text {p}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>Q</mi> <mtext>p</mtext> </msub> </math></EquationSource> </InlineEquation>), transferred angular momenta (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\ell \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> </InlineEquation>), spectroscopic factors (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(S_\text {p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mtext>p</mtext> </msub> </math></EquationSource> </InlineEquation>), and deformation parameters of parent and daughter nuclei. Physics-motivated descriptors encode barrier penetration trends (<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(Z_{\text {d}}/\sqrt{Q_{\text {p}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>Z</mi> <mtext>d</mtext> </msub> <mo stretchy="false">/</mo> <msqrt> <msub> <mi>Q</mi> <mtext>p</mtext> </msub> </msqrt> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\((Z_{\text {d}} Z_{\text {c}})/\sqrt{Q_{\text {p}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mo stretchy="false">(</mo> <msub> <mi>Z</mi> <mtext>d</mtext> </msub> <msub> <mi>Z</mi> <mtext>c</mtext> </msub> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> <msqrt> <msub> <mi>Q</mi> <mtext>p</mtext> </msub> </msqrt> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\ell (\ell +1)/\sqrt{Q_{\text {p}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ℓ</mi> <mrow> <mo stretchy="false">(</mo> <mi>ℓ</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">/</mo> <msqrt> <msub> <mi>Q</mi> <mtext>p</mtext> </msub> </msqrt> </mrow> </math></EquationSource> </InlineEquation>) together with shell effects, pairing correlations, isospin asymmetry, and deformation-driven barrier modifications. These inputs, rooted in the WKB barrier penetration framework and spectroscopic overlaps, ensure that the learned patterns reflect nuclear structure behavior rather than statistical artifacts. The calculated half-lives show close agreement with experimental data, demonstrating that the adopted approach reliably incorporates essential nuclear structure effects. Systematic trends clearly reflect the role of pairing correlations, which manifest in the odd-even staggering of half-lives, and the influence of shell closures, where enhanced stability leads to longer decay times. Variations with mass number also highlight the impact of quadrupole and higher order deformations, particularly in midshell regions where collective motion becomes significant. The effective spectroscopic factor extracted from the analysis trace experimental patterns and provide new evidence for configuration mixing, indicating the interplay between single-particle states and collective degrees of freedom. The predictions further suggest regions of rapid structural change, driven by shell evolution and shape coexistence, which may strongly affect decay probabilities. Extending the calculations to unexplored nuclei, we identify candidates near the drip lines whose half-lives fall in a measurable range, offering promising cases for future investigation at next-generation radioactive-ion beam facilities. Overall, the study establishes a quantitatively reliable and physically grounded approach for connecting proton emission systematics with underlying nuclear structure and for supporting the exploration of exotic nuclei far from stability.</p>

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Systematics of proton radioactivity half-lives using machine learning regression models

  • Nishu Jain,
  • Raj Kumar

摘要

Proton radioactivity, a rare quantum tunneling decay mode occurring in nuclei beyond the proton drip line, provides a sensitive probe of nuclear structure through its dependence on proton-decay energy, angular momentum, deformation, and spectroscopic overlaps. The present work aims to investigate the influence of nuclear structure effects such as shell closures, deformation, and pairing correlations on proton emission half-lives, and to provide reliable predictions for nuclei beyond current experimental limits using gradient boosting regressors as a supportive tool. The dataset includes all known proton emitters with measured proton-decay energies ( \(Q_{\text {p}}\) Q p ), transferred angular momenta ( \(\ell \) ), spectroscopic factors ( \(S_\text {p}\) S p ), and deformation parameters of parent and daughter nuclei. Physics-motivated descriptors encode barrier penetration trends ( \(Z_{\text {d}}/\sqrt{Q_{\text {p}}}\) Z d / Q p , \((Z_{\text {d}} Z_{\text {c}})/\sqrt{Q_{\text {p}}}\) ( Z d Z c ) / Q p , \(\ell (\ell +1)/\sqrt{Q_{\text {p}}}\) ( + 1 ) / Q p ) together with shell effects, pairing correlations, isospin asymmetry, and deformation-driven barrier modifications. These inputs, rooted in the WKB barrier penetration framework and spectroscopic overlaps, ensure that the learned patterns reflect nuclear structure behavior rather than statistical artifacts. The calculated half-lives show close agreement with experimental data, demonstrating that the adopted approach reliably incorporates essential nuclear structure effects. Systematic trends clearly reflect the role of pairing correlations, which manifest in the odd-even staggering of half-lives, and the influence of shell closures, where enhanced stability leads to longer decay times. Variations with mass number also highlight the impact of quadrupole and higher order deformations, particularly in midshell regions where collective motion becomes significant. The effective spectroscopic factor extracted from the analysis trace experimental patterns and provide new evidence for configuration mixing, indicating the interplay between single-particle states and collective degrees of freedom. The predictions further suggest regions of rapid structural change, driven by shell evolution and shape coexistence, which may strongly affect decay probabilities. Extending the calculations to unexplored nuclei, we identify candidates near the drip lines whose half-lives fall in a measurable range, offering promising cases for future investigation at next-generation radioactive-ion beam facilities. Overall, the study establishes a quantitatively reliable and physically grounded approach for connecting proton emission systematics with underlying nuclear structure and for supporting the exploration of exotic nuclei far from stability.