<p>The decay properties of Hassium isotopes are examined through a detailed analysis of their half-lives for various decay modes, including <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-decay, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta ^{-}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>β</mi> <mo>-</mo> </msup> </math></EquationSource> </InlineEquation>-decay, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq3.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta ^{+}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>β</mi> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation>-decay, and spontaneous fission. <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-decay half-lives are calculated using the Unified Fission Model with a Woods–Saxon potential, while analytical formulas are employed for <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-decay and spontaneous fission. A preliminary comparison of four mass models (LDM, DZ28, WS4, FRDM), enhanced via machine learning techniques, identifies the improved WS4 model as the most accurate for predicting <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-decay Q-values. Using this model, the competition between decay modes in Hassium isotopes is systematically investigated. Results reveal that <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq3.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta ^{+}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>β</mi> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq2.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta ^{-}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>β</mi> <mo>-</mo> </msup> </math></EquationSource> </InlineEquation> decays are far less competitive compared to <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-decay and spontaneous fission, both of which exhibit significantly shorter half-lives. Neutron-deficient and neutron-rich isotopes are found to predominantly undergo spontaneous fission, whereas intermediate isotopes (<InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq10.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{259}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>259</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Hs and <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq11.gif" Format="GIF" Height="11" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{261-275}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mrow> <mn>261</mn> <mo>-</mo> <mn>275</mn> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>Hs) primarily decay via <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-emission. Notably, the possibility of <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq3.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta ^{+}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>β</mi> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation>-decay is identified around <InlineEquation ID="IEq14"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3647_Article_IEq14.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(^{269}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mrow /> <mn>269</mn> </mmultiscripts> </math></EquationSource> </InlineEquation>Hs. A total of 16 decay chains have been constructed, along with their associated decay modes and half-lives. The predicted decay modes exhibit strong agreement with available experimental observations, thereby reinforcing confidence in the reliability of the calculated decay chains that have not yet been experimentally confirmed.</p>

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Radioactive decay investigation of Hassium isotopes

  • R. Belhaddouf,
  • M. R. Oudih,
  • M. Fellah,
  • N. H. Allal

摘要

The decay properties of Hassium isotopes are examined through a detailed analysis of their half-lives for various decay modes, including \(\alpha\) α -decay, \(\beta ^{-}\) β - -decay, \(\beta ^{+}\) β + -decay, and spontaneous fission. \(\alpha\) α -decay half-lives are calculated using the Unified Fission Model with a Woods–Saxon potential, while analytical formulas are employed for \(\beta\) β -decay and spontaneous fission. A preliminary comparison of four mass models (LDM, DZ28, WS4, FRDM), enhanced via machine learning techniques, identifies the improved WS4 model as the most accurate for predicting \(\alpha\) α -decay Q-values. Using this model, the competition between decay modes in Hassium isotopes is systematically investigated. Results reveal that \(\beta ^{+}\) β + and \(\beta ^{-}\) β - decays are far less competitive compared to \(\alpha\) α -decay and spontaneous fission, both of which exhibit significantly shorter half-lives. Neutron-deficient and neutron-rich isotopes are found to predominantly undergo spontaneous fission, whereas intermediate isotopes ( \(^{259}\) 259 Hs and \(^{261-275}\) 261 - 275 Hs) primarily decay via \(\alpha\) α -emission. Notably, the possibility of \(\beta ^{+}\) β + -decay is identified around \(^{269}\) 269 Hs. A total of 16 decay chains have been constructed, along with their associated decay modes and half-lives. The predicted decay modes exhibit strong agreement with available experimental observations, thereby reinforcing confidence in the reliability of the calculated decay chains that have not yet been experimentally confirmed.