Theoretical evaluation of decay mode of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>Th</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mrow> <mml:mn>229</mml:mn> <mml:mi>m</mml:mi> </mml:mrow> </mml:mmultiscript

The excitation energy of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mmultiscripts> <a:mi>Th</a:mi> <a:mprescripts/> <a:none/> <a:mrow> <a:mn>229</a:mn> <a:mi>m</a:mi> </a:mrow> </a:mmultiscripts> </a:math> is extremely low at <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>8.4</b:mn> <b:mspace width="0.28em"/> <b:mi>eV</b:mi> </b:mrow> </b:math> ; thus, this isotope exhibits changes in its decay modes depending on the chemical state, specifically the outermost electronic states. However, the reported half-lives of the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mi>γ</d:mi> </d:math> -ray transition are not consistent among the previous experiments. In this study, we investigate the chemical states of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mmultiscripts> <e:mi>Th</e:mi> <e:mprescripts/> <e:none/> <e:mrow> <e:mn>229</e:mn> <e:mi>m</e:mi> </e:mrow> </e:mmultiscripts> </e:math> by density functional theory calculations. Based on these results, we evaluate the relationship between the experimental half-life of each sample and the electronic state of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>Th</f:mi> </f:math> . The calculation results indicate that ion trap method, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msub> <g:mi>CaF</g:mi> <g:mn>2</g:mn> </g:msub> </g:mrow> </g:math> model, and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:msub> <h:mi>MgF</h:mi> <h:mn>2</h:mn> </h:msub> </h:mrow> </h:math> one decay only via the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi>γ</i:mi> </i:math> -ray transition, whereas <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:msub> <j:mi>LiSrAlF</j:mi> <j:mn>6</j:mn> </j:msub> </j:mrow> </j:math> one decays via the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mi>γ</k:mi> </k:math> -ray transition and has a possibility of decay via internal conversion and electron bridge.