Search for a shape isomer in $$^{233}$$Th

Abstract A search for a shape isomer in $$^{233}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>233</mml:mn> </mml:mmultiscripts> </mml:math> Th via delayed $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> decay was performed using the Heidelberg–Darmstadt Crystal Ball spectrometer together with a $$\varDelta E$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:mi>E</mml:mi> </mml:mrow> </mml:math> – E telescope for light charged particle identification. Excited states in $$^{233}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>233</mml:mn> </mml:mmultiscripts> </mml:math> Th were populated through the $$^{232}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>232</mml:mn> </mml:mmultiscripts> </mml:math> Th( d , p ) reaction. The search for isomeric $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> decay was based on a total-energy reconstruction method: prompt energy deficits $$E_{\textrm{Miss}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mtext>Miss</mml:mtext> </mml:msub> </mml:math> indicated possible long-lived isomeric states. Corresponding delayed summed energies $$E^{\textrm{Sum}}_{\textrm{del}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>E</mml:mi> <mml:mtext>del</mml:mtext> <mml:mtext>Sum</mml:mtext> </mml:msubsup> </mml:math> were recorded with the Crystal Ball. A two-dimensional analysis of $$E_{\textrm{Miss}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mtext>Miss</mml:mtext> </mml:msub> </mml:math> versus $$E^{\textrm{Sum}}_{\textrm{del}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>E</mml:mi> <mml:mtext>del</mml:mtext> <mml:mtext>Sum</mml:mtext> </mml:msubsup> </mml:math> was carried out for various prompt and delayed multiplicities and for delayed time intervals up to 200 ns within the excitation-energy range $$E^{x} = 3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>E</mml:mi> <mml:mi>x</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> –7 MeV. No evidence of isomeric $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> decay was observed. The branching ratio for the population of a potential shape isomer in the second minimum of $$^{233}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>233</mml:mn> </mml:mmultiscripts> </mml:math> Th relative to the first minimum is constrained to $$ &lt; 10^{-6}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>&lt;</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> , for isomeric states with energies $$E^{x} = 2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>E</mml:mi> <mml:mi>x</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> <