Lifetimes of low-lying levels in $$^{158}$$Gd

Abstract The low-lying structure of the well-deformed nucleus $$^{158}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>158</mml:mn> </mml:mmultiscripts> </mml:math> Gd has been revisited to elucidate the nature of the low-lying states in $$^{158}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>158</mml:mn> </mml:mmultiscripts> </mml:math> Gd. Earlier ( p , t ) studies identified numerous 0 $$^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>+</mml:mo> </mml:mmultiscripts> </mml:math> states below 4.3 MeV, prompting questions about whether these states correspond to collective vibrations or shape coexistence. New and previously reported ( $$n,n^\prime \gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> ) measurements are combined, including $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> - $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> coincidences, excitation functions, and angular distributions, to extract lifetimes and transition probabilities for 44 excited states up to 2.7 MeV, including 32 previously unmeasured levels. Our results confirm or revise $$\gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>γ</mml:mi> </mml:math> -ray placements and provide detailed transition strengths, revealing both weakly collective and strongly enhanced B(E2) and B(E1) transition probabilities. In particular, a tentative 0 $$^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>+</mml:mo> </mml:mmultiscripts> </mml:math> state at 2437.8 keV exhibits a strong interband B(E2) transition, which may be a candidate for a possible two-phonon ( $$\beta \beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> ) excitation. Systematic comparisons with neighboring Gd isotopes, Hartree–Fock–Bogoliubov, and interacting-boson model predictions suggest that the first excited 0 $$^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>+</mml:mo> </mml:mmultiscripts> </mml:math> state in $$^{158}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>158</mml:mn> </mml:mmultiscripts> </mml:math> Gd is predicted to be a $$\beta $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> -vibration, although it is weakly collective. We also present results for lifetimes and transition probabilities for a number of negative parity states, including $$\hbox {K}^{\pi }=0^-,1^-,2^-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mtext>K</mml:mtext> <mml:mi>π</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:msup> <mml:mn>0</mml:mn> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>1</mml:mn> <mml:mo>-</mml:mo> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>2</mml:mn> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> sequences, perhaps providing insight into octupole collectivity and the interplay between quadrupole and octupole vibrations in deformed nuclei. The systematic presence of low-lying negative-parity bands and their interband transition strengths suggest that $$^{158}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts>