Structural evolution of octupole-deformed radium isotopes within a coupled-channels method

We have systematically investigated the spectroscopic properties in even-even <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mmultiscripts> <a:mi>Ra</a:mi> <a:mprescripts/> <a:none/> <a:mrow> <a:mn>222</a:mn> <a:mo>−</a:mo> <a:mn>228</a:mn> </a:mrow> </a:mmultiscripts> </a:math> by introducing the cluster degrees of freedom within the coupled-channels method, which allows the core <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mmultiscripts> <b:mi>Pb</b:mi> <b:mprescripts/> <b:none/> <b:mn>208</b:mn> </b:mmultiscripts> </b:math> to occupy the octupole <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msup> <c:mn>3</c:mn> <c:mo>−</c:mo> </c:msup> </c:math> state (Calc. I), as well as both the octupole <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msup> <d:mn>3</d:mn> <d:mo>−</d:mo> </d:msup> </d:math> and quadrupole <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msup> <e:mn>2</e:mn> <e:mo>+</e:mo> </e:msup> </e:math> states (Calc. II), along with multipole interactions. Excellent agreement has been achieved between our calculated results and available data on energy spectra, reduced electromagnetic <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>E</f:mi> <f:mi>λ</f:mi> </f:mrow> </f:math> transition-matrix elements, and intrinsic electric dipole, quadrupole, and octupole <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:msub> <g:mi>Q</g:mi> <g:mi>λ</g:mi> </g:msub> </g:math> moments, pointing to the existence of strong octupole correlations in this region. The description of parity-doublet bands and electromagnetic-transition properties in both calculations is consistent with each other and with experimental data, which confirms the reliability of the coupled-channels formalism based on the cluster-core configuration in heavy nuclei. The enhanced <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>E</h:mi> <h:mn>2</h:mn> </h:mrow> </h:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mrow> <i:mi>E</i:mi> <i:mn>3</i:mn> </i:mrow> </i:math> matrix elements in both calculations for <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mmultiscripts> <j:mi>Ra</j:mi> <j:mprescripts/> <j:none/> <j:mrow> <j:mn>222</j:mn> <j:mo>−</j:mo> <j:mn>226</j:mn> </j:mrow> </j:mmultiscripts> </j:math> suggest that these three nuclei can exhibit static octupole deformation in both positive- and negative-parity bands. On the other hand, the accurate reproduction of the higher negative-parity bandhead and the derived <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:msub> <k:mi>Q</k:mi> <k:mn>3</k:mn> </k:msub> </k:math> moments in nucleus <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mmultiscripts> <l:mi>Ra</l:mi> <l:mprescripts/> <l:none/> <l:mn>228</l:mn> </l:mmultiscripts> </l:math> is consistent with the interpretation of this nucleus as a deformed rotor exhibiting dynamic/soft octupole vibrations. We hope that the present work may open new avenues for exploring octupole collectivity and cluster correlations in heavy nuclei.