Quadrupole strength in isobaric triplets

The dependence of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mi>E</a:mi> <a:mn>2</a:mn> </a:mrow> </a:math> matrix elements on isospin projection <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>T</b:mi> <b:mi>z</b:mi> </b:msub> </b:math> is linked to the conservation of the isospin symmetry. To study this conjecture, we calculated the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>B</c:mi> <c:mo>(</c:mo> <c:mi>E</c:mi> <c:mn>2</c:mn> <c:mo>:</c:mo> <c:msup> <c:mn>2</c:mn> <c:mo>+</c:mo> </c:msup> <c:mo>→</c:mo> <c:msup> <c:mn>0</c:mn> <c:mo>+</c:mo> </c:msup> <c:mo>)</c:mo> </c:mrow> </c:math> rates for the even-even <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>T</d:mi> <d:mo>=</d:mo> <d:mn>1</d:mn> </d:mrow> </d:math> mirror nuclei with 42 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mo>≤</e:mo> <e:mo> </e:mo> <e:mi>A</e:mi> <e:mo> </e:mo> <e:mo>≤</e:mo> </e:math> 98 within nuclear density functional theory, employing the generalized Bohr Hamiltonian, and carrying out angular momentum projection. We demonstrated that collective effects are crucial for describing experimental data near the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:mi>N</f:mi> <f:mo>=</f:mo> <f:mi>Z</f:mi> </f:mrow> </f:math> line without invoking explicit beyond-Coulomb isospin symmetry-breaking corrections. We also determined the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>B</g:mi> <g:mo>(</g:mo> <g:mi>E</g:mi> <g:mn>2</g:mn> <g:mo>↓</g:mo> <g:mo>)</g:mo> </g:mrow> </g:math> values for odd-odd <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:msub> <h:mi>T</h:mi> <h:mi>z</h:mi> </h:msub> <h:mo>=</h:mo> <h:mn>0</h:mn> </h:mrow> </h:math> nuclei <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mmultiscripts> <i:mi>Br</i:mi> <i:mprescripts/> <i:none/> <i:mn>70</i:mn> </i:mmultiscripts> </i:math> and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mmultiscripts> <j:mi mathvariant="normal">Y</j:mi> <j:mprescripts/> <j:none/> <j:mn>78</j:mn> </j:mmultiscripts> </j:math> in doubly blocked configurations. We discussed the requirements for accurately describing isobaric analog states and emphasized how current theoretical results should be interpreted within the study of isospin symmetry across isospin triplets.