Competing shape evolution, crossing configurations, and single particle levels in nuclei

The evolution of shape in the even-even zirconium (Zr) isotopes has been the subject of study for many years. However, the odd-mass isotopes have not been investigated as extensively due to limited experimental accessibility and computational challenges. This work, employing the interacting boson-fermion model with configuration mixing, examines the effect of rapid shape evolution and normal-intruder configuration crossing, both identified as quantum phase transitions, alongside evolution in single particle energies, on the positive-parity spectrum of odd-mass <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msup><a:mrow/><a:mrow><a:mn>93</a:mn><a:mtext>--</a:mtext><a:mn>103</a:mn></a:mrow></a:msup><a:mi>Zr</a:mi></a:mrow></a:math> isotopes. Calculated energy levels, magnetic moments, <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>B</b:mi><b:mo>(</b:mo><b:mi>E</b:mi><b:mn>2</b:mn><b:mo>)</b:mo></b:mrow></b:math> values, and quadrupole moments are compared to experimental data, showing good agreement. This agreement emphasizes the unique role of the odd neutron in the data. The special case of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mmultiscripts><c:mi mathvariant="normal">Zr</c:mi><c:mprescripts/><c:none/><c:mn>99</c:mn></c:mmultiscripts></c:mrow></c:math>, which lies near the critical point of both quantum phase transitions, is also addressed, offering a new interpretation of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mn>7</e:mn><e:mo>/</e:mo><e:msubsup><e:mn>2</e:mn><e:mn>1</e:mn><e:mo>+</e:mo></e:msubsup></e:mrow></e:math> isomeric state and the occurrence of the type II shell evolution, in light of recent debates.