Band terminations and maximum spin values with up to 18 aligned particles (and holes) in the Z,N=50 to 82 shells

Observed rotational bands that terminate or appear to terminate at very high spin are analyzed within the configuration constrained cranked Nilsson-Strutinsky (unpaired CNS or CNSB with pairing) formalism. Spin values for the nuclei discussed reach or come close to the maximum spin that can be built within the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>Z</a:mi><a:mo>,</a:mo><a:mi>N</a:mi><a:mo>=</a:mo><a:mn>50</a:mn><a:mo>–</a:mo><a:mn>82</a:mn></a:mrow></a:math> shells. Configurations are distinguished not only by the number of particles in high-<b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>j</b:mi></b:math> and low-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>j</c:mi></c:math> shells within each <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi mathvariant="script">N</d:mi></d:math> shell but, in some cases, also by the number of particles in pseudospin partners like <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:msub><f:mi>d</f:mi><f:mrow><f:mn>5</f:mn><f:mo>/</f:mo><f:mn>2</f:mn></f:mrow></f:msub><f:msub><f:mi>g</f:mi><f:mrow><f:mn>7</f:mn><f:mo>/</f:mo><f:mn>2</f:mn></f:mrow></f:msub></f:mrow></f:math> and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:msub><g:mi>s</g:mi><g:mrow><g:mn>1</g:mn><g:mo>/</g:mo><g:mn>2</g:mn></g:mrow></g:msub><g:msub><g:mi>d</g:mi><g:mrow><g:mn>3</g:mn><g:mo>/</g:mo><g:mn>2</g:mn></g:mrow></g:msub></g:mrow></g:math>. Configurations in <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mmultiscripts><h:mi>Dy</h:mi><h:mprescripts/><h:none/><h:mn>156</h:mn></h:mmultiscripts></h:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mmultiscripts><i:mi>Hf</i:mi><i:mprescripts/><i:none/><i:mn>164</i:mn></i:mmultiscripts></i:math>, which terminate at <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi>I</j:mi><j:mo>≈</j:mo><j:mn>60</j:mn></j:mrow></j:math>, are well understood in terms of their occupation of open <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mi>j</k:mi></k:math> shells or groups of <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mi>j</l:mi></l:math> shells. The bands in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mmultiscripts><m:mi>Dy</m:mi><m:mprescripts/><m:none/><m:mn>156</m:mn></m:mmultiscripts></m:math> are tentatively observed up to termination while the bands in <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"><n:mmultiscripts><n:mi>Hf</n:mi><n:mprescripts/><n:none/><n:mn>164</n:mn></n:mmultiscripts></n:math> are still a few spin units away. These terminating states are built with up to 18 aligned particles or 18 <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mtext>particles</o:mtext><o:mo>+</o:mo><o:mtext>holes</o:mtext></o:math> outside a core. The core is built from nucleons in filled <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"><p:mi>j</p:mi></p:math> shells, which gives no contribution to the spin. Analysis of the high-spin bands in <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"><q:mmultiscripts><q:mi>Xe</q:mi><q:mprescripts/><q:none/><q:mrow><q:mn>125</q:mn><q:mo>,</q:mo><q:mn>126</q:mn></q:mrow></q:mmultiscripts></q:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"><r:mmultiscripts><r:mi>Ce</r:mi><r:mprescripts/><r:none/><r:mrow><r:mn>131</r:mn><r:mo>,</r:mo><r:mn>132</r:mn></r:mrow></r:mmultiscripts></r:math> suggests that bands in <s:math xmlns:s="http://www.w3.org/1998/Math/MathML"><s:mmultiscripts><s:mi>Xe</s:mi><s:mprescripts/><s:none/><s:mn>126</s:mn></s:mmultiscripts></s:math> and <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"><t:mmultiscripts><t:mi>Ce</t:mi><t:mprescripts/><t:none/><t:mn>132</t:mn></t:mmultiscripts></t:math> are observed to terminate at similar spin values, where terminating bands in <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"><u:mmultiscripts><u:mi>Xe</u:mi><u:mprescripts/><u:none/><u:mn>126</u:mn></u:mmultiscripts></u:math> are observed high above yrast. It is remarkable that the deformed mean field, plus single-particle configurations, is able to provide such a comprehensive description of known experimental levels in nuclei up to spin <v:math xmlns:v="http://www.w3.org/1998/Math/MathML"><v:mrow><v:mn>60</v:mn><v:mi>ℏ</v:mi></v:mrow></v:math> and beyond. It is also impressive that the model can relate alignments of single-particle spin vectors to changes in shape with the nuclear spin.