High precision measurement of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi>Tc</mml:mi><mml:mprescripts/><mml:none/><mml:mn>99</mml:mn></mml:mmultiscripts><mml:mspace width="0.16em"/><mml:mi>β</mml:

Highly precise measurements of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mmultiscripts><a:mi>Tc</a:mi><a:mprescripts/><a:none/><a:mn>99</a:mn></a:mmultiscripts><a:mspace width="4pt"/><a:mi>β</a:mi></a:math> spectrum were performed in two laboratories using metallic magnetic calorimeters. Independent sample preparations, evaluation methods, and analyses yielded consistent results and the spectrum could be measured down to less than <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>1</c:mn><c:mspace width="0.16em"/><c:mi mathvariant="normal">k</c:mi><c:mi mathvariant="normal">e</c:mi><c:mi mathvariant="normal">V</c:mi></c:mrow></c:math>. Consistent <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mi>β</h:mi></h:math> spectra were also obtained via cross evaluations of the experimental data sets. An additional independent measurement with silicon detectors in a <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mrow><i:mn>4</i:mn><i:mi>π</i:mi></i:mrow></i:math> configuration confirms the spectrum shape above <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mn>25</j:mn><j:mspace width="0.16em"/><j:mi mathvariant="normal">k</j:mi><j:mi mathvariant="normal">e</j:mi><j:mi mathvariant="normal">V</j:mi></j:mrow></j:math>. Detailed theoretical calculations were performed using the nuclear shell model and including atomic effects. The spectrum shape was found to be sensitive to the effective value of the axial-vector coupling constant. Combining measurements and predictions, we extracted <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"><o:mrow><o:msub><o:mi>Q</o:mi><o:mi>β</o:mi></o:msub><o:mo>=</o:mo><o:mn>295.82</o:mn><o:mrow><o:mo>(</o:mo><o:mn>16</o:mn><o:mo>)</o:mo></o:mrow><o:mspace width="0.16em"/><o:mi mathvariant="normal">k</o:mi><o:mi mathvariant="normal">e</o:mi><o:mi mathvariant="normal">V</o:mi></o:mrow></o:math>, <t:math xmlns:t="http://www.w3.org/1998/Math/MathML"><t:mrow><t:msubsup><t:mi>g</t:mi><t:mi>V</t:mi><t:mtext>eff</t:mtext></t:msubsup><t:mo>=</t:mo><t:mn>0.376</t:mn><t:mrow><t:mo>(</t:mo><t:mn>5</t:mn><t:mo>)</t:mo></t:mrow></t:mrow></t:math>, and <u:math xmlns:u="http://www.w3.org/1998/Math/MathML"><u:mrow><u:msubsup><u:mi>g</u:mi><u:mi>A</u:mi><u:mtext>eff</u:mtext></u:msubsup><u:mo>=</u:mo><u:mn>0.574</u:mn><u:mrow><u:mo>(</u:mo><u:mn>36</u:mn><u:mo>)</u:mo></u:mrow></u:mrow></u:math>, which seems to solve an inconsistency of the quenched coupling constants between first and higher forbidden nonunique transitions. Furthermore, we derived the mean energy of the <v:math xmlns:v="http://www.w3.org/1998/Math/MathML"><v:mi>β</v:mi></v:math> spectrum, <w:math xmlns:w="http://www.w3.org/1998/Math/MathML"><w:mrow><w:msub><w:mover><w:mi>E</w:mi><w:mo>¯</w:mo></w:mover><w:mi>β</w:mi></w:msub><w:mo>=</w:mo><w:mn>98.51</w:mn><w:mrow><w:mo>(</w:mo><w:mn>23</w:mn><w:mo>)</w:mo></w:mrow><w:mspace width="0.16em"/><w:mi mathvariant="normal">k</w:mi><w:mi mathvariant="normal">e</w:mi><w:mi mathvariant="normal">V</w:mi></w:mrow></w:math>, <bb:math xmlns:bb="http://www.w3.org/1998/Math/MathML"><bb:mrow><bb:mo form="prefix">log</bb:mo><bb:mi>f</bb:mi><bb:mo>=</bb:mo><bb:mo>−</bb:mo><bb:mn>0.47660</bb:mn><bb:mo>(</bb:mo><bb:mn>22</bb:mn><bb:mo>)</bb:mo></bb:mrow></bb:math>, and <db:math xmlns:db="http://www.w3.org/1998/Math/MathML"><db:mrow><db:mo form="prefix">log</db:mo><db:mi>f</db:mi><db:mi>t</db:mi><db:mo>=</db:mo><db:mn>12.3478</db:mn><db:mo>(</db:mo><db:mn>23</db:mn><db:mo>)</db:mo></db:mrow></db:math>. Published by the American Physical Society 2024