Total absorption spectroscopy of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> decay of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Zr</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>101</mml:mn><mml:mo>,</mml:mo><mml:mn>102</mml:mn></mml:mrow></mml:mmultiscripts></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Tc</mml:mi><mml:mprescripts /><mml:none…

The $\ensuremath{\beta}$ decay of $^{101,102}\mathrm{Zr}$ and $^{109}\mathrm{Tc}$ was studied using the technique total absorption spectroscopy. experiment performed at National Superconducting Cyclotron Laboratory Summing NaI(Tl) (SuN) detector in first-ever application spectroscopy with a fast beam produced via projectile fragmentation. $\ensuremath{\beta}$-decay feeding intensity Gamow-Teller transition strength distributions were extracted for these three decays. compared to different quasiparticle random-phase approximation (QRPA) models based on mean-field potentials. A comparison calculations from one QRPA learn about ground-state shape parent nucleus. For $^{101}\mathrm{Zr}$ $^{102}\mathrm{Zr}$, assuming pure configuration (oblate or prolate) not able reproduce distributions. These results may indicate that some type mixture between oblate prolate shapes is necessary $^{109}\mathrm{Tc}$, suggests dominant configuration. other two are commonly used provide properties $r$-process network calculations. This work shows importance making comparisons experimental theoretical distributions, rather than just half-lives $\ensuremath{\beta}$-delayed neutron emission probabilities, as close path possible.