<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>z</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo>→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math>decays of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Ni</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>54</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">Fe</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>50</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">Cr</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>46</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">Ti</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>42</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>and comparison with mirror<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mmultiscripts><mml:mi mathvariant="normal">He</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:mmultiscripts><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:math>measurements

We have studied the $\ensuremath{\beta}$ decay of the ${T}_{z}=\ensuremath{-}1,{f}_{7/2}$ shell nuclei $^{54}\mathrm{Ni},^{50}\mathrm{Fe},^{46}\mathrm{Cr}$, and $^{42}\mathrm{Ti}$ produced in fragmentation reactions. The proton separation energies in the daughter ${T}_{z}=0$ nuclei are relatively large $(\ensuremath{\approx}4$--5 MeV) so studies of the $\ensuremath{\gamma}$ rays are essential. The experiments were performed at GSI as part of the Stopped-beam campaign with the RISING setup consisting of 15 Euroball Cluster Ge detectors. From the newly obtained high precision $\ensuremath{\beta}$-decay half-lives, excitation energies, and $\ensuremath{\beta}$ branching ratios, we were able to extract Fermi and Gamow-Teller transition strengths in these $\ensuremath{\beta}$ decays. With these improved results it was possible to compare in detail the Gamow-Teller (GT) transition strengths observed in beta decay including a sensitivity limit with the strengths of the ${T}_{z}=+1$ to ${T}_{z}=0$ transitions derived from high resolution $({}^{3}\mathrm{He},t)$ reactions on the mirror target nuclei at RCNP, Osaka. The accumulated $B$(GT) strength obtained from both experiments looks very similar although the charge exchange reaction provides information on a broader energy range. Using the ``merged analysis'' one can obtain a full picture of the $B$(GT) over the full ${Q}_{\ensuremath{\beta}}$ range. Looking at the individual transitions some differences are observed, especially for the weak transitions. Their possible origins are discussed.

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