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In recent years a number of correlation measurements in nuclear $\beta$ decay have been performed reaching a precision of the order of 1\% and below and it is expected that even higher precision will be reached in the near future. At these levels of precision higher-order corrections due to e.g. recoil terms induced by the strong interaction and radiative corrections cannot necessarily be neglected anymore when interpreting these results in terms of new physics or extracting a value for the $V_{ud}$ quark-mixing matrix element. We provide here an update of the $\mathcal{F} t$ values of the $T=1/2$ mirror $\beta$ decays as well as an overview of current experimental and theoretical knowledge of the most important recoil term, weak magnetism, for both the $T=1/2$ mirror $\beta$ transitions and a large set of $\beta$ decays in higher isospin multiplets. The matrix elements determining weak magnetism were calculated in the nuclear shell model and cross-checked against experimental data, showing overall good agreement. Additionally, we show that further insight can be obtained from properly deformed nuclear potentials, in particular for mirror $T=1/2$ decays.. The results provide new insights in the size of weak magnetism, extending the available information to $\beta$ transitions of nuclei with masses up to $A =$ 75. This provides important guidance for the planning and interpretation of ongoing and new precise correlation measurements in nuclear $\beta$ decay searching for new physics or to extract the $V_{ud}$ quark-mixing matrix element in mirror $\beta$ decays. This more detailed knowledge of weak magnetism can also be of interest for further theoretical work related to the reactor neutrino problem., Comment: 64 pages, 21 figures

A new value for the hyperfine magnetic field of copper impurities in iron is obtained by combining resonance frequencies from experiments involving {\beta}-NMR on oriented nuclei on 59-Cu, 69-Cu, and 71-Cu with magnetic moment values from collinear laser spectroscopy measurements on these isotopes. The resulting value, i.e., Bhf(CuFe) = -21.794(10) T, is in agreement with the value adopted until now but is an order of magnitude more precise. It is consistent with predictions from ab initio calculations. Comparing the hyperfine field values obtained for the individual isotopes, the hyperfine anomalies in Fe were determined to be 59{\Delta}69=0.15(9)% and 71{\Delta}69=0.07(11)%., Comment: 6 pages, 2 figures, 3 tables

The half-life of the $\alpha$ decaying nucleus $^{221}$Fr was determined in different environments, i.e. embedded in Si at 4 K, and embedded in Au at 4 K and about 20 mK. No differences in half-life for these different conditions were observed within 0.1%. Furthermore, we quote a new value for the absolute half-life of $^{221}$Fr of t$_{1/2}$ = 286.1(10) s, which is of comparable precision to the most precise value available in literature.

The $\beta$-asymmetry parameter $\widetilde{A}$ for the Gamow-Teller decay of $^{60}$Co was measured by polarizing the radioactive nuclei with the brute force low-temperature nuclear-orientation method. The $^{60}$Co activity was cooled down to milliKelvin temperatures in a $^3$He-$^4$He dilution refrigerator in an external 13 T magnetic field. The $\beta$ particles were observed by a 500 ${\mu}m$ thick Si PIN diode operating at a temperature of about 10 K in a magnetic field of 0.6 T. Extensive GEANT4 Monte-Carlo simulations were performed to gain control over the systematic effects. Our result, $\widetilde{A} = -1.014(12)_{stat}(16)_{syst}$, is in agreement with the Standard-Model value of $-0.987(9)$, which includes recoil-order corrections that were addressed for the first time for this isotope. Further, it enables limits to be placed on possible tensor-type charged weak currents as well as other physics beyond the Standard Model.

The beta asymmetry parameter A for the pure Gamow-Teller decay of 114In is reported. The low temperature nuclear orientation method was combined with a GEANT4 based simulation code allowing for the first time to address in detail the effects of scattering and of the magnetic field. The result, A = -0.994 +/- 0.010stat +/- 0.010syst, constitutes the most accurate value for the asymmetry parameter of a nuclear beta transition to date. The value is in agreement with the Standard Model prediction of A = -1 and provides new limits on tensor type charged weak currents., Comment: 11 pages, 2 figures; additional information was added on systematic effects, the magnetic field map and the calculation of the Qcos(theta) values