Accurate Masses and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>-Decay Schemes for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">P</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>34</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Si</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>33</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

By using delayed $\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}$ coincidence techniques, the mass excesses of $^{34}\mathrm{P}$ and $^{33}\mathrm{Si}$ have been measured to be -24 546 \ifmmode\pm\else\textpm\fi{} 45 and -20 569 \ifmmode\pm\else\textpm\fi{} 50 keV, respectively, representing improvements in precision of a factor of 2 for $^{34}\mathrm{P}$ and a factor of 4 for $^{33}\mathrm{Si}$ over previous measurements. The first measurements of the high-energy $\ensuremath{\gamma}$ rays from $^{34}\mathrm{P}$ decay with a Ge(Li) detector are presented, revealing three new $\ensuremath{\beta}$ branches. $\ensuremath{\gamma}$-ray energies (in keV) and relative intensities for the $^{34}\mathrm{S}$ daughter transitions are 1787 \ifmmode\pm\else\textpm\fi{} 1 (0.30 \ifmmode\pm\else\textpm\fi{} 0.10), 1947.1 \ifmmode\pm\else\textpm\fi{} 1.5 (0.28 \ifmmode\pm\else\textpm\fi{} 0.10), 1987.2 \ifmmode\pm\else\textpm\fi{} 1.0 (1.0 \ifmmode\pm\else\textpm\fi{} 0.2), 2127.4 (100.0 \ifmmode\pm\else\textpm\fi{} 0.3), 4073.4 \ifmmode\pm\else\textpm\fi{} 1.5 (0.46 \ifmmode\pm\else\textpm\fi{} 0.06), and 4114.0 \ifmmode\pm\else\textpm\fi{} 1.5 (1.2 \ifmmode\pm\else\textpm\fi{} 0.2). The $^{34}\mathrm{S}$ excitation energies and relative $\ensuremath{\beta}$ branches are 2127.4 (100 \ifmmode\pm\else\textpm\fi{} 0.3), 3303.7 (0.26), 3914.2 (0.30 \ifmmode\pm\else\textpm\fi{} 0.10), 4073.0 (0.76 \ifmmode\pm\else\textpm\fi{} 0.12), and 4114.5 (2.2 \ifmmode\pm\else\textpm\fi{} 0.3). For the decay of $^{33}\mathrm{Si}$, energies and relative intensities of $\ensuremath{\gamma}$ rays were measured to be 415.8 \ifmmode\pm\else\textpm\fi{} 0.6 (6.7 \ifmmode\pm\else\textpm\fi{} 0.6), 1431.4 (13.1 \ifmmode\pm\else\textpm\fi{} 1.0), 1847.5 (100 \ifmmode\pm\else\textpm\fi{} 1), and 2537.5 (9.3 \ifmmode\pm\else\textpm\fi{} 0.8), representing excitation energies and relative $\ensuremath{\beta}$-ray intensities to the $^{33}\mathrm{P}$ daughter states of 1431.4 (${5.1}_{\ensuremath{-}2.4}^{+1.0}$), 1847.5 (${100}_{\ensuremath{-}2.8}^{+1.0}$), and 2537.6 (10.5 \ifmmode\pm\else\textpm\fi{} 1.0). The half-lives of $^{34}\mathrm{P}$ and $^{33}\mathrm{Si}$ were determined by multiscaling $\ensuremath{\gamma}$-ray yields to be 12.45 \ifmmode\pm\else\textpm\fi{} 0.10 and 6.11 \ifmmode\pm\else\textpm\fi{} 0.21 sec, respectively. Combined with an earlier result, a half-life of 6.18 \ifmmode\pm\else\textpm\fi{} 0.18 sec is adopted for $^{33}\mathrm{Si}$. The transverse mass relationship of Garvey, using the present measurements for $^{34}\mathrm{P}$ and $^{33}\mathrm{Si}$, predicts a mass excess of -20 251 \ifmmode\pm\else\textpm\fi{} 90 keV for the ${T}_{z}=3$ nuclide $^{34}\mathrm{Si}$.

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