Spectroscopy of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>3</mml:mn><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mn>5</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">Si</mml:mi></mml:math>by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>decay:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi><mml:mi>d</mml:mi><mml:mo>−</mml:mo><mml:mi>f</mml:mi><mml:mi>p</mml:mi></mml:math>shell gap and single-particle states

The ${}^{34,35}\mathrm{Al}$ $\ensuremath{\beta}$ decays have been studied at the CERN online mass separator ISOLDE by \ensuremath{\beta}-\ensuremath{\gamma}, \ensuremath{\beta}-\ensuremath{\gamma}-\ensuremath{\gamma}, and $\ensuremath{\beta}\ensuremath{-}n\ensuremath{-}\ensuremath{\gamma}$ measurements in order to corroborate the low-level description of ${}^{34}\mathrm{Si}$ and to obtain the first information on the level structure of the $N=21$ isotope ${}^{35}\mathrm{Si}.$ Earlier observed $\ensuremath{\gamma}$ lines in ${}^{34}\mathrm{Al}$ decay were confirmed and new $\ensuremath{\gamma}$ transitions following both $\ensuremath{\beta}$ decay and $\ensuremath{\beta}\ensuremath{-}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{d}$ neutron emission have been established. The first level scheme of ${}^{35}\mathrm{Si}$ includes three excited states at 910, 974, and 2168 keV. Indication is found for ${J}^{\ensuremath{\pi}}{=(3/2)}^{\ensuremath{-}}$ and ${(3/2)}^{+}$ for the first two excited states, respectively. Beta-decay half-life of ${T}_{1/2}=38.6(4) \mathrm{ms}$ and $\ensuremath{\beta}\ensuremath{-}\mathrm{d}\mathrm{e}\mathrm{l}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{d}$ neutron branching value ${P}_{n}=41(13)%$ were measured unambiguously. The significance of the single-particle energy determination at $N=21,$ $Z=14$ for assessing the effective interaction in $\mathrm{sd}\ensuremath{-}\mathrm{fp}$ shell-model calculations is discussed and illustrated by predictions for different neutron-rich isotopes.