<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mi>He</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mmultiscripts> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> </mml:mro

Resonances in $^{7}\mathrm{Be}$ which decay into the $^{3}\mathrm{He}+\ensuremath{\alpha}$ exit channel have been measured with improved precision using preexisting data sets. The energy and width of the ${J}^{\ensuremath{\pi}}=7/{2}^{\ensuremath{-}}$ state have been extracted from an invariant-mass study of projectile-breakup products originating from interactions of an $E/A=10.7\ensuremath{-}\mathrm{MeV}^{10}\mathrm{C}$ beam on Be and C targets. The excitation energy of this state (from the pole of the $S$ matrix) is determined to be ${E}^{*}=4.545(6)$ MeV, a factor of 8 improvement in precision as compared to the ENSDF value. This improvement is enabled by fine tuning the detector calibrations using calibration resonances in $^{6}\mathrm{Li}, ^{7}\mathrm{Li}, ^{6}\mathrm{Be}, ^{9}\mathrm{B}$, and $^{12}\mathrm{C}$ whose decay energies are known to high precision. The ${J}^{\ensuremath{\pi}}=7/{2}^{\ensuremath{-}}$ resonance in $^{7}\mathrm{Be}$ can now itself be used as a calibration resonance in invariant-mass experiments. This utility is particularly helpful for $^{3}\mathrm{He}$ energy calibrations of CsI(Tl) detectors which are often used in detector arrays employed for measurements with fast beams. This utility is demonstrated with a data set associated with $E/A=70$-MeV $^{7}\mathrm{Be}$ beams which are inelastically excited to the $7/{2}^{\ensuremath{-}}$ and $5/{2}_{1}^{\ensuremath{-}}$ resonances. Again using the pole of the $S$ matrix as the definition of the resonance parameters, the fitted excitation energy of the $5/{2}_{1}^{\ensuremath{-}}$ resonance is 6.376(17) MeV, approximately 300 keV lower than the ENSDF value. Its width of 565(4) keV is roughly half of the ENSDF value.