Shape coexistence and signature splitting in ${}_{}{}^{77}{}_{}{}^{}\mathrm{Br}$

High angular momentum states in ${}_{}{}^{77}{}_{}{}^{}\mathrm{Br}$ were populated via the ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}$${(}^{18}$O,α2n${)}^{77}$Br reaction at 65 MeV using the Florida State University (FSU) FN Tandem-LINAC accelerator. The Pitt-FSU array with 9 Compton-suppressed high purity Ge detectors was used to measure prompt γ-γ coincidences. Analysis of the coincidences led to an extension of the positive- and negative-parity bands to spins of (41/$2^{+}$) and (43/$2^{\mathrm{-}}$). Directional correlation of oriented nuclei ratios have been deduced where possible, and spin assignments made accordingly. A cranked-shell-model analysis shows that in the positive-parity band the ν${\mathit{g}}_{9/2}$ alignment occurs at the same frequency as in the neighboring isotopes, ${}_{}{}^{75,79}{}_{}{}^{}\mathrm{Br}$, but with a larger interaction strength. In the negative-parity bands the lower π${\mathit{g}}_{9/2}$ crossing also occurs at about the same frequency as in ${}_{}{}^{75}{}_{}{}^{}\mathrm{Br}$, but with a smaller interaction. The higher frequency ν${\mathit{g}}_{9/2}$ crossing is delayed in ${}_{}{}^{77}{}_{}{}^{}\mathrm{Br}$. Hartree-Fock-Bogolyubov cranking calculations predict considerable γ softness in ${}_{}{}^{77}{}_{}{}^{}\mathrm{Br}$, and particle-rotor model calculations support the interpretation of γ softness or variations in triaxiality within the bands.