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Pseudo spin doublet bands and Gallagher Moszkowski doublet bands in $^{100}$Y

New transitions in neutron rich $^{100}$Y have been identified in a $^9$Be+$^{238}$U experiment with mass- and Z- gates to provide full fragment identification. These transitions and high spin levels of $^{100}$Y have been investigated by analyzing the high statistics $γ$-$γ$-$γ$ and $γ$-$γ$-$γ$-$γ$ coincidence data from the spontaneous fission of $^{252}$Cf at the Gammasphere detector array. Two new bands, 14 new levels and 23 new transitions have been identified. The $K^π=4^+$ new band decaying to an 1s isomeric state is assigned to be the high-$K$ Gallagher-Moszkowski (GM) partner of the known $K^π=1^+$ band, with the $π5/2[522] \otimes ν3/2[411]$ configuration. This 4$^+$ band is also proposed to be the pseudo spin partner of the new $K^π=5^+$ band with a 5$^{+}$ $π5/2[422] \otimes ν5/2[413]$ configuration, to form a $π5/2[422] \otimes ν[312$ $5/2,3/2]$ neutron pseudospin doublet. Constrained triaxial covariant density functional theory and quantal particle rotor model calculations have been applied to interpret the band structure and available electromagnetic transition probabilities and are found in good agreement with experimental values.