High-spin lifetime measurements in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>=</mml:mo><mml:mi>Z</mml:mi></mml:mrow></mml:math>nucleus<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Kr</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>72</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>

High-spin states in the $N=Z$ nucleus $^{72}\mathrm{Kr}$ have been populated in the $^{40}\mathrm{Ca}$($^{40}\mathrm{Ca}$, 2\ensuremath{\alpha})$^{72}\mathrm{Kr}$ fusion-evaporation reaction at a beam energy of 165 MeV using the Gammasphere array for \ensuremath{\gamma}-ray detection coupled to the Microball array for charged particle detection. The previously observed bands in $^{72}\mathrm{Kr}$ were extended to an excitation energy of \ensuremath{\sim}24 MeV and angular momentum of 30\ensuremath{\hbar}. Using the Doppler shift attenuation method the lifetimes of high-spin states were measured for the first time. Excellent agreement between the results of calculations within the isovector mean field theory and experiment is observed both for rotational and deformation properties. No enhancement of quadrupole deformation expected in the presence of isoscalar $t=0$ $\mathit{np}$ pairing is observed. Current data do not show any evidence for the existence of the isoscalar $\mathit{np}$ pairing.

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