Experimental evidence of exact E(5) symmetry in Kr82

Abstract

The low-lying positive-parity structures of $^{82}\mathrm{Kr}$ have been investigated following their population in the $^{76}\mathrm{Ge}(^{9}\mathrm{Be},3n)$ reaction at ${\mathrm{E}}_{\mathrm{lab}}\ensuremath{\approx}31\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and using a large array of Compton suppressed HPGe clovers as the detection setup. Apart from other spectroscopic measurements, level lifetimes of the states have been extracted using the Doppler shift attenuation method. The level energies and the associated transition probabilities exhibit superlative overlap with the calculations in the framework of the interaction boson approximation and the E(5) model. The $^{82}\mathrm{Kr}$ nucleus, thus, exemplifies the critical point of phase (shape) transition from the U(5) (spherical vibrator) to the O(6) ($\ensuremath{\gamma}$-soft rotor) paradigms of nuclear structure.