Effects of high-$j$ orbitals, pairing and deformed neutron shells on upbendings of ground-state bands in neutron-rich even-even isotopes $^{170-184}$Hf

Abstract

The ground-state bands (GSBs) in the even-even hafnium isotopes 170−184 Hf are investigated by using the cranked shell model (CSM) with pairing correlations treated by the particle-number conserving (PNC) method. The experimental kinematic moments of inertia are reproduced very well by theoretical calculations. The second upbending of the GSB at high frequency ω ≈ 0.5 MeV observed (predicted) in 172 Hf ( 170,174−178 Hf) attributes to the sudden alignments of the proton high-j orbitals π1i 13/2 (1/2 + [660]), π1h 9/2 (1/2 − [541]) and orbital π1h 11/2 (7/2 − [523]). The first upbendings of GSBs at low frequency ω = 0.2 − 0.3 MeV in 170−178 Hf, which locate below the deformed neutron shell N = 108, attribute to the alignment of the neutron orbital ν1i 13/2 . For the heavier even-even isotopes 180−184 Hf, compared to the lighter isotopes, the first band-crossing is delayed to the high frequency due to the existence of the deformed shells N = 108, 116. The upbendings of GSBs in 180−184 Hf are predicted to occur at ω ≈ 0.5MeV, which come from the sharp raise of the simultaneous alignments of both proton π1i 13/2 , π1h 9/2 and neutron ν2g 9/2 orbitals. The pairing correlation plays a very important role in the rotational properties of GSBs in even-even isotopes 180−184 Hf. Its effects on upbendings and band-crossing frequencies are investigated.