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Register a new userDeformation and its influence on $K$ isomerism in neutron-rich Hf nuclei
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We investigate the influence of deformation on the possible occurrence of long-lived $K$ isomers in Hf isotopes around N=116, using configuration-constrained calculations of potential-energy surfaces. Despite having reduced shape elongation, the multi-quasiparticle states in $^{186,188}$Hf remain moderately robust against triaxial distortion, supporting the long expected occurrence of exceptionally long-lived isomers. The calculations are compared with available experimental data.
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We review the impact of nuclear forces on matter at neutron-rich extremes. Recent results have shown that neutron-rich nuclei become increasingly sensitive to three-nucleon forces, which are at the forefront of theoretical developments based on effective field theories of quantum chromodynamics. This includes the formation of shell structure, the spectroscopy of exotic nuclei, and the location of the neutron dripline. Nuclear forces also constrain the properties of neutron-rich matter, including the neutron skin, the symmetry energy, and the structure of neutron stars. We first review our understanding of three-nucleon forces and show how chiral effective field theory makes unique predictions for many-body forces. Then, we survey results with three-nucleon forces in neutron-rich oxygen and calcium isotopes and neutron-rich matter, which have been explored with a range of many-body methods. Three-nucleon forces therefore provide an exciting link between theoretical, experimental and observational nuclear physics frontiers.
Inspired by the newly discovered isomeric states in the rare-earth neutron-rich nuclei, high-$K$ isomeric states in neutron-rich samarium and gadolinium isotopes are investigated within the framework of the cranked shell model (CSM) with pairing correlation treated by a particle-number-conserving (PNC) method. The experimental multi-particle state energies and moments of inertia are reproduced quite well by the PNC-CSM calculations. A remarkable effect from the high-order deformation $varepsilon_{6}$ is demonstrated. Based on the occupation probabilities, the configurations are assigned to the observed high-$K$ isomeric states. The lower $5^-$ isomeric state in $^{158}$Sm is preferred as the two-proton state with configuration $pifrac{5}{2}^{+}[413]otimespifrac{5}{2}^{-}[532]$. More low-lying two-particle states are predicted. The systematics of the electronic quadrupole transition probabilities, $B(E2)$ values along the neodymium, samarium, gadolinium and dysprosium isotopes and $N=96,98,100,102$ isotones chains is investigated to reveal the midshell collectivities.
Interference effect of neutron capture cross section between the compound and direct processes is investigated. The compound process is calculated by resonance parameters and the direct process by the potential mode. The interference effect is tested for neutron-rich $^{82}$Ge and $^{134}$Sn nuclei relevant to $r$-process and light nucleus $^{13}$C which is neutron poison in the $s$-process and produces long-lived radioactive nucleus $^{14}$C ($T_{1/2}=5700$ y). The interference effects in those nuclei are significant around resonances, and low energy region if $s$-wave neutron direct capture is possible. Maxwellian averaged cross sections at $kT=30$ and $300$ keV are also calculated, and the interference effect changes the Maxwellian averaged capture cross section largely depending on resonance position.
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 $hbaromegaapprox0.5$ MeV observed (predicted) in $^{172}$Hf ($^{170,174-178}$Hf) attributes to the sudden alignments of the proton high-$j$ orbitals $pi1i_{13/2}$ $(1/2^{+}[660])$, $pi1h_{9/2}$ $(1/2^{-}[541])$ and orbital $pi1h_{11/2}$ $(7/2^{-}[523])$. The first upbendings of GSBs at low frequency $hbaromega=0.2-0.3$ MeV in $^{170-178}$Hf, which locate below the deformed neutron shell $N=108$, attribute to the alignment of the neutron orbital $ u1i_{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 $hbaromegaapprox0.5$MeV, which come from the sharp raise of the simultaneous alignments of both proton $pi1i_{13/2}$, $pi1h_{9/2}$ and neutron $ u2g_{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.
Pauli blocking is carefully investigated for the processes of $NN rightarrow N Delta$ and $Delta rightarrow N pi$ in heavy-ion collisions, aiming at a more precise prediction of the $pi^-/ pi^+$ ratio which is an important observable to constrain the high-density symmetry energy. We use the AMD+JAM approach, which combines the antisymmetrized molecular dynamics for the time evolution of nucleons and the JAM model to treat processes for $Delta$ resonances and pions. As is known in general transport-code simulations, it is difficult to treat Pauli blocking very precisely due to unphysical fluctuations and additional smearing of the phase-space distribution function, when Pauli blocking is treated in the standard method of JAM. We propose an improved method in AMD+JAM to use the Wigner function precisely calculated in AMD as the blocking probability. Different Pauli blocking methods are compared in heavy-ion collisions of neutron-rich nuclei, ${}^{132}mathrm{Sn}+{}^{124}mathrm{Sn}$, at 270 MeV/nucleon. With the more accurate method, we find that Pauli blocking is stronger, in particular for the neutron in the final state in $NN rightarrow N Delta$ and $ Delta to Npi$, compared to the case with a proton in the final state. Consequently, the $pi^-/pi^+$ ratio becomes higher when the Pauli blocking is improved, the effect of which is found to be comparable to the sensitivity to the high-density symmetry energy.
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