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Register a new userCovariant density functional analysis of shape evolution in $N =40$ isotones
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The structure of low-lying excitation states of even-even $N=40$ isotones is studied using a five-dimensional collective Hamiltonian with the collective parameters determined from the relativistic mean-field plus BCS method with the PC-PK1 functional in the particle-hole channel and a separable paring force in the particle-particle channel. The theoretical calculations can reproduce not only the systematics of the low-lying states along the isotonic chain but also the detailed structure of the spectroscopy in a single nucleus. We find a picture of spherical-oblate-prolate shape transition along the isotonic chain of $N=40$ by analyzing the potential energy surfaces. The coexistence of low-lying excited $0^+$ states has also been shown to be a common feature in neutron-deficient $N=40$ isotones.
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The structure of low-energy collective states in proton-deficient N=28 isotones is analyzed using structure models based on the relativistic energy density functional DD-PC1. The relativistic Hartree-Bogoliubov model for triaxial nuclei is used to calculate binding energy maps in the $beta$-$gamma$ plane. The evolution of neutron and proton single-particle levels with quadrupole deformation, and the occurrence of gaps around the Fermi surface, provide a simple microscopic interpretation of the onset of deformation and shape coexistence. Starting from self-consistent constrained energy surfaces calculated with the functional DD-PC1, a collective Hamiltonian for quadrupole vibrations and rotations is employed in the analysis of excitation spectra and transition rates of $^{46}$Ar, $^{44}$S, and $^{42}$Si. The results are compared to available data, and previous studies based either on the mean-field approach or large-scale shell-model calculations. The present study is particularly focused on $^{44}$S, for which data have recently been reported that indicate pronounced shape coexistence.
Background: The $K^pi=2^-$ excited band emerges systematically in $N=150$ isotones raging from Pu to No with even-$Z$ numbers, and a sharp drop in energies was observed in Cf. Purpose: I attempt to uncover the microscopic mechanism for the appearance of such a low-energy $2^-$ state in $^{248}$Cf. Furthermore, I investigate the possible occurrence of the low-energy $K^pi=2^+$ state to elucidate the mechanism that prefers the simultaneous breaking of the reflection and axial symmetry to the breaking of the axial symmetry alone in this mass region. Method: I employ a nuclear EDF method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random-phase approximation are used to describe the ground state and the transition to excited states. Results: The Skyrme-type SkM* and SLy4 functionals reproduce the fall in energy, but not the absolute value, of the $K^pi=2^-$ state at $Z=98$, where the proton 2qp excitation $[633]7/2 otimes [521]3/2$ plays a decisive role for the peculiar isotonic dependence. I find interweaving roles by the pairing correlation of protons and the deformed shell closure at $Z=98$. The SkM* model predicts the $K^pi=2^-$ state appears lower in energy in $^{246}$Cf than in $^{248}$Cf as the Fermi level of neutrons is located in between the $[622]5/2$ and $[734]9/2$ orbitals. Except for $^{250}$Fm in the SkM* calculation, the $K^pi=2^+$ state is predicted to appear higher in energy than the $K^pi=2^-$ state because the quasi-proton $[521]1/2$ orbital is located above the $[633]7/2$ orbital. Conclusions: A systematic study of low-lying collective states in heavy actinide nuclei provides a rigorous testing ground for microscopic nuclear models. The present study shows a need for improvements in the EDFs to describe pairing correlations and shell structures in heavy nuclei, that are indispensable in predicting the heaviest nuclei.
The rich phenomena of deformations in neutron-deficient krypton isotopes such as the shape evolution with neutron number and the shape coexistence attract the interests of nuclear physicists for decades. It will be interesting to study such shape phenomena using a novel way, i.e., by thermally exciting the nucleus. So in this work, we develop the finite temperature covariant density functional theory for axially deformed nuclei with the treatment of pairing correlations by BCS approach, and apply this approach for the study of shape evolutions in $^{72,74}$Kr with increasing temperatures. For $^{72}$Kr, with temperature increasing, the nucleus firstly experiences a relatively quick weakening in oblate deformation at temperature $T sim0.9$ MeV, and then changes from oblate to spherical at $T sim2.1$ MeV. For $^{74}$Kr, its global minimum locates at quadroupole deformation $beta_2 sim -0.14$ and abruptly changes to spherical at $Tsim 1.7$ MeV. The proton pairing transition occurs at critical temperature 0.6 MeV following the rule $T_c =0.6 Delta_p (0)$ where $Delta_p(0)$ is the proton pairing gap at zero temperature. The signatures of the above pairing transition and shape changes can be found in the curve of the specific heat. The single-particle level evolutions with the temperature are presented.
Spin-orbit splitting is an essential ingredient for our understanding of the shell structure in nuclei. One of the most important advantages of relativistic mean-field (RMF) models in nuclear physics is the fact that the large spin-orbit (SO) potential emerges automatically from the inclusion of Lorentz-scalar and -vector potentials in the Dirac equation. It is therefore of great importance to compare the results of such models with experimental data. We investigate the size of $2p$ and $1f$ splittings for the isotone chain $^{40}$Ca, $^{38}$Ar, $^{36}$S, and $^{34}$Si in the framework of various relativistic and nonrelativistic density functionals. They are compared with the results of nonrelativistic models and with recent experimental data.
Excited states in the $N=40$ isotone $^{62}$Ti were populated via the $^{63}$V$(p,2p)$$^{62}$Ti reaction at $sim$200~MeV/u at the Radioactive Isotope Beam Factory and studied using $gamma$-ray spectroscopy. The energies of the $2^+_1 rightarrow 0^{+}_{mathrm{gs}}$ and $4^+_1 rightarrow 2^+_1$ transitions, observed here for the first time, indicate a deformed $^{62}$Ti ground state. These energies are increased compared to the neighboring $^{64}$Cr and $^{66}$Fe isotones, suggesting a small decrease of quadrupole collectivity. The present measurement is well reproduced by large-scale shell-model calculations based on effective interactions, while ab initio and beyond mean-field calculations do not yet reproduce our findings. The shell-model calculations for $^{62}$Ti show a dominant configuration with four neutrons excited across the $N=40$ gap. Likewise, they indicate that the $N=40$ island of inversion extends down to $Z=20$, disfavoring a possible doubly magic character of the elusive $^{60}$Ca.
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