Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSpin-orbit splittings of neutron states in $N = 20$ isotones from covariant density functionals and their extensions
283
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
Neutron $2p$ and $1f$ spin--orbit splittings were recently measured in the isotones $^{37}$S and $^{35}$Si by $(d,p)$ transfer reactions. Values were reported by using the major fragments of the states. An important reduction of the $p$ splitting was observed, from $^{37}$S to $^{35}$Si, associated to a strong modification of the spin--orbit potential in the central region of the nucleus $^{35}$Si. We analyze $2p$ and $1f$ neutron spin--orbit splittings in the $N=20$ isotones $^{40}$Ca, $^{36}$S, and $^{34}$Si. We employ several Skyrme and Gogny interactions, to reliably isolate pure spin--orbit and tensor--induced contributions, within the mean--field approximation. We use interactions (i) without the tensor force; (ii) with the tensor force and with tensor parameters adjusted on top of existing parametrizations; (iii) with the tensor force and with tensor and spin--orbit parameters adjusted simultaneously on top of existing parametrizations. We predict in cases (ii) and (iii) a non negligible reduction of both $p$ and $f$ splittings, associated to neutron--proton tensor effects, from $^{40}$Ca to $^{36}$S. The two splittings are further decreased for the three types of interactions, going from $^{36}$S to $^{34}$Si. This reduction is produced by the spin--orbit force and is not affected by tensor--induced contributions. For both reductions, from $^{40}$Ca to $^{36}$S and from $^{36}$S to $^{34}$Si, we predict in all cases that the modification is more pronounced for $p$ than for $f$ splittings. The measurement of the centroids for neutron $2p$ and $1f$ states in the nuclei $^{36}$S and $^{34}$Si would be interesting to validate this prediction experimentally. We show the importance of using interactions of type (iii), because they provide $p$ and $f$ splittings in the nucleus $^{40}$Ca which are in agreement with the corresponding experimental values.
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.
The latest experimental data on nuclei at $^{132}$Sn permit us for the first time to determine the spin-orbit splittings of neutrons and protons in identical orbits in this neutron-rich doubly-magic region and compare the case to that of $^{208}$Pb. Using the new results, which are now consistent for the two neutron-rich doubly magic regions, a theoretical analysis defines the isotopic dependence of the mean field spin-orbit potential and leads to a simple explicit expression for the difference between the spin-orbit splittings of neutrons and protons. The isotopic dependence is explained in the framework of different theoretical approaches.
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.
Coexistence of different geometric shapes at low energies presents a universal structure phenomenon that occurs over the entire chart of nuclides. Studies of the shape coexistence are important for understanding the microscopic origin of collectivity and modifications of shell structure in exotic nuclei far from stability. The aim of this work is to provide a systematic analysis of characteristic signatures of coexisting nuclear shapes in different mass regions, using a global self-consistent theoretical method based on universal energy density functionals and the quadrupole collective model. The low-energy excitation spectrum and quadrupole shape invariants of the two lowest $0^{+}$ states of even-even nuclei are obtained as solutions of a five-dimensional collective Hamiltonian (5DCH) model, with parameters determined by constrained self-consistent mean-field calculations based on the relativistic energy density functional PC-PK1, and a finite-range pairing interaction. The theoretical excitation energies of the states: $2^+_1$, $4^+_1$, $0^+_2$, $2^+_2$, $2^+_3$, as well as the $B(E2; 0^+_1to 2^+_1)$ values, are in very good agreement with the corresponding experimental values for 621 even-even nuclei. Quadrupole shape invariants have been implemented to investigate shape coexistence, and the distribution of possible shape-coexisting nuclei is consistent with results obtained in recent theoretical studies and available data. The present analysis has shown that, when based on a universal and consistent microscopic framework of nuclear density functionals, shape invariants provide distinct indicators and reliable predictions for the occurrence of low-energy coexisting shapes. This method is particularly useful for studies of shape coexistence in regions far from stability where few data are available.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
