SEMICLASSICAL ORIGIN OF SHELL STRUCTURES IN DEFORMED NUCLEI: DEPENDENCE ON SURFACE DIFFUSENESS AND EFFECT OF SPIN-ORBIT COUPLINGS

2004 ◽  
Vol 13 (01) ◽  
pp. 191-202 ◽  
Author(s):  
KEN-ICHIRO ARITA
Keyword(s):  
Periodic Orbit ◽  
Mean Field ◽  
Orbit Coupling ◽  
Shell Structures ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Periodic Orbit Theory ◽  
Shell Effects ◽  
Surface Diffuseness ◽  
Type Potential

Shell structures in nuclear mean field potentials are analyzed using semiclassical periodic-orbit theory. rα-type potential model is taken as an approximation of Woods-Saxon model, and spin-orbit coupling is also taken into account. Using this model, we examine shell structure as functions of deformation, nuclear size (diffuseness), and spin-orbit coupling strength. Significant roles of periodic orbit bifurcations for strong deformed shell effects are clarified. Special attentions will be paid to bifurcations of the 'bridge orbits', which emerge from symmetric orbits and then submerge in other symmetric orbits by varying a potential parameter.

scholarly journals Critical Temperature in the BCS-BEC Crossover with Spin-Orbit Coupling

2021 ◽  
Vol 6 (2) ◽  
pp. 16
Author(s):  
Luca Dell’Anna ◽  
Stefano Grava
Keyword(s):  
Critical Temperature ◽  
Mean Field ◽  
Bound State ◽  
Field Approximation ◽  
Einstein Condensate ◽  
Orbit Coupling ◽  
Mean Field Approximation ◽  
Integral Approach ◽  
Spin Orbit Coupling ◽  
Spin Orbit

We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen–Cooper–Schrieffer (BCS) superconducting phase to a Bose–Einstein condensate (BEC), also in the presence of a spin–orbit coupling. Below a critical temperature the system is characterized by an order parameter. Generally a mean field approximation cannot reproduce the correct behavior of the critical temperature Tc over the whole crossover. We analyze the crucial role of quantum fluctuations beyond the mean-field approach useful to find Tc along the crossover in the presence of a spin–orbit coupling, within a path integral approach. A formal and detailed derivation for the set of equations useful to derive Tc is performed in the presence of Rashba, Dresselhaus and Zeeman couplings. In particular in the case of only Rashba coupling, for which the spin–orbit effects are more relevant, the two-body bound state exists for any value of the interaction, namely in the full crossover. As a result the effective masses of the emerging bosonic excitations are finite also in the BCS regime.

scholarly journals Spin-Orbit Coupling Descriptions of Magnetic Excitations in Lanthanide Complexes

2020 ◽  
Author(s):  
Shashank Vittal Rao ◽  
MATTEO PICCARDO ◽  
Alessandro Soncini
Keyword(s):  
Crystal Field ◽  
Electron Spin ◽  
Single Molecule ◽  
Lanthanide Complexes ◽  
Mean Field ◽  
Orbit Coupling ◽  
Ligand Field ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Magnetic Excitations

We present a number of computationally cost-effective approaches to calculate magnetic excitations (i.e. crystal field energies and magnetic anisotropies in the lowest spin-orbit multiplet) in lanthanide complexes. In particular, we focus on the representation of the spin-orbit coupling term of the molecular Hamiltonian, which has been implemented within the quantum chemistry package CERES using various approximations to the Breit-Pauli Hamiltonian. The approximations include the (i) bare one-electron approximation, (ii) atomic mean field and molecular mean field approximations of the two-electron term, (iii) full representation of the Breit-Pauli Hamiltonian. Within the framework of the CERES implementation, the spin-orbit Hamiltonian is always fully diagonalized together with the electron repulsion Hamiltonian (CASCI-SO) on the full basis of Slater determinants arising within the 4f ligand field space. For the first time, we make full use of the Cholesky decomposition of two-electron spin-orbit integrals to speed up the calculation of the two-electron spin-orbit operator. We perform an extensive comparison of the different approximations on a set of lanthanide complexes varying both the lanthanide ion and the ligands. Surprisingly, while our results confirm the need of at least a mean field approach to accurately describe the spin-orbit coupling interaction within the ground Russell-Saunders term, we find that the simple bare one-electron spin-orbit Hamiltonian performs reasonably well to describe the crystal field split energies and <sub>g</sub> tensors within the ground spin-orbit multiplet, which characterize all the magnetic excitations responsible for lanthanide-based single-molecule magnetism.<br>

scholarly journals Spin-Orbit Coupling Descriptions of Magnetic Excitations in Lanthanide Complexes

2020 ◽  
Author(s):  
Shashank Vittal Rao ◽  
MATTEO PICCARDO ◽  
Alessandro Soncini
Keyword(s):  
Crystal Field ◽  
Electron Spin ◽  
Single Molecule ◽  
Lanthanide Complexes ◽  
Mean Field ◽  
Orbit Coupling ◽  
Ligand Field ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Magnetic Excitations

We present a number of computationally cost-effective approaches to calculate magnetic excitations (i.e. crystal field energies and magnetic anisotropies in the lowest spin-orbit multiplet) in lanthanide complexes. In particular, we focus on the representation of the spin-orbit coupling term of the molecular Hamiltonian, which has been implemented within the quantum chemistry package CERES using various approximations to the Breit-Pauli Hamiltonian. The approximations include the (i) bare one-electron approximation, (ii) atomic mean field and molecular mean field approximations of the two-electron term, (iii) full representation of the Breit-Pauli Hamiltonian. Within the framework of the CERES implementation, the spin-orbit Hamiltonian is always fully diagonalized together with the electron repulsion Hamiltonian (CASCI-SO) on the full basis of Slater determinants arising within the 4f ligand field space. For the first time, we make full use of the Cholesky decomposition of two-electron spin-orbit integrals to speed up the calculation of the two-electron spin-orbit operator. We perform an extensive comparison of the different approximations on a set of lanthanide complexes varying both the lanthanide ion and the ligands. Surprisingly, while our results confirm the need of at least a mean field approach to accurately describe the spin-orbit coupling interaction within the ground Russell-Saunders term, we find that the simple bare one-electron spin-orbit Hamiltonian performs reasonably well to describe the crystal field split energies and <sub>g</sub> tensors within the ground spin-orbit multiplet, which characterize all the magnetic excitations responsible for lanthanide-based single-molecule magnetism.<br>

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