Ground State Properties of an Anderson Hamiltonian with Splitting Due to Crystal Field and Spin-Orbit Interactions

1984 ◽  
Vol 53 (8) ◽  
pp. 2697-2702 ◽  
Author(s):  
Fusayoshi J. Ohkawa
Keyword(s):  
Crystal Field ◽  
Ground State ◽  
Spin Orbit ◽  
Anderson Hamiltonian ◽  
Ground State Properties ◽  
Spin Orbit Interactions

scholarly journals Wigner SU(4) symmetry, clustering, and the spectrum of $$^{12}$$C

2021 ◽  
Vol 57 (9) ◽  
Author(s):  
Shihang Shen ◽  
Timo A. Lähde ◽  
Dean Lee ◽  
Ulf-G. Meißner
Keyword(s):  
Excited States ◽  
Ground State ◽  
Nucleon Nucleon ◽  
Irreducible Representations ◽  
Spin Orbit ◽  
Hoyle State ◽  
Nucleon Interaction ◽  
Model Calculations ◽  
Nucleon Nucleon Interaction ◽  
Spin Orbit Interactions

AbstractWe present lattice calculations of the low-lying spectrum of $$^{12}$$ 12 C using a simple nucleon–nucleon interaction that is independent of spin and isospin and therefore invariant under Wigner’s SU(4) symmetry. We find strong signals for all excited states up to $$\sim 15$$ ∼ 15  MeV above the ground state, and explore the structure of each state using a large variety of $$\alpha $$ α cluster and harmonic oscillator trial states, projected onto given irreducible representations of the cubic group. We are able to verify earlier findings for the $$\alpha $$ α clustering in the Hoyle state and the second $$2^+$$ 2 + state of $$^{12}$$ 12 C. The success of these calculations to describe the full low-lying energy spectrum using spin-independent interactions suggest that either the spin-orbit interactions are somewhat weak in the $$^{12}$$ 12 C system, or the effects of $$\alpha $$ α clustering are diminishing their influence. This is in agreement with previous findings from ab initio shell model calculations.

scholarly journals Quanty4RIXS: a program for crystal field multiplet calculations of RIXS and RIXS–MCD spectra usingQuanty

2018 ◽  
Vol 25 (3) ◽  
pp. 899-905 ◽  
Author(s):  
Patric Zimmermann ◽  
Robert J. Green ◽  
Maurits W. Haverkort ◽  
Frank M. F. de Groot
Keyword(s):  
Transition Metal ◽  
Metal Ions ◽  
Crystal Field ◽  
Transition Metal Ions ◽  
Quantum Mechanical ◽  
Spin Orbit ◽  
Hartree Fock ◽  
Spin Orbit Interactions

Some initial instructions for theQuanty4RIXSprogram written in MATLAB®are provided. The program assists in the calculation of 1s 2p RIXS and 1s 2p RIXS–MCD spectra usingQuanty. Furthermore, 1s XAS and 2p 3d RIXS calculations in different symmetries can also be performed. It includes the Hartree–Fock values for the Slater integrals and spin–orbit interactions for several 3dtransition metal ions that are required to create the .lua scripts containing all necessary parameters and quantum mechanical definitions for the calculations. The program can be used free of charge and is designed to allow for further adjustments of the scripts.

scholarly journals Pressure Effects on the Magnetic Phase Diagram of the CeNMSb2 (NM: Au and Ag): A DFT Study

Materials ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2237
Author(s):  
Mowafaq Mohammad Alsardia ◽  
Jaekyung Jang ◽  
Joo Yull Rhee
Keyword(s):  
Ground State ◽  
Noble Metals ◽  
Easy Axis ◽  
Magnetic Phase ◽  
Magnetic Phase Diagram ◽  
Pressure Effects ◽  
Spin Orbit ◽  
Magnetic Ground State ◽  
Magnetic Easy Axis ◽  
Spin Orbit Interactions

We explore the influence of pressure on the magnetic ground state of the heavy-fermion antiferromagnet (ferromagnet) CeAuSb 2 (CeAgSb 2 ) using first-principles calculations. The total-energy differences obtained by including the spin-orbit interactions and the on-site Coulomb potential for the Ce-derived 4f-orbitals are necessary to realize the accurate magnetic ground state of CeNMSb 2 (NM: Au and Ag). According to our results, the appearance of a new magnetic phase of CeAuSb 2 (CeAgSb 2 ) at the pressure of 2.1 GPa (3.5 GPa) is due to the rotation of the magnetic easy axis from the <001> to the <100> direction. Additionally, our data confirm that CeAgSb 2 is antiferromagnetic (AFM) above a critical pressure P c , and such a tendency is expected for CeAuSb 2 and remains to be seen. Through the spin-orbit-coupling Hamiltonian and detailed information on the occupation of individual 4f-orbitals of the Ce atom obtained by the electronic-structure calculations, we can deduce the rotation of the magnetic easy axis upon the application of pressure. According to the present and previous studies, the differences among the magnetic properties of CeNMSb 2 (NM: Cu, Ag and Au) compounds are not due to the different noble metals, but due to the subtle differences in the relative position of Ce atoms and, in turn, different occupations of Ce 4f-orbitals.

Potential-energy curves, zero-field splittings, and radiative lifetimes for low-lying states of AsH

1987 ◽  
Vol 65 (2) ◽  
pp. 155-164 ◽  
Author(s):  
Toshio Matsushita ◽  
Christel M. Marian ◽  
Rainer Klotz ◽  
Sigrid D. Peyerimhoff
Keyword(s):  
Fine Structure ◽  
Potential Energy ◽  
Ground State ◽  
Zero Order ◽  
Potential Energy Curves ◽  
Basis Set ◽  
Zero Field ◽  
Spin Orbit ◽  
Spin Orbit Interactions ◽  
Π State

Large-scale multireference configuration-interaction (MRD-CI) calculations in an atomic-orbital (AO) basis set containing up to f functions on As and d on hydrogen are employed to study the potential-energy curves of the π2(X3Σ−, a1Δ, b1Σ+), the σ → π, and the π → σ3.1Π states; a large number of σ → σ* states; and the lowest π → s,p Rydberg series. The σ → σ* states are strongly repulsive and exhibit numerous interactions with the Rydberg members causing predissociation. The probabilities for the spin-forbidden transitions from b1Σ+and a1Δ to the X3Σ−ground state as well as the zero-field splittings of theX3Σ−and A3Π states have been evaluated by employing a variational perturbation scheme in which the zero-order wave functions are MRD-CI expansions. The perturber states are determined by their spin-orbit interactions, which are calculated by employing the Breit–Pauli one- and two-electron spin-orbit operator. The radiative lifetime of the b1Σ+ state is predicted to be 0.35 ms, whereby the dominant mechanism is deactivation to the ms = ±1 component.The parallel transition is found to be much weaker. The lifetime of a1Δ is calculated to be 22 ms, whereby the process [Formula: see text] is favored. Both b–X and a–X transitions borrow their intensity primarily from the A3Π–X3Σ− transition and, furthermore, the 1Π–a1Δ and higher 3,1Π state spin-allowed transitions. The probability for the quadrupole b–a transition is evaluated to be three orders of magnitude smaller than the b–X transition. The calculated zero-field splitting of the X3Σ− ground state amounts to 101.4 cm−1, and the fine-structure splitting between the 2, 1, and 0+ components of the A3Π state evaluated to be 544.5 and 674.4 cm−1, respectively, in good accord with experimental results; whereas the calculated Λ doubling of the0+–0− fine-structure levels of the A3Π state (35.2 cm−1 vs. 44.72 cm−1) is too small in the present treatment. The dependence of spin-orbit effects and transition probabilities on AO basis sets and relativistic corrections to the zero-order Hamiltonian are discussed, and it is concluded that lifetime calculations for spin-forbidden processes in first- and second-row molecules can be extended in a fairly straightforward manner to systems with considerable spin-orbit interactions.

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