A Model Study of Instabilities Present in the Mean-Field Description and in Linearized Correlation Schemes

1989 ◽  
Vol 44 (2) ◽  
pp. 117-124
Author(s):  
Michael C. Böhm ◽  
Gerd Bubeck ◽  
Andrzej M. Oles
Keyword(s):  
Theoretical Calculations ◽  
Mean Field ◽  
Numerical Data ◽  
Local Approach ◽  
Stability Range ◽  
Hartree Fock ◽  
Model Study ◽  
Correlation Models ◽  
The Stability ◽  
Hf Wave

Abstract In this work we discuss the cooperative occurrence of instabilities in the Hartree-Fock (HF) approximation and linearized correlation models. Both breakdown phenomena can be analyzed via eigenvalues of characteristic matrices. The well known HF instabilities follow from a quasidegeneracy between the symmetry-adapted mean-field state and singly excited configurations. Quasi-degeneracies between the HF wave function and doubly excited configurations restrict the applicability of linearized correlation models. In the theoretical calculations the method of the local approach (LA) has been employed to derive the correlated ground state. For a system of the general topology XH2 (X = C, Si, etc.) the bond orbital approximation (BOA) has been used to derive analytic formulae indicating the stability range of linearized correlation schemes. Numerical calculations on the basis of a simple model-Hamiltonian are given for the π systems C2H4 and C2H2, respectively, which have been studied as a function of the CC bondlength. The comparison of the respective numerical data indicates that both breakdown phenomena are enhanced via coupling terms between strongly correlated bonds.

Shape evolution and energy spectra of Pt isotopes

2016 ◽  
Vol 25 (02) ◽  
pp. 1650012
Author(s):  
Yu Kun ◽  
Xianrong Zhou ◽  
Jiwei Cui
Keyword(s):  
Energy Surface ◽  
Theoretical Calculations ◽  
Mean Field ◽  
Energy Spectra ◽  
Shape Evolution ◽  
Excitation Spectra ◽  
Hartree Fock ◽  
The Mean ◽  
Stable Shape ◽  
Good Agreement

The shapes and low-energy spectra of [Formula: see text]Pt isotopes are discussed by a nonrelativistic Skyrme–Hartree–Fock (SHF) approach plus a density-dependent pairing in the BCS approximation. Two different Skyrme parameters SLy5 and SGII are used to perform constrained triaxial mean-field calculations of energy surface. The calculations beyond mean field are introduced by a projection of mean-field intrinsic wave functions onto good angular momentum. Theoretical calculations exhibit the evolution of shapes from triaxial in light Pt isotopes to [Formula: see text] soft for medium Pt isotopes, and finally oblate shapes in heavy isotopes. In particular, the calculated excitation spectra are in good agreement with available data and the trend of experimental [Formula: see text] is reproduced. The mean-field calculations indicate a stable shape evolution with SLy5 and SGII interactions, respectively. In the present SHF approach, the lighter nuclei Pt isotopes present a slightly triaxial shapes.

scholarly journals Stability analysis of the coexistence equilibrium of a balanced metapopulation model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shodhan Rao ◽  
Nathan Muyinda ◽  
Bernard De Baets
Keyword(s):  
Equilibrium Point ◽  
Mathematical Proof ◽  
Mean Field ◽  
Patch Dynamics ◽  
System Modelling ◽  
Metapopulation Model ◽  
Ode System ◽  
Homogeneous Network ◽  
The Stability ◽  
Coexistence Equilibrium

AbstractWe analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another through dispersal or migration. We assume that the inter-patch migrations are detailed balanced and that the patches are identical with intra-patch dynamics governed by a mean-field ODE system with a coexistence equilibrium. By making use of an appropriate Lyapunov function coupled with LaSalle’s invariance principle, we are able to show that the coexistence equilibrium point within each patch is locally asymptotically stable if the inter-patch dispersal network is heterogeneous, whereas it is neutrally stable in the case of a homogeneous network. These results provide a mathematical proof confirming the existing numerical simulations and broaden the range of networks for which they are valid.

THE INNER CRUST OF NEUTRON STARS IN RELATIVISTIC MEAN FIELD APPROACH

2008 ◽  
Vol 17 (09) ◽  
pp. 1765-1773 ◽  
Author(s):  
JIGUANG CAO ◽  
ZHONGYU MA ◽  
NGUYEN VAN GIAI
Keyword(s):  
Boundary Conditions ◽  
Neutron Stars ◽  
Mean Field ◽  
Bcs Theory ◽  
Neutron Density ◽  
Field Approach ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Density Distributions ◽  
Rmf Model

The microscopic properties and superfluidity of the inner crust in neutron stars are investigated in the framework of the relativistic mean field(RMF) model and BCS theory. The Wigner-Seitz(W-S) cell of inner crust is composed of neutron-rich nuclei immersed in a sea of dilute, homogeneous neutron gas. The pairing properties of nucleons in the W-S cells are treated in BCS theory with Gogny interaction. In this work, we emphasize on the choice of the boundary conditions in the RMF approach and superfluidity of the inner crust. Three kinds of boundary conditions are suggested. The properties of the W-S cells with the three kinds of boundary conditions are investigated. The neutron density distributions in the RMF and Hartree-Fock-Bogoliubov(HFB) models are compared.

scholarly journals RELATIVE MOTION CORRECTION TO FISSION BARRIERS

2008 ◽  
Vol 17 (01) ◽  
pp. 151-159 ◽  
Author(s):  
J. SKALSKI
Keyword(s):  
Relative Motion ◽  
Cluster Model ◽  
Motion Correction ◽  
Mean Field Theory ◽  
Mean Field ◽  
Ternary Fission ◽  
Skyrme Interaction ◽  
Hartree Fock ◽  
Fission Barriers ◽  
The Mean

We discuss the effect of kinetic energy of the relative motion becoming spurious for separate fragments on the selfconsistent mean-field fission barriers. The treatment of the relative motion in the cluster model is contrasted with the necessity of a simpler and approximate approach in the mean-field theory. A scheme of the energy correction to the Hartree-Fock is proposed. The results obtained with the effective Skyrme interaction SLy 6 show that the correction, previously estimated as ~ 8 MeV in A = 70 - 100 nuclei, amounts to 4 MeV in the medium heavy nucleus 198 Hg and to null in 238 U . However, the corrected barrier implies a shorter fission half-life of the latter nucleus. The same effect is expected to lower barriers for multipartition (i.e. ternary fission, etc) and make hyperdeformed minima less stable.

Sternheimer Antishielding Functions ß(r) and γ(r) for Rare Earth Atoms

1986 ◽  
Vol 41 (1-2) ◽  
pp. 37-46 ◽  
Author(s):  
K. D. Sen ◽  
P. C. Schmidt ◽  
Alarich Weiss
Keyword(s):  
Rare Earth ◽  
Valence State ◽  
Wave Functions ◽  
Electric Field Gradients ◽  
Hartree Fock ◽  
Field Gradients ◽  
Lanthanide Atoms ◽  
Hf Wave ◽  
Self Consistency ◽  
Consistency Effects

The Sternheimer shielding-antishielding functions ß(r) and γ(r) are reported for all the fourteen lanthanide atoms at the uncoupled Hartree-Fock level of theory. Each atom is considered in two valence state configurations, 4fn 5d0 and 4 fn-1 5d1, and the nonrelativistic HF wave functions have been used. The 5d1 configuration leads to a smaller net antishielding than the 4fn configuration by ~ 6-12% in the series. The electron-electron self consistency effects are found to be less than 5% in the series. The importance of the calculated antishielding functions in the antishielding theory of electric field gradients in noncubic metals is discussed.

scholarly journals Carbon Substitution on N24Cages: Crossover between Triangular and Hexagonal Structures

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Carrie Sanders ◽  
Douglas L. Strout
Keyword(s):  
Theoretical Calculations ◽  
High Energy ◽  
Energy Materials ◽  
Cylindrical Structures ◽  
High Energy Materials ◽  
Energy Applications ◽  
Carbon Substitution ◽  
Complex Forms ◽  
The Stability ◽  
Carbon Inclusion

Complex forms of nitrogen are of interest for their potential as high-energy materials, but many all-nitrogen systems lack the stability for practical high-energy applications. Inclusion of carbon atoms in an otherwise all-nitrogen structure can increase stability. Nitrogen cages are known for energetically preferring cylindrical structures with triangular endcaps, but carbon cages prefer the pentagon-hexagon structure of the fullerenes. Previous calculations on N22C2have shown that carbon inclusion narrows the gap between triangular and fullerene-like structures. In the current study, three isomers of N24are used as frameworks for carbon substitution. Theoretical calculations are carried out on isomers of N20C4, N18C6, and N16C8, with the goal of determining what level of carbon substitution causes the carbon fullerene-like structures to become energetically preferred.

scholarly journals Influence of the Al content on the phase transformations in Cu-Al-Ag alloys

2003 ◽  
Vol 28 (1) ◽  
pp. 33-38 ◽  
Author(s):  
A. T. Adorno ◽  
A. V. Benedetti ◽  
R. A. G. da Silva ◽  
M. Blanco
Keyword(s):  
Thermal Analysis ◽  
Differential Thermal Analysis ◽  
Transition Temperature ◽  
Phase Transformations ◽  
Decomposition Reaction ◽  
Phase Decomposition ◽  
Stability Range ◽  
X Ray ◽  
Al Content ◽  
The Stability

The influence of the Al content on the phase transformations in Cu-Al-Ag alloys was studied by classical differential thermal analysis (DTA), optical microscopy (OM) and X-ray diffractometry (XRD). The results indicated that the increase in the Al content and the presence of Ag decrease the rate of the <FONT FACE=Symbol>b</font>1 phase decomposition reaction and contribute for the raise of this transition temperature, thus decreasing the stability range of the perlitic phase resulted from the b1 decomposition reaction.

scholarly journals Structural Properties of G,T-Parallel Duplexes

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Anna Aviñó ◽  
Elena Cubero ◽  
Raimundo Gargallo ◽  
Carlos González ◽  
Modesto Orozco ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Structural Properties ◽  
Theoretical Calculations ◽  
Md Simulations ◽  
Theoretical Studies ◽  
Duplex Structure ◽  
Strong Stabilization ◽  
The Stability ◽  
The Impact

The structure of G,T-parallel-stranded duplexes of DNA carrying similar amounts of adenine and guanine residues is studied by means of molecular dynamics (MD) simulations and UV- and CD spectroscopies. In addition the impact of the substitution of adenine by 8-aminoadenine and guanine by 8-aminoguanine is analyzed. The presence of 8-aminoadenine and 8-aminoguanine stabilizes the parallel duplex structure. Binding of these oligonucleotides to their target polypyrimidine sequences to form the corresponding G,T-parallel triplex was not observed. Instead, when unmodified parallel-stranded duplexes were mixed with their polypyrimidine target, an interstrand Watson-Crick duplex was formed. As predicted by theoretical calculations parallel-stranded duplexes carrying 8-aminopurines did not bind to their target. The preference for the parallel-duplex over the Watson-Crick antiparallel duplex is attributed to the strong stabilization of the parallel duplex produced by the 8-aminopurines. Theoretical studies show that the isomorphism of the triads is crucial for the stability of the parallel triplex.

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