scholarly journals Shape Coexistence In The Neutron-Deficient Lead Isotopes, As Seen From Within Complimentary Models

2019 ◽  
Vol 14 ◽  
pp. 59
Author(s):  
Ruben Fossion ◽  
G. A. Lalazissis
Keyword(s):  
Lead Isotopes ◽  
Mean Field ◽  
Interacting Boson Model ◽  
Shape Coexistence ◽  
Excitation Energies ◽  
Excitation Mode ◽  
Theoretical Approaches ◽  
Mean Field Models ◽  
The Mean ◽  
Boson Model

In the neutron-deficient lead isotopes, at low excitation energies, the nucleus does not have one preferred excitation mode. Instead, three different coexisting "families" of excitation states are found in the excitation spectrum. Theoretical approaches are offered within the mean-field models (both relativistic and non-relativistic) and within the Interacting Boson Model (IBM). Recently, a third approach using bosoncoherent states has shown to offer a possible bridge between the former two approaches.

Energy Levels and Electromagnetic Transition of 90-94mo Nuclei Using Ibm-1

2020 ◽  
pp. 149-152
Keyword(s):  
Experimental Data ◽  
Transition Probability ◽  
Energy Levels ◽  
Dynamical Symmetry ◽  
Interacting Boson Model ◽  
Excitation Energies ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Energy States ◽  
Good Agreement

The energy states for the J , b , ɤ bands and electromagnetic transitions B (E2) values for even – even molybdenum 90 – 94 Mo nuclei are calculated in the present work of "the interacting boson model (IBM-1)" . The parameters of the equation of IBM-1 Hamiltonian are determined which yield the best excellent suit the experimental energy states . The positive parity of energy states are obtained by using IBS1. for program for even 90 – 94 Mo isotopes with bosons number 5 , 4 and 5 respectively. The" reduced transition probability B(E2)" of these neuclei are calculated and compared with the experimental data . The ratio of the excitation energies of the 41+ to 21+ states ( R4/2) are also calculated . The calculated and experimental (R4/2) values showed that the 90 – 94 Mo nuclei have the vibrational dynamical symmetry U(5). Good agreement was found from comparison between the calculated energy states and electric quadruple probabilities B(E2) transition of the 90–94Mo isotopes with the experimental data .

scholarly journals Population dynamics with spatial structure and an Allee effect

2020 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael Plank ◽  
Matthew Simpson
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Short Range ◽  
Allee Effect ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Continuum Approximation ◽  
Spatial Moment ◽  
Mean Field Models ◽  
The Mean

AbstractAllee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

Shape coexistence in $^{76}$Se within the neutron-proton interacting boson model

2021 ◽  
Author(s):  
Chengfu Mu ◽  
Dali Zhang
Keyword(s):  
Experimental Data ◽  
Energy Spectrum ◽  
Excitation Energy ◽  
Energy Levels ◽  
Spherical Shape ◽  
Interacting Boson Model ◽  
Shape Coexistence ◽  
Electromagnetic Transition ◽  
Boson Model ◽  
Good Agreement

Abstract We have investigated the low-lying energy spectrum and electromagnetic transition strengths in even-even $^{76}$Se using the proton-neutron interacting boson model (IBM-2). The theoretical calculation for the energy levels and $E2$ and $M1$ transition strengths is in good agreement with the experimental data. Especially, the excitation energy and $E2$ transition of $0^+_2$ state, which is intimately associated with shape coexistence, can be well reproduced. The analysis on low-lying states and some key structure indicators indicates that there is a coexistence between spherical shape and $\gamma$-soft shape in $^{76}$Se.

scholarly journals Invariant cone and synchronization state stability of the mean field models

2018 ◽  
Vol 34 (3) ◽  
pp. 422-433 ◽  
Author(s):  
W. Oukil ◽  
Ph. Thieullen ◽  
A. Kessi
Keyword(s):  
Mean Field ◽  
Invariant Cone ◽  
Mean Field Models ◽  
The Mean

Formulating the interacting boson model by mean-field methods

2010 ◽  
Vol 81 (4) ◽  
Author(s):  
Kosuke Nomura ◽  
Noritaka Shimizu ◽  
Takaharu Otsuka
Keyword(s):  
Mean Field ◽  
Interacting Boson Model ◽  
Field Methods ◽  
Boson Model ◽  
Mean Field Methods
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