scholarly journals Review of Shape Phase Transition Studies for Bose-Fermi Systems: The Effect of the Odd-Particle on the Bosonic Core

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 215
Author(s):  
M. Böyükata ◽  
C. E. Alonso ◽  
J. M. Arias ◽  
L. Fortunato ◽  
A. Vitturi
Keyword(s):  
Phase Transition ◽  
Critical Points ◽  
Potential Energy Surfaces ◽  
Energy Levels ◽  
Model Space ◽  
Fermi Systems ◽  
Energy Surfaces ◽  
Shape Phase Transition ◽  
Intrinsic Frame ◽  
Transition Studies

The quantum phase transition studies we have done during the last few years for odd-even systems are reviewed. The focus is on the quantum shape phase transition in Bose-Fermi systems. They are studied within the Interacting Boson-Fermion Model (IBFM). The geometry is included in this model by using the intrinsic frame formalism based on the concept of coherent states. First, the critical point symmetries E(5/4) and E(5/12) are summarized. E(5/4) describes the case of a single j=3/2 particle coupled to a bosonic core that undergoes a transition from spherical to γ-unstable. E(5/12) is an extension of E(5/4) that describes the multi-j case (j=1/2,3/2,5/2) along the same transitional path. Both, E(5/4) and E(5/12), are formulated in a geometrical context using the Bohr Hamiltonian. Similar situations can be studied within the IBFM considering the transitional path from UBF(5) to OBF(6). Such studies are also presented. No critical points have been proposed for other paths in odd-even systems as, for instance, the transition from spherical to axially deformed shapes. However, the study of such shape phase transition can be done easily within the IBFM considering the path from UBF(5) (spherical) to SUBF(3) (axial deformed). Thus, in a second part, this study is presented for the multi-j case. Energy levels and potential energy surfaces obtained within the intrinsic frame formalism of the IBFM Hamiltonian are discussed. Finally, our recent works within the IBFM for a single-j fermion coupled to a bosonic core that performs different shape phase transitional paths are reviewed. All significant paths in the model space are studied: from spherical to γ-unstable shape, from spherical to axially deformed (prolate and oblate) shapes, and from prolate to oblate shape passing through the γ-unstable shape. The aim of these applications is to understand the effect of the coupled fermion on the core when moving along a given transitional path and how the coupled fermion modifies the bosonic core around the critical points.

Searching critical points of fitted potential energy surfaces

1996 ◽  
Vol 371 ◽  
pp. 85-90 ◽  
Author(s):  
Jaime Fernández Rico ◽  
Alfredo Aguado ◽  
Miguel Paniagua
Keyword(s):  
Potential Energy ◽  
Critical Points ◽  
Potential Energy Surfaces ◽  
Energy Surfaces

scholarly journals Formation of Van Der Waals Complexes in Concerted Unimolecular Elimination Processes

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Faina Dubnikova ◽  
Assa Lifshitz
Keyword(s):  
Potential Energy ◽  
Transition State ◽  
Potential Energy Surfaces ◽  
Energy Levels ◽  
Van Der Waals ◽  
State Theory ◽  
Van Der Waals Interactions ◽  
Decomposition Products ◽  
Quantum Chemical Methods ◽  
Energy Surfaces

Potential energy surfaces for three unimolecular elimination reactions: , , and were calculated using a variety of quantum chemical methods. It was shown that, in all the three cases, the transition state in the first step of the reaction leads to the production of the complex intermediates based on van der Waals interactions. In addition to the fact that the three complexes appear as intermediates on the potential energy surfaces, which means that they are not free entities, the entropy values of the two elimination products are far above those of the complexes due to their additional Sackur-Tetrode entropy. Moreover, the three vibrational frequencies of the H2O group in the (CH3)3COH complex and the H–Cl and H–F stretch frequencies in CH3CF3 and CH3CH2CH2Cl are quite different (see the various tables). The energy levels of the complexes were found to be below those of the corresponding decomposition products. Rate constants for the elimination processes were calculated from the potential energy surfaces using transition-state theory and were compared to available experimental data.

Vibrational energies of H3+ and Li3+ based on the diatomics-in-molecules potentials

1986 ◽  
Vol 51 (10) ◽  
pp. 2057-2062 ◽  
Author(s):  
Jan Vojtík ◽  
Vladimír Špirko ◽  
Per Jensen
Keyword(s):  
Potential Energy ◽  
Ab Initio ◽  
Potential Energy Surfaces ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Vibrational Motion ◽  
Variational Calculations ◽  
Vibrational Energies ◽  
Vibrational Energy Levels ◽  
Energy Surfaces

The present publication reports variational calculations of the vibrational energy levels for H3+, D3+, 6Li3+, and 7Li3+, starting from potential energy surfaces generated by the DIM scheme. The vibrational energies obtained agree semiquantitatively with those based on the best ab initio potentials available. The results seem to indicate that an analogous approach might be useful in describing the vibrational motion of heavier alkali cluster cations A3+.

POTENTIAL ENERGY SURFACES AND MICROWAVE SPECTRA FOR 20Ne–13C16O2, 22Ne–12C16O2 and 22Ne–13C16O2 COMPLEXES

2012 ◽  
Vol 11 (06) ◽  
pp. 1175-1182 ◽  
Author(s):  
RONG CHEN ◽  
HUA ZHU
Keyword(s):  
Potential Energy ◽  
Potential Energy Surfaces ◽  
Global Minimum ◽  
Energy Levels ◽  
Three Dimensional ◽  
Lanczos Algorithm ◽  
Potential Surfaces ◽  
Microwave Spectra ◽  
Stretching Vibration ◽  
Energy Surfaces

We report averaged potential energy surfaces for isotopic Ne–CO2 complexes (20 Ne –13 C 16 O 2, 22 Ne –12 C 16 O 2 and 22 Ne –13 C 16 O 2). According to the latest ab initio potential of 20 Ne –12 C 16 O 2 (Chen R, Jiao EQ, Zhu H, Xie DQ, J Chem Phys133:104302, 2010) including the Q3 normal mode for the υ3 antisymmetric stretching vibration of the CO2 molecule. We obtain the averaged potentials for 20 Ne –13 C 16 O 2, 22 Ne –12 C 16 O 2 and 22 Ne –13 C 16 O 2 by the integration of the three-dimensional potential over the Q3 coordinate. The averaged potential surfaces are found to have a T-shaped global minimum and two equivalent linear local minima. The radial DVR/angular FBR method and the Lanczos algorithm are applied to calculate the rovibrational energy levels. Comparison with the available observed values showed an overall excellent agreement for all spectroscopic parameters and the microwave spectra.

Vibrationally Averaged Potential Energy Surfaces and Microwave Spectra for Isotopic Ne-CO2 Complexes

2014 ◽  
Vol 670-671 ◽  
pp. 235-239
Author(s):  
Rong Chen ◽  
Xiao Ling Luo
Keyword(s):  
Potential Energy ◽  
Normal Mode ◽  
Potential Energy Surfaces ◽  
Energy Levels ◽  
Chem Phys ◽  
Lanczos Algorithm ◽  
Potential Surfaces ◽  
Microwave Spectra ◽  
Stretching Vibration ◽  
Energy Surfaces

Averaged potential energy surfaces for isotopic Ne–CO2complexes (20Ne–18O13C16O,20Ne–17O12C16O and22Ne–17O12C16O) are presented. According to the latestab initiopotential of20Ne–12C16O2(R. Chen, H. Zhu, D. Q. Xie, J. Chem. Phys, 133, 2010, 104302,) which incorporates its dependence on theQ3normal mode for the antisymmetric stretching vibration of the CO2molecule, we obtain the averaged potentials for20Ne–18O13C16O,20Ne–17O12C16O and22Ne–17O12C16O complexes by integrating the potential energy surface overQ3normal mode. Each averaged potential surfaces are found to have a T-shaped global minimum and two equivalent linear local minima. The radial DVR/angular FBR method and the Lanczos algorithm are applied to calculate the rovibrational energy levels. Comparison with the available experimental values showed an overall excellent agreement for all spectroscopic parameters and the microwave spectra.

Investigation of shape phase transition in the U(5) ↔ SO(6) transitional region by catastrophe theory and critical exponents of some quantities

2014 ◽  
Vol 23 (09) ◽  
pp. 1450045 ◽  
Author(s):  
H. Fathi ◽  
M. Ghadami ◽  
H. Sabri ◽  
N. Fouladi ◽  
M. A. Jafarizadeh
Keyword(s):  
Phase Transition ◽  
Critical Exponents ◽  
Catastrophe Theory ◽  
Least Square ◽  
Transitional Region ◽  
Least Square Fitting ◽  
Boson Model ◽  
Energy Surfaces ◽  
Thermodynamic Phase ◽  
Shape Phase Transition

In this paper, we have analyzed the critical behavior of even–even Ru and Pd isotopes between U(5) and SO(6) limits of interacting boson model via Catastrophe Theory in combination with a coherent state formalism to generate energy surfaces. The parameters of the Hamiltonian are determined via least-square fitting to the experimental data for different Ru and Pd isotopes. Our results suggest a second-order phase transition in these isotopic chains and propose the best candidates for E(5) critical symmetry. Also, the analogy between the critical exponents of ground state quantum phase transition and Landau values for the critical exponents of thermodynamic phase transitions are described.

Reduced-dimensional surface hopping with offline–online computations

2021 ◽  
Author(s):  
Zachary Morrow ◽  
Hyuk-Yong Kwon ◽  
Carl Tim Kelley ◽  
Elena Jakubikova
Keyword(s):  
Molecular Dynamics ◽  
Potential Energy ◽  
Molecular Dynamics Simulations ◽  
Potential Energy Surfaces ◽  
Energy Levels ◽  
Surface Hopping ◽  
Dynamics Simulations ◽  
Energy Surfaces ◽  
Nuclear Geometry ◽  
Dimensional Surface

Molecular dynamics simulations often classically evolve the nuclear geometry on adiabatic potential energy surfaces (PESs), punctuated by random hops between energy levels in regions of strong coupling, in an algorithm...

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