CORRELATION OF KINETIC MOMENT OF INERTIA WITH POWER FORMULA INDEX

2012 ◽  
Vol 21 (10) ◽  
pp. 1250082
Author(s):  
RAJESH KUMAR ◽  
VIKAS KATOCH ◽  
S. SHARMA ◽  
J. B. GUPTA
Keyword(s):  
Phase Transition ◽  
Good Accuracy ◽  
Power Index ◽  
Moment Of Inertia ◽  
Light Nuclei ◽  
Index Formula ◽  
Ground Band ◽  
Shape Phase Transition ◽  
Kinetic Moment

The level energies of ground band of even Z, even N nuclei may be reproduced well with good accuracy by using the power index formula E = aIb. In an earlier study of the dependence of the kinetic moment of inertia (MoI) J(1) on spin I, a possible correlation of the MoI J(1) with power index "b" was suggested. Here we illustrate that the slope of the kinetic MoI versus spin I corresponds to the magnitude of the index "b" for several isotopes in the A = 100–150 region. The validity of the formula is illustrated for light nuclei in A = 100 region and its use for studying shape phase transition at N = 60.

ANHARMONICITY VERSUS LINEARITY RELATION AND MALLMANN PLOT

2013 ◽  
Vol 22 (08) ◽  
pp. 1350064 ◽  
Author(s):  
J. B. GUPTA
Keyword(s):  
Phase Transition ◽  
Nuclear Structure ◽  
Power Index ◽  
Energy Ratio ◽  
Index Formula ◽  
Alternative Form ◽  
Shape Phase Transition

The anharmonity in shape transitional nuclei, observed earlier, is studied and an alternative form is derived. The dichotomy of a constant anharmonicity along with a changing nuclear structure is resolved. The evolution of the collective nuclear structure from the spherical vibrator to the deformed rotor is studied through the variation of energy ratio R10/2(E10/E2) with R4/2, for Ba – Dy and for Dy – Hf (N<104) and R12/2. The role of the Z = 64 subshell and the N = 88–90 shape phase transition are illustrated in the Mallmann plot. The relative merits of the empirical formulae: rotation–vibration linearity model, the soft rotor formula and the power index formula are compared.

Systematic study of the nature of gamma bands in A = 100–200 mass nuclei

2018 ◽  
Vol 33 (21) ◽  
pp. 1850118 ◽  
Author(s):  
Monica Karday ◽  
H. M. Mittal ◽  
Rohit Mehra
Keyword(s):  
Phase Transition ◽  
Systematic Study ◽  
Excited Level ◽  
Equilibrium Structure ◽  
Excitation Energies ◽  
Ground Band ◽  
Level Sequence ◽  
Shape Signature ◽  
Shape Phase Transition

The [Formula: see text]-bands are analyzed through the variation of the energy of the [Formula: see text] excitation and the energies of excited level sequence of [Formula: see text]-bands with respect to various parameters. The shape phase transition observed at N = 88–90 is reviewed through its influence on the energies of [Formula: see text]-band. The correlation of the [Formula: see text] excitation energies with the collective shape signature observable [Formula: see text] indicates a connection with the nuclear equilibrium structure. The study of excited level sequence in the [Formula: see text]-band with respect to the ground band signifies that the two bands differ in deformation.

NEW PERSPECTIVE IN ROTATION–VIBRATION INTERACTION

2013 ◽  
Vol 22 (05) ◽  
pp. 1350023 ◽  
Author(s):  
J. B. GUPTA
Keyword(s):  
Linear Relation ◽  
Power Index ◽  
Index Formula ◽  
Level Energy ◽  
Ground Band ◽  
Single Term ◽  
Approximate Relationship ◽  
Energy Ratios ◽  
New Perspective ◽  
Universal Scale

A linear relation for the level energy ratios in the ground band of even–even nuclei, based on the rotation–vibration expression, is derived and its application on a universal scale, including the O(6), E(5) and X(5) symmetries, is illustrated. A microscopic view of this relation and of the collective model is given. Also, an approximate relationship with single term power index formula E = aIb is demonstrated.

Moments of inertia and B(E2;01+→21+)s in the NpNn scheme

2015 ◽  
Vol 93 (7) ◽  
pp. 711-715
Author(s):  
Rajesh Kumar ◽  
S. Sharma
Keyword(s):  
Nuclear Structure ◽  
Strong Dependence ◽  
Moment Of Inertia ◽  
Nucleon Pair ◽  
Valence Nucleon ◽  
Moments Of Inertia ◽  
Ground Band ◽  
Neutron Interaction ◽  
Medium Mass

We examine the collective nuclear structure of light and medium mass (Z = 50–82, N = 82–126) even–even nuclei using valence nucleon pair product (NpNn). We discuss the role of proton–neutron interaction in light mass nuclei and illustrate the variation of observables of collectivity and deformation (i.e., ground band moment of inertia) and B(E2) values with N and NpNn). The plot of these observables against NpNn vividly displays the formation of isotonic multiplets in quadrant I, strong dependence on NpNn in quadrant II and weak constancy with Z in quadrant III is illustrated.

Moment of Inertia in Light Nuclei

1968 ◽  
Vol 174 (4) ◽  
pp. 1316-1319 ◽  
Author(s):  
S. Das Gupta ◽  
A. Van Ginneken
Keyword(s):  
Moment Of Inertia ◽  
Light Nuclei

Mechanism of dynamic phase transition and synchronous stability in Hindmarsh–Rose neuronal network

2018 ◽  
Vol 32 (28) ◽  
pp. 1850308
Author(s):  
Shi-Dong Liang ◽  
Haoqi Li ◽  
Yuefan Deng
Keyword(s):  
Phase Transition ◽  
Parameter Space ◽  
Lyapunov Stability ◽  
Neuronal Network ◽  
Neuronal Model ◽  
Index Formula ◽  
Neuronal Dynamics ◽  
Dynamical Phase ◽  
Dynamic Phase ◽  
Dynamic Phase Transition

The neuronal dynamics plays an important role in understanding the neurological phenomena. We study the mechanism of the dynamic phase transition and its Lyapunov stability of a single Hindmarsh–Rose (HR) neuronal model. We propose an index [Formula: see text] to express the dynamical phase of the HR neurons. When [Formula: see text] the neuron is in the pure resting state, and when [Formula: see text] the neuron closes to the pure spiking phase, while when [Formula: see text] the neuron runs in the bursting phase. Based on this method, we investigate numerically the phase diagram of the HR neuronal model in the parameter space. We find that two mechanisms governed the HR neuronal dynamic phase transition, the phase transition and crossover transition in the different regions of the parameter space. Moreover, we analyze the equilibrium point stability of the HR neuronal model based on the Lyapunov stability method. We study the synchronous stability of the HR neuronal network based on the master stability function method and give the phase diagrams of the maximum Lyapunov exponents in the parameter space of networks. The regions of the synchronous stabilities in the parameter space depend on the couplings of the HR neurons of the membrane potential and the flux of the fast ion channel between the HR neurons. These results help to understand the HR neuronal dynamics and the synchronous stability of the HR neuronal networks.

scholarly journals Variational procedure leading from Davidson potentials to the E(5)and X(5) critical point symmetries

2020 ◽  
Vol 13 ◽  
pp. 10
Author(s):  
Dennis Bonatsos ◽  
D. Lenis ◽  
N. Minkov ◽  
D. Petrellis ◽  
P. P. Raychev ◽  
...  
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Ground State ◽  
Nuclear Energy ◽  
Energy Spectra ◽  
Variational Procedure ◽  
Ground State Band ◽  
Sharp Maximum ◽  
State Band ◽  
Shape Phase Transition

Davidson potentials of the form β^2 + β0^4/β^2, when used in the original Bohr Hamiltonian for γ-independent potentials bridge the U(5) and 0(6) symmetries. Using a variational procedure, we determine for each value of angular momentum L the value of β0 at which the derivative of the energy ratio RL = E(L)/E(2) with respect to β0 has a sharp maximum, the collection of RL values at these points forming a band which practically coincides with the ground state band of the E(5) model, corresponding to the critical point in the shape phase transition from U(5) to Ο(6). The same potentials, when used in the Bohr Hamiltonian after separating variables as in the X(5) model, bridge the U(5) and SU(3) symmetries, the same variational procedure leading to a band which practically coincides with the ground state band of the X(5) model, corresponding to the critical point of the U(5) to SU(3) shape phase transition. A new derivation of the Holmberg-Lipas formula for nuclear energy spectra is obtained as a by-product.

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