scholarly journals Identification of highly deformed even–even nuclei in the neutron- and proton-rich regions of the nuclear chart from the B(E2)↑ and E2 predictions in the generalized differential equation model

2015 ◽  
Vol 24 (12) ◽  
pp. 1550091
Author(s):  
R. C. Nayak ◽  
S. Pattnaik
Keyword(s):  
Differential Equation ◽  
Large Deformations ◽  
Transition Probability ◽  
Electric Quadrupole ◽  
Mass Region ◽  
Equation Model ◽  
Generalized Differential Equation ◽  
Predicted Values ◽  
Generalized Differential ◽  
Physical Quantities

We identify here the possible occurrence of large deformations in the neutron- and proton-rich ([Formula: see text]-rich and [Formula: see text]-rich) regions of the nuclear chart from extensive predictions of the values of the reduced quadrupole transition probability [Formula: see text] for the transition from the ground state to the first [Formula: see text] state and the corresponding excitation energy [Formula: see text] of even–even nuclei in the recently developed generalized differential equation (GDE) model exclusively meant for these physical quantities. This is made possible from our analysis of the predicted values of these two physical quantities and the corresponding deformation parameters derived from them such as the quadrupole deformation [Formula: see text], the ratio of [Formula: see text] to the Weisskopf single-particle [Formula: see text] and the intrinsic electric quadrupole moment [Formula: see text], calculated for a large number of both known as well as hitherto unknown even–even isotopes of oxygen to fermium (0 to FM; [Formula: see text]–100). Our critical analysis of the resulting data convincingly support possible existence of large collectivity for the nuclides [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], whose values of [Formula: see text] are found to exceed 0.3 and even 0.4 in some cases. Our findings of large deformations in the exotic [Formula: see text]-rich regions support the existence of another “island of inversion” in the heavy-mass region possibly caused by breaking of the [Formula: see text] subshell closure.

scholarly journals ${\rm B(E2)}\uparrow (0_{1}^{+} \rightarrow 2_{1}^{+})$ predictions for even–even nuclei in the differential equation model

2015 ◽  
Vol 24 (02) ◽  
pp. 1550011 ◽  
Author(s):  
R. C. Nayak ◽  
S. Pattnaik
Keyword(s):  
Differential Equation ◽  
Transition Probability ◽  
Electric Quadrupole ◽  
Equation Model ◽  
Quadrupole Transition ◽  
Differential Equation Model ◽  
Recursion Relations ◽  
Electric Quadrupole Transition ◽  
Wide Range

We use the recently developed differential equation model (DEM) for the reduced electric quadrupole transition probability B(E2)↑ for the transition from the ground to the first 2+ state for predicting its values for a wide range of even–even nuclides almost throughout the nuclear landscape from Neon to Californium. This is made possible as the principal equation in the model, namely, the differential equation connecting the B(E2)↑ value of a given even–even nucleus with its derivatives with respect to the neutron and proton numbers, provides two different recursion relations, each connecting three different neighboring even–even nuclei from lower- to higher-mass numbers and vice versa. These relations are primarily responsible in extrapolating from known to unknown terrain of the B(E2)↑-landscape and thereby facilitate the predictions throughout. As a result, we have succeeded in predicting its hitherto unknown value for the adjacent 251 isotopes lying on either side of the known B(E2)↑ database.

scholarly journals A differential equation for the transition probability B(E2)↑ and the resulting recursion relations connecting even–even nuclei

2014 ◽  
Vol 23 (04) ◽  
pp. 1450022 ◽  
Author(s):  
S. Pattnaik ◽  
R. C. Nayak
Keyword(s):  
Differential Equation ◽  
Transition Probability ◽  
Electric Quadrupole ◽  
Energy Relation ◽  
Local Energy ◽  
Many Body ◽  
Recursion Relations ◽  
Many Body Theory ◽  
Electric Quadrupole Transition ◽  
Atomic Nuclei

We obtain here a new relation for the reduced electric quadrupole transition probability B(E2)↑ of a given nucleus in terms of its derivatives with respect to neutron and proton numbers based on a similar local energy relation in the Infinite Nuclear Matter (INM) model of atomic nuclei, which is essentially built on the foundation of the Hugenholtz–Van Hove (HVH) theorem of many-body theory. Obviously, such a relation in the form of a differential equation is expected to be more powerful than the usual algebraic difference equations. Although the relation for B(E2)↑ has been perceived simply on the basis of a corresponding differential equation for the local energy in the INM model, its theoretical foundation otherwise has been clearly demonstrated. We further exploit the differential equation in using the very definitions of the derivatives to obtain two different recursion relations for B(E2)↑, connecting in each case three neighboring even–even nuclei from lower to higher mass numbers and vice versa. We demonstrate their numerical validity using available data throughout the nuclear chart and also explore their possible utility in predicting B(E2)↑ values.

scholarly journals Fixed Point Theorems for Generalized Set-Valued Weak θ-Contractions in Complete Metric Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Seong-Hoon Cho
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Generalized Differential Equation ◽  
Generalized Differential

In this paper, the notion of generalized set-valued weak θ-contractions is introduced and a new fixed point theorem for such contractions is established in the setting metric spaces. The main result is a generalization of fixed point theorems in the literature. An example and an application to generalized differential equation are given to support the validity of the main theorem.

scholarly journals On the Oscillatory Behavior of Some Qeneralized Differential Equation

2021 ◽  
pp. 73-82
Author(s):  
Juan E. Napoles Valdes´ ◽  
Yusif S. Gasimov ◽  
Aynura R. Aliyeva
Keyword(s):  
Differential Equation ◽  
Oscillatory Behavior ◽  
Oscillatory Nature ◽  
Type Transformation ◽  
Generalized Differential Equation ◽  
Generalized Differential

In this article, using the Riccati-type transformation, we study the oscillatory nature of the solutions of the generalized differential equation and give some criteria of the Kamenev type that generalizes several well-known results on the topic.

scholarly journals Properties of the solution set of a generalized differential equation

1972 ◽  
Vol 6 (3) ◽  
pp. 379-398 ◽  
Author(s):  
J.L. Davy
Keyword(s):  
Differential Equation ◽  
Additional Assumption ◽  
Initial Conditions ◽  
Upper Semicontinuity ◽  
The State ◽  
Solution Set ◽  
Initial Time ◽  
State Variable ◽  
Generalized Differential Equation ◽  
Generalized Differential

We prove that the solution set of a generalized differential equation is connected and that points on the boundary of the solution funnel are peripherally attainable. This is done without the additional assumption of continuity in the state variable required in previous results. The result on upper semicontinuity of the solution set with respect to initial conditions is extended to include variations of initial time.

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