scholarly journals Root Mean Square Radius of 6Li Nucleus using Cluster Model Wavefunction

2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Neelam Sinha
Keyword(s):  
Root Mean Square ◽  
Single Particle ◽  
Cluster Model ◽  
Center Of Mass ◽  
High Energy ◽  
Nuclear Charge Radius ◽  
Group Method ◽  
Mean Square ◽  
Generator Coordinate ◽  
Alpha Cluster

The calculation of root mean square nuclear charge radius is one of the most important nuclear parameters regarding the size and structure of the nucleus. In this paper calculations for root mean square (r.m.s.) radius of the ground state of 6Li nucleus using high energy electron scattering is presented. The initial work involves writing first the cluster model wavefunction employing the resonating group method, generator coordinate method and complex generator coordinate technique. The wavefunction is written with definite parity, spin, total angular momentum and relative motion between the alpha cluster and deuteron cluster and the center-of-mass of the two clusters. The application of complex generator coordinate technique transforms the cluster model wavefunction into antisymmetrized products of single particle wavefunction written in terms of single particle co-ordinates, the centerof-mass coordinates, parameter coordinates and generator coordinates. The width parameters of alpha and deuteron clusters are adjusted to obtain predictions close to experimental values.

scholarly journals CLUSTER SHELL MODEL WAVE FUNCTION: STRUCTURE OF 6LI NUCLEUS

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Neelam Sinha ◽  
Piyush Sinha
Keyword(s):  
Wave Function ◽  
Shell Model ◽  
Single Particle ◽  
Cluster Model ◽  
Center Of Mass ◽  
Group Method ◽  
Model Wave Function ◽  
Model Wave ◽  
Generator Coordinate ◽  
Particle Wave Function

In this paper cluster model wave function for 6Li using Shell Model with definite parity and angular momentum is written along with cluster co-ordinates, which are relative to the center-of-mass of various clusters and involve with parameters. These parameters can be adjusted to some extent to obtain predictions close to experimental properties. The cluster model wave function is written along with resonating group method (RGM) and the Complex Generator Coordinate Technique (CGCT). The Complex Generator Coordinate Technique allows the transformation of the cluster model wave function written in terms of cluster co-ordinates into anti-symmetrized product of single particle wave function. This wave function is written in terms of single particle co-ordinates, the center-of-mass co-ordinates, parameter coordinates and generator coordinates.

scholarly journals Use of Microscopic Theoretical Methods for The Construction of The Nuclear Wavefunction of 7Li

2021 ◽  
Vol 16 (2) ◽  
Author(s):  
Neelam Sinha ◽  
Piyush Sinha
Keyword(s):  
Center Of Mass ◽  
Light Nuclei ◽  
Mass Motion ◽  
Group Method ◽  
Generator Coordinate Method ◽  
Generator Coordinate ◽  
Nuclear Cluster ◽  
Neutron Cluster ◽  
Alpha Cluster ◽  
Antisymmetrized Product

Microscopic theoretical studies of scattering and reaction problems for light nuclei have been extensively carried out using resonating group method. In this paper we have used the nuclear cluster model, the resonating group method, the generator coordinate method and complex generator coordinate technique for the construction of microscopic antisymmetrized nuclear wavefunction of 7Li nucleus. This wavefunction can be further used to calculate the structural properties of the nucleus. The 7Li nucleus in ground state is considered as a nuclear system consisting of three clusters namely an alpha cluster, a deuteron cluster and a neutron cluster. We have chosen spatial, spin and isospin function of cluster internal functions. The arguments of internal wavefunction include the parameter coordinates. These parameters can be adjusted to some extent to obtain predictions close to experimental results. The wavefunction is written using shell model with definite parity and angular momentum. The complex generator coordinate technique allows this wavefunction to write it as an antisymmetrized product of seven single particle functions after inclusion of the wavefunction for the center- of -mass motion

scholarly journals Elastic scattering and breakup reactions with light proton- and neutron-rich exotic nuclei

2018 ◽  
Vol 194 ◽  
pp. 07002
Author(s):  
M.K. Gaidarov ◽  
V.K. Lukyanov ◽  
D.N. Kadrev ◽  
E.V. Zemlyanaya ◽  
A.N. Antonov ◽  
...  
Keyword(s):  
Experimental Data ◽  
Elastic Scattering ◽  
Cross Sections ◽  
Cluster Model ◽  
Microscopic Analysis ◽  
High Energy ◽  
The Real ◽  
Optical Potentials ◽  
Generator Coordinate ◽  
Energy Approximation

A microscopic analysis of the optical potentials (OPs) and cross sections of elastic scattering of 8B on 12C, 58Ni, and 208Pb targets at energies 20 < E < 170 MeV and 12,14Be on 12C at 56 MeV/nucleon is carried out. The real part of the OP is calculated by a folding procedure and the imaginary part is obtained on the base of the high-energy approximation (HEA). The density distributions of 8B evaluated within the variational Monte Carlo (VMC) model and the three-cluster model (3CM) are used to construct the potentials. The 14Be densities obtained in the framework of the the generator coordinate method (GCM) are used to calculate the optical potentials, while for the same purpose both the VMC model and GCM densities of 12Be are used. In the hybrid model developed and explored in our previous works, the only free parameters are the depths of the real and imaginary parts of OP obtained by fitting the experimental data. The use of HEA to estimate the imaginary OP at energies just above the Coulomb barrier is discussed. In addition, cluster model, in which 8B consists of a p-halo and the 7Be core, is applied to calculate the breakup cross sections of 8B nucleus on 9Be, 12C, and 197Au targets, as well as momentum distributions of 7Be fragments. A good agreement of the theoretical results with the available experimental data is obtained. It is concluded that the reaction studies performed in this work may provide supplemental information on the internal spatial structure of the proton- and neutron-halo nuclei.

Estimating Center of Mass Kinematics During Perturbed Human Standing Using Accelerometers

2021 ◽  
pp. 1-10
Author(s):  
Sandra K. Hnat ◽  
Musa L. Audu ◽  
Ronald J. Triolo ◽  
Roger D. Quinn
Keyword(s):  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Mean Squared Error ◽  
Balance Control ◽  
Center Of Mass ◽  
Coefficient Of Determination ◽  
Mean Square ◽  
Cord Injury ◽  
Movement Type

Estimating center of mass (COM) through sensor measurements is done to maintain walking and standing stability with exoskeletons. The authors present a method for estimating COM kinematics through an artificial neural network, which was trained by minimizing the mean squared error between COM displacements measured by a gold-standard motion capture system and recorded acceleration signals from body-mounted accelerometers. A total of 5 able-bodied participants were destabilized during standing through: (1) unexpected perturbations caused by 4 linear actuators pulling on the waist and (2) volitionally moving weighted jars on a shelf. Each movement type was averaged across all participants. The algorithm’s performance was quantified by the root mean square error and coefficient of determination (R2) calculated from both the entire trial and during each perturbation type. Throughout the trials and movement types, the average coefficient of determination was 0.83, with 89% of the movements with R2 > .70, while the average root mean square error ranged between 7.3% and 22.0%, corresponding to 0.5- and 0.94-cm error in both the coronal and sagittal planes. COM can be estimated in real time for balance control of exoskeletons for individuals with a spinal cord injury, and the procedure can be generalized for other gait studies.

scholarly journals Deterministic and Probabilistic Foundation Forces Resulting From an Unbalanced Turbine

1976 ◽  
Author(s):  
L. Boyce ◽  
T. J. Kozik
Keyword(s):  
Root Mean Square ◽  
Center Of Mass ◽  
Random Variable ◽  
Degree Of Freedom ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Principal Mode ◽  
Single Degree ◽  
Rotating Machine ◽  
Mean Square Response

This paper considers the problem of the unbalanced rotating turbine as a single degree of freedom system, wherein the principal mode of vibration is a translation in the direction of the machine supports. The distance from the center of mass of the rotating mass to the geometric axis, also known as the effective eccentricity, is modeled as a random variable. The expression for the root mean square response of the rotating machine is derived and related to the statistical analog for the deterministic expression for the foundation force. These results are numerically compared to their equivalent deterministic values.

THE STUDY OF DIBARYON SYSTEMS WITH STRANGENESS ON CHIRAL QUARK MODEL

2005 ◽  
Vol 20 (01) ◽  
pp. 69-77
Author(s):  
HOURONG PANG ◽  
JIALUN PING ◽  
XIAOHUA WU
Keyword(s):  
Binding Energy ◽  
Quark Model ◽  
Root Mean Square ◽  
Bound State ◽  
Group Method ◽  
Chiral Quark Model ◽  
Mean Square ◽  
Narrow Resonance ◽  
The Masses

We expand Salamanca SU (2) chiral quark model to SU (3) one and calculate promising dibaryon candidates with strangeness S=-3,-6 in the framework of resonating group method. We find that, besides ΩΩ, the mass of NΩ state is about 23–38 MeV lower than its threshold, it might appear as a bound state or a narrow resonance. The effect of K and η exchanges on the masses of strangeness and nonstrangeness systems has been studied and found to be negligible for nonstrangeness systems. However this effect brings some changes (about tens of MeV) on the masses of strangeness systems. We have also studied the sensitivities of binding energy and root mean square radius to the mass of s-quark.

Evolution of few-cycle pulses in nonlinear dispersive media: Velocity of the center of mass and root-mean-square duration

2016 ◽  
Vol 94 (3) ◽  
Author(s):  
Yury A. Kapoyko ◽  
Arkadiy A. Drozdov ◽  
Sergei A. Kozlov ◽  
Xi-Cheng Zhang
Keyword(s):  
Root Mean Square ◽  
Center Of Mass ◽  
Dispersive Media ◽  
Mean Square

EFFECT OF THE PARTICLE-NUMBER SYMMETRY RESTORATION ON ROOT MEAN SQUARE RADII OF EVEN–EVEN NEUTRON-DEFICIENT NUCLEI IN THE ISOVECTOR PAIRING CASE

2012 ◽  
Vol 21 (04) ◽  
pp. 1250046 ◽  
Author(s):  
M. DOUICI ◽  
N. H. ALLAL ◽  
M. FELLAH ◽  
N. BENHAMOUDA ◽  
M. R. OUDIH
Keyword(s):  
Experimental Data ◽  
Root Mean Square ◽  
Single Particle ◽  
Particle Number ◽  
Mean Field ◽  
Second Step ◽  
Mean Square ◽  
The One ◽  
Proton Pairing

The effect of the particle-number symmetry restoration on the root mean square (rms) proton and neutron radii of neutron-deficient nuclei is studied in the isovector pairing case. As a first step, an expression of the nuclear radii which includes the neutron–proton pairing effects and which strictly conserves the particle-number has been established using the SBCS (Sharp BCS) method. It is shown that this expression generalizes the one obtained in the pairing between like-particles case. As a second step, the proton and neutron rms radii are numerically evaluated for even–even nuclei such as 16⩽Z⩽56 and 0⩽(N-Z)⩽4 using the single-particle energies of a Woods–Saxon mean-field. The results are compared with experimental data when available and with the results obtained when one considers only the pairing between like-particles.

scholarly journals Validity and Reliability of a Tool for Accelerometric Assessment of Balance in Scholar Children

2021 ◽  
Vol 10 (1) ◽  
pp. 137
Author(s):  
Jesús García-Liñeira ◽  
Raquel Leirós-Rodríguez ◽  
Vicente Romo-Pérez ◽  
Jose L. García-Soidán
Keyword(s):  
Root Mean Square ◽  
Center Of Mass ◽  
Healthy Children ◽  
Mean Square ◽  
Functional Tests ◽  
Clinical Tests ◽  
Validity And Reliability ◽  
Balance Test ◽  
Cross Sectional ◽  
Bar Test

In Pediatrics, balance is assessed through low-sensitivity clinical tests which identify developmental alterations at already advanced stages that cannot be detected at earlier stages. Therefore, the aim of this study was to develop an easily applicable quantitative tool that can be used to evaluate postural control. Consequently, a cross-sectional study was carried out with 91 healthy children. All of them performed a series of six accelerometric functional tests and four clinical tests of balance (Modified Flamingo Test, Bar Test, Babinski–Weil Test, and Fukuda Stepping Test). The Bar Test obtained mild inverse correlations with accelerations produced in the mediolateral axis and the root mean square of all the tests in monopodal support. The Flamingo Test obtained direct correlations with the root mean square of the tests in monopodal support and with the mediolateral axis of the monopodal tests and gait. The pediatric balance assessment scale consists of three factors and eleven items extracted from five accelerometric functional tests: the monopodal balance test with six items, normal gait test with three items, and bipodal balance test with two items. This tool is easy to apply and allows analysis in the evaluation of the balance state based on the accelerations of the center of mass.

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