scholarly journals The harmonic oscillator energy level spacing for neutrons and protons in nuclei

2019 ◽  
Vol 3 ◽  
pp. 76
Author(s):  
G. A. Lalazissis ◽  
C. P. Panos
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Density Distribution ◽  
Periodic Table ◽  
Neutron Number ◽  
Level Spacing ◽  
Proton Number ◽  
The Difference ◽  
Closed Shells ◽  
Approximate Expressions

Approximate expressions of hw for neutrons and protons separately, as functions of the neutron number Ν and the proton number Ζ respectively, are derived. The dependence of hωn{hωp) on N(Z) is established using a rather recently proposed semi-phenomenological density distribution based on the separation energies of the last neutron or proton. The corresponding curves of hω show "discontinuities in the slope" at the closed shells throughout the periodic table. The difference hωn — hωΛ is also discussed

scholarly journals The variation of the Ηωwith the particle number and the appearance of "kinks" for atomic clusters

2020 ◽  
Vol 9 ◽  
pp. 306
Author(s):  
B. A. Kotsos ◽  
M. E. Grypeos
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Particle Number ◽  
Atomic Clusters ◽  
Level Spacing ◽  
Fermi Distribution ◽  
Sodium Clusters ◽  
Electronic Densities ◽  
Closed Shells

The dependence of the harmonic oscillator (HO) energy level spacing Ηω on the particle number Ν is studied analytically for atomic clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to "kinks", that is to "marked discontinuities in the slope" of Ηω at the closed shells. These discontinuities diminish as Ν increases.

The dependence of the harmonic oscillator energy level spacing on the mass number of nuclei

1983 ◽  
Vol 121 (2-3) ◽  
pp. 91-95 ◽  
Author(s):  
C.B. Daskaloyannis ◽  
M.E. Grypeos ◽  
C.G. Koutroulos ◽  
S.E. Massen ◽  
D.S. Saloupis
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Mass Number ◽  
Level Spacing

ISOSPIN DEPENDENT OSCILLATOR SPACING FOR NEUTRONS AND PROTONS IN NUCLEI USING HF-BCS RADII

1996 ◽  
Vol 05 (04) ◽  
pp. 669-679 ◽  
Author(s):  
G.A. LALAZISSIS ◽  
C.P. PANOS
Keyword(s):  
Root Mean Square ◽  
Neutron Number ◽  
Asymptotic Formulas ◽  
Mean Square ◽  
Heavy Nuclei ◽  
Nuclear Radius ◽  
Proton Number ◽  
The Mean ◽  
The Difference

The oscillator spacing for neutrons (ħωn) and protons (ħωp) is calculated as a function of the neutron number N and the proton number Z. The dependence of ħωn(ħωp) on N and Z is established employing a parametrization for the mean square nuclear radius obtained from HF-BCS calculations. It turns out that the difference ħωn−ħωp is appreciable, because ħω amplifies small differences of root mean square radii. It is also seen that the correction due to valence nucleons is important for relatively light and medium heavy nuclei. Satisfactory and simple approximate asymptotic formulas for ħωn(N, Z) and ħωp(N, Z) are also derived, which can be used in practice. Finally, the validity of our various approaches is checked and a possible application is also discussed.

JUSTIFICATION OF EFFECTIVE PARTICLE NUMBERS FOR DESCRIBING INTRUDER BANDS

1992 ◽  
Vol 07 (16) ◽  
pp. 1391-1398
Author(s):  
BRUCE R. BARRETT
Keyword(s):  
Neutron Number ◽  
Theoretical Explanation ◽  
Ground Band ◽  
Major Shell ◽  
Effective Particle ◽  
The Difference ◽  
Closed Shells

The standard theoretical explanation of low-lying, deformed, intruder bands in even-even nuclei near closed shells is in terms of two-particle, two-hole excitations across the major-shell gap. One normally ignores the difference between particles and holes and assumes that the effective proton (or neutron) number has increased by four. We provide a justification of this approximation by comparing two F-spin multiplets having the same F value, where one multiplet is for the ground-band levels of a set of nuclei, while the second multiplet is for the intruder-band levels of another set of nuclei.

scholarly journals Determination of the Harmonic Oscillator Energy Level Spacing for Atomic Clusters

2019 ◽  
Vol 7 ◽  
pp. 63
Author(s):  
M. E. Grypeos ◽  
B. A. Kotsos
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Particle Number ◽  
Model Potential ◽  
Atomic Clusters ◽  
Level Spacing ◽  
Jellium Model ◽  
Sodium Clusters ◽  
Good Agreement

The harmonic oscillator energy level spacing Κω for atomic clusters as a function of the particle number Ν is expressed analytically in terms of the parameters of a Woods-Saxon (or Symmetrized Woods-Saxon) potential which approximates the effective spherical self-consistent jellium model potential. The expressions derived depend an the particular scheme adopted to approximate the potential by the harmonic oscillator one and on the assumed dependence of the potential radius R on N. It is also observed, considering the case of sodium clusters,that for large Ν the expressions of Ηω are in good agreement with the well known expression of Ηω in terms of the Wigner-Seitz radius.

scholarly journals The oscillator spacing of nuclei as function of Ν and Ζ

2020 ◽  
Vol 6 ◽  
pp. 212
Author(s):  
G. A. Lalazissis ◽  
C. P. Panos
Keyword(s):  
Energy Level ◽  
Harmonic Oscillator ◽  
Mean Square ◽  
Level Spacing ◽  
Neutron Excess ◽  
Asymptotic Formulae ◽  
The Mean ◽  
Isospin Dependence ◽  
Better Than

New improved expressions for the harmonic oscillator energy level spacing Κω as function of Ν and Ζ are derived. The isospin dependence is introduced by using new expressions for the mean square radius of nuclei, which fit the experimental mean square radii and the isotopie shifts of even-even nuclei much better than other frequently used relations. The effect of the neutron excess an hω is studied. Very accurate approximate asymptotic formulae for Ηω are also derived, which are suitable for practical use.

Discussion of several analytical approximate expressions for the eigenvalues of the bounded harmonic oscillator and hydrogen atom

1983 ◽  
Vol 24 (2) ◽  
pp. 169-184 ◽  
Author(s):  
Gustavo A. Arteca ◽  
Sergio A. Maluendes ◽  
Francisco M. Fernández ◽  
Eduardo A. Castro
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Approximate Expressions

scholarly journals Quantitative electroencephalography as a tool for objective neurophysiological seizure diagnosis: A retrospective study

2020 ◽  
Vol 0 ◽  
pp. 1-6
Author(s):  
Rajesh Kumar ◽  
Tribhuwan Kumar ◽  
Kamlesh Jha ◽  
Yogesh Kumar
Keyword(s):  
Energy Level ◽  
Matched Control ◽  
Age Groups ◽  
Quantitative Electroencephalography ◽  
Beta Band ◽  
Significant Difference ◽  
Males And Females ◽  
The Mean ◽  
The Difference ◽  
Electrical Activities

Objectives: Seizure is the fourth most common neurological disorder in the world; it affects all age groups with equal possibility of occurrence in both males and females. Many antiepileptic drugs are available today, but its diagnosis is challenging. The present study attempted to see if seizure activities could be predicted by analyzing the pre-seizure electrical activities. The prediction may help in taking preventive measures appropriately beforehand in the individuals with seizure proneness. Material and Methods: We selected 11 generalized seizure patients and 19 control patients out of total 115 patients referred for electro-diagnostics for various reasons. EEG of the subjects recorded, segmented as per protocol, and analyzed using MATLAB and EEGLAB tools. Results: The mean energy level in alpha and beta band of the study subject was significantly lower (P = 0.04 and 0.004, respectively) as compared to the age matched control subjects. Theta and delta bands did not show any significant difference between the groups. The difference between the pre- and post-electrical seizure energy and entropy was statistically insignificant. Conclusion: The study shows that the energy level remains low in the seizure patients in the alpha and beta bands. This further goes down when electrophysiological seizure activities starts. The randomness or entropy does not alter significantly among the seizure subjects in comparison to non-seizure subjects.

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