MODIFIED BETHE–WEIZSÄCKER MASS FORMULA WITH ISOTONIC SHIFT AND NEW DRIPLINES

Nuclear masses are calculated using the modified Bethe–Weizsäcker mass formula in which the isotonic shifts have been incorporated. The results are compared with the improved liquid drop model with isotonic shift. Mass excesses predicted by this method compares well with the microscopic–macroscopic model while being much more simple. The neutron and proton drip lines have been predicted using this modified Bethe–Weizsäcker mass formula with isotonic shifts.

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The Study of Modified Semi-Empirical Mass Formula (SEMF) by Considering Isospin Effects in Liquid Drop Model

Proceeding International Conference on Science and Engineering ◽

10.14421/icse.v2.76 ◽

2019 ◽

Vol 2 ◽

pp. 153-160

Author(s):

Sinta Ayu Sakinah ◽

Eko Tri Sulistyani

Keyword(s):

Mass Formula ◽

Liquid Drop ◽

Experimental Results ◽

Macroscopic Model ◽

Model Parameters ◽

Liquid Drop Model ◽

Protons And Neutrons ◽

Symmetry Properties ◽

K 12 ◽

Semi Empirical

We do theoretically study of Modified Semi-Empirical Mass Formula (SEMF) based on macroscopic approach in liquid drop model by considering isospin effects. Isospin is one of internal symmetry properties in hadron group, particularly the nucleon multiplet, it represented by SU(2) isospin group. Hadron is a group of elementary particles take place in the strong interaction. The role of strong interactions represents homogeneous nuclear force, interactions between proton-proton (Fpp) , proton-neutron (Fpn), and neutron-neutron (Fnn) are same. In other words, protons and neutrons are indistinguishable because mass (energy) between protons and neutrons is almost the same, by removing charge between them (charge independent). The dependence of isospin effects on nuclear symmetry term and odd-even (pairing) term made the formulation of SEMF should be modificated, in order to obtain nuclear mass and binding energy of a nucleus close to the experimental results. We do two accuracy testing. First, by comparing |Mexp - Mth| for nuclei Pb82208 using SEMF before and after being modified, the result shows that using SEMF before modification the value of |Mexp - Mth|≈ 0,0204 u and for modified SEMF we obtained |Mexp - Mth|≈ 0,0203 u at k=12 . The value of |Mexp - Mth| for modified SEMF is smaller than before modification, it indicates that Modified SEMF is a good formula to calculate the mass of nuclei. Second, by comparing Modified SEMF with other models such as FRDM, HFB-14, and HFB-17 using accuracy parameter in the form of rms deviation and number of model parameters ). The results show that rms deviation decrease 21% to 0,516 and number of model parameters ) decrease to 15, consists of 13 macroscopic model parameters and two microscopic model parameters and �). The value of model parameters was obtained by fitting to experimental results, as a reason it is called semi-empiric.

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THE ART OF PREDICTING NUCLEAR MASSES

International Journal of Modern Physics E ◽

10.1142/s0218301308012014 ◽

2008 ◽

Vol 17 (supp01) ◽

pp. 398-411 ◽

Cited By ~ 9

Author(s):

JORGE G. HIRSCH ◽

IRVING MORALES ◽

JOEL MENDOZA-TEMIS ◽

ALEJANDRO FRANK ◽

JUAN CARLOS LOPEZ-VIEYRA ◽

...

Keyword(s):

Theoretical Analysis ◽

Predictive Model ◽

Iterative Process ◽

Short Range ◽

Mass Formula ◽

Predictive Power ◽

Liquid Drop ◽

Liquid Drop Model ◽

Nuclear Mass ◽

Nuclear Masses

A review of recent advances in the theoretical analysis of nuclear mass models and their predictive power is presented. After introducing two tests which probe the ability of nuclear mass models to extrapolate, three models are analyzed in detail: the liquid drop model (LDM), the liquid drop model plus empirical shell corrections (LDMM) and the Duflo–Zuker mass formula (DZ). The DZ model is exhibited as the most predictive model. The Garvey–Kelson mass relations are also discussed. It is shown that their fulfillment probes the consistency of the most commonly used mass formulae, and that they can be used in an iterative process to predict nuclear masses in the neighborhood of nuclei with measured masses, offering a simple and reproducible procedure for short range mass predictions.

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FISSION BARRIERS WITHIN THE LIQUID DROP MODEL WITH THE SURFACE-CURVATURE TERM

International Journal of Modern Physics E ◽

10.1142/s0218301304001801 ◽

2004 ◽

Vol 13 (01) ◽

pp. 107-112 ◽

Cited By ~ 21

Author(s):

K. POMORSKI ◽

J. DUDEK

Keyword(s):

Liquid Drop ◽

Surface Curvature ◽

Fission Barrier ◽

Macroscopic Model ◽

Liquid Drop Model ◽

Barrier Heights ◽

Curvature Term ◽

Fission Barriers ◽

The Masses ◽

Weak Influence

The recently revised liquid drop model (PRC 67(2003) 044316) containing the curvature term reproduces the masses of 2766 experimentally known isotopes having Z≥8 and N≥8 with the r.m.s. deviation equal to 0.698 MeV when the microscopic corrections of Moeller et al. is used. The influence of the congruence energy as well as the compression term on the barrier heights is discussed within this new macroscopic model. The r.m.s. deviation of the fission barrier heights of 40 isotopes with Z≥34 is 1.73 MeV only when deformation-dependent congruence energy is included. The effect of the compression term in the liquid drop energy has rather weak influence on the barrier heights.

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PREDICTING NUCLEAR MASSES BY IMAGE RECONSTRUCTION

International Journal of Modern Physics E ◽

10.1142/s0218301306005228 ◽

2006 ◽

Vol 15 (08) ◽

pp. 1855-1867 ◽

Cited By ~ 2

Author(s):

IRVING MORALES ◽

ALEJANDRO FRANK ◽

JUAN CARLOS LÓPEZ-VIEYRA ◽

JOSÉ BAREA ◽

JORGE G. HIRSCH ◽

...

Keyword(s):

Fourier Transform ◽

Liquid Drop ◽

Nuclear Deformation ◽

Two Dimensional ◽

Deconvolution Method ◽

Liquid Drop Model ◽

Unstable Nuclei ◽

Shell Closures ◽

Nuclear Masses ◽

Potential Applications

The differences between measured masses and Liquid Drop Model (LDM) predictions have well known regularities, which can be analyzed as a two-dimensional texture on the N-Z plane. The remaining microscopic effects, obtained after removing the smooth LDM mass contributions, have proved difficult to model. They contain all the information related to shell closures, nuclear deformation and the residual nuclear interactions, and display a well defined pattern. In the present work the more than 2000 known nuclear masses are studied as an array in the N-Z plane viewed through a mask, behind which the approximately 7000 unknown unstable nuclei that can exist between the proton and neutron drip lines are hidden. Employing a Fourier transform deconvolution method these masses can be predicted. Measured masses are reconstructed with and r.m.s. error of less than 100 keV. Potential applications of the present approach are outlined.

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Coefficients and terms of the liquid drop model and mass formula

Physical Review C ◽

10.1103/physrevc.73.067302 ◽

2006 ◽

Vol 73 (6) ◽

Cited By ~ 24

Author(s):

G. Royer ◽

C. Gautier

Keyword(s):

Mass Formula ◽

Liquid Drop ◽

Liquid Drop Model

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PREDICTIONS OF NUCLEAR MASSES IN DIFFERENT MODELS

International Journal of Modern Physics E ◽

10.1142/s0218301307005909 ◽

2007 ◽

Vol 16 (02) ◽

pp. 474-482 ◽

Cited By ~ 2

Author(s):

BOŻENA NERLO–POMORSKA ◽

KRZYSZTOF POMORSKI ◽

MONIKA ZWIERZCHOWSKA

Keyword(s):

Field Theory ◽

Liquid Drop ◽

Mean Field Theory ◽

Mean Field ◽

Liquid Drop Model ◽

Hartree Fock ◽

Relativistic Mean Field ◽

Bogoliubov Theory ◽

Nuclear Masses ◽

Nuclear Stability

The modern version of the liquid-drop model is compared to the macroscopic Thomas-Fermi (TF) energy and the macroscopic part of the binding energy evaluated within the Hartree-Fock-Bogoliubov theory with the Gogny force and the relativistic mean field theory. The limits of nuclear stability predicted by these models are discussed.

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