THE ART OF PREDICTING 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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MODIFIED BETHE–WEIZSÄCKER MASS FORMULA WITH ISOTONIC SHIFT AND NEW DRIPLINES

Modern Physics Letters A ◽

10.1142/s021773230501666x ◽

2005 ◽

Vol 20 (21) ◽

pp. 1605-1618 ◽

Cited By ~ 6

Author(s):

P. ROY CHOWDHURY ◽

C. SAMANTA ◽

D. N. BASU

Keyword(s):

Mass Formula ◽

Liquid Drop ◽

Macroscopic Model ◽

Liquid Drop Model ◽

Nuclear Masses

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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Modification of the nuclear landscape in the inverse problem framework using the generalized Bethe–Weizsäcker mass formula

International Journal of Modern Physics E ◽

10.1142/s0218301318500155 ◽

2018 ◽

Vol 27 (02) ◽

pp. 1850015 ◽

Cited By ~ 4

Author(s):

S. Cht. Mavrodiev ◽

M. A. Deliyergiyev

Keyword(s):

Inverse Problem ◽

Mass Formula ◽

Maximum Deviation ◽

Model Parameters ◽

Magic Numbers ◽

Systems Of Equations ◽

Nonlinear Systems Of Equations ◽

Nuclear Mass ◽

Nuclear Masses ◽

Semi Empirical

We formalized the nuclear mass problem in the inverse problem framework. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The inverse problem was formulated for the numerically generalized semi-empirical mass formula of Bethe and von Weizsäcker. It was solved in a step-by-step way based on the AME2012 nuclear database. The established parametrization describes the measured nuclear masses of 2564 isotopes with a maximum deviation less than 2.6[Formula: see text]MeV, starting from the number of protons and number of neutrons equal to 1.The explicit form of unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified least [Formula: see text] procedure, that realized in the algorithms which were developed by Lubomir Aleksandrov to solve the nonlinear systems of equations via the Gauss–Newton method, lets us to choose the better one between two functions with same [Formula: see text]. In the obtained generalized model, the corrections to the binding energy depend on nine proton (2, 8, 14, 20, 28, 50, 82, 108, 124) and ten neutron (2, 8, 14, 20, 28, 50, 82, 124, 152, 202) magic numbers as well on the asymptotic boundaries of their influence. The obtained results were compared with the predictions of other models.

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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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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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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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Nuclear mass measurements with radioactive ion beams

International Journal of Modern Physics E ◽

10.1142/s0218301319300054 ◽

2019 ◽

Vol 28 (04) ◽

pp. 1930005 ◽

Cited By ~ 2

Author(s):

Michael A. Famiano

Keyword(s):

Mass Measurement ◽

Measurement Techniques ◽

Nuclear Mass ◽

Mass Measurements ◽

Future Directions ◽

Advantages And Disadvantages ◽

Nuclear Masses ◽

Under Construction ◽

Very High ◽

Practical Constraints

Nuclear masses are the most fundamental of all nuclear properties, yet they can provide a wealth of knowledge, including information on astrophysical sites, constraints on existing theory, and fundamental symmetries. In nearly all applications, it is necessary to measure nuclear masses with very high precision. As mass measurements push to more short-lived and more massive nuclei, the practical constraints on mass measurement techniques become more exacting. Various techniques used to measure nuclear masses, including their advantages and disadvantages are described. Descriptions of some of the world facilities at which the nuclear mass measurements are performed are given, and brief summaries of planned facilities are presented. Future directions are mentioned, and conclusions are presented which provide a possible outlook and emphasis on upcoming plans for nuclear mass measurements at existing facilities, those under construction, and those being planned.

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A Compact UWB Indoor and Through-Wall Radar with Precise Ranging and Tracking

International Journal of Antennas and Propagation ◽

10.1155/2012/678590 ◽

2012 ◽

Vol 2012 ◽

pp. 1-11 ◽

Cited By ~ 11

Author(s):

Yinan Yu ◽

Jian Yang ◽

Tomas McKelvey ◽

Borys Stoew

Keyword(s):

Signal Processing ◽

Theoretical Analysis ◽

Short Range ◽

Indoor Environment ◽

Low Cost ◽

Moving Target ◽

Radiation Characteristics ◽

Uwb Radar ◽

Signal Processing Algorithms ◽

Processing Algorithms

Ultrawideband (UWB) technology has many advantages compared to its narrowband counterpart in many applications. We present a new compact low-cost UWB radar for indoor and through-wall scenario. The focus of the paper is on the development of the signal processing algorithms for ranging and tracking, taking into account the particular properties of the UWB CMOS transceiver and the radiation characteristics of the antennas. Theoretical analysis for the algorithms and their evaluations by measurements are presented in the paper. The ranging resolution of this UWB radar has achieved 1-2 mm RMS accuracy for a moving target in indoor environment over a short range, and Kalman tracking algorithm functions well for the through-wall detection.

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