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Nuclear binding energy per nucleon
Source publication
In this paper, the integrated nuclear model is introduced and a binding energy formula based on this model is presented. The
binding energies of most nuclides in this model are compared with available experimental values and also with values from
the liquid drop model (LDM).
Contexts in source publication
Context 1
... Table 1, the nuclear binding energy for all nuclides is given using Equation 6 and has been compared with the results of liquid drop models (LDMs) and with ex- perimental results. The nuclear binding energies per nu- cleon obtained using Equation 6 are in good agreement with the existing experimental data and also with LDM for all mass numbers as shown in Figures 1, 2, 3. ...
Context 2
... semi-empirical Equation 1, based upon only liquid drop model, contains at least five terms to be calculated, whereas in our Equation 6, only two terms are calcu- lated. Careful consideration of Table 1 and Figures 2 and 3 reveals the meaningful accuracy of our integrated model compared to liquid drop model with respect to experimental data (Figure 1). Special features of the ex- perimental diagram such as having maximum value for Fe and its local extrema coincide with the calculated values from Equation 6. ...
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Citations
... (3) and (4), it is possible to notice that if the parity term is included in a function employed in a model the contribution of parity will be weighted by the coefficients found by the algorithm. Dataset 1-Tritium and 254 most stable nuclides from AME2020 also used in Ref. 22 According to IAEA, an isotope is considered stable when it is non-radioactive. The Nuclear Data Services provided by IAEA (International Atomic Energy Agency) defines 243 stable isotopes in the Nuclear Chart (see Supplementary Material). ...
... The Nuclear Data Services provided by IAEA (International Atomic Energy Agency) defines 243 stable isotopes in the Nuclear Chart (see Supplementary Material). However, in 22 , the authors used a reduced number of nuclides in their study, a total of 109 nuclides (see Supplementary Material). They used 96 stable isotopes and included 12 long-lived isotopes and the tritium in their selection of stable isotopes, all inclusions are described and their measured or estimated half-lives are indicated in Supplementary Material. ...
... To help with further comparisons we opted to select the isotopes from 22 for the training subset due to the reduced number of elements, allowing us to demonstrate the performance of our method even when using a smaller number of observations. This training subset was the one used in the first example of symbolic regression by applying the Thomson problem to find an alternative numerical approximation of the binding energy per nucleon for highly stable nuclei. ...
Understanding nuclear behaviour is fundamental in nuclear physics. This paper introduces a data-driven approach, Continued Fraction Regression (cf-r), to analyze nuclear binding energy (B(A, Z)). Using a tailored loss function and analytic continued fractions, our method accurately approximates stable and experimentally confirmed unstable nuclides. We identify the best model for nuclides with A≥200\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\ge 200$$\end{document}, achieving precise predictions with residuals smaller than 0.15 MeV. Our model’s extrapolation capabilities are demonstrated as it converges with upper and lower bounds at the nuclear mass limit, reinforcing its accuracy and robustness. The results offer valuable insights into the current limitations of state-of-the-art data-driven approaches in approximating the nuclear binding energy. This work provides an illustration on the use of analytical continued fraction regression for a wide range of other possible applications.
... The constants of these terms are fitting parameters that are found experimentally to be equal to next: α n = 15.5 MeV, α s ∼ 18 MeV, α c = 0.691 MeV, α asym = 23 MeV. The details about Liquid Drop Model (LDM), discussion about other binding models, and references could be found, e.g., in [23], [24]. Note that the fourth term in Equation 8 is an asymmetry term in which it is taken into account the asymmetry in protons and neutrons. ...
A concept of ensemble averaged stellar reactors is developed to study the dynamics of processes occurring in stars, allocated in the ∼ 200 pc solar neighborhood. According to the effective temperature value, four stellar classes are identified, for which the correlation coefficients and standard deviation are counted. The theory of the buoyancy terrestial elements is generalized to stellar systems. It was suggested that stars are overheated due to the shift parameters of the nuclear processes occurring inside the stars, which leads to the synthesis of transuranium elements until the achievement of a critical nuclear mass and star explosion. The heavy transuranium elements sink downward and are concentrated in the stellar depth layers. The physical explanation of the existence of the critical Chandrasekhar star limit has been offered. Based on the spatial analysis of overheated stars, it was suggested that the withdrawal of the stellar reactor from the equilibrium state is a consequence of extragalactic compression inside the galaxy arm due to the arm spirality (not to be confused with the spirality of the galaxy itself).
... The constants of these terms are fitting parameters that are found experimentally to be equal to next: α n = 15.5 MeV, α s ∼ 18 MeV, α c = 0.691 MeV, α asym = 23 MeV. The details about Liquid Drop Model (LDM), discussion about other binding models, and references could be found e.g., in [36], [37]. Note that the asymmetry term is thus a correction term that tries to consider the asymmetry in amount of protons and neutrons. ...
Chemical elements in space can be synthesized by stellar nuclear reactors. Studying the dynamics of processes occurring in the stars introduces a concept of the ensemble-averaged stellar reactor. For future interstellar missions, the terrestrial and solar abundances were compared with considerable number of stars allocated in the ∼ 200 pc solar neighborhood. According to the value of the effective temperature, four stellar classes are distinguished, for which the correlation coefficients and standard deviation are calculated. The statement about the possibility of transferring heavy elements synthesized by stars over long distances in space has been completely refuted. There is no immutability of the distribution of elements on neighboring stars and in the Solar System. It is shown that chemical elements are mainly synthesized inside each stellar reactor. The theory of the buoyancy of elements is generalized to stars. It has been suggested that stars overheat due to a shift in the parameters of nuclear processes occurring inside stars, which leads to the synthesis of heavy elements.
... Model inti tetes cairan memaparkan bahwa inti atom yang diasumsikan sebagai suatu tetes cairan yang mempunyai kerapatan konstan, dengan meninjau efek-efek pada inti atom yakni efek volume, efek permukaan, efek coulomb, efek asimetri dan efek pasangan (Ghahramany et al., 2011). Model inti tetes cairan berhasil menganalisis sifat inti yakni rata-rata energi ikat per nukleon, namun untuk sifat inti lainnya, seperti energi dalam keadaan tereksitasi dan momen magnet inti memerlukan model inti yang secara mikroskopik dalam tinjauan perilaku nukleon secara individu (Sirma et al., 2020). ...
The purpose of this study was to calculate the activity, binding energy, and disintegration energy produced by the decay of radioactive substances in the Neptunium series based on the liquid drop core model. The research steps: 1) prepare supporting data for research on activity and binding energy on nuclear stability decay; 2) review the material that has been obtained; 3) perform calculation simulations; 4) analyze and discuss the calculation results; 5) conclude the research results. The conclusion in this study is that the activity value has increased linearly with a range of values from Bq to Bq. The binding energy decreased linearly with values ranging from 1797.4088 MeV to 1627.7112 MeV. Meanwhile, the binding energy of the nucleons increases linearly. The disintegration energy in the Neptunium series has the largest positive value (Q>0) of 5.2712 MeV and the smallest disintegration energy of Radium-225 which is -0.4317 MeV. Keyword : The activity, binding energy, liquid drop model
... The B-WSEMF is written as [12,[15][16][17]; B-WSEMF is credited for being the first phenomenological semi-empirical mass formula, that explains some crucial nuclear properties such as the mass parabola, binding fractions, fusion, fission and alpha-decay barrier potential [8,18,19]. However, B-WSEMF is limited in describing other nuclear properties such as magic numbers, nuclear magnetic moments, nuclear excited states and binding energies of light nuclei that are away from the line of stability [20,21]. In regard to this, several modifications of B-WSEMF have been undertaken with a view of formulating a model that mirrors the experimental data for both light and deformed super heavy nuclei [8,[22][23][24][25][26]. ...
... In comparison with other nuclear models for calculating binding energies, the INM is the simplest because it depends only on three basic nuclear parameters namely the atomic number (Z), neutron number (N) and mass number (A). Moreover, the calculations of binding fractions obtained from INM are relatively closer to the experimental data than other nuclear models for nuclei with 92 Z [20]. On the contrary, accurate results are not obtained when INM is used to calculate the binding fraction of nuclei having 92 Z (Transuranic elements and transactinides). ...
... The binding energy equation for nuclei derived by Ghahramany and his group is written as [20,[34][35]; ...
A modified integrated nuclear model (MINM) for calculating the binding energies of finite nuclei is proposed. The model is an improvement of the integrated nuclear model (INM) that was formulated based on the theory of quantum chromodynamics. MINM is a simple model that depends on the proton and neutron numbers, and a variable stability coefficient factor denoted by λ. The variable λ rectifies the inequality in the neutron to proton ratio that results from the increase in the size of the nucleus. The results of the binding fraction obtained from MINM were compared with the existing experimental data obtained from atomic mass evaluation tables, AME2016. It was found that, the root mean square deviation for the binding fractions obtained from MINM is 0.2267 MeV with respect to the experimental data, while the root mean square deviation for the binding fraction obtained from INM is 1.5801 MeV. The root mean square deviation for MINM is very small. This supports the validity of the MINM and the consequent accuracy in the values of the binding fraction for different nuclei, especially in the region whereby A>220.
... Based on quark theory, Ghahramany and team members [1][2][3][4] and Khanna and team members [5] developed simple nuclear binding energy formulae. Recently, we developed four different formulae for estimating binding energy of isotopes [6,7] by considering actual Up and Down quark masses [8] and electroweak [9] interaction coefficient of magnitude 0.0016 ...
... Important point to be noted is that, this relation is also free from arbitrary numbers and arbitrary energy coefficients. To compare the estimated nuclear binding energy data prepared with relations (1), (2) and (3), we have taken the following most advanced semi empirical mass formulae i.e relations (4) and (5) as references [13,14]. Readers are encouraged to refer recent semi empirical formulae [15,16] ...
... , Table 1 for the estimated nuclear binding energy of isotopes of Z = 3, 10, 17, 24,…122. With respect to relation (4), starting from Z=3 to 122 and considering 7246 atomic nuclides, root mean square error for relations (1), (2) and (3) ...
In this paper we present 3 unified formulae for estimating nuclear binding energy associated with strong and weak interactions. Our approach is entirely different from currently believed semi empirical mass formulae. Based on the three formulae, it can be understood that, increasing number of up and down quarks helps in increasing nuclear binding energy and electroweak interaction helps in reducing nuclear binding energy.
... In addition, an integrated nuclear model was proposed, and through it, a new version of the nuclear binding energy was presented according to this model. The binding energies of all nuclides in this model were compared with the available practical data, along with the energies values according to the liquid drop model [12]. The same researcher employed another form of nuclear binding energy to complement the integrated nuclear model. ...
... It deviates from the nuclei that have closed shells. This behavior of Qα-value for all the proposed models is consistent with others [5,6,11,12,19]. As for a certain isotope, the energy of decay decreases with an increase in mass number as shown in Figure ( These results were consistent with the half-life study of some isotopes. The results revealed that the half-life decreases with the increase in the mass of the same isotopes as well as the increase in the nuclear binding energy. ...
... So . This behavior of average binding energy for all the proposed models is consistent with others [5,6,10,12,19). ...
The nuclear binding energy calculated by the quark model has been used in the current research to quantify alpha decay energy (Qα- value). The research dealt with the odd-even and even - even type of heavy and super-heavy nuclei within the range (78≤ Z ≤ 118). By knowing the number of Z and N for a given nucleus, regardless of its mass, it became possible to calculate the energy of alpha decay. By correlating the experimental nuclear binding energy values of the parent nucleus and its daughters with the theoretically computed values, the quark model was adapted. Graphically extracted calibration equations have been used to produce a modern version of the alpha decay energy by linear and logarithmic matching. As essential statistical instruments, the square root rate and standard deviation were determined to show the utility of adjusted models in testing decay energy and nuclear binding energy. The analyses revealed that the experimental results have been approved.
... Since nuclear force is mediated via quarks and gluons, it is necessary and compulsory to study the nuclear binding energy scheme in terms of nuclear coupling constants. In this direction, N. Ghahramany and team members have taken a great initiative in exploring the secrets of nuclear binding energy and magic numbers [6,7] with reference to quarks. A very interesting point of their study is that -nuclear binding energy can be understood with two or three terms having a single variable energy coefficient. ...
An attempt is made toa model the atomic nucleus as a combination of bound and free or unbound nucleons. Due to strong interaction, bound nucleons help in increasing nuclear binding energy and due to electroweak interaction, free or unbound nucleons help in decreasing nuclear binding energy. In this context, with reference to proposed 4G model of final unification and strong interaction, recently we have developed a unified nuclear binding energy scheme with four simple terms, one energy coefficient of 10.1 MeV and two small numbers 0.0016 and 0.0019. In this paper, by eliminating the number 0.0019, we try to fine tune the estimation procedure of number of free or unbound nucleons pertaining to the second term with an energy coefficient of 11.9 MeV. Interesting observation is that, Z can be considered as a characteristic representation of range of number of bound isotopes of Z.
... Since nuclear force is mediated via quarks and gluons, it is necessary and compulsory to study the nuclear binding energy scheme in terms of nuclear coupling constants. In this direction, N. Ghahramany and team members have taken a great initiative in exploring the secrets of nuclear binding energy and magic numbers [6,7] with reference to quarks. Very interesting point of their study is that -nuclear binding energy can be understood with two or three terms having single variable energy coefficient. ...
With reference to proposed 4G model of final unification and strong interaction, recently we have developed a unified nuclear binding energy scheme with four simple terms, one energy coefficient of 10.1 MeV and two small numbers 0.0016 and 0.0019. In this paper, by eliminating the number 0.0019, we try to fine tune the estimation procedure of number of free or unbound nucleons pertaining to the second term with an energy coefficient of 11.9 MeV. It seems that, some kind of electroweak interaction is playing a strange role in maintaining free or unbound nucleons within the nucleus. It is possible to say that, strong interaction plays a vital role in increasing nuclear binding energy and electroweak interaction plays a vital role in reducing nuclear binding energy. Interesting observation is that, Z can be considered as a characteristic representation of range of number of bound isotopes of Z. For medium, heavy and super heavy atoms, beginning and ending mass numbers pertaining to bound states can be understood with 2Z+0.004Z^2 and 3Z+0.004Z^2 respectively. With further study, neutron drip lines can be understood. Based on this kind of data fitting procedure, existence of our 4G model of electroweak fermion of rest energy 584.725 GeV can be confirmed indirectly.
... The most stable isobars which are determined for an isobaric family with odd and even mass number (A) equals to (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) from the parabolic relationship between binding energies (B.E) and atomic number (Z) as shown in the figures (3-1) and are ( 15 N, 17 O, 19 F, 21 Ne, 23 Na, 25 Mg, 27 Al & 29 Si) nuclides for isobars with an odd mass number (A), while for isobars with even mass number (A) the most stable isobars for odd-odd nuclide are ( 16 N, 18 F, 20 F, 22 Na, 24 Na, 26 Al, 28 Al & 30 Al ) and for even-even nuclide( 16 O, 18 O, 20 Ne, 22 Ne, 24 Mg, 26 Mg, 28 Si & 30 Si) . ...
... The most stable isobars which are determined for an isobaric family with odd and even mass number (A) equals to (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) from the parabolic relationship between binding energies (B.E) and atomic number (Z) as shown in the figures (3-1) and are ( 15 N, 17 O, 19 F, 21 Ne, 23 Na, 25 Mg, 27 Al & 29 Si) nuclides for isobars with an odd mass number (A), while for isobars with even mass number (A) the most stable isobars for odd-odd nuclide are ( 16 N, 18 F, 20 F, 22 Na, 24 Na, 26 Al, 28 Al & 30 Al ) and for even-even nuclide( 16 O, 18 O, 20 Ne, 22 Ne, 24 Mg, 26 Mg, 28 Si & 30 Si) . ...
... The most stable isobars which are determined for an isobaric family with odd and even mass number (A) equals to (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) from the parabolic relationship between binding energies (B.E) and atomic number (Z) as shown in the figures (3-1) and are ( 15 N, 17 O, 19 F, 21 Ne, 23 Na, 25 Mg, 27 Al & 29 Si) nuclides for isobars with an odd mass number (A), while for isobars with even mass number (A) the most stable isobars for odd-odd nuclide are ( 16 N, 18 F, 20 F, 22 Na, 24 Na, 26 Al, 28 Al & 30 Al ) and for even-even nuclide( 16 O, 18 O, 20 Ne, 22 Ne, 24 Mg, 26 Mg, 28 Si & 30 Si) . ...
