Bethe–Weizsäcker semiempirical mass formula coefficients 2019 update based on AME2016

With reference to authors recently proposed three virtual atomic gravitational constants and nuclear elementary charge, close to stable mass numbers, it is possible to show that, squared neutron number plays a major role in reducing nuclear binding energy. In this context, Z=30 onwards, ‘inverse of the strong coupling constant’, can be inferred as a representation of the maximum strength of nuclear interaction and 10.09 MeV can be considered as a characteristic nuclear binding energy coefficient. Coulombic energy coefficient being 0.695 MeV, semi empirical mass formula - volume, surface, asymmetric and pairing energy coefficients can be shown to be 15.29 MeV, 15.29 MeV, 23.16 MeV and 10.09 MeV respectively. Volume and Surface energy terms can be represented with (A-A2/3-1)*15.29 MeV. With reference to nuclear potential of 1.162 MeV and coulombic energy coefficient, close to stable mass numbers, nuclear binding energy can be fitted with two simple terms having an effective binding energy coefficient of  [10.09-(1.162+0.695)/2] = 9.16 MeV. Nuclear binding energy can also be fitted with five terms having a single energy coefficient of 10.09 MeV. With further study, semi empirical mass formula can be simplified with respect to strong coupling constant.

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On the Role of Squared Neutron Number in Reducing Nuclear Binding Energy in the Light of Electromagnetic, Weak and Nuclear Gravitational Constants – A Review

The phenomenon of liquid-gas phase transition occurring in heavy-ion collisions at intermediate energies is a subject of contemporary interest. In statistical models of fragmentation, the liquid drop model is generally used to calculate the ground-state binding energies of the fragments. It is well known that the surface and symmetry energy of the hot fragments at the low-density freeze-out can be considerably modified. In addition to this, the level-density parameter also has a wide variation. The effect of variation of these parameters is studied on fragmentation observables which are related to the nuclear liquid-gas phase transition. The canonical thermodynamical model which has been very successful in describing the phenomenon of fragmentation is used for the study. The shift in transition temperature owing to the variation in liquid drop model parameters has been examined.

Effect of liquid drop model parameters on nuclear liquid gas phase transition

A modified phenomenological formula for the ground state binding energy in the region of light nuclei is proposed. Since binding energy is proportional to the volume of a nuclide, the new formula contains a volume term proportional to the mass number A and expresses asymmetry energy and coulomb repulsion energy between protons in a much simpler form than the way it is presented in the liquid drop model. The formula is used to calculate nuclear binding energy using three terms only, namely mass number A, neutron number, N and atomic number, Z. The correspondence with the conventional Liquid drop model and with the experimental results is highly satisfactory for light nuclei. Considering a set of 60 light nuclei for A ≤ 55, the formula yields root mean square deviation of 0.541 MeV, with respect to experimental values. This is better than conventional Liquid drop model which gives a root mean square deviation of 3.485 MeV over the same range of nuclei. The value of f is comparatively smaller for even-odd nuclei when compared to the corresponding even-even nuclei. Thus even-even nuclei are more strongly bound than odd-odd or even-odd nuclei making them more stable.

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Modified Phenomenological Formula for the Ground State Energy of Light Nuclei

As there exist no repulsive forces in strong interaction, in a hypothetical approach, strong interaction can be assumed to be equivalent to a large gravitational coupling. Based on this concept, strong coupling constant can be defined as a ratio of the electromagnetic force and the gravitational force associated with proton, neutron, up quark and down quark. With respect to the product of strong coupling constant and fine structure ratio, we review our recently proposed two semi empirical relations and coefficients 0.00189 and 0.00642 connected with nuclear stability and binding energy. We wish to emphasize thatby classifying nucleons as ‘free nucleons’ and ‘active nucleons’, nuclear binding energy can be fitted with a new class of ‘three term’ formula having one unique energy coefficient. Based on the geometry and quantum nature, currently believed harmonic oscillator and spin orbit magic numbers can be considered as the lower and upper “mass limits” of quark clusters.

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Hypothetical Role of Large Nuclear Gravity in Understanding the Significance and Applications of the Strong Coupling Constant

The dependence on the structure functions and Z, N numbers of the nuclear binding energy is investigated within the inverse problem(IP) approach. This approach allows us to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. The IP was formulated for the numerical generalization of the semi-empirical mass formula of BW. It was solved in 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 MeV, starting from the number of protons and number of neutrons equal to 1. The set of parameters $\{a_{i}\}$, $i=1,\dots, {\mathcal{N}}_{\rm{param}}$ of our fit represent the solution of an overdetermined system of nonlinear equations, which represent equalities between the binding energy $E_{B,j}^{\rm{Expt}}(A,Z)$ and its model $E_{B,j}^{\rm{Th}}(A,Z,\{a_{i}\})$, where $j$ is the index of the given isotope. The solution of the overdetermined system of nonlinear equations has been obtained with the help of the Aleksandrov's auto-regularization method of Gauss-Newton(GN) type for ill-posed problems. The efficiency of the above methods was checked by comparing relevant results with the results obtained independently. The explicit form of unknown functions was discovered in a step-by-step way using the modified least $\chi^{2}$ procedure, that realized in the algorithms which were developed by Aleksandrov to solve nonlinear systems of equations via the GN method, lets us to choose between two functions with same $\chi^{2}$ the better one. 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.

Modification of the Nuclear Landscape in the Inverse Problem Framework using the Generalized Bethe-Weizs\"{a}cker Mass Formula

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 o...

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

Some time ago the possibility of classical (without Gamow tunneling) universal description of radioactive nuclei decay was demonstrated. Such possibility is basis on the classical interpretation of Bohmian Psi-field reality in Bohmian-Chetaev mechanics and the hypothesis for the presence of dissipative forces, generated from the Gryzinski translational precession of the charged particles spin, in Langevin- Kramers diffusion mechanism. In this paper is present an unified model of proton, alpha decay, cluster radioactivity and spontaneous fission half-life as explicit function which depends on the total decay energy and kinetic energy, the number of protons and neutrons of daughter product, the number of protons and neutrons of mother nuclei and from a set) unknown digital parameters. The Half- lifes of the 573 nuclei taken from NuDat database together with the recent experimental data from Oganessian provide a basis for discovering the explicit form of the Kramers solution of Langevin type equation in a framework of inverse problem with the help of the Alexandrov dynamic auto-regularization method (FORTRAN program REGN-Dubna). The procedure LCH in program REGN permitts to reduce the number of unknown digital parameters from 137 to 79. The model describes 424 decays quantities with deviation of order one in years power scale.

Unified description of the proton, alpha, cluster decays and spontaneously fissions half- life

In the framework of Bohmian quantum mechanics supplemented with the Chetaev theorem on stable trajectories in dynamics in the presence of dissipative forces we have shown the possibility of the classical (without tunneling) universal description of radioactive decay of heavy nuclei, in which under certain conditions so called noise-induced transition is generated or, in other words, the stochastic channel of alpha decay, cluster radioactivity and spontaneous fission conditioned by the Kramers diffusion mechanism. Based on the ENSDF database we have found the parametrized solutions of the Kramers equation of Langevin type by Alexandrov dynamic auto-regularization method (FORTRAN program REGN-Dubna). These solutions describe with high-accuracy the dependence of the half-life (decay probability) of heavy radioactive nuclei on total kinetic energy of daughter decay products. The verification of inverse problem solution in the framework of the universal Kramers description of the alpha decay, cluster radioactivity and spontaneous fission, which was based on the newest experimental data of alpha-decay of even-even super heavy nuclei (Z=114, 116, 118) have shown the good coincidence of the experimental and theoretical half-life depend upon of alpha-decay energy.

M. A. Deliyergiyev

Papers

Modification of the Nuclear Landscape in the Inverse Problem Framework using the Generalized Bethe-Weizs\"{a}cker Mass Formula

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

Unified description of the proton, alpha, cluster decays and spontaneously fissions half- life

The Schrodinger-Chetaev Equation in Bohmian Quantum Mechanics and Diffusion Mechanism for Alpha Decay, Cluster Radioactivity and Spontaneous Fission

Numerical Generalization of the Bethe-Weizs\"{a}cker Mass Formula