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

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

In the binary-driven hypernova model of long gamma-ray bursts, a carbon–oxygen star explodes as a supernova in the presence of a neutron star binary companion in close orbit. Hypercritical (i.e., highly super-Eddington) accretion of the ejecta matter onto the neutron star sets in, making it reach the critical mass with consequent formation of a Kerr black hole. We have recently shown that, during the accretion process onto the neutron star, fast neutrino flavor oscillations occur. Numerical simulations of the above system show that a part of the ejecta stays bound to the newborn Kerr black hole, leading to a new process of hypercritical accretion. We address herein, also for this phase of the binary-driven hypernova, the occurrence of neutrino flavor oscillations given the extreme conditions of high density (up to 1012 g cm−3) and temperatures (up to tens of MeV) inside this disk. We estimate the behavior of the electronic and non-electronic neutrino content within the two-flavor formalism (νeνx) under the action of neutrino collective effects by neutrino self-interactions. We find that in the case of inverted mass hierarchy, neutrino oscillations inside the disk have frequencies between ∼(105–109) s−1, leading the disk to achieve flavor equipartition. This implies that the energy deposition rate by neutrino annihilation (ν+ν¯→e−+e+) in the vicinity of the Kerr black hole is smaller than previous estimates in the literature not accounting for flavor oscillations inside the disk. The exact value of the reduction factor depends on the νe and νx optical depths but it can be as high as ∼5. The results of this work are a first step toward the analysis of neutrino oscillations in a novel astrophysical context, and as such, deserve further attention.

Neutrino Oscillations in Neutrino-Dominated Accretion Around Rotating Black Holes

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A modified nuclear model for binding energy of nuclei

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 observations from the model parameters. The inverse problem was formulated for the numericaly generalized the semi-empirical mass formula of Bethe and von Weizs\"{a}cker. It was solved in step by step way based on the AME2012 nuclear database. 
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 type for ill-posed problems. 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. These results help us to evaluate the borders of the nuclear landscape and show their limit. The efficiency of the applied approach was checked by comparing relevant results with the results obtained independently.

S. Cht. Mavrodiev

Papers

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

Computation of the Binding Energies in the Inverse Problem Framework

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