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\title{\myfont{\textbf{Comparison of binding energy from Atomic Mass Evaluation (AME-2020) with statistical model calculations}.}}
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%\author[1,2]{}
\author[1,2]{\fontsize{12}{10}R. Sariyal}
\affil[1]{\fontsize{12}{10}Department of Physics, Panjab University, Chandigarh 160014, India.}
\affil[2]{\fontsize{12}{10}Department of Atomic and Nuclear Physics,Tata Institute of Fundamental Research, Mumbai 400005, India.}
\date{}
\maketitle{}
\section{\hspace{5.5cm}Abstract}
Realistic model calculations are fundamental to any physical problem. Statistical model continues to remain one of the important theoretical basis formalism in nuclear reaction and structure field, which is based on the assumption that once compound nucleus (CN) is formed with different projectile and target combination above coulomb barrier with certain excitation energy is fully equilibrated in all degrees of freedom (i.e. energy, angular momentum) before the decay takes place. In this letter, we have compared the recently measured binding energies from The Atomic Mass Evaluation 2020 \cite{AMC-2020} with calculated values based on FORTRAN code known as CASCADE\cite{pul}. This comparison becomes very important from the fact that code calculates everything from excitation energy, Q-value of reaction to cross-sections based on binding energy and is used frequently by nuclear research community throughout the world. We have given brief explanation on how code calculates and comparison of calculated Binding energy with recently measured binding energies from The Atomic Mass Evaluation 2020 \cite{AMC-2020}. A total of 254 stable nuclides binding energies are compared.
%\section{Q-Value:}
\
Q-value is one of the very important ingredient which determines whether nuclear reaction process will take place or not. It may be defined as the mass difference between initial reactants and products. In terms of binding energy it can be defined as difference of binding energy of products and reactants.
Q-value of nuclear reaction can be given by: $$ a + b \hspace{3mm}{\rightarrow} \hspace{3mm}c $$
\begin{equation} \label{1}
Q = [m(a) + m (b) - m(c) ]c^2
\end{equation}
\hspace{7cm}Or
\begin{equation} \label{2}
Q = B(c) - B(b) - B(a)
\end{equation}
where B is binding energy.
CASCADE calculates Q value of reaction using binding energy of reactants and products. So, it is crucial to compare experimental binding energy value with calculated ones. The National Nuclear Data Center, Brookhaven National Laboratory which is a repository of nuclear data e.g. nuclear structure, decay, and reaction data, publishes atomic masses from time to time. Recently masses are updated and published as a part of Atomic Mass Evaluation-2020 by Meng Wang et. al \cite{AMC-2020}. Binding energy per nucleon of 254 stable nuclides are compared and shown in figure \ref{fig1}.\begin{figure}
\centering
\includegraphics[width=10cm, height=6cm]{comparison.eps}
\caption{Comparison of experimental binding energy per nucleon with calculated values from CASCADE. }
\label{fig1}
\end{figure}
Binding energy of nuclei is calculated by s using Myers and Swiatecki \cite{myers}
\begin{equation} \label{3}
(B)_{A,Z}= - c_1 A + c_2 A^{2/3} + \frac{c_3 Z^2}{A^{1/3}} - \frac{c_4 Z^2}{A} + \delta
\end{equation}
where $c_1 , c_2,c_3,c_4,\delta$ are different variables.
Calculated values are almost same within the error bar.
\begin{thebibliography}{}
\bibitem{AMC-2020} Meng Wang, W.J. Huang, F.G. Kondev, G. Audi and S. Naimi, Chinese Phys. C \textbf{45}, 030003 (2021).
\bibitem{myers}W. D. Myers and W. J. Swiatecki, Nucl. Phys. \textbf{81}, 1 (1966).
\bibitem{pul}F.Puhlhofer, Nucl. Phys. A \textbf{280},267 (1977).
\end{thebibliography}
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