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The pairing energies (PE) of nonmagic atomic nuclei with $A \geq 50$ can be derived from the odd nuclei masses $M$ provided it is possible to present $M$ as a sum of two terms [1]:
1) a smooth function of nucleon numbers having the same form of Tailor series expansion for even-even and odd nuclei;
2) PE: $P_{n}\left(N^{\prime}, Z\right)$ and $P_{p}\left(N, Z^{\prime}\right)$, where $N\left(N^{\prime}\right)$ and $Z\left(Z^{\prime}\right)$ denote even (odd) numbers of neutrons and protons and indices $n(p)$ refer to neutron (proton) $\mathrm{PE}$.
Traditionally the masses of two adjacent odd nuclei is used for calculations of $\mathrm{PE}$ and this procedure smoothes out the influence of the state of odd nucleon on $\mathrm{PE}$. To overcome this problem, we have proposed [2] the expression for PE, which includes only one odd nucleon mass. This expression is based on the assumptions 1), 2) and Taylor series expansion of mass surface up to the third order in the number of nucleons. For example,
$P_{n}\left(N^{\prime}, Z\right)=M\left(N^{\prime}, Z\right)-\frac{9}{16}\left[M\left(N^{\prime}+1, Z\right)+M\left(N^{\prime}-1, Z\right)\right]+$
$\hspace{2.1cm} +\frac{1}{16}\left[M\left(N^{\prime}+3, Z\right)+M\left(N^{\prime}-3, Z\right)\right]$
The results of calculations of pairing energies of deformed $\mathrm{U}(\mathrm{Z}=92)$ and Pu$(\mathrm{Z}=94)$ actinide nuclei with Nilsson quantum numbers $K^{\pi}\left[N n_{z} \lambda\right]$ of odd neutron quasiparticles are given in the
Table. The masses of nuclei are taken from Atomic Mass Evaluation - AME2020 [3]. The results obtained confirm our conclusion about the dependence of $\mathrm{PE}$ on the state of an odd nucleon.
$
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline N^{\prime} & Z & P_{n}, \mathrm{keV} & K^{\pi}\left[N n_{z} \lambda\right] \text{neutrons} & N^{\prime} & Z & P_{n}, \mathrm{keV} & K^{\pi}\left[N n_{z} \lambda\right] \text{neutrons} \\
\hline 141 & 92 & 573 & 5 / 2^{+}[633] & 143 & 94 & 564 & 7 / 2^{-}[743] \\
143 & 92 & 626 & 7 / 2^{-}[743] & 145 & 94 & 520 & 1 / 2^{+}[631] \\
145 & 92 & 578 & 1 / 2^{+}[631] & 147 & 94 & 551 & 5 / 2^{+}[622] \\
147 & 92 & 574 & 5 / 2^{+}[622] & 149 & 94 & 454 & 7 / 2^{+}[624] \\
\hline
\end{array}
$
References:
1. D.G. Madland, J.R. Nix, Nucl. Phys. A 476, 1 (1988).
2. A.K. Vlasnikov, A.I. Zippa, V.M. Mikhajlov, Bull. Russ. Acad. Sci.: Phys. 80, 905 (2016); 81, 1185 (2017); 84, 919 (2020); 84, 1191 (2020); 84, 1309 (2020).
3. https://www-nds.iaea.org/amdc/
