Strong correlations of the Garvey-Kelson mass relations

Rapid Communication

Strong correlations of the Garvey-Kelson mass relations

Y. Y. Cheng, Y. M. Zhao, and A. Arima

Phys. Rev. C 89, 061304(R) – Published 11 June 2014

Abstract

In this Rapid Communication we point out strong correlations between the Garvey-Kelson mass relations (GKs). These correlations are originated from the statistical odd-even feature of the interaction between the last proton and the last neutron in atomic nuclei and are instructive in reducing the deviations of the GKs in applications.

Received 14 January 2014
Revised 23 April 2014

DOI:https://doi.org/10.1103/PhysRevC.89.061304

Authors & Affiliations

Y. Y. Cheng^1,2, Y. M. Zhao^1,3,4,*, and A. Arima^1,5

¹Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
²School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
³Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator, Lanzhou 730000, China
⁴CCAST, World Laboratory, P.O. Box 8730, Beijing 100080, China
⁵Musashi Gakuen, 1-26-1 Toyotamakami Nerima-ku, Tokyo 176-8533, Japan

^*Corresponding author: ymzhao@sjtu.edu.cn

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Vol. 89, Iss. 6 — June 2014

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Figure 1
The schematic diagram of the Garvey-Kelson relations, the GKL (left panel) and the GKT (right panel). The plus and minus signs are consistent with the GKL and GKT in Eq. (1), and the two nuclei with star symbols in these two panels are called the reference nuclei.
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Figure 2
Average deviations $\bar{D}$ vs $N$ (based on the AME2012 database [18]), for even-even, even-odd, odd-even, and odd-odd reference nuclei, respectively. ${\bar{D}}_{L}$ (ee) denotes $\bar{D}$ of the GKL with even values for both $N$ and $Z$ , ${\bar{D}}_{L}$ (oe) denotes $\bar{D}$ of the GKL with an odd value of $N$ and an even value of $Z$ , and so on.
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Figure 3
The schematic diagram of the relations $R_{i}$ $(i = 1, 2, \dots, 12$ ) in Eq. (4). By using the GKL and GKT, one has maximally twelve relations $R_{i}$ to evaluate the mass of a given nucleus, depending on its relative position with respect to the other five. Here the numbers inside boxes correspond to $R_{i}$ ; for instances, number “1” in the left panel corresponds to $R_{1}$ in Eq. (4), number “8” in the right panel corresponds to $R_{8}$ in Eq. (4), and so on.
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Figure 4
Schematic diagrams of the three cases for combinatorial (joint) Garvey-Kelson mass relations for $n = 2$ . In this figure we assume that the nucleus represented by a solid circle in green is an even-even nucleus. In the left panel, we exemplify the first case in which the cancellation is best done by using the joint relation of $R_{2}$ and $R_{3}$ . Here the joint relation of $R_{2}$ and $R_{3}$ is equivalent to $δ V$ of an odd- $N$ -even- $Z$ nucleus subtracted by that of an even- $N$ -odd- $Z$ nucleus (i.e., $δ V (oe) - δ V (eo)$ ), plus that of an even- $N$ -odd- $Z$ nucleus subtracted by that of an odd- $N$ -even- $Z$ nucleus (i.e., $δ V (eo) - δ V (oe)$ ), and thus one achieves the smallest RMSD. The second and third cases are exemplified by using joint relations ( $R_{1}, R_{2}$ ) and $(R_{2}, R_{8}$ ), respectively. Here $D_{R_{1}, R_{2}} = \frac{1}{2} (δ V (oo) - δ V (eo) + δ V (oe) - δ V (ee))$ , and $D_{R_{2}, R_{8}} = δ \bar{V} (oe) - δ V (eo)$ . It is therefore expected that the RMSD in the first case is the smallest, and that in the third case is the largest.
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Figure 5
The RMSD of the GKs for $n = 2$ . There are totally sixty-six ( $\frac{12 \times 11}{2} = 66$ ) combinations, among which there are eighteen cases belong to the first case, thirty-six belong to the second case, and twelve belong to the third case. Refer to Figure 4 and the text for explanation of the three cases. One sees that the first case gives the smallest RMSD, and the third gives the largest RMSD, as expected. The RMSD in the second case is intermediate between the first and the third cases. See the text for details.
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Physical Review C

covering nuclear physics

Strong correlations of the Garvey-Kelson mass relations

Y. Y. Cheng, Y. M. Zhao, and A. Arima

Phys. Rev. C 89, 061304(R) – Published 11 June 2014

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Physical Review C

covering nuclear physics

Strong correlations of the Garvey-Kelson mass relations

Y. Y. Cheng, Y. M. Zhao, and A. Arima

Phys. Rev. C 89, 061304(R) – Published 11 June 2014

Abstract

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