Why does the recently proposed simple empirical formula for the lowest excitation energies work so well?

It has recently been shown that a simple empirical formula, in terms of the mass number and the valence nucleon numbers, is able to describe the main trends of the lowest excitation energies of the natural parity even multipole states up to $10^+$ in even-even nuclei throughout the entire periodic table. In an effort to understand why such a simple formula is so capable, we investigate the possibility of associating each term of the empirical formula with the specific part of the measured excitation energy graph.Comment: 9 pages, 3 figure

Spin-dependent empirical formula for the lowest excitation energies of the natural parity states in even-even nuclei

We present an empirical expression which holds for the lowest excitation energy of the natural parity states in even-even nuclei throughout the entire periodic table. This formula contains spin-dependent factors so that it is applied to different multipole states with the same model parameters in contrast to the recently proposed empirical expression where the model parameters had to be fitted for each multipole separately.Comment: 9 pages, 5 figure

NpNnN_pN_n scheme and the valence proton-neutron interaction

We examine the common belief that the $N_pN_n$ scheme is manifested as a direct consequence of the valence proton-neutron interaction which has proven to be a dominant factor in developing collectivity in nuclei. We show that the simplification of the $N_pN_n$-plot of the lowest $2^+$ excitation energy is introduced merely because the excitation energy always decreases when the valence nucleon number becomes larger.Comment: 10 pages, 6 figure

N_pN_n dependence of empirical formula for the lowest excitation energy of the 2^+ states in even-even nuclei

We examine the effects of the additional term of the type $\sim e^{- \lambda' N_pN_n}$ on the recently proposed empirical formula for the lowest excitation energy of the $2^+$ states in even-even nuclei. This study is motivated by the fact that this term carries the favorable dependence of the valence nucleon numbers dictated by the $N_pN_n$ scheme. We show explicitly that there is not any improvement in reproducing $E_x(2_1^+)$ by including the extra $N_pN_n$ term. However, our study also reveals that the excitation energies $E_x(2_1^+)$, when calculated by the $N_pN_n$ term alone (with the mass number $A$ dependent term), are quite comparable to those calculated by the original empirical formula.Comment: 14 pages, 5 figure

Empirical formula applied to the lowest excitation energies of the natural parity odd multipole states in even-even nuclei

We applied our recently proposed empirical formula, a formula quite successful in describing essential trends of the lowest excitation energies of the natural parity even multipole states, to the lowest excitation energies of the natural parity odd multipole states in even-even nuclei throughout the entire periodic table. Even though the systematic behavior of the lowest excitation energies of odd multipole states is quite different from those of even multipole states, we have shown that the same empirical formula also holds reasonably well for the odd multipole states with the exception of a few certain instances.Comment: 23 pages, 11 figure

Technical Summary of Rice Yield Exceeding 10 Tons per Hectare for Three Consecutive Years

In Heilongjiang Province, rice planting area increased year by year. However, due to improper cultivation methods, farmers did not have knowledge about characteristics of rice varieties, there was still no complete cultivation technology system. The yield of different regions varied widely. The increase in rice yield was relatively low, and yield per hectare remained at 7 tons. Through the recent three years of large-scale demonstration, it is known that at the same time of promoting high-yield rice varieties, it is recommended to promote high-yield cultivation method. In the cultivation process, it is recommended to take reliable, effective, and simple and feasible technical procedures

Evolutionary Game Dynamics for Financial Risk Decision-Making in Global Supply Chain

This paper focuses on the game evolution process and its influencing factors of financial risk cooperation behavior between suppliers and manufacturers in global supply chain system. Using two-population evolutionary game theory, the performance of supply chain members under financial risk environment is modeled. Further, the proposed financial risk game model is applied to simulation cases of global supply chain. Based on the theory analysis and simulation results, it is shown that the cooperation strategy is the optimal evolutionarily stable strategy (ESS) for all supply chain members, when facing the high financial risk. The financial risk-sharing coefficient can be regarded as an adjuster that affects risk ESS of both suppliers and manufacturers under the low financial risk setting. By reducing the financial risk-sharing ratio of one supply chain player, his intention of adopting cooperation strategy would be enhanced. Finally, it is observed that financial risk sharing approach may lead to the alignment among supply chain members. Therefore, setting up an effective financial risk-sharing mechanism is beneficial to realize sustainable development of global supply chain