Bingding Energies for the r-th Power Potential Model and Its Application to the Yrast Excitation Energies

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We assume a global potential for nucleons inside a nucleus and check its validity for the Yrast energies of 2+ states in even-even nuclei, whose nucleon numbers are between 90 and 200. This check is done for a wide range of nuclei rather than for a specific nucleus. We model a r-dependent potential for the nucleons inside the nucleus, which gives the best fit for the lowest excitation energies of natural parity even multipole states in even-even nuclei. For this purpose, we first assume that the potential has a power form in the distance r and derive the general energy levels by using Heisenbergis uncertainty relation. We check the validity of this formulation for r?1, r, r2, and ~ r0, and conclude that our formulations are valid for a wide range of r?1 ~ r2. Finally, we apply our formula to the lowest excitation energies of natural parity even multipole states in even-even nuclei and show that the nucleon potentials are about r?0.234 ~ r?0.909. We also try to search for the tendencies of the NpNn scheme but cannot find any clear indication that the NpNn scheme is valid.