Towards Understanding Energy Levels of Two Identical Nucleons with Delta Interaction

δ相互作用下两个全同核子能级的进一步理解

In this paper we study a given system of two identical nucleons in the presence of an attractiveδinteraction.We derive the formulas for energies of identical nucleons with the configuration|j_1j_2J>explicitly,and explain all empirical rules of the energy level ordering with spin J and parity,deep understandings of which have been desirable for a few decades.We also proved analytically that the energy interval between the lowest level and the second lowest level is larger than the sum of intervals of all other successive levels,thus present a sound explanation of the large energy gap between the ground state and the first excited state of such system.

本文研究由两个全同费米子构成的系统,这两个费米子之间存在吸引的δ相互作用。推导了两个全同核子|j_(1)j_(2)J>组态的能量解析公式,解释了给定自旋J和宇称的能级次序所有经验规律,这些规律在过去几十年里都没有得到深入理解。还解析证明了最低能级和次低能级之间的能量差大于所有其它能级之间的能量差之和,从而对于这类系统的基态和第一激发态之间存在很大能隙的现象提供了一个完美的解释。