核的巨单极激发的求和规则和核物质的不可压缩性系数

Sum Rule in Nuclear Giant Monopole Resonance and Incompressibility of Nuclear Matter

采用近来在研究核基态中极为成功的相对论模型研究有限核的同位旋巨单极共振 ,从而给出核物质的不可压缩性系数 .讨论了建立在相对论平均场基态上的相对论无规位相近似的自洽处理 .自洽要求基态和巨共振激发态的研究从同一个有效拉氏量出发 .与相对论平均场的无海近似自洽 ,相对论无规位相近似不仅要包含正能态的粒子 -空穴激发 ,还必须考虑 Fermi海核子态和 Dirac海核子态激发的贡献 .用约束的相对论平均场方法得到核的巨单极共振的能量逆权重的求和规则 ,验证 Dirac海核子态的贡献 .比较理论计算和实验测量的巨单极共振的能量得到核物质的不可压缩性系数为 2 5 0 - 2 70 Me V.

The isoscalar giant monopole resonance for finite nuclei and the nuclear matter incompressibility are studied in a consistent relativistic approach, which achieves a great success in describing the properties of nuclear ground states. The consistency in the relativistic random phase approximation (RRPA) built on the relativistic mean field (RMF) ground states are investigated. The RMF wave function of nucleus and the particle-hole residual interactions in RRPA are calculated from a same effective Lagrangian. A fully consistent treatment of RRPA with the RMF approximation, i.e. no sea approximation, has to include not only the positive particle-hole excitation, but also the pairs formed from the Dirac states and Fermi states. The energy inverse weighted sum rule for the isoscalar giant monopole resonance is studied in the constrained RMF, which verifies the important contribution from the Dirac state. A comparison between experimental and calculated energies of isoscalar giant monopole energies points to a value of 250-270 MeV for the nuclear matter incompressibility.