$^{40}$Ca + $^{208}$Pb双核构型中核子密度的库仑与核极化
Coulomb and nuclear polarization of the nucleon density in the dinuclear configuration of the $^{40}$Ca + $^{208}$Pb system
AI总结：
该研究基于形变Woods–Saxon平均场，计算了$^{40}$Ca + $^{208}$Pb双核系统的核子密度极化，明确了库仑与核场的作用及单中心描述的适用范围。
AI中文摘要：
在形变Woods–Saxon平均场框架下，研究了固定中心距下第二个重核的存在引起的重核核子密度分布变化。对其中一个核的单粒子问题，通过柱形简谐振子基对角化求解，对角化前哈密顿量中已包含伙伴核的外场；该外场由伙伴电荷分布的库仑势，以及与双核系统方法中所用形式相同的、由Migdal密度相关有效核子-核子相互作用双折叠得到的核部分组成。针对$^{40}$Ca + $^{208}$Pb系统，在间距$R = 15.5$~$20$ fm时，计算了诱导密度变化$\boldsymbol{\rho}(\boldsymbol r;R)$及对应的四极矩、均方根半径、相互作用能变化。将结果与同一外场的一阶（线性响应）处理对比，发现两个伙伴核的极化由排斥性库仑潮汐场主导，其产生密度的扁椭形变，而吸引性核场作用相反，在最小间距下部分抵消库仑贡献；极化能为偶极量，诱导四极形变仅贡献其百分之几，还定量确定了单中心描述的适用范围。
英文摘要：
The change of the nucleon density distribution of a heavy nucleus caused by the presence of a second nucleus at a fixed centre-to-centre distance is studied in the framework of the deformed Woods--Saxon mean field. The single-particle problem of one nucleus has been solved by diagonalization in a cylindrical harmonic oscillator basis with the external field of the partner nucleus included in the Hamiltonian before diagonalization. The external field consists of the Coulomb potential of the partner charge distribution and of the nuclear part obtained by double folding of the Migdal density-dependent effective nucleon-nucleon interaction, in the same form as it is used in the dinuclear system approach. The induced density change $δρ(\boldsymbol r;R)$ and the corresponding changes of the quadrupole moment, of the mean-square radius and of the interaction energy have been calculated for the $^{40}$Ca + $^{208}$Pb system at separations $R = 15.5$--$20$ fm. The results are compared with the first-order (linear-response) treatment of the same external field. The polarization of both partners is found to be dominated by the repulsive Coulomb tidal field, which produces an oblate deformation of the density, while the attractive nuclear field acts in the opposite sense and partially cancels the Coulomb contribution at the smallest separations. The polarization energy is found to be a dipole quantity, the induced quadrupole deformation contributing only a few percent of it. The limits of validity of the one-centre description are established quantitatively.
