A many-body Hamiltonian consisting of a spherical shell model mean-field term, a pairing interaction for alike nucleons and a dipole–dipole interaction, with the dipole operator involving a cubic term in the radial coordinate, was studied within a quasiparticle random-phase approximation and applied numerically to five even–even isotopes of Sm. The resulting wavefunctions were further used to calculate the B(E1) values, which at their turn were employed to calculate the photoabsorption cross section, integrated moments of the cross section and energy weighted sum rule (EWSR). The calculated cross section and its integrated moments were compared with the available data, and a good agreement was observed. Two regions were distinguished: one corresponding to the pygmy dipole resonance (PDR) (1–10 MeV) and the other to the giant dipole resonance (GDR) (10–20 MeV), which were studied separately. The peaks belonging to each of the two ranges were analyzed in detail. The PDR states were located around the neutron separation energy and were mainly formed by the collective isoscalar and neutron collective states. The PDR states describe oscillations of the neutron excess against protons from the isospin-saturated core. The character of the states from the GDR region, isoscalar or isovector, is also pointed out. The PDR states carry only 0.8%–2.7% of the total EWSR and 0.4%–5.9% of the total E1 strength. The dependence of the dipole strength on nuclear deformation is evidenced. A comment on the cross section splitting into two branches for deformed isotopes is included. The r-cubic term and nuclear deformation have opposite effects on the dipole strength. In addition, it diminishes the effect of nonconservation of the center of mass momentum. The famous Thomas–Reiche–Kuhn sum rule formula is generalized to the case of the Schiff dipole momentum. The new sum rule is well satisfied. The projected spherical single-particle basis used in our formalism allows for a unified description of spherical transitional and deformed isotopes.

中文翻译：

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寻找偶偶核中侏儒偶极子共振的新方法。适用于同位素 144,148,150,152,154Sm

在准粒子随机相中研究了由球壳模型平均场项、相似核子的配对相互作用和偶极-偶极相互作用组成的多体哈密顿量，偶极算子涉及径向坐标中的立方项近似并在数值上应用于钐的五种偶数同位素。由此产生的波函数进一步用于计算乙（乙1）值，这些值依次用于计算光吸收截面、截面积分矩和能量加权和规则（EWSR）。将计算的横截面及其积分矩与现有数据进行比较，观察到良好的一致性。区分了两个区域：一个对应于侏儒偶极子共振（PDR）（1-10 MeV），另一个对应于巨偶极子共振（GDR）（10-20 MeV），分别进行了研究。详细分析了属于两个范围中的每一个的峰。 PDR态位于中子分离能附近，主要由集体等标量态和中子集体态组成。 PDR 状态描述了中子过剩对来自同位旋饱和核心的质子的振荡。还指出了东德地区国家的特征，即等标量或等矢量。 PDR 州仅占总 EWSR 的 0.8%–2.7% 和总 E1 强度的 0.4%–5.9%。偶极子强度对核变形的依赖性是有证据的。包括对变形同位素横截面分成两个分支的评论。这r-三次项和核变形对偶极子强度具有相反的影响。此外，它还减弱了质心动量不守恒的影响。著名的 Thomas-Reiche-Kuhn 和规则公式被推广到希夫偶极动量的情况。新的总和规则得到了很好的满足。我们的形式主义中使用的投影球形单粒子基础允许对球形过渡和变形同位素进行统一描述。