Quantum Phase Crossover in the Spherical Mean-field plus Q·Q and Pairing Model within a Single-j Shell
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摘要: 介绍了单j壳的球形平均场加几何四极-四极和标准对力模型的量子相交叉行为。在单j=15/2的壳内，计算了随模型控制参数变化的多个物理量如低激发能级、激发态间重叠积分、低激发态间的B（E2）比值和电四极矩比值。结果显示，在类转动到对激发相的演化中，多个物理量在交叉区存在非常明显的变化，如B（E2；41 → 21）/B（E2；21 → 0g），B（E2；42 → 21）/B（E2；21 → 0g）等，并且这些变化在核子数达到半满壳时尤为显著。此外，尽管当j较小时，由几何四极-四极相互作用得到的低激发能级不满足转动谱规律，但当j值足够大时，这些低激发能级满足转动谱规律。
The analysis of the quantum phase crossover behavior in the spherical shell model mean-field plus the geometric quadrupole-quadrupole (Q·Q) and standard pairing model within a single-j shell is reported. Several quantities, such as low-lying excitation energies, the overlaps of excited states, ratios of some B(E2) and electric quadrupole moments of some low-lying states as functions of the control parameter of the model in a j=15/2 shell are calculated. The results show that there are noticeable changes in the crossover region of the rotational-like to the pair-excitation phase transition, such as B(E2;41 → 21)/B(E2;21 → 0g) and B(E2;42 → 21)/B(E2;21 → 0g), especially in the half-filling case. Though the low-lying excitation energies generated from the geometric quadrupole-quadrupole interaction not satisfy the pattern of a rotational spectrum when j is small, these energies follow the pattern of a rotational spectrum when j is sufficiently large.Abstract: The analysis of the quantum phase crossover behavior in the spherical shell model mean-field plus the geometric quadrupole-quadrupole (Q·Q) and standard pairing model within a single-j shell is reported. Several quantities, such as low-lying excitation energies, the overlaps of excited states, ratios of some B(E2) and electric quadrupole moments of some low-lying states as functions of the control parameter of the model in a j=15/2 shell are calculated. The results show that there are noticeable changes in the crossover region of the rotational-like to the pair-excitation phase transition, such as B(E2;41 → 21)/B(E2;21 → 0g) and B(E2;42 → 21)/B(E2;21 → 0g), especially in the half-filling case. Though the low-lying excitation energies generated from the geometric quadrupole-quadrupole interaction not satisfy the pattern of a rotational spectrum when j is small, these energies follow the pattern of a rotational spectrum when j is sufficiently large.-
Key words:
- shell model /
- quadrupole-quadrupole interaction /
- single-j shell
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