一个集体angular momentum消失的单轴转动微观曲柄模型
A microscopic cranking model for uni-axial rotation with vanishing collective angular momentum
摘要：
推广了微观曲柄模型（MCRM）中的刚性-无旋流变换，讨论了原子核集体绕单轴转动及其与内禀运动的耦合。这种推广使我们能够考虑当集体转动惯量保持有限时，集体角速度和集体角动量的极限都非常小。在这个极限中，集体流变得很大，并且相互对抗，共同导致集体角动量的消失。在这个极限下，内禀波函数的角动量约束的MCRM方程变得与传统的曲柄模型（CCRM）相同。在此极限下，MCRM薛定谔方程也变得与增加无旋流动能分量的CCRM方程相同。在这个极限下，MCRM薛定谔方程的时间反演不变性被破坏。求解了两个MCRM方程（无自由参数），得到了核中基态转动带的简形变谐振子势。预测的激发能和四极矩接近经验观察到的，与差异似乎可归因于在模型中，在低角动量和科里奥利力诱导的准粒子旋转对齐在较高的角动量配对相关的情况下。基态终端（截止）角动量预测为10，而不是8经验观察和预测的CCRM。假设配对关联会减小截止角动量。
英文摘要：
The rigid-irrotational flow transformation in the previous microscopic cranking model (MCRM) for nuclear collective rotation about a single axis and its coupling to intrinsic motion is generalized. This generalization allow us to consider the limit of vanishingly small collective angular velocity and hence collective angular momentum while the collective moment of inertia remains finite. In this limit, the collective flow become large and oppose one another collaborating the vanishing of the collective angular momentum. In this limit, the MCRM equation for the angular-momentum constraint on the intrinsic wavefunction becomes identical to that of the conventional cranking model (CCRM). In this limit, the MCRM Schrodinger equation also becomes identical to that of the CCRM with an added irrotational-flow kinetic energy component. In this limit, the time-reversal invariance of the MCRM Schrodinger equation is destroyed. The two MCRM equations (with no free parameters) are solved for the ground-state rotational band in the nucleus for a simple deformed harmonic oscillator potential. The predicted excitation energy and quadrupole moment are close to those observed empirically, with the differences seemingly attributable to the absence, in the model, of pairing correlations at low angular momenta and Coriolis-force induced quasi-particle rotation alignment at higher angular momenta. The ground-state terminal (cut-off) angular momentum is predicted to be 10 instead of 8 observed empirically and predicted by the CCRM. It is assumed that pairing correlations would reduce the cut-off angular momentum.
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