Analytical continuation from bound to resonant states in the Dirac equation with quadrupole-deformed potentials
Analytical continuation from bound to resonant states in the Dirac equation with quadrupole-deformed potentials
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具有四极变形势的狄拉克方程中从束缚态到共振态的解析延拓
DOI：
10.1103/physrevc.92.024324
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发表时间：
2015-08
影响因子：
3.1
通讯作者：
Li Z. P.
中科院分区：
文献类型：
--
作者：
Xu Xu-Dong;Zhang Shi-Sheng;Signoracci A. J.;Smith M. S.;Li Z. P.
工作背景：具有明显单粒子特征的共振对于定量描述滴线附近和滴线之外的奇异核至关重要，并且经常影响晕的形成和核子衰变过程。由于大多数原子核都是形变的，形变和阈值附近的轨道结构之间的相互作用可以改善对奇异核的描述。目的：发展一种研究具有四极形变Woods-Saxon势的Dirac方程中单粒子共振轨道结构的方法。在这个方案中，确定结合和共振能级与变形的结构演化，并研究在松散结合系统中对晕形成的影响，重点是最近的晕候选核Mg-37。方法：本文在具有变形Woods-Saxon势的Dirac方程的基础上，发展了耦合常数解析延拓（ACCC）方法。变形势中的标量和矢量项由价中子和附近轨道的能量确定，这些能量是从具有PC-PK 1密度泛函的自洽相对论Hartree-Bogoliubov（RHB）计算中提取的。结果如下：我们比较的能量和宽度的共振轨道在最近的晕核候选人Mg-37使用ACCC方法的基础上的狄拉克耦合通道方程的散射相移（SPS）方法确定的。结果发现，从两种方法的结果吻合较好的窄共振，而SPS方法失败的宽共振。从ACCC方法的束缚和共振轨道的Nilsson水平计算在很宽的范围内的变形，并显示出一些决定性的提示晕形成的Mg-37。结论：在我们的耦合通道狄拉克方程变形势的ACCC模型中，组态1/2[321]和5/2[312]轨道在约0.5变形处的交叉增加了占据来自2 p（3/2）的1/2[321]轨道的概率，从而解释了最近在Mg-37中观察到的p波单中子晕组态。共振1/2[301]组态在A = 40以上的镁同位素的晕形成中起着至关重要的作用，对于大于0.2的宽范围的变形。
Background: Resonances with pronounced single-particle characteristics are crucial for quantitative descriptions of exotic nuclei near and beyond the drip lines, and often impact halo formation and nucleon decay processes. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold can lead to improved descriptions of exotic nuclei. Purpose: Develop a method to study single-particle resonant orbital structure in the Dirac equation with a quadrupole-deformed Woods-Saxon potential. Determine the structure evolution of bound and resonant levels with deformation in this scheme, and examine the impact on halo formation in loosely bound systems, with a focus on the recent halo candidate nucleus Mg-37. Method: Analytical continuation of the coupling constant (ACCC) method is developed on the basis of the Dirac equation with a deformed Woods-Saxon potential. The scalar and vector terms in the deformed potential are determined by the energies of the valence neutron and nearby orbitals, which are extracted from a self-consistent relativistic Hartree-Bogoliubov (RHB) calculation with the PC-PK1 density functional. Results: We compare the energies and widths of resonant orbitals in the recent halo nucleus candidate Mg-37 using the ACCC method based on the Dirac coupled-channel equations with those determined from the scattering phase shift (SPS) method. It is found that the results from the two methods agree well for narrow resonances, whereas the SPS method fails for broad resonances. Nilsson levels for bound and resonant orbitals from the ACCC method are calculated over a wide range of deformations and show some decisive hints of halo formation in Mg-37. Conclusions: In ourACCC model for deformed potentials in the coupled-channelDirac equations, the crossing of the configuration 1/2[321] and 5/2[312] orbitals at a deformation of approximately 0.5 enhances the probability to occupy the 1/2[321] orbital coming from 2p(3/2) thereby explaining the recent observation of a p-wave one-neutron halo configuration in Mg-37. The resonant 1/2[301] configuration plays a crucial role in halo formation in the magnesium isotopes beyond A = 40 for a wide range of deformations larger than 0.2.