arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1002.3200nucl-th
收藏

核物理中的混合对称壳模型计算

Mixed-Symmetry Shell-Model Calculations in Nuclear Physics

V. G. Gueorguiev

摘要:

我们考虑一种新的方法来核壳模型。本文利用盒子中的一维谐振子引入了双基壳模型理论的概念。通过实现大型矩阵对角化的Lanczos方法和求解广义特征值问题的Cholesky算法,将该方法应用于核。混合对称基结合了传统的球壳模型态和SU(3)集体组态。我们在24 Mg和44 Ti上测试了这种混合对称方案的有效性。使用Wilthental USD交叉点在小于全空间10%的空间中获得的24 Mg的结果,在2%内再现了结合能,以及准确再现了低能谱和态结构- 90%与精确本征态重叠。相比之下,对于m格式计算,需要大约60%的全空间来获得兼容的结果。对44 Ti的计算支持混合模方案,尽管具有很少的非重复的纯SU(3)计算不如标准m方案计算好。SU(3)对称性的强破缺导致组合基内相对较小的增强。然而,在全pf壳空间的50%中的一个pf基计算与在该空间的80%中的一个通常的m格式计算一样好。利用Kuo-Brown-3相互作用对低pf壳层核44- 48 Ti和48 Cr的计算结果表明,该区域的SU(3)对称性破缺是由单粒子自旋轨道分裂驱动的.在我们的研究中,我们观察到一些有趣的相干结构,如基态的相干混合,玩具模型中的准微扰行为,以及增强的B(E2)强度接近SU(3)极限,即使SU(3)似乎是相当严重的破坏。

英文摘要:

We consider a novel approach to the nuclear shell model. The one-dimensional harmonic oscillator in a box is used to introduce the concept of an oblique-basis shell-model theory. By implementing the Lanczos method for diagonalization of large matrices, and the Cholesky algorithm for solving generalized eigenvalue problems, the method is applied to nuclei. The mixed-symmetry basis combines traditional spherical shell-model states with SU(3) collective configurations. We test the validity of this mixed-symmetry scheme on 24Mg and 44Ti. Results for 24Mg, obtained using the Wilthental USD intersection in a space that spans less than 10% of the full-space, reproduce the binding energy within 2% as well as an accurate reproduction of the low-energy spectrum and the structure of the states - 90% overlap with the exact eigenstates. In contrast, for an m-scheme calculation, one needs about 60% of the full space to obtain compatible results. Calculations for 44Ti support the mixed-mode scheme although the pure SU(3) calculations with few irreps are not as good as the standard m-scheme calculations. The strong breaking of the SU(3) symmetry results in relatively small enhancements within the combined basis. However, an oblique-basis calculation in 50% of the full pf-shell space is as good as a usual m-scheme calculation in 80% of the space. Results for the lower pf-shell nuclei 44-48Ti and 48Cr, using the Kuo-Brown-3 interaction, show that SU(3) symmetry breaking in this region is driven by the single-particle spin-orbit splitting. In our study we observe some interesting coherent structures, such as coherent mixing of basis states, quasi-perturbative behavior in the toy model, and enhanced B(E2) strengths close to the SU(3) limit even though SU(3) appears to be rather badly broken.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑