Probing ab initio emergence of nuclear rotation

Abstract

Structural phenomena in nuclei, from shell structure and clustering to superfluidity and collective rotations and vibrations, reflect emergent degrees of freedom. Ab initio theory describes nuclei directly from a fully microscopic formulation. We can therefore look to ab initio theory as a means of exploring the emergence of effective degrees of freedom in nuclei. For the illustrative case of emergent rotational bands in the Be isotopes, we establish an understanding of the underlying oscillator space and angular momentum (orbital and spin) structure. We consider no-core configuration interaction (NCCI) calculations for 7,9,11 Be with the Dae-jeon16 internucleon interaction. Although shell model or rotational degrees of freedom are not assumed in the ab initio theory, the NCCI results are suggestive of the emergence of effective shell model degrees of freedom (0 ω and 2 ω excitations) and LS-scheme rotational degrees of freedom, consistent with an Elliott-Wilsdon SU(3) description. These results provide some basic insight into the connection between emergent effective collective rotational and shell model degrees of freedom in these light nuclei and the underlying ab initio microscopic description. arXiv:1912.00083v1 [nucl-th]

A Guided Tour of ab initio Nuclear Many-Body Theory

“…An exact diagonalization in such a symmetry-adapted basis will offer a much more efficient description of nuclear states with intrinsic deformation than the conventional NCSM, which would need to use massive model spaces with manyparticle-many-hole excitations. This reduction of the model space dimensions also allows such symmetry-adapted NCSM [139,140] and NCCI approaches [141] to reach heavier nuclei than the conventional versions.…”

“…Emergence of collectivity. Both NCCI and VS-IMSRG calculations with chiral NN+3N interactions have demonstrated that these interactions do indeed produce the telltale features of collective behavior in nuclear spectra [26,141,213,261,262]. Upon a bit of reflection, it is not surprising that reasonable results on rotational bands, for instance, should be found in these approaches: While they rely on particle-hole type expansions, the exact diagonalization is done in a complete model space of up to A v hA v p excitations, where A v is the number of valence nucleons.…”

Symmetry and Shape Coexistence in 10Be

“…Moreover, ab initio calculated wave functions have been found [15,16] to have dominant components with specific Elliott SU(3) [17,18] or Sp(3, R) [19] symmetry. Ab initio calculations can thus give insight into the nature of collective states by exposing the symmetry structure of calculated wave functions [20][21][22].…”

“…In a contribution [23] to the proceedings of the previous workshop in this series, we explored the rotational features of the ab initio calculated spectrum of 10 Be. The ab initio NCCI calculated spectrum from Ref.…”

The descriptions of rotational bands in <sup>10</sup>Be and <sup>12</sup>Be withshell-model calculations

“…Johnson [30] 使用L-S分解方法来分解jj耦合下的壳模型计算结果，并使用唯象Cohen-Kurath相互作用壳模型 [31] 和现实 核力无核芯壳模型 [32] 分别研究了 9 Be中的转动带信息。Caprio等人 [33] 使用基于第一性原理的无核芯壳模型和L-S分解 进一步研究了 7,9,11 Be中的转动带信息。 原子核壳模型理论广泛用于轻重核的研究中 [26,34] 。该方法在计算Be同位素中具有集团结构或大形变原子核时， 需要考虑跨壳激发的影响，通常使用包含0p 3/2 , 0p 1/2 , 0d 5/2 , 1s 1/2 和0d 3/2 轨道的p-sd模型空间有效相互作用，如MK [35] 、 WBP [36] 、WBT [36] 、YSOX [37] 等。本文主要使用WBP [36] 和YSOX [37] 在p-sd跨壳模型空间内研究 10 Be和 12 Be的能谱以及 可能存在的转动带信息。考虑到跨壳激发下的质心修正，在谐振子基矢下使用Gloeckner和Lawson [38] 提出的方法来 消除质心运动带来的伪态，其中倍增系数β=10。 在原子核壳模型计算中，jj耦合方法主要考虑核子单粒子轨道间的耦合，而ls耦合方法可以体现原子核集体的 轨道角动量l与自旋角动量s间的耦合，从而更清晰地描述原子核集体结构的性质。常用的壳模型方法通常采用jj耦 合的方式 [39] ，因此我们将jj耦合方法计算出的波函数通过L-S分解得到ls耦合下的波函数信息，从而分析原子核集体 特征。以L分解为例，该方法以L 2 算符构建一个厄米矩阵，将波函数ψ作为初始向量v 1 构建Lanczos算法 [40] ： 10 Be. The composition distribution of the orbital quantum number L at different energy levels is obtained 10 Be 的实验研究中发现了两条以 0 In these light nuclei around the dripline, the intruded higher single-particle orbitals often occur in the ground states and mix with the normal single-particle orbitals.…”