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arXiv 2111.01461nucl-thphysics.comp-ph
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核III的多参考多体微扰理论--PGCM-PT的二级从头计算

Multi-reference many-body perturbation theory for nuclei III -- Ab initio calculations at second order in PGCM-PT

Mikael Frosini, Thomas Duguet, Jean-Paul Ebran, Benjamin Bally, Heiko Hergert, Tomás R. Rodríguez, Robert Roth, Jiangming Yao, Vittorio Somà

摘要:

尽管缺少动力学相关,投影生成坐标方法(PGCM)最近被证明是一个合适的方法来处理复杂核的低激发态光谱。尽管如此,描述绝对结合能和达到高精度最终需要在PGCM之上包含动力学相关性。在这种情况下,本工作讨论了第一个现实的结果,一种新的多参考微扰理论(PGCM-PT),可以做到这一点,在一个保守的计划为地面和低洼的激发态。首先,在小($e_{\mathrm{max}}=4$)模型空间中的原理证明计算表明,闭合-(\nucl{O}{16})和开壳层(\nucl{O}{18},\nucl{Ne}{20})核的精确结合能在$0.5-1.5\%$中以二级重现,即通过PGCM-PT(2)。此外,PGCM-PT(2)利用多参考介质内相似重整化群变换对哈密顿量进行预处理,可以在比未演化哈密顿量更小的模型空间内达到收敛值.这样做,PGCM-PT(2)捕获的动力学相关性显示出对低位激发能的必要修正,这些激发能在前导级变得过于膨胀,即,在严格的PGCM水平。目前的工作奠定了基础,更好地理解的最佳方式来把握静态和动态的相关性在一个一致的方式,通过从头计算多体方法的目的是准确地描述复杂的核的基态和激发态。

英文摘要:

In spite of missing dynamical correlations, the projected generator coordinate method (PGCM) was recently shown to be a suitable method to tackle the low-lying spectroscopy of complex nuclei. Still, describing absolute binding energies and reaching high accuracy eventually requires the inclusion of dynamical correlations on top of the PGCM. In this context, the present work discusses the first realistic results of a novel multi-reference perturbation theory (PGCM-PT) that can do so within a symmetry-conserving scheme for both ground and low-lying excited states. First, proof-of-principle calculations in a small ($e_{\mathrm{max}}=4$) model space demonstrate that exact binding energies of closed- (\nucl{O}{16}) and open-shell (\nucl{O}{18}, \nucl{Ne}{20}) nuclei are reproduced within $0.5-1.5\%$ at second order, i.e. through PGCM-PT(2). Moreover, profiting from the pre-processing of the Hamiltonian via multi-reference in-medium similarity renormalization group transformations, PGCM-PT(2) can reach converged values within smaller model spaces than with an unevolved Hamiltonian. Doing so, dynamical correlations captured by PGCM-PT(2) are shown to bring essential corrections to low-lying excitation energies that become too dilated at leading order, i.e., at the strict PGCM level. The present work is laying the foundations for a better understanding of the optimal way to grasp static and dynamical correlations in a consistent fashion, with the aim of accurately describing ground and excited states of complex nuclei via ab initio many-body methods.

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