Reply to Comment on ``Ab Initio Study of 40-Ca with an Importance Truncated No-Core Shell Model''
R. Roth, P. Navratil
我们回应Dean等人（arXiv：0709.0449）对我们最近信件（Phys.Rev.Lett.99：092501，2007）的评论.
We respond to Comment on our recent letter (Phys.Rev.Lett.99:092501,2007) by Dean et al (arXiv:0709.0449).
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Comment on "Ab Initio study of 40-Ca with an importance-truncated no-core shell model"
在最近的一封信[物理。99，092501（2007）]，Roth和Navratil提出了一种无核壳模型的重要性截断格式。作者声称，他们的截断方案导致收敛的结果为基态的40-Ca。我们认为，不能从信中提出的结果得出这一结论。此外，声称的收敛性与多体理论的预期不符。特别是，耦合集群计算表明，一个显着的相关能量的一部分是失踪。
Ab Initio Study of 40Ca with an Importance Truncated No-Core Shell Model
我们提出了一个重要的截断计划的无核壳模型，使收敛计算远远超出p壳层的核。它是基于一个先验的措施，通过多体微扰理论构建的单个基态的重要性。只有物理上相关的状态的无核心模型空间被认为是，这导致了显着减少的基础维度。我们分析了这种截断方案的有效性和效率，使用不同的现实核子-核子相互作用，并比较传统的无核壳模型计算4 He和16 O。然后，我们提出了第一个收敛计算的基态40 Ca的非核心模型空间内，包括多达16个\hbar Ω-激发使用现实的低动量相互作用。该方案具有普适性，可方便地应用于其它量子多体问题。
We study the use of truncated normal-ordered three-nucleon interactions in ab initio nuclear structure calculations starting from chiral two- plus three-nucleon Hamiltonians evolved consistently with the similarity renormalization group (SRG). We present three key steps: (i) a rigorous benchmark of the normal-ordering approximation in the importance-truncated no-core shell model (IT-NCSM) for 4-He, 16-O, and 40-Ca; (ii) a direct comparison of the IT-NCSM results with coupled-cluster calculations at the singles and doubles level (CCSD) for 16-O; and (iii) first applications of SRG-evolved chira…
The problem of center-of-mass (CM) contaminations in ab initio nuclear structure calculations using configuration interaction (CI) and coupled-cluster (CC) approaches is analyzed. A rigorous and quantitative scheme for diagnosing the CM contamination of intrinsic observables is proposed and applied to ground-state calculations for He-4 and O-16. The CI and CC calculations for O-16 based on model spaces defined via a truncation of the single-particle basis lead to sizable CM contaminations, while the importance-truncated no-core shell model based on the $N_{\max}\hbarΩ$ space is virtually free …
We propose an importance-truncation scheme for the large-scale nuclear shell model that extends its range of applicability to larger valence spaces and mid-shell nuclei. It is based on a perturbative measure for the importance of individual basis states that acts as an additional truncation for the many-body model space in which the eigenvalue problem of the Hamiltonian is solved numerically. Through a posteriori extrapolations of all observables to vanishing importance threshold, the full shell-model results can be recovered. In addition to simple threshold extrapolations, we explore extrapol…
We discuss the building blocks for a consistent inclusion of chiral three-nucleon (3N) interactions into ab initio nuclear structure calculations beyond the lower p-shell. We highlight important technical developments, such as the similarity renormalization group (SRG) evolution in the 3N sector, a JT-coupled storage scheme for 3N matrix elements with efficient on-the-fly decoupling, and the importance truncated no-core shell model with 3N interactions. Together, these developments make converged ab initio calculations with explicit 3N interactions possible also beyond the lower p-shell. We an…
We formulate the In-Medium Similarity Renormalization Group (IM-SRG) for open-shell nuclei using a multi-reference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multi-reference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of even oxygen isotopes with chiral NN and 3N Hamiltonians, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the Importance-Truncated No-Core Shell Model and the Coupled Cluster …
Importance Truncation for Large-Scale Configuration Interaction Approaches
我们引入了一个迭代的重要性截断计划，其目的是通过先验选择物理上最相关的基态来降低组态相互作用方法的模型空间的维数。使用来自多组态微扰理论与重要性阈值相结合的重要性措施，我们构建了一个模型空间优化的一个给定的哈密顿量的单个本征态的描述。我们详细讨论了各种技术方面和改进的重要性截断，如微扰校正排除的基态，阈值外推技术，和不同的迭代模型空间更新计划。我们在无核壳模型（NCSM）的上下文中应用重要性截断的思想，对核的基态进行从头计算。在一系列的基准计算封闭和开放壳层核O-16，我们比较的基态能量的重要性截断NCSM完整的NCSM。所有的计算表明，一个很好的协议的重要性截断和充分NCSM的所有情况下，后者是可行的。结果表明，重要性截断的NCSM在保留了完整NCSM的大部分优点的同时，提供了更大的N_max*hbar*Omega空间和更重的核.用这种方法，我们能够对C-12和O-16等核进行重要截断的NCSM计算，直到N_max=22。
Ab initio no-core configuration interaction (NCCI) calculations for the nuclear many-body problem have traditionally relied upon an antisymmetrized product (Slater determinant) basis built from harmonic oscillator orbitals. The accuracy of such calculations is limited by the finite dimensions which are computationally feasible for the truncated many-body space. We therefore seek to improve the accuracy obtained for a given basis size by optimizing the choice of single-particle orbitals. Natural orbitals, which diagonalize the one-body density matrix, provide a basis which maximizes the occupat…
We explore the systematics of ground-state and excitation energies in singly-strange hypernuclei throughout the helium and lithium isotopic chains --- from $^5_Λ$He to $^{11}_Λ$He and from $^7_Λ$Li to $^{12}_Λ$Li --- in the ab initio no-core shell model with importance truncation. All calculations are based on two- and three-baryon interaction from chiral effective field theory and we employ a similarity renormalization group transformation consistently up to the three-baryon level to improve the model-space convergence. While the absolute energies of hypernuclear states show a systematic vari…
Most nuclear structure calculations, even for full configuration interaction approaches, are performed within truncated model spaces. These require consistent transformations of the Hamiltonian and operators to account for the missing physics beyond the active space, so that several recent efforts have been devoted to find compatible derivations of the effective operators. The effective charges employed in the shell-model calculations, and fitted to reproduce experimental data, can be seen as the phenomenological counterpart of such renormalization for electromagnetic operators. Here, we make …
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