Geometry of effective Hamiltonians

Kvaal, Simen

doi:10.1103/physrevc.78.044330

Cited by 26 publications

(52 citation statements)

References 32 publications

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“…As noted above, the Lee-Suzuki procedure makes the small-space eigenvectors as close as possible to projections of the full eigenvectors without sacrificing orthogonality. In other words, it constructs the orthonormal set {|k } that minimizes the quantity [23] …”

Section: Methodsmentioning

confidence: 99%

Nonperturbative renormalization of the neutrinoless double-βoperator inp-shell nuclei

2011

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Section: Methodsmentioning

confidence: 99%

Nonperturbative renormalization of the neutrinoless double-βoperator inp-shell nuclei

2011

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“…In this work we compute the ground state of the A c nucleus using the coupled-cluster method in the singles-and-doubles approximation with the Λ-triples correction treated perturbatively (Λ-CCSD(T)) [46,47], while the one-and two-particle-attached equation-of-motion coupled-cluster (EOM-CC) methods are used to compute the ground and excited states of the A c + 1 and A c + 2 nuclei [48][49][50][51]. In this work we define our valence space by the sdshell, and we use the Okubo-Lee-Suzuki similarity transformation [52][53][54] to project the one-and two-particleattached EOM-CC eigenstates with the largest overlap with the model space onto two-body valence-space states.…”

mentioning

confidence: 99%

Opensd-shell nuclei from first principles

et al. 2016

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We extend the ab initio coupled-cluster effective interaction (CCEI) method to open-shell nuclei with protons and neutrons in the valence space, and compute binding energies and excited states of isotopes of neon and magnesium. We employ a nucleon-nucleon and three-nucleon interaction from chiral effective field theory evolved to a lower cutoff via a similarity renormalization group transformation. We find good agreement with experiment for binding energies and spectra, while charge radii of neon isotopes are underestimated. For the deformed nuclei 20 Ne and 24 Mg we reproduce rotational bands and electric quadrupole transitions within uncertainties estimated from an effective field theory for deformed nuclei, thereby demonstrating that collective phenomena in sd-shell nuclei emerge from complex ab initio calculations.Introduction -Nuclei are complex many-body systems that present us with a wealth of interesting quantum mechanical phenomena that emerge along the entire chart of nuclei. These phenomena involve: exotic clustering behavior and extended density distributions of loosely bound nuclei [1, 2], melting and re-organization of shellstructure in neutron nuclei [3][4][5], Borromean nuclei [6,7], and emergence of collective behavior in nuclei, such as rotational and vibrational states [8,9] as well as nuclear super conductivity and pairing [10].Recently there has been an explosion of nuclear manybody methods with a sufficiently soft computational scaling to allow a reliable description of binding energies and spectra in nuclei up through the sd-shell starting from nucleon-nucleon and three-nucleon forces from chiral effective field theory (EFT) [11][12][13][14][15][16]. In spite of this progress, emergence of collective phenomena in nuclei still poses significant challenges to ab initio methods. Rotational states in p-shell nuclei have been successfully computed in the no-core shell-model and in Green'sfunction Monte-Carlo approaches [17][18][19][20][21], while in the sd-shell, deformed nuclei have only been accurately described in shell-model calculations using phenemenological interactions [22]. A symplectic approach has been proposed [23] to enable extension of the no-core shellmodel to larger model spaces and higher-mass nuclei, yet prototypical deformed nuclei like 20 Ne and 48 Cr remain out of reach in the aforementioned approaches. Furthermore, as deformed nuclei are truly open-shell, they

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“…If we look more closely, we see that the reference Λ-CCSD(T) results in 21,22 is not yet converged; it moves down by ∼ 150 keV when we increase the model space size from N = 10 to N = 12 oscillator shells. The 2 + state changes only by ∼ 5 keV indicating that it, by contrast, is well converged.…”

Section: The Ab Initio Shell Modelmentioning

confidence: 94%

“…Perform a "Lee-Suzuki" mapping [17,18,19,20] of the low-lying states in these nuclei onto states in the valence shell containing one and two (and eventually, three) nucleons. The mapping is designed to maximize the overlap of the full ab initio eigenstates with their shell-model images, while preserving orthogonality of the images [21]. 4.…”

Section: The Ab Initio Shell Modelmentioning

confidence: 99%

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Nuclear matrix elements for double-β decay

Engel¹

2015

AIP Conference Proceedings

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Abstract. Recent progress in nuclear-structure theory has been dramatic. I describe applications in progress of ab inito calculations to double-beta decay, and discuss the recent and future application of generator-coordinate methods to the same problem. I also discuss the old and vexing problem of the renormalization of the weak nuclear axial-vector coupling constant "in medium" and plans to resolve it.

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Geometry of effective Hamiltonians

Cited by 26 publications

References 32 publications

Nonperturbative renormalization of the neutrinoless double-βoperator inp-shell nuclei

Nonperturbative renormalization of the neutrinoless double-βoperator inp-shell nuclei

Opensd-shell nuclei from first principles

Nuclear matrix elements for double-β decay

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