Shell model in the complex energy plane

Michel, N.; Nazarewicz, W.; Płoszajczak, M.; Vertse, T.

doi:10.1088/0954-3899/36/1/013101

Cited by 258 publications

(397 citation statements)

References 226 publications

(475 reference statements)

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“…‡ To include continuum degrees of freedom, i.e., resonant and scattering states, we would have to treat the nucleus as an open quantum system in a so-called rigged Hilbert space [111,112]. This setting also creates opportunities for a completely microscopic description of nuclear reactions, see, e.g., [113,114].…”

Section: References States and Many-body Basesmentioning

confidence: 99%

In-medium similarity renormalization group for closed and open-shell nuclei

Hergert¹

2016

Phys. Scr.

145

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Abstract. We present a pedagogical introduction to the In-Medium Similarity Renormalization Group (IMSRG) framework for ab initio calculations of nuclei. The IMSRG performs continuous unitary transformations of the nuclear many-body Hamiltonian in second-quantized form, which can be implemented with polynomial computational effort. Through suitably chosen generators, it is possible to extract eigenvalues of the Hamiltonian in a given nucleus, or drive the Hamiltonian matrix in configuration space to specific structures, e.g., band-or block-diagonal form.Exploiting this flexibility, we describe two complementary approaches for the description of closed-and open-shell nuclei: The first is the Multireference IMSRG (MR-IMSRG), which is designed for the efficient calculation of nuclear ground-state properties. The second is the derivation of nonempirical valence-space interactions that can be used as input for nuclear Shell model (i.e., configuration interaction (CI)) calculations. This IMSRG+Shell model approach provides immediate access to excitation spectra, transitions, etc., but is limited in applicability by the factorial cost of the CI calculations.We review applications of the MR-IMSRG and IMSRG+Shell model approaches to the calculation of ground-state properties for the oxygen, calcium, and nickel isotopic chains or the spectroscopy of nuclei in the lower sd shell, respectively, and present selected new results, e.g., for the ground-and excited state properties of neon isotopes.Submitted to: Phys. Scr.

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Section: References States and Many-body Basesmentioning

confidence: 99%

In-medium similarity renormalization group for closed and open-shell nuclei

Hergert¹

2016

Phys. Scr.

145

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“…The principal difficulty in the formulation of the CSM is the treatment of the unbound space of states, i.e., resonances and the non-resonant continuum [19,20,28]. Therefore, whatever strategy is adopted to formulate the configuration interaction approach for OQSs, the key points are: (i) the treatment of the s.p.…”

Section: Continuum Shell Model Description Of Ancs In Mirror Sysmentioning

confidence: 99%

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

et al. 2012

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Background: An asymptotic normalization coefficient (ANC) characterizes the asymptotic form of a one-nucleon overlap integral required for description of nucleon-removal reactions.Purpose: We investigate the impact of the particle continuum on proton and neutron ANCs for mirror systems from p-and sd-shell regions. Method:We use the real-energy and complex-energy continuum shell model approaches.Results: We studied the general structure of the single-particle ANCs as a function of the binding energy and orbital angular momentum. We computed ANCs in mirror nuclei for different physical situations, including capture reactions to weakly-bound and unbound states. Conclusions:We demonstrated that the single-particle ANCs exhibit generic behavior that is different for charged and neutral particles. We verified the previously proposed relation [1] between proton and neutron mirror ANCs. We find minor modifications if the spectroscopic strength is either localized in a single state or broadly distributed. For cases when several states couple strongly to the decay channel, these modifications may reach 30%.

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“…The role of the continuum is expected to be important close to the drip line, as seen in Refs. [20,[26][27][28]. For this purpose we use a Berggren representation [29] for the neutron s 1/2 , d 3/2 , and d 5/2 partial waves.…”

mentioning

confidence: 99%

“…The Berggren ensemble has been successfully used within the Gamow shell model, see for example Ref. [27] for a recent review, and in coupled-cluster calculations of energies and lifetimes in Refs. [20,22].…”

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confidence: 99%

Closed-shell properties ofO24withab initiocoupled-cluster theory

et al. 2011

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We present a microscopic calculation of spectroscopic factors for neutron and proton removal from 24 O using the coupled-cluster method and a state-of-the-art chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order. In order to account for the coupling to the scattering continuum we use a Berggren single-particle basis that treats bound, resonant, and continuum states on an equal footing. We report neutron removal spectroscopic factors for the 23 O states J π = 1/2 + , 5/2 + , 3/2 − and 1/2 − , and proton removal spectroscopic factors for the 23 N states 1/2 − and 3/2 − . Our calculations support the accumulated experimental evidence that 24 O is a closed-shell nucleus.PACS numbers: 21.10.Jx, 21.60. De, 21.10.Pc, 31.15.bw, 24.10.Cn Introduction The study of nuclei far from stability is a leading direction in nuclear physics, experimentally and theoretically. It represents a considerable intellectual challenge to our understanding of the stability of matter itself, with potential implications for the synthesis of elements. An important aspect of this research direction is to understand how magic numbers and shells appear and evolve with increasing numbers of neutrons or protons. The structure and properties of barely stable nuclei at the limits of stability, have been demonstrated to deviate dramatically from the established patterns for ordinary and stable nuclei, see Ref.[1] and references therein for a recent review. One of the striking features of nuclei close to the drip line is the adjustment of shell gaps, giving rise to different magic numbers [2]. The way shell closures and single-particle properties evolve as functions of the number of nucleons forms one of the greatest challenges to our understanding of the basic features of nuclei, and thereby the stability of matter.The chain of oxygen isotopes up to 28 O is particularly interesting since these are the heaviest nuclei for which the drip line is well established. Two out of four stable even-even isotopes exhibit a doubly magic nature, namely 22 O (Z=8,N =14) and 24 O (Z=8, N =16). Several recent experiments [3-6] bring evidence that 24 O is the last stable oxygen isotope. This is remarkable, in particular if one considers the fact that the addition of a single proton on top of the Z = 8 closed shell brings the drip line of the fluorine isotopes to 31 F. Recent measurements [3] also suggest that 24 O has a spherical neutron configuration. The isotopes 25−28 O are all believed to be unstable towards neutron emission, even though 28 O is a doubly magic nucleus within the standard shell-model picture. This indicates that the magic number at the neutron drip line for the oxygen isotopes is not at N = 20 but rather at N = 16.Although spectroscopic factors are not observable quantities [9,10], they can be used to address shell closure properties within the context of a given model. Experimentally, spectroscopic factors are defined as the ratio of the observed reaction rate with respect to the same

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Shell model in the complex energy plane

Cited by 258 publications

References 226 publications

In-medium similarity renormalization group for closed and open-shell nuclei

In-medium similarity renormalization group for closed and open-shell nuclei

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

Closed-shell properties ofO24withab initiocoupled-cluster theory

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