Harmonic oscillator eigenfunction expansions, quantum dots, and effective interactions

Kvaal, Simen

doi:10.1103/physrevb.80.045321

Cited by 22 publications

(56 citation statements)

References 43 publications

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“…However, in all these many-body approaches, the size of the actual model space grows combinatorially with the number of active particles and singleparticle states taken, which is not the case for DFT. In a recent work, the exponential convergence of wavefunctions expanded in a HO basis has in fact been related to its weak differentiability properties [134]. It has been argued therein that this may be a generic property of systems with exponentially decaying wave-functions.…”

Section: B Estimation Of Theoretical Errorsmentioning

confidence: 99%

Surface symmetry energy of nuclear energy density functionals

et al. 2011

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We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutronrich matter and description of fission rates for r-process nucleosynthesis.

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Section: B Estimation Of Theoretical Errorsmentioning

confidence: 99%

Surface symmetry energy of nuclear energy density functionals

et al. 2011

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“…These values of the ir cutoff can be lowered (thereby increasing the reliability of the extrapolation) only by increasing N ; a computational challenge which gets harder the larger the number of particles in the nucleus. For example, the largest N achievable with ANTOINE 39 for the nuclei 6 Li and Notice that the slopes of the light p-shell nuclei 6 He and 6 Li are intermediate between those of the more massive s-shell nuclei and the slope of the deuteron which has an unnaturally small binding energy on a hadronic scale. It is tempting to try to understand the slopes in Figures 10 and 11 with the aid of the scale of Q; the experimental binding momentum of each nucleus.…”

Section: Dependence Of Ir Extrapolation Upon Nucleus and N N Interactionmentioning

confidence: 99%

“…In this example, N = N max , the maximum of the total HO quanta shared by all nucleons above the lowest HO configuration of the nucleus 6 Li. This truncation, a characteristic feature of the NCSM, is at the level of total energy quanta ("total-energy-cut space"), which is different from the configuration-interaction calculations used in atomic and molecular problems, that are often truncated at the single-particle level ("single-particle-cut space").…”

Section: 13mentioning

confidence: 99%

“…Let us illustrate this distinction with two examples. 6 He is an open shell nucleus with N 0 = 1 since both valence neutrons occupy the 0p shell in the lowest energy many-body configuration. Assigning a single neutron the entire N max = 4 quanta means that the highest occupied single-particle state is in the N = 5 shell.…”

Section: Ultraviolet and Infrared Cutoffs Inherent To The Finite Ho Bmentioning

confidence: 99%

“…4,5 In addition, a recent discussion of the configuration-interaction method in a HO basis analyzes convergence for many-electron systems trapped in a harmonic oscillator (a typical model for a quantum dot). 6 The convergence rates of the functional analysis theorems (inverse power laws in N for "non smooth" potentials such as Yukawas with strong short range correlations and exponential in N for "smooth" potentials such as gaussians) were demonstrated numerically in Ref. 4 for the HO expansion and in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Properties of infrared extrapolations in a harmonic oscillator basis

Coon

Kruse

2016

Int. J. Mod. Phys. E

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The success and utility of effective field theory (EFT) in explaining the structure and reactions of few-nucleon systems has prompted the initiation of EFT-inspired extrapolations to larger model spaces in ab initio methods such as the no-core shell model (NCSM). In this contribution, we review and continue our studies of infrared (ir) and ultraviolet (uv) regulators of NCSM calculations in which the input is phenomenological N N and N N N interactions fitted to data. We extend our previous findings that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful, not only for the eigenstates of the Hamiltonian but also for expectation values of operators, such as r 2 , considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a possible extrapolation of ground state energies in the uv cutoff when the ir cutoff is below the intrinsic ir scale is not robust and does not agree with the ir extrapolation of the same data or with independent calculations using other methods.

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Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

et al. 2018

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a b s t r a c tWe consider the one-dimensional Hamiltonian with a V-shaped, decorated with a point impurity of either δ-type, or local δ ′ -type or even nonlocal δ ′ -type, thus yielding three exactly solvable models. We analyse the behaviour of the change in the energy levels when an interaction of the type −λ δ(x) or −λ δ(x − x 0 ) is switched on. In the first case, even energy levels, pertaining to antisymmetric bound states, remain invariant with respect to λ even though odd energy levels, pertaining to symmetric bound states, decrease as λ increases. In the second, all energy levels decrease when the factor λ increases. A similar study has been performed for the so-called nonlocal δ ′ interaction, requiring a coupling constant renormalisation, which implies the replacement of the form factor λ by a renormalised form factor β. In terms of β, odd energy levels are unchanged. However, we show the existence of level crossings: after a fixed value of β the energy of each even level, with the natural exception of the first one, becomes lower than the constant energy of the previous odd level. Finally, we consider an interaction of the type −λδ(x)+µδ ′ (x), and analyse in detail the discrete spectrum of the resulting selfadjoint Hamiltonian.

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Harmonic oscillator eigenfunction expansions, quantum dots, and effective interactions

Cited by 22 publications

References 43 publications

Surface symmetry energy of nuclear energy density functionals

Surface symmetry energy of nuclear energy density functionals

Properties of infrared extrapolations in a harmonic oscillator basis

Spectroscopy of a one-dimensional V-shaped quantum well with a point impurity

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