Localization landscape for Dirac fermions

Lemut, G.; Pacholski, M. J.; Ovdat, Omrie; Grabsch, Aurélien; Tworzydło, J.; Beenakker, C. W. J.

doi:10.1103/physrevb.101.081405

Cited by 18 publications

(28 citation statements)

References 31 publications

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“…2 ever, it should be noted that there is still a significant energy gap from the data points at 100-500 keV to the solar Gamow energy, E Gamow = 27 keV. Summing detector data from LUNA reach down to the lowest energies hitherto measured, E = 70 keV, and provide a value for the total S-factor, summed from all transitions, of S(E = 70 keV)=1.74±0.14 stat ±0.14 syst keV barn [33,36]. However, by design the summing data cannot constrain the partial S-factor for capture to the 6.79 MeV level very well.…”

Section: Introductionmentioning

confidence: 98%

Astrophysical S factor of the N14(p,γ)O15

et al. 2018

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The 14 N(p,γ) 15 O reaction is the slowest reaction of the carbon-nitrogen cycle of hydrogen burning and thus determines its rate. The precise knowledge of its rate is required to correctly model hydrogen burning in asymptotic giant branch stars. In addition, it is a necessary ingredient for a possible solution of the solar abundance problem by using the solar 13 N and 15 O neutrino fluxes as probes of the carbon and nitrogen abundances in the solar core. After the downward revision of its cross section due to a much lower contribution by one particular transition, capture to the ground state in 15 O, the evaluated total uncertainty is still 8%, in part due to an unsatisfactory knowledge of the excitation function over a wide energy range. The present work reports precise S-factor data at twelve energies between 0.357-1.292 MeV for the strongest transition, capture to the 6.79 MeV excited state in 15 O, and at ten energies between 0.479-1.202 MeV for the second strongest transition, capture to the ground state in 15 O. An R-matrix fit is performed to estimate the impact of the new data on astrophysical energies. The recently suggested slight enhancement of the 6.79 MeV transition at low energy could not be confirmed. The present extrapolated zero-energy S-factors are S6.79(0) = 1.24±0.11 keV barn and SGS(0) = 0.19±0.05 keV barn.

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Section: Introductionmentioning

confidence: 98%

Astrophysical S factor of the N14(p,γ)O15

et al. 2018

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“…The understanding that the pure tunnelling picture in LLT is only applicable at very low energies is novel, and establishes when and how one can use LLT in a useful manner. Two very recent papers [67,68] have developed generalisations of LLT to allow treatment of systems with internal degrees of freedom, with [68] explicitly extending their technique to arbitrary energies, while the method in [67] is amenable to such an extension [68]. These generalisations of course come at the price of added complexity, but have additional advantages as well: for example, the method of [68] removes the constraint that the physical potential cannot be negative on any part of the system domain, and yields some helpful features arising from the different normalisation of the eigenstates chosen therein.…”

Section: Breakdown At Higher Energiesmentioning

confidence: 99%

Computing the eigenstate localisation length at very low energies from Localisation Landscape Theory

et al. 2021

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While Anderson localisation is largely well-understood, its description has traditionally been rather cumbersome. A recently-developed theory -Localisation Landscape Theory (LLT) -has unparalleled strengths and advantages, both computational and conceptual, over alternative methods. To begin with, we demonstrate that the localisation length cannot be conveniently computed starting directly from the exact eigenstates, thus motivating the need for the LLT approach. Then, we confirm that the Hamiltonian with the effective potential of LLT has very similar low energy eigenstates to that with the physical potential, justifying the crucial role the effective potential plays in our new method. We proceed to use LLT to calculate the localisation length for very low-energy, maximally localised eigenstates, as defined by the length-scale of exponential decay of the eigenstates, (manually) testing our findings against exact diagonalisation. We then describe several mechanisms by which the eigenstates spread out at higher energies where the tunnelling-in-the-effective-potential picture breaks down, and explicitly demonstrate that our method is no longer applicable in this regime. We place our computational scheme in context by explaining the connection to the more general problem of multidimensional tunnelling and discussing the approximations involved. Our method of calculating the localisation length can be applied to (nearly) arbitrary disordered, continuous potentials at very low energies.

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“…The low background conditions observed in underground experiments can only be fully exploited for accelerator-based studies if there is no additional background induced by the ion beam. As the Felsenkeller accelerator is not yet running, this point has been addressed in a recent experiment using an intensive, 9 particle-µA, 12 C beam at the surface-based HZDR 3 MV Tandetron accelerator in Rossendorf ( Figure 5).…”

Section: Background Studies With Ion Beammentioning

confidence: 99%

“…With the same approach, the 14 N(p,γ) 15 O reaction controlling the CNO cycle in the Sun [11,12], the reactions controlling Big Bang production of 6 Li [13,14] and 7 Li [6], and several reactions of higher hydrogen burning have recently been studied.…”

Section: Introductionmentioning

confidence: 99%

The new Felsenkeller 5 MV underground accelerator

et al. 2019

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The field of nuclear astrophysics is devoted to the study of the creation of the chemical elements. By nature, it is deeply intertwined with the physics of the Sun. The nuclear reactions of the proton-proton cycle of hydrogen burning, including the 3 He(α,γ) 7 Be reaction, provide the necessary nuclear energy to prevent the gravitational collapse of the Sun and give rise to the by now wellstudied pp, 7 Be, and 8 B solar neutrinos. The not yet measured flux of 13 N, 15 O, and 17 F neutrinos from the carbon-nitrogen-oxygen cycle is affected in rate by the 14 N(p,γ) 15 O reaction and in emission profile by the 12 C(p,γ) 13 N reaction. The nucleosynthetic output of the subsequent phase in stellar evolution, helium burning, is controlled by the 12 C(α,γ) 16 O reaction.In order to properly interpret the existing and upcoming solar neutrino data, precise nuclear physics information is needed. For nuclear reactions between light, stable nuclei, the best available technique are experiments with small ion accelerators in underground, low-background settings. The pioneering work in this regard has been done by the LUNA collaboration at Gran Sasso/Italy, using a 0.4 MV accelerator.The present contribution reports on a higher-energy, 5.0 MV, underground accelerator in the Felsenkeller underground site in Dresden/Germany. Results from γ-ray, neutron, and muon background measurements in the Felsenkeller underground site in Dresden, Germany, show that the background conditions are satisfactory for nuclear astrophysics purposes. The accelerator is in the commissioning phase and will provide intense, up to 50 µA, beams of 1 H + , 4 He + , and 12 C + ions, enabling research on astrophysically relevant nuclear reactions with unprecedented sensitivity.

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Localization landscape for Dirac fermions

Cited by 18 publications

References 31 publications

Astrophysical S factor of the N14(p,γ)O15

Astrophysical S factor of the N14(p,γ)O15

Computing the eigenstate localisation length at very low energies from Localisation Landscape Theory

The new Felsenkeller 5 MV underground accelerator

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