Collective Models of the Nucleus

Davidson, J. P.; Moszkowski, S. A.

doi:10.1119/1.1975889

Cited by 59 publications

(17 citation statements)

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“…Upon inspection of the level scheme of 94 Zr, the first excited state can be interpreted as a consequence of collective behaviour of the nucleus in terms of a dipole vibration. Interpreted in the spherical shell model with explicit vibrational degrees of freedom, the nuclear wave function can be decomposed into a combination of Slater determinants and a vibrational wave function [58]. Neglecting higher-order corrections, the former is the same as that of the 0 + ground state.…”

Section: Numerical Resultsmentioning

confidence: 99%

First-forbidden transitions in the reactor anomaly

et al. 2019

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We describe here microscopic calculations performed on the dominant forbidden transitions in reactor antineutrino spectra above 4 MeV using the nuclear shell model. By taking into account Coulomb corrections in the most complete way, we calculate the shape factor with the highest fidelity and show strong deviations from allowed approximations and previously published results. Despite small differences in the ab initio electron cumulative spectra, large differences on the order of several percents are found in the antineutrino spectra. Based on the behaviour of the numerically calculated shape factors we propose a parametrization of forbidden spectra. Using Monte Carlo techniques we derive an estimated spectral correction and uncertainty due to forbidden transitions. We establish the dominance and importance of forbidden transitions in both the reactor anomaly and spectral shoulder analysis. Based on these results, we conclude that a correct treatment of forbidden transitions is indispensable in both the normalization anomaly and spectral shoulder.

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Section: Numerical Resultsmentioning

confidence: 99%

First-forbidden transitions in the reactor anomaly

et al. 2019

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“…Its ground state is 1/2 + , consistent with a deformation of β 2 = 0.269 of Möller et al (2015), meaning the unpaired nucleon sits in the 1/2 + [220] orbital. From Davidson (1968), we find the wave function is dominated by the 1d 5/2 harmonic oscillator function, combined with parts from 2s 1/2 and 1d 3/2 . From our deliberations of Eq.…”

Section: Deformed Single-particle Matrix Elementsmentioning

confidence: 93%

“…with β 2 the traditional measure of quadrupole deformation (Davidson, 1968;Eisenberg and Greiner, 1975). In the case β 2 > 0, the nucleus has a prolate shape while it is oblate for β 2 < 0.…”

Section: L0(z W )mentioning

confidence: 99%

“…In the case of nuclear deformation, our initial harmonic oscillator wave functions are not any more good approximations of the nuclear wave function, as l is not a good quantum number. The single-particle wave function is then a normalized linear combination (Davidson, 1968) χ…”

Section: Deformed Single-particle Matrix Elementsmentioning

confidence: 99%

“…The coefficients C jΩ are tabulated by e.g. Nilsson (1955) and Davidson (1968) for different values of β 2 . The φ(jΩ) are solutions of the spherical single-particle orbital with the proper spin-angular functions…”

Section: Deformed Single-particle Matrix Elementsmentioning

confidence: 99%

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High precision analytical description of the allowed β spectrum shape

et al. 2018

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A fully analytical description of the allowed β spectrum shape is given in view of ongoing and planned measurements. Its study forms an invaluable tool in the search for physics beyond the standard electroweak model and the weak magnetism recoil term. Contributions stemming from finite size corrections, mass effects, and radiative corrections are reviewed. A particular focus is placed on atomic and chemical effects, where the existing description is extended and analytically provided. The effects of QCD-induced recoil terms are discussed, and cross-checks were performed for different theoretical formalisms. Special attention was given to a comparison of the treatment of nuclear structure effects in different formalisms. Corrections were derived for both Fermi and Gamow-Teller transitions, and methods of analytical evaluation thoroughly discussed. In its integrated form, calculated f values were in agreement with the most precise numerical results within the aimed for precision. We stress the need for an accurate evaluation of weak magnetism contributions, and note the possible significance of the oft-neglected induced pseudoscalar interaction. Together with improved atomic corrections, we then present an analytical description of the allowed β spectrum shape accurate to a few parts in 10 −4 down to 1 keV for low to medium Z nuclei, thereby extending the work by previous authors by nearly an order of magnitude.

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