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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[atomic, energy, nuclear, optics] The magnetic moment as a result of the nuclear spin with respect to protons, neutron is linked to the nuclear spin angular momentum (Ispin) as μn=gn(μN/ℏ)Ispin, where μN=eℏ/2mp the nuclear magneton, and ℏ=h/2π with h = 6.62606957 × 10−34m2kg/s the Planck’s constant, mp the proton mass, and e = 1.60217657 × 10−19C the electron charge. It is also referred to as nucleong-factor.
Magnetic properties of materials
Published in David Jiles, Introduction to the Electronic Properties of Materials, 2017
The magnetic properties of materials arise almost exclusively from the motion of the electrons. This motion, in the form of electron spin and electron orbital motion, generates a magnetic moment associated with the electron. Much weaker magnetic moments arise from the nucleus, but these are three orders of magnitude smaller. Compare, for example, the size of the nuclear magneton μn = 5.051 × 10−27 Am2 with the Bohr (electron) magneton μß = 9.274 × 10−24 Am2.
Important components for accurate hyperfine coupling constants: electron correlation, dynamic contributions, and solvation effects
Published in Molecular Physics, 2020
Sigurd Vogler, Johannes C. B. Dietschreit, Laurens D. M. Peters, Christian Ochsenfeld
The isotropic HFCC can be calculated in the absence of spin-orbit coupling [55]: where is the permeability of the vacuum, is the electronic and is the nuclear g-factor of nucleus k, is the Bohr magneton, is the nuclear magneton, and is the mean value of in the current electronic state. is the Fermi-contact integral (real-space spin density), which is given by: where is the difference between the α- and β-electron density matrices of the basis functions and , and the nucleus is located at .
Sympathetic cooling of protons and antiprotons with a common endcap Penning trap
Published in Journal of Modern Optics, 2018
M. Bohman, A. Mooser, G. Schneider, N. Schön, M. Wiesinger, J. Harrington, T. Higuchi, H. Nagahama, C. Smorra, S. Sellner, K. Blaum, Y. Matsuda, W. Quint, J. Walz, S. Ulmer
Experiments that compare the basic properties of matter/antimatter counterparts with high precision provide stringent tests of charge-parity-time (CPT) invariance. As the fundamental symmetry of the Standard Model, any measured CPT-violation will provide a clear indication of new physics. Current experimental limits constrain CPT violating effects to a fractional precision of for leptons [1,2], for mesons [3] and for hydrogen and antihydrogen [4,5]. Our experiments target comparisons of the fundamental properties of protons (p) and antiprotons (), chiefly by measuring charge-to-mass ratios and magnetic moments in Penning traps. To determine the antiproton-to-proton charge-to-mass ratio we compare cyclotron frequencies of negative hydrogen ions and antiprotons in the magnetic field of a Penning trap. Based on such measurements was determined with an experimental uncertainty of [6]. Magnetic moment measurements, however, rely on the determination of and the spin precession frequency , where is the nuclear magneton. The determination of relies on the continuous Stern–Gerlach effect [7] for non-destructive detection of the particle’s spin eigenstate. This method has been applied successfully in measurements of the magnetic moments of the electron and the positron [1], and later, in determinations of the g-factor of the bound electron [8,9]. However, the mass of the proton reduces the magnetic moment by a factor of 660, making the application of the continuous Stern–Gerlach effect much more difficult.
Hydrogen states in mixed-cation CuIn(1−x)Ga x Se2 chalcopyrite alloys: a combined study by first-principles density-functional calculations and muon-spin spectroscopy
Published in Philosophical Magazine, 2021
A. G. Marinopoulos, R. C. Vilão, H. V. Alberto, E. F. M. Ribeiro, J. M. Gil, P. W. Mengyan, M. R. Goeks, M. Kauk-Kuusik, J. S. Lord
In order to examine quantitatively the degree of atomic character of the neutral hydrogen state, calculations of the hyperfine tensor were performed [45]. In particular the isotropic part of the hyperfine constant (Fermi-contact term), A, can serve as a measure of the electron-spin localisation of the unpaired electron. The expression for the Fermi-contact term for neutral hydrogen is given by:[46] where g is the electron g-factor, the Bohr magneton, g the hydrogen nuclear gyromagnetic ratio and its nuclear magneton. The spin density at the hydrogen-nucleus site, , is given by: = ( – ); namely, as the difference between the spin-up and spin-down electron densities. The isotropic constant was calculated by means of the hybrid HSE06 functional, with convergence calculations performed also with a higher kinetic-energy cutoff (550 eV). The resulting value was equal to 460 MHz (± 10 MHz) for the H configuration in the CIS compound [see Figure 5(a)]. This value corresponds to % of the free-atom value of the hydrogen atom (1420 MHz) [47], verifying the presence of at least some partial atomic character in these neutral paramagnetic states. This value is also very similar to the isotropic hyperfine constants of muonium (after scaling for the respective nuclear magnetic moments) in other copper-based compounds, such as CuO and the cuprous halides where magnitudes in the range between 25 % and 40 % of the free-atom value were reported [48–50]. Interestingly, first-principles calculations of hydrogen states and their spin densities in CuO showed that interstitial hydrogen has a similar quasi-atomic character, with a significant delocalisation of the electron-spin density to the nearest copper neighbours [51]. This finding is consistent with the present results in CIS and CIGS, lending also a plausible explanation for the existence of a moderate (not exceptionally high) value of the isotropic hyperfine constant for neutral hydrogen.