Introduction

Arfken, George B.

doi:10.1016/b978-0-12-059820-5.50008-2

Cited by 312 publications

(422 citation statements)

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“…Making use of the wave functions (19) and (23) in Eqs. (8) and (9) we computed the numbers for position-and momentum-space Fisher information. The results for the values of F ρ and F γ are presented in Table 3.…”

Section: Results For Shannon Entropy and Fisher Informationmentioning

confidence: 99%

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Shannon entropies and Fisher information of K-shell electrons of neutral atoms

Sekh¹,

Saha

Talukdar

2018

Physics Letters A

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We represent the two K-shell electrons of neutral atoms by Hylleraas-type wave function which fulfils the exact behavior at the electron-electron and electron-nucleus coalescence points and, derive a simple method to construct expressions for single-particle position-and momentum-space charge densities, ρ(r) and γ(p) respectively. We make use of the results for ρ(r) and γ(p) to critically examine the effect of correlation on bare (uncorrelated) values of Shannon information entropies (S) and of Fisher information (F ) for the K-shell electrons of atoms from helium to neon. Due to inter-electronic repulsion the values of the uncorrelated Shannon position-space entropies are augmented while those of the momentum-space entropies are reduced. The corresponding Fisher information are found to exhibit opposite behavior in respect of this. Attempts are made to provide some plausible explanation for the observed response of S and F to electronic correlation.

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Section: Results For Shannon Entropy and Fisher Informationmentioning

confidence: 99%

“…But we need the Fourier transform of the constructed position-space wave function to study properties of S and F in the momentum-space. The required transform can be taken by making judicious use of the standard integrals [8] 1 ξ e −α ξ+i β·ξ dξ = 4π…”

Section: Introductionmentioning

confidence: 99%

Shannon entropies and Fisher information of K-shell electrons of neutral atoms

Sekh¹,

Saha

Talukdar

2018

Physics Letters A

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“…When the total charge remains constant, the explanation for this behavior is not obvious. However, one aspect of the decrease in precursor ion intensity can be understood by considering that the bandwidth of the auxiliary signal (the inverse of its duration) diminishes with exposure [19]. Each collision disrupts the phase relationship between an ion's secular motion and the auxiliary signal.…”

Section: Duration Of Exposurementioning

confidence: 99%

Resonant excitation in a low-pressure linear ion trap

Collings¹,

Stott²,

Londry³

2003

J. Am. Soc. Mass Spectrom.

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It has been shown that through the process of resonant excitation the fragmentation of ions confined in a low-pressure (Ͻ0.05 mTorr) linear ion trap (LIT) can be accomplished while maintaining both high fragmentation efficiency and high resolution of excitation. The ion reserpine, 609.23 Da, has been fragmented with efficiencies greater than 90% while a higher mass ion, a homogeneously substituted triazatriphosphorine of mass 2721.89 Da, has been fragmented with 48% efficiency. This was accomplished by extended resonant excitation by low-amplitude auxiliary RF signals. Computer modelling of ion trajectories and analysis of the trapping potentials have demonstrated that a reduction in neutralization of ions on the rods (or losses on the rods) and increased fragmentation is a consequence of higher order terms in the potential introduced by the round-rod geometry of the LIT. (LIT), leading to neutralization on the rods and/or fragmentation, has been demonstrated previously using both quadrupolar and dipolar auxiliary RF signals [1][2][3][4]. Typically, these experiments were carried out using nitrogen collision gas, at pressures ranging from 1.5 to 7 mTorr, with exposures to resonant excitation of a few milliseconds. At these pressures and exposures it was possible to obtain increased resolutions of excitation from 75 to 250 as the pressure in the LIT was decreased [3]. In those experiments, resolution decreased as the amplitude of the auxiliary signal was increased. However, the auxiliary amplitude required for either neutralization on the rods or fragmentation was dependent upon the pressure of the buffer gas. When the auxiliary amplitude was too low, thermalizing collisions reduced ion energies, both translational and internal, at a rate greater than energy was added by the auxiliary signal. In consequence, there existed a threshold for the auxiliary amplitude below which neutralization/fragmentation did not occur [5,6]. When the auxiliary amplitude was only slightly above this threshold, resolution of excitation was high, but the degree of neutralization/fragmentation was low [3]. In order to achieve a high degree of neutralization/fragmentation, it was necessary to increase the auxiliary amplitude and suffer the decreased resolution.The range of frequencies, about the secular frequency, to which ions respond (frequency response) increases with pressure. This behavior is predicted by the theory of a forced damped harmonic oscillator (FDHO). Models based on the FDHO theory have been used to describe the behavior of ions confined in a Paul trap at pressures in the mTorr regime [7,8]. However, when excited on-resonance at pressures below one mTorr, it has been assumed generally that ions would be lost on the rods before significant fragmentation occurred. In contrast, it is well known that effective fragmentation at low pressures (1 ϫ 10 Ϫ4 to 1 ϫ 10 Ϫ6 torr) can be achieved through the use of off-resonance excitation, as demonstrated in sustained off-resonance irradiation (SORI) experiments in FT-ICR [9 -11].In t...

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“…10). For small y we may expand (51) into a Taylor series in y and for large w 2 + (2 |z| − t) 2 λ we may use the asymptotic expansion for the Bessel functions [36], which gives…”

Section: The Transverse Field Of Multi-polar Stripsmentioning

confidence: 99%

Closed Analytical Formulae for Multi-Pole Magnetic Rings

Ausserlechner¹

2012

PIER B

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Abstract-Multi-pole permanent magnetic encoders are used for wheel speed sensing in automotive systems. This paper discusses rings and discs magnetized along axial direction. The vector field is calculated analytically in 3D as sums over all poles. For the case of discs with vanishing inner and infinite outer diameter the summation is done in closed form with a new summation formula. The results are discussed and several plots of field patterns are given in normalized form: At very small air-gap the field shows an overshoot. At moderate and large air-gaps it is a sine-function with exponentially decaying amplitude. The amplitude versus air gap, reading radius, thickness of the magnetic layer, and number of poles is studied and excellent agreement with measurements is found. The effect of a steel-back on the field is explained. It is also shown how to maximize the torque transmitted in axially magnetized couplings.

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Introduction

Cited by 312 publications

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Shannon entropies and Fisher information of K-shell electrons of neutral atoms

Shannon entropies and Fisher information of K-shell electrons of neutral atoms

Resonant excitation in a low-pressure linear ion trap

Closed Analytical Formulae for Multi-Pole Magnetic Rings

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