Magnetic Dipole Amplitude Research Articles

Dynamics of a magnetic pendulum in the presence of an oscillating conducting plate

AbstractA pendulum with an attached permanent magnet moving near a conductor is a typical experiment for the demonstration of electromagnetic braking. When the conductor itself moves, it can transfer energy to the pendulum. We study a simple but exact analytical model where the conductor is a horizontally unbounded flat plate. For this geometry, eddy currents and induced Lorentz force due to the motion of a magnetic dipole are known analytically in the quasistatic limit. A vertical oscillation of such a horizontal plate located beneath the magnet is considered. In this setup, the vertical position of the pendulum is an equilibrium point when the magnetic moment of the magnet is perpendicular to its plane of motion. Depending on the strength of the magnetic dipole moment, the frequency and amplitude of the plate as well as the distance between plate and magnet, the plate oscillation can destabilize the equilibrium. The stability limits for weak electromagnetic coupling are computed analytically using the harmonic balancing method. For stronger coupling, the stability limits are obtained numerically using Floquet analysis. Chaotic motions with finite amplitudes are also found.

Radiative transition properties of singly charged magnesium, calcium, strontium and barium ions

Accurate values of electric dipole (E1) amplitudes along with their uncertainties for a number of transitions among low-lying states of Mg+, Ca+, Sr+, and Ba+ are listed by carrying out calculations using a relativistic all-order many-body method. By combining experimental wavelengths with these amplitudes, we quote transition probabilities, oscillator strengths and lifetimes of many short-lived excited states of the above ions. The uncertainties in these radiative properties are also quoted. We also give electric quadrupole (E2) and magnetic dipole (M1) amplitudes of the metastable states of the Ca+, Sr+, and Ba+ ions by performing similar calculations. Using these calculated E1, E2 and M1 matrix elements, we have estimated the transition probabilities, oscillator strengths and lifetimes of a number of allowed and metastable states. These quantities are further compared with the values available from the other theoretical studies and experimental data in the literature. The present data will be useful for the astrophysical observations, laboratory analysis and simulations of spectral properties in the above considered alkaline-earth metal ions.

Measurements of theγ*p→Δreaction at lowQ2: Probing the mesonic contribution

The determination of nonspherical angular momentum amplitudes in nucleons at long ranges (low Q{sup 2}) was accomplished through the p(e-vector,e{sup '}p){pi}{sup 0} reaction in the {delta} region at Q{sup 2}=0.060, 0.127, and 0.200 (GeV/c){sup 2} at the Mainz Microtron with an accuracy for the cross sections of 4%. The results for the dominant transition magnetic dipole amplitude and the quadrupole to dipole ratios have been obtained with an estimated model uncertainty that is approximately the same as the experimental uncertainty. Lattice and effective field theory predictions agree with our data within the relatively large estimated theoretical uncertainties. Phenomenological models are in good agreement with experiment when the resonant amplitudes are adjusted to the data. To check reaction model calculations additional data were taken for center-of-mass energies below resonance and for the {sigma}{sub LT{sup '}} structure function. These results confirm the dominance, and general Q{sup 2} variation, of the pionic contribution at large distances.

Virtual Compton scattering measurements in theγ*N→Δtransition

We report on new H(e,e{sup '}p){gamma} measurements in the {delta}(1232) resonance at Q{sup 2}=0.06 (GeV/c){sup 2} carried out simultaneously with H(e,e{sup '}p){pi}{sup 0}. It is the lowest Q{sup 2} for which the virtual Compton scattering (VCS) reaction has been studied in the first resonance region. The VCS measured cross sections are well described by dispersion-relation calculations in which the multipole amplitudes derived from H(e,e{sup '}p){pi}{sup 0} data are used as input, thus confirming the compatibility of the results. The derived resonant magnetic dipole amplitude M{sub 1+}{sup 3/2}=(40.60{+-}0.70{sub stat+sys})(10{sup -3}/m{sub {pi}{sup +}}) at W=1232 MeV is in excellent agreement with the value extracted from H(e,e{sup '}p){pi}{sup 0} measurements.

STUDYING γ*N→Δ→πN WITH CROSS SECTIONS AND POLARIZATION OBSERVABLES

Preliminary results are presented of the reaction γ*N→Δ→πN that was studied at the Jefferson Laboratory for transferred four momentum of 1.0 (GeV/c)2. Angular distributions of the cross sections and polarizations were measured over much of the available phase space. Out of the eighteen response functions involved in this reaction, fourteen separate responses and two additional response combinations were extracted. All resonant and background multipole amplitudes were decomposed for s- and p-waves as well as several of the d-wave multipole amplitudes. The responses and multipoles were compared to model calculations. Significant differences were observed between the experimental values and those of the models for several of the responses and multipoles. The ratios of the electric and longitudinal quadrupole amplitudes to the magnetic dipole amplitude were extracted. These values are different from previously reported values.

NtoΔelectromagnetic transition form factors from lattice QCD

The magnetic dipole, the electric quadrupole, and the Coulomb quadrupole amplitudes for the transition $\ensuremath{\gamma}\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\Delta}$ are evaluated both in quenched lattice QCD at $\ensuremath{\beta}=6.0$ and using two dynamical Wilson fermions simulated at $\ensuremath{\beta}=5.6.$ The dipole transition form factor is accurately determined at several values of momentum transfer. On the lattices studied in this work, the electric quadrupole amplitude is found to be nonzero, yielding a negative value for the ratio ${R}_{\mathrm{EM}}$ of electric quadrupole to magnetic dipole amplitudes at three values of momentum transfer.

γN → Δ transition form factors in quenched and NF = 2 QCD

Abstract Calculations of the magnetic dipole, electric quadrupole and Coulomb quadrupole amplitudes for the transition γN → Δ are presented both in quenched QCD and with two flavours of degenerate dynamical quarks.

Calculation of the N to Δ electromagnetic transition matrix element

We present results on the ratio of electric quadrupole to magnetic dipole amplitudes, R EM =G E2/G M1 , for the transitionλN → Δ from lattice QCD. We consider both the quenched and the 2-flavor theory.

The electroproduction of the Δ(1232) in the chiral quark–soliton model

We calculate the ratios E2 / M1 and C2 / M1 for the electroproduction of the Δ(1232) in the region of photon virtuality 0<− q 2<1 GeV 2 . The magnetic dipole amplitude M1 is also presented. The theory used is the chiral quark–soliton model, which is based on the instanton vacuum of the QCD. The calculations are performed in flavours SU(2) and SU(3) taking rotational ( 1/ N c ) corrections into account. The results for the ratios agree qualitatively with the available data, although the magnitude of both ratios seems to underestimate the latest experimental results.

Effective Lagrangian approach to the theory of eta photoproduction in the N*(1535) region.

We investigate theoretical uncertainties and model dependence in the extraction of the nucleon-{Delta}(1232) electromagnetic transition amplitudes from the multipole data base. Our starting point is an effective Lagrangian incorporating chiral symmetry, which includes, at the tree level, the pseudovector nucleon Born terms, leading {ital t}-channel vector-meson exchanges, and {ital s}- and {ital u}-channel {Delta} exchanges. We express the nucleon-{Delta} transition magnetic dipole ({ital M}1) and electric quadrupole ({ital E}2) amplitudes in terms of two independent gauge couplings at the {gamma}{ital N}{Delta} vertex, and fit these to various multipole data sets. We find a large sensitivity to the method used in unitarizing the amplitude, and extract the {ital E}2/{ital M}1 ratio (EMR) to be {ital negative}, with a magnitude of around 1.5%. The resonant amplitudes in this work are of interest to the test of topical hadron models inspired by QCD: the sign of the EMR, extracted by us, is in accord with that predicted by most realistic models, and its magnitude lies between the predictions of the quark shell model and the Skyrmion model. Finally, our work provides a phenomenologically satisfying unitary amplitude for pion photoproduction off nucleons, which can be used as a realistic starting point for theoretical studiesmore » of this process in complex nuclei.« less

Dependence of the electromagnetic ratio of electric quadrupole to magnetic dipole Delta N gamma couplings on the Delta + mass in single-pion photoproduction.

We investigate the role of the ${\mathrm{\ensuremath{\Delta}}}^{+}$ mass and the magnetic dipole coupling parameters in the extraction of the ratio of electric quadrupole to magnetic dipole amplitudes (EMR) in the ${\mathrm{\ensuremath{\Delta}}}^{+}$\ensuremath{\rightarrow}r\ensuremath{\gamma} transition. We show that existing data on single-pion photoproduction do not allow as wide a range (\ifmmode\pm\else\textpm\fi{}5% ) of values for the EMR as concluded in a recent paper by Slaughter and Oneda [Phys. Rev. D 49, 323 (1994)].

Calculation of the Delta +p gamma photon-decay amplitude A1/2 and the E1+/M1+ ratio in single-pion electroproduction: An algebraic approach.

A [ital nonperturbative] calculation of the [Delta][sup +][r arrow][ital P]+[gamma] transverse one-half helicity transition form factor [ital h][sub 3]([ital q][sup 2]) and the [ital A][sub 1/2] [Delta][sup +][ital P][gamma] photon-decay amplitude is made with results in good agreement with experiment. The ratio of the electric quadrupole amplitude to the magnetic dipole amplitude at resonance is calculated as a function of [ital G][sub [ital M]][sup *](0) and the [Delta][sup +] mass. We confirm that [ital G][sub [ital M]][sup *]([ital q][sup 2]) decreases more rapidly than the nucleon dipole form factor in the region where [ital G][sub [ital E]][sup *]([ital q][sup 2]) is known to be small. Our treatment is completely relativistic and current conservation is guaranteed.

Effective-Lagrangian approach to the theory of pion photoproduction in the Delta (1232) region.

We investigate theoretical uncertainties and model dependence in the extraction of the nucleon-$\ensuremath{\Delta}(1232)$ electromagnetic transition amplitudes from the multipole data base. Our starting point is an effective Lagrangian incorporating chiral symmetry, which includes, at the tree level, the pseudovector nucleon Born terms, leading $t$-channel vector-meson exchanges, and $s$- and $u$-channel $\ensuremath{\Delta}$ exchanges. We express the nucleon-$\ensuremath{\Delta}$ transition magnetic dipole ($M1$) and electric quadrupole ($E2$) amplitudes in terms of two independent gauge couplings at the $\ensuremath{\gamma}N\ensuremath{\Delta}$ vertex, and fit these to various multipole data sets. We find a large sensitivity to the method used in unitarizing the amplitude, and extract the $\frac{E2}{M1}$ ratio (EMR) to be negative, with a magnitude of around 1.5%. The resonant amplitudes in this work are of interest to the test of topical hadron models inspired by QCD: the sign of the EMR, extracted by us, is in accord with that predicted by most realistic models, and its magnitude lies between the predictions of the quark shell model and the Skyrmion model. Finally, our work provides a phenomenologically satisfying unitary amplitude for pion photoproduction off nucleons, which can be used as a realistic starting point for theoretical studies of this process in complex nuclei.

High-Q2 Delta (1232) electroproduction and QCD predictions.

Analyses of the electroproduction of pions in the {Delta}(1232) region have been taken to suggest that the dominance of the magnetic dipole amplitude persists up to the highest momentum transfer available. Actually, magnetic dipole dominance is consistent with the data but is not required by it. We show that the high-momentum-transfer QCD prediction of equality, modulo notation, between the electric quadrupole and magnetic dipole amplitudes is also consistent with the high-momentum-transfer data. Thus, while the present data do restrict the multipole amplitudes, to distinguish the two main possibilities further measurements are needed, and we comment on these.

Magnetic dipole and electric quadrupole amplitudes induced by the hyperfine interaction in the Cesium 6S-7S transition and the parity violation calibration

A possible way to calibrate the Cesium 6S→7S parity violating electric dipole amplitude E 1 (p.v) is to make use of the ratio E 1 (p.v)/M 1 (h.f) where M 1 (h.f) is the magnetic dipole amplitude induced by the hyperfine interaction V(h.f). We show by evaluating relativistic and many-body effects that M 1 (h.f) is given, to better than 3•10 −3 , by the geometrical mean of the 6S and 7S hyperfine splittings and thus provides a very good calibration of E 1 (p.v.). It one wishes to reach the 1% accuracy, it may be no longer legitimate to ignore the electric quadrupole amplitude E 2 (h.f) which can also be induced by V(h.f). We have shown that E 2 (h.f), computed within a one-particle model, is strongly suppressed by an approximate selection rule. This rule, however, does not work in general for many-body effects. Consequently we have made an estimate of the ratio E 2 (h.f)/M 1 (h.f) to first order in the electron-electron interaction; we have found a value which confirms the necessity of including the quadrupole amplitude E 2 (h.f) in the 6S→7S radiative amplitude, as it is suggested by a recent phenomenological analysis of the experimental data. This quadrupole amplitude E 2 (h.f.) is by itself an interesting quantity since it is governed almost exclusively by man Demonstration de la possibilite de calibrer l'amplitude electrique dipolaire violant la parite E 1 (p.v.) a mieux que 3•10 −3 en utilisant le rapport E 1 (p.v.)/M 1 (h.f.), ou M 1 (h.f.), amplitude dipolaire magnetique induite par l'interaction hyperfine V(h.f.), est donnee par la moyenne geometrique des ecarts hyperfins des etats 6S et 7S, en tenant compte des corrections relativistes et des effets a N corps. A cette precision, necessite d'introduire l'amplitude quadripolaire electrique E 2 (h.f.) que l'on calcule a l'aide d'un modele a une particule: elle est fortement inhibee par une regle de selection approchee, qui ne s'applique pas en general aux effets a N corps

Study of the collisional broadening of the bismuth line 648 nn hyperfine components by faraday rotation spectroscopy

The spootral profiles of the Faraday effect for the hyperfine multiplet4S3/2–2D5/2 λ648 nm in atomic bismuth have been measured accurately using the tunable dye-laser and computer controlled experimental apparatus. The collisional line broadening and shift rate constants are determined for perturbation by helium, nitrogen, argon and xenon. The more accurate value is obtained for the ratio of the electric quadrupole and the magnetic dipole amplitudes for this transition.

Ratio of electric quadrupole to magnetic dipole amplitudes in the nucleon-delta transition.

We have analyzed available data on magnetic dipole and electric quadrupole amplitudes for the photoproduction of pions around the delta region, in the framework of a phenomenological ..gamma..N..delta.. interaction and background. The unitarity constraint via Watson's theorem limits severely the range of allowed gauge couplings in the ..gamma..N..delta.. vertex. We obtain (-1.5 +- 0.2)% as the ratio of the electric quadrupole to magnetic dipole resonant amplitudes, a value of the same order of magnitude as predicted in the skyrmion model of baryons. This ratio suggests a deformed structure of the nucleon and the delta isobar.

The multipole E1+(3/2)of photopion production on nucleons and its double zero at the resonance Δ(1232)

The multipole E1+(3/2) of photoproduction of pions on nucleons in the region of the first resonance has been calculated with the use of relativistic dispersion relations supplemented with the values of pion-nucleon scattering phase-shifts at moderate energies and with summary information on the dynamics in the region of higher energies. This approach, which has previously been applied successfully to the magnetic dipole amplitude M1+(3/2) of photo- and electroproduction of pion on nucleons, is shown to work remarkably well in the case of E1+(3/2) also.

Observation of the interference between the magnetic and electric dipole amplitudes of the caesium 6S-7S transition in an electric field. measurement of the transition magnetic moment

Observation of the interference between the magnetic and electric dipole amplitudes of the caesium 6S-7S transition in an electric field. measurement of the transition magnetic moment

Parity violation induced by weak neutral currents in atomic physics. part II

The first part of this paper gives a detailed account of the evaluation of the electric dipole amplitude induced in alkali one-photon S-S transitions, by the parity violating electron-nucleus short range potential Vp.v. associated with the weak neutral currents. Two methods are presented : the first involves an explicit sum over the contributions of the P-states admixed with the S-states and incorporates the best information available on S-P electric dipole amplitudes. The second method, mathematically more elegant, avoids with the help of Green's function techniques any explicit sum over the P states, and, provided that some spin-orbit corrections are neglected, leads to a fairly simple formula involving Coulomb integrals tabulated in the literature and the interpolated quantum defects for S and P waves. The second part is devoted to a description of possible ways to detect parity violation induced in radiative S-S transitions, with a brief discussion of physical processes which could be a source of experimental difficulty. The last section of the paper deals with a theoretical analysis of the influence of a static electric field on the radiative S-S transitions. An evaluation of the induced electric dipole amplitude in the case of cesium indicates that it will compete with the magnetic dipole amplitude for electric fields larger than 10 V/cm. An interference effect between these two amplitudes gives rise to an electronic polarization in the final atomic state proportional to the vector product of the static electric field by the photon momentum which, in a typical case, could be as large as 64 %; the measurement of this interesting and rather peculiar effect will lead to a determination of the sign of the magnetic dipole amplitude. Moreover parity violation could manifest itself by a dependence of this electron polarization on the state of circular polarization of the incident photon.