Experiments in Neutrino Mass and Mixing: Part I - New Limits on Heavy Neutrino Emission in Nuclear Beta Decay. Part II - Fast Neutron Backgrounds for the San Onofre Neutrino Detector

In Part I of this thesis, a new magnetic spectrometer experiment which measured the β spectrum of ^(35)S is described. New limits on heavy neutrino emission in nuclear β decay were set, for a heavy neutrino mass range between 12 and 22 keV. In particular, this measurement rejects the hypothesis that a 17 keV neutrino is emitted, with sin^2 θ = 0.0085, at the 6δ statistical level. In addition, an auxiliary experiment was performed, in which an artificial kink was induced in the β spectrum by means of an absorber foil which masked a fraction of the source area. In this measurement, the sensitivity of the magnetic spectrometer to the spectral features of heavy neutrino emission was demonstrated.

In Part II, a measurement of the neutron spallation yield and multiplicity by the Cosmic-ray Underground Background Experiment is described. The production of fast neutrons by muons was investigated at an underground depth of 20 meters water equivalent, with a 200 liter detector filled with 0.09% Gd-loaded liquid scintillator. We measured a neutron production yield of (3.4 ± 0.7) x 10^(-5) neutrons per muon-g/cm^2, in agreement with other experiments. A single-to-double neutron multiplicity ratio of 4:1 was observed. In addition, stopped π^+ decays to µ^+ and then e^+ were observed as was the associated production of pions and neutrons, by the muon spallation interaction. It was seen that practically all of the π^+ produced by muons were also accompanied by at least one neutron. These measurements serve as the basis for neutron background estimates for the San Onofre neutrino detector.

The deuteron-deuteron reaction and the stopping cross section of D_2O ice below 600 kev

The energy loss of protons and deuterons in D_2O ice has been measured over the energy range, E_p 18 - 541 kev. The double focusing magnetic spectrometer was used to measure the energy of the particles after they had traversed a known thickness of the ice target. One method of measurement is used to determine relative values of the stopping cross section as a function of energy; another method measures absolute values. The results are in very good agreement with the values calculated from Bethe’s semi-empirical formula. Possible sources of error are considered and the accuracy of the measurements is estimated to be ± 4%.

The D(dp)H^3 cross section has been measured by two methods. For E_D = 200 - 500 kev the spectrometer was used to obtain the momentum spectrum of the protons and tritons. From the yield and stopping cross section the reaction cross section at 90° has been obtained.

For E_D = 35 – 550 kev the proton yield from a thick target was differentiated to obtain the cross section. Both thin and thick target methods were used to measure the yield at each of ten angles. The angular distribution is expressed in terms of a Legendre polynomial expansion. The various sources of experimental error are considered in detail, and the probable error of the cross section measurements is estimated to be ± 5%.

Primary cosmic-ray positrons and negatrons in 1968 at energies between 11 and 204 MeV

The cosmic-ray positron and negatron spectra between 11 and 204 MeV have been measured in a series of 3 high-altitude balloon flights launched from Fort Churchill, Manitoba, on July 16, July 21, and July 29, 1968. The detector system consisted of a magnetic spectrometer utilizing a 1000-gauss permanent magnet, scintillation counters, and a lucite Čerenkov counter.

Launches were timed so that the ascent through the 100 g/cm² level of residual atmosphere occurred after the evening geomagnetic cutoff transition. Data gathered during ascent are used to correct for the contribution of atmospheric secondary electrons to the flux measured at float altitude. All flights floated near 2.4 g/cm².

A pronounced morning intensity increase was observed in each flight. We present daytime positron and negatron data which support the interpretation of the diurnal flux variation as a change in the local geomagnetic cutoff. A large diurnal variation was observed in the count rate of positrons and negatrons with magnetic rigidities less than 11 MV and is evidence that the nighttime cutoff was well below this value.

Using nighttime data we derive extraterrestrial positron and negatron spectra. The positron-to-total-electron ratio which we measure indicates that the interstellar secondary, or collision, source contributes ≾50 percent of the electron flux within this energy interval. By comparing our measured positron spectrum with the positron spectrum calculated for the collision source we derive the absolute solar modulation for positrons in 1968. Assuming negligible energy loss during modulation, we derive the total interstellar electron spectrum as well as the spectrum of directly accelerated, or primary, electrons. We examine the effect of adiabatic deceleration and find that many of the conclusions regarding the interstellar electron spectrum are not significantly altered for an assumed energy loss of up to 50 percent of the original energy.

Nuclear reactions leading to energy levels of Ar37 and K37

In view of recent interest in the Cl³⁷ (ʋ solar’^e-)Ar³⁷ reaction cross section, information on some aspects of mass 37 nuclei has been obtained using the K³⁹ (d, ∝) Ar³⁷ and Cl³⁵ (He³, p) Ar³⁷ reactions. Ar³⁷ levels have been found at 0, 1.41, 1.62, 2.22, 2.50, 2.80, 3.17, 3.27, 3.53, 3.61, 3.71, (3.75), (3.90), 3.94, 4.02, (4.21), 4.28, 4.32, 4.40, 4.45, 4.58, 4.63, 4.74, 4.89, 4.98, 5.05, 5.10, 5.13, 5.21, 5.35, 5.41, 5.44, 5.54, 5.58, 5.67, 5.77, and 5.85 MeV (the underlined values correspond to previously tabulated levels). The nuclear temperature calculated from the Ar³⁷ level density is 1.4 MeV. Angular distributions of the lowest six levels with the K³⁹ (d, ∝) Ar³⁷ reaction at E_d = 10 MeV indicate a dominant direct interaction mechanism and the inapplicability of the 2I + 1 rule of the statistical model. Comparison of the spectra obtained with the K³⁹ (d, ∝) Ar³⁷ and Cl³⁵ (He³, p) Ar³⁷ reactions leads to the suggestion that the 5.13-MeV level is the T = 3/2 Cl³⁷ ground state analog. The ground state Q-value of the Ca⁴⁰ (p, ∝) K³⁷ reaction has been measured: -5179 ± 9 keV. This value implies a K³⁷ mass excess of -24804 ± 10 keV. Description of a NMR magnetometer and a sixteen-detector array used in conjunction with a 61-cm double-focusing magnetic spectrometer are included in appendices.

Mass measurements of some proton-rich nuclei

The Q values and 0^o cross sections of (He³, n) reactions forming seven proton-rich nuclei have been measured with accuracies varying from 6 to 18 keV. The Q values (in keV) are: Si²⁶ (85), S³⁰ (-573), Ar³⁴ (-759), Ti⁴² (-2865), Cr⁴⁸ (5550), Ni⁵⁶ (4513) and Zn⁶⁰ (818). At least one excited state was found for all but Ti⁴². The first four nuclei complete isotopic spin triplets; the results obtained agree well with charge-symmetry predictions. The last three, all multiples of the α particle, are important in the α and e-process theories of nucleo-synthesis in stars. The energy available for β decay of these three was found by magnetic spectrometer measurements of the (He³, p) Q values of reactions leading to V⁴⁸, Co⁵⁶, and Cu⁶⁰. Many excited states were seen: V⁴⁸ (3), Co⁵⁶ (15), Cu⁶⁰ (23). The first two states of S³⁰ are probably 0⁺ and 2⁺ from (He³, n) angular distribution measurements. Two NaI γ-ray measurements are described: the decay of Ar³⁴ (measured ^Ƭ1/2 = 1.2 ± 0.3s) and the prompt γ-ray spectrum from Fe⁵⁴(He³, nγ)Ni⁵⁶. Possible collective structure in Ni⁵⁶ and Ca⁴⁰, both doubly magic, is discussed.

The (He³, n) neutron energy and yield measurements utilized neutron-induced nuclear reactions in a silicon semiconductor detector. Cross sections for the most important detection processes, Si²⁸ (n, α) Mg²⁵ and Si²⁸ (n, p) Al²⁸, are presented for reactions leading to the first four states of both residual nuclei for neutron energies from 7.3 to 16.4 MeV. Resolution and pulse-height anomalies associated with recoil Mg²⁵ and Al²⁸ ions are discussed. The 0^o cross section for Be⁹ (α, n) C¹², used to provide calibration neutrons, has been measured with a stilbene spectrometer for n_o (5.0 ≤ E_α ≤ 12 MeV), n₁ (4.3 ≤ E_α ≤ 12.0 MeV) and n₂ (6.0 ≤ E_α ≤ 10.1 MeV). Resonances seen in the n_o yield may correspond to nine new levels in C¹³.

Electromagnetic decay of the 1.7- and 2.43-MeV levels in ^9Be

The 1.7- and 2.43-MeV levels in ⁹Be were populated with the reaction ¹¹B(d, α)⁹Be* by bombarding thin boron on carbon foils with 1.7-MeV deuterons. The alpha particles were analyzed in energy with a surface-barrier counter set at the unique kinematically determined angle and the recoiling ⁹Be nuclei at 90^o were analyzed in rigidity with a magnetic spectrometer, in energy by a surface-barrier counter at the spectrometer focus, and in velocity by the time delay between an alpha and a ⁹Be count. When a pulse from the spectrometer counter was in the appropriate delayed coincidence with a pulse from the alpha counter, the two pulses were recorded in a two-dimensional pulse height analyzer. Most of the ⁹Be* decay by particle breakup. Only those that gamma decay are detected by the spectrometer counter. Thus the experiment provides a direct measurement of Γ_rad/Γ. Analysis of 384 observed events gives Γ_rad/Γ = (1.16 ± 0.14) X 10^-4 for the 2.43-MeV level. Combining this ratio with the value of Γ_rad = 0.122 ± 0.015 eV found from inelastic electron scattering gives Γ = (1.05 ± 0.18) keV. For the 1.7-MeV level, an upper limit, Γ_rad/Γ ≤ 2.4 = 10^-5, was determined.

An investigation of the three-body reaction He^3(He^3, 2p)He^4

Reactions produced by the He³ bombardment of the He³ have been investigated for bombarding energies from 1 to 20 MeV using a tandem Van de Graaff accelerator. Proton spectra from the three-body reaction He³(He³, 2p)He⁴ have been measured with a counter telescope at 13 angles for 9 bombarding energies between 3 and 18 MeV. The results are compared with a model for the reaction which includes a strong p-He⁴ final-state interaction. Alpha-particle spectra have been obtained at 12 and 18 MeV for forward angles with a magnetic spectrometer. These spectra indicate a strongly forward-peaked mechanism involving the ¹S₀ p-p interaction in addition to the p-He⁴ interaction. Measurements of p-He⁴ and p-p coincidence spectra at 10 MeV confirm these features of the reaction mechanism. Deuteron spectra from the reaction of He³(He³, d)pHe³ have been measured at 18 MeV. A triton spectrum from the reaction He³(He³, t)3p at 20 MeV and 4⁰ is interpreted in terms of a sequential decay through an excited state of the alpha particle at 20.0 MeV. No effects are observed which would indicate an interaction in the residual (3p) system. Below 3 MeV the He³(He³, 2p)He⁴ reaction mechanism is observed to be changing and further measurements are suggested in view of the importance of this reaction in stellar interiors.

Energy loss of light ions channeling in silicon

Experimental measurements of rate of energy loss were made for protons of energy .5 to 1.6 MeV channeling through 1 μm thick silicon targets along the <110>, <111>, and <211> axial directions, and the {100}, {110}, {111}, and {211} planar directions. A .05% resolution automatically controlled magnetic spectrometer was used. The data are presented graphically along with an extensive summary of data in the literature. The data taken cover a wider range of channels than has previously been examined, and are in agreement with the data of F. Eisen, et al., Radd. Eff. 13, 93 (1972).

The theory in the literature for channeling energy loss due to interaction with local electrons, core electrons, and distant valence electrons of the crystal atoms is summarized. Straggling is analyzed, and a computer program which calculates energy loss and straggling using this theory and the Moliere approximation to the Thomas Fermi potential, V_TF, and the detailed silicon crystal structure is described. Values for the local electron density Z_loc in each of the channels listed above are extracted from the data by graphical matching of the experimental and computer results.

Zeroth and second order contributions to Z_loc as a function of distance from the center of the channel were computed from ∇²V_TF = 4πρ for various channels in silicon. For data taken in this work and data of F. Eisen, et al., Rad. Eff. 13, 93 (1972), the calculated zeroth order contribution to Z_loc lies between the experimentally extracted Z_loc values obtained by using the peak and the leading edge of the transmission spectra, suggesting that the observed straggling is due both to statistical fluctuations and to path variation.

π+ photoproduction at angles from 6° to 90° C.M. and energies from 589 to 1269 MeV

The differential cross section for the reaction γp → π⁺n was measured at 32 laboratory photon energies between 589 and 1269 MeV at the Caltech Synchrotron. At each energy, data have been obtained at typically fifteen π⁺ c.m. angles between 6° and 90°. A magnetic spectrometer was used to detect the π⁺ photo-produced in a liquid hydrogen target. Two Cherenkov counters were used to reject the background of positrons and protons. The data clearly show the presence of a pole in the production amplitude due to the one pion exchange. Moravcsik fits to the 32 angular distributions, including data from another experiment, are presented. The extrapolation of these fits to the pole gives a value for the pion-nucleon coupling constant of 14.5 which is consistent with the accepted value. The second and third pion-nucleon resonances are evident as peaks in the total cross section and as changes in the shape of the angular distributions. At the third resonance there is evidence for both a D5/2 and an F5/2 amplitude. The absence of large variations in the 0° and 180° cross sections implies that the second and third resonances are mostly produced from an initial state with helicity ± 3/2.

Nonexistence of looping trajectories in hydromagnetic waves of finite amplitude. Breaking of waves in a cold collision-free plasma in a magnetic field. On stabilities of periodic waves in a cold collision-free plasma in a magnetic field.

This dissertation consists of three parts. In Part I, it is shown that looping trajectories cannot exist in finite amplitude stationary hydromagnetic waves propagating across a magnetic field in a quasi-neutral cold collision-free plasma. In Part II, time-dependent solutions in series expansion are presented for the magnetic piston problem, which describes waves propagating into a quasi-neutral cold collision-free plasma, ensuing from magnetic disturbances on the boundary of the plasma. The expansion is equivalent to Picard's successive approximations. It is then shown that orbit crossings of plasma particles occur on the boundary for strong disturbances and inside the plasma for weak disturbances. In Part III, the existence of periodic waves propagating at an arbitrary angle to the magnetic field in a plasma is demonstrated by Stokes expansions in amplitude. Then stability analysis is made for such periodic waves with respect to side-band frequency disturbances. It is shown that waves of slow mode are unstable whereas waves of fast mode are stable if the frequency is below the cutoff frequency. The cutoff frequency depends on the propagation angle. For longitudinal propagation the cutoff frequency is equal to one-fourth of the electron's gyrofrequency. For transverse propagation the cutoff frequency is so high that waves of all frequencies are stable.

Psychobiophysics of transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a technique that stimulates the brain using a magnetic coil placed on the scalp. Since it is applicable to humans non-invasively, directly interfering with neural electrical activity, it is potentially a good tool to study the direct relationship between perceptual experience and neural activity. However, it has been difficult to produce a clear perceptible phenomenon with TMS of sensory areas, especially using a single magnetic pulse. Also, the biophysical mechanisms of magnetic stimulation of single neurons have been poorly understood.

In the psychophysical part of this thesis, perceptual phenomena induced by TMS of the human visual cortex are demonstrated as results of the interactions with visual inputs. We first introduce a method to create a hole, or a scotoma, in a flashed, large-field visual pattern using single-pulse TMS. Spatial aspects of the interactions are explored using the distortion effect of the scotoma depending on the visual pattern, which can be luminance-defined or illusory. Its similarity to the distortion of afterimages is also discussed. Temporal interactions are demonstrated in the filling-in of the scotoma with temporally adjacent visual features, as well as in the effective suppression of transient visual features. Also, paired-pulse TMS is shown to lead to different brightness modulations in transient and sustained visual stimuli.

In the biophysical part, we first develop a biophysical theory to simulate the effect of magnetic stimulation on arbitrary neuronal structure. Computer simulations are performed on cortical neuron models with realistic structure and channels, combined with the current injection that simulates magnetic stimulation. The simulation results account for general and basic characteristics of the macroscopic effects of TMS including our psychophysical findings, such as a long inhibitory effect, dependence on the background activity, and dependence on the direction of the induced electric field.

The perceptual effects and the cortical neuron model presented here provide foundations for the study of the relationship between perception and neural activity. Further insights would be obtained from extension of our model to neuronal networks and psychophysical studies based on predictions of the biophysical model.

Studies of ambient and chamber aerosol composition using the aerosol mass spectrometer

This thesis presents composition measurements for atmospherically relevant inorganic and organic aerosol from laboratory and ambient measurements using the Aerodyne aerosol mass spectrometer. Studies include the oxidation of dodecane in the Caltech environmental chambers, and several aircraft- and ground-based field studies, which include the quantification of wildfire emissions off the coast of California, and Los Angeles urban emissions.

The oxidation of dodecane by OH under low NO conditions and the formation of secondary organic aerosol (SOA) was explored using a gas-phase chemical model, gas-phase CIMS measurements, and high molecular weight ion traces from particle- phase HR-TOF-AMS mass spectra. The combination of these measurements support the hypothesis that particle-phase chemistry leading to peroxyhemiacetal formation is important. Positive matrix factorization (PMF) was applied to the AMS mass spectra which revealed three factors representing a combination of gas-particle partitioning, chemical conversion in the aerosol, and wall deposition.

Airborne measurements of biomass burning emissions from a chaparral fire on the central Californian coast were carried out in November 2009. Physical and chemical changes were reported for smoke ages 0 – 4 h old. CO₂ normalized ammonium, nitrate, and sulfate increased, whereas the normalized OA decreased sharply in the first 1.5 - 2 h, and then slowly increased for the remaining 2 h (net decrease in normalized OA). Comparison to wildfire samples from the Yucatan revealed that factors such as relative humidity, incident UV radiation, age of smoke, and concentration of emissions are important for wildfire evolution.

Ground-based aerosol composition is reported for Pasadena, CA during the summer of 2009. The OA component, which dominated the submicron aerosol mass, was deconvolved into hydrocarbon-like organic aerosol (HOA), semi-volatile oxidized organic aerosol (SVOOA), and low-volatility oxidized organic aerosol (LVOOA). The HOA/OA was only 0.08–0.23, indicating that most of Pasadena OA in the summer months is dominated by oxidized OA resulting from transported emissions that have undergone photochemistry and/or moisture-influenced processing, as apposed to only primary organic aerosol emissions. Airborne measurements and model predictions of aerosol composition are reported for the 2010 CalNex field campaign.

One-dimensional models for organic magnetic materials

In the preparation of small organic paramagnets, these structures may conceptually be divided into spin-containing units (SCs) and ferromagnetic coupling units (FCs). The synthesis and direct observation of a series of hydrocarbon tetraradicals designed to test the ferromagnetic coupling ability of m-phenylene, 1,3-cyclobutane, 1,3- cyclopentane, and 2,4-adamantane (a chair 1,3-cyclohexane) using Berson TMMs and cyclobutanediyls as SCs are described. While 1,3-cyclobutane and m-phenylene are good ferromagnetic coupling units under these conditions, the ferromagnetic coupling ability of 1,3-cyclopentane is poor, and 1,3-cyclohexane is apparently an antiferromagnetic coupling unit. In addition, this is the first report of ferromagnetic coupling between the spins of localized biradical SCs.

The poor coupling of 1,3-cyclopentane has enabled a study of the variable temperature behavior of a 1,3-cyclopentane FC-based tetraradical in its triplet state. Through fitting the observed data to the usual Boltzman statistics, we have been able to determine the separation of the ground quintet and excited triplet states. From this data, we have inferred the singlet-triplet gap in 1,3-cyclopentanediyl to be 900 cal/mol, in remarkable agreement with theoretical predictions of this number.

The ability to simulate EPR spectra has been crucial to the assignments made here. A powder EPR simulation package is described that uses the Zeeman and dipolar terms to calculate powder EPR spectra for triplet and quintet states.

Methods for characterizing paramagnetic samples by SQUID magnetometry have been developed, including robust routines for data fitting and analysis. A precursor to a potentially magnetic polymer was prepared by ring-opening metathesis polymerization (ROMP), and doped samples of this polymer were studied by magnetometry. While the present results are not positive, calculations have suggested modifications in this structure which should lead to the desired behavior.

Source listings for all computer programs are given in the appendix.

Trapped ion magnetic resonance: concepts and designs

A novel spectroscopy of trapped ions is proposed which will bring single-ion detection sensitivity to the observation of magnetic resonance spectra. The approaches developed here are aimed at resolving one of the fundamental problems of molecular spectroscopy, the apparent incompatibility in existing techniques between high information content (and therefore good species discrimination) and high sensitivity. Methods for studying both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) are designed. They assume established methods for trapping ions in high magnetic field and observing the trapping frequencies with high resolution (<1 Hz) and sensitivity (single ion) by electrical means. The introduction of a magnetic bottle field gradient couples the spin and spatial motions together and leads to a small spin-dependent force on the ion, which has been exploited by Dehmelt to observe directly the perturbation of the ground-state electron's axial frequency by its spin magnetic moment.

A series of fundamental innovations is described m order to extend magnetic resonance to the higher masses of molecular ions (100 amu = 2x 10^5 electron masses) and smaller magnetic moments (nuclear moments = 10^(-3) of the electron moment). First, it is demonstrated how time-domain trapping frequency observations before and after magnetic resonance can be used to make cooling of the particle to its ground state unnecessary. Second, adiabatic cycling of the magnetic bottle off between detection periods is shown to be practical and to allow high-resolution magnetic resonance to be encoded pointwise as the presence or absence of trapping frequency shifts. Third, methods of inducing spindependent work on the ion orbits with magnetic field gradients and Larmor frequency irradiation are proposed which greatly amplify the attainable shifts in trapping frequency.

The dissertation explores the basic concepts behind ion trapping, adopting a variety of classical, semiclassical, numerical, and quantum mechanical approaches to derive spin-dependent effects, design experimental sequences, and corroborate results from one approach with those from another. The first proposal presented builds on Dehmelt's experiment by combining a "before and after" detection sequence with novel signal processing to reveal ESR spectra. A more powerful technique for ESR is then designed which uses axially synchronized spin transitions to perform spin-dependent work in the presence of a magnetic bottle, which also converts axial amplitude changes into cyclotron frequency shifts. A third use of the magnetic bottle is to selectively trap ions with small initial kinetic energy. A dechirping algorithm corrects for undesired frequency shifts associated with damping by the measurement process.

The most general approach presented is spin-locked internally resonant ion cyclotron excitation, a true continuous Stern-Gerlach effect. A magnetic field gradient modulated at both the Larmor and cyclotron frequencies is devised which leads to cyclotron acceleration proportional to the transverse magnetic moment of a coherent state of the particle and radiation field. A preferred method of using this to observe NMR as an axial frequency shift is described in detail. In the course of this derivation, a new quantum mechanical description of ion cyclotron resonance is presented which is easily combined with spin degrees of freedom to provide a full description of the proposals.

Practical, technical, and experimental issues surrounding the feasibility of the proposals are addressed throughout the dissertation. Numerical ion trajectory simulations and analytical models are used to predict the effectiveness of the new designs as well as their sensitivity and resolution. These checks on the methods proposed provide convincing evidence of their promise in extending the wealth of magnetic resonance information to the study of collisionless ions via single-ion spectroscopy.

Charged pion contribution to the anomalous magnetic moment of the muon

The model dependence inherent in hadronic calculations is one of the dominant sources of uncertainty in the theoretical prediction of the anomalous magnetic moment of the muon. In this thesis, we focus on the charged pion contribution and turn a critical eye on the models employed in the few previous calculations of $a_\mu^{\pi^+\pi^-}$. Chiral perturbation theory provides a check on these models at low energies, and we therefore calculate the charged pion contribution to light-by-light (LBL) scattering to $\mathcal{O}(p^6)$. We show that the dominant corrections to the leading order (LO) result come from two low energy constants which show up in the form factors for the $\gamma\pi\pi$ and $\gamma\gamma\pi\pi$ vertices. Comparison with the existing models reveal a potentially significant omission - none include the pion polarizability corrections associated with the $\gamma\gamma\pi\pi$ vertex. We next consider alternative models where the pion polarizability is produced through exchange of the $a_1$ axial vector meson. These have poor UV behavior, however, making them unsuited for the $a_\mu^{\pi^+\pi^-}$ calculation. We turn to a simpler form factor modeling approach, generating two distinct models which reproduce the pion polarizability corrections at low energies, have the correct QCD scaling at high energies, and generate finite contributions to $a_\mu^{\pi^+\pi^-}$. With these two models, we calculate the charged pion contribution to the anomalous magnetic moment of the muon, finding values larger than those previously reported: $a_\mu^\mathrm{I} = -1.779(4)\times10^{-10}\,,\,a_\mu^\mathrm{II} = -4.892(3)\times10^{-10}$.