Application of magnetic field over-modulation for improved EPR linewidth measurements using probes with Lorentzian lineshape

Magnetic field modulation in CW electron paramagnetic resonance (EPR) is used for signal detection. However, it can also distort signal lineshape. In experiments where the linewidth information is of particular importance, small modulation amplitude is usually used to limit the lineshape distortion. The use of small modulation amplitude, however, results in low signal-to-noise ratio and therefore affects the precision of linewidth measurements. Recently, a new spectral simulation model has been developed enabling accurate fitting of modulation-broadened EPR spectra in liquids. Since the use of large modulation amplitude (over-modulation) can significantly enhance the EPR signal, the precision of linewidth measurements is therefore greatly improved. We investigated the over-modulation technique in EPR oximetry experiments using the oxygen-sensing probe lithium octa-n-butoxy-substitued naphthalocyanine (LiNc-BuO). Modulation amplitudes 2-18 times the intrinsic linewidth of the probe were applied to increase the spectral signal-to-noise ratio. The intrinsic linewidth of the probe at different oxygen concentrations was accurately extracted through curve fitting from the enhanced spectra. Thus, we demonstrated that the over-modulation model is also applicable to particulate oxygen-sensing probes such as LiNc-BuO and that the lineshape broadening induced by oxygen is separable from that induced by over-modulation. Therefore, the over-modulation technique can be used to enhance sensitivity and improve linewidth measurements for EPR oximetry with particulate oxygen-sensing probes with Lorentzian lineshape. It should be particularly useful for in vivo oxygen measurements, in which direct linewidth measurements may not be feasible due to inadequate signal-to-noise ratio.     

Nonequivalent spectra of unpaired electrons in field and frequency modulation

We report a difference in the spectral lineshapes of continuous-wave (CW) electron paramagnetic resonance (EPR) spectroscopy between field and frequency modulation. This finding addresses the long-standing question of the effect of modulation in EPR absorption. We compared the first-derivative EPR spectra at 1.1 GHz for lithium phthalocyanine crystals, which have a single narrow linewidth in the EPR absorption spectrum, using field and frequency modulation. The experimental findings suggest that unpaired electrons have different behaviors under perturbation due to field and frequency modulation.     

A parametric approach to spectral-spatial EPR imaging

Continuous wave electron paramagnetic resonance imaging for in vivo mapping of spin distribution and spectral shape requires rapid data acquisition. A spectral-spatial imaging technique is presented that provides an order of magnitude reduction in acquisition time, compared to iterative tomographic reprojection. The proposed approach assumes that spectral shapes in the sample are well-approximated by members from a parametric family of functions. A model is developed for the spectra measured with magnetic field modulation. Parameters defining the spin distribution and spectral shapes are then determined directly from the measurements using maximum a posteriori probability estimation. The approach does not suffer approximation error from limited sweep width of the main magnetic field and explicitly incorporates the variability in signal-to-noise ratio versus strength of magnetic field gradient. The processing technique is experimentally demonstrated on a one-dimensional phantom containing a nitroxide spin label with constant g-factor. Using an L-band EPR spectrometer, spectral shapes and spin distribution are accurately recovered from two projections and a spectral window which is comparable to the maximum linewidth of the sample.     

Absorption line CW EPR using an amplitude modulated longitudinal field

In standard continuous wave electron paramagnetic resonance (CW-EPR) experiments, the first derivative of absorption lines is detected. This type of a line shape is caused by the magnetic field modulation and is usually an undesired feature, since the sensitivity of CW-EPR drastically decreases with increasing linewidth. A new approach is introduced, which allows for the measurement of absorption line EPR spectra in systems with broad inhomogeneous lines. The method makes use of multiple-photon transitions that are induced in spin systems when a transverse microwave and a longitudinal radio frequency field are simultaneously applied. The absorption lines are obtained by using amplitude modulation of the radio frequency field and slight saturation of the spectral lines. The basics of the new approach are discussed and experimental examples are given.     

Interaction-enhanced double resonance in cold gases

A new type of double-resonance spectroscopy of a quantum gas based on interaction-induced frequency modulation of a probe transition has been considered. Interstate interaction of multilevel atoms causes a coherence-dependent collisional shift of the transition between the atomic states |1〉 and |2〉 due to a nonzero population of the state |3〉. Thus, the frequency of the probe transition |1〉?|2〉 experiences oscillations associated with the Rabi oscillations between the states |1〉 and |3〉 under continuous excitation of the drive resonance |1〉?|3〉. Such a dynamic frequency shift leads to a change in the electromagnetic absorption at the probe frequency and, consequently, greatly enhances the sensitivity of double-resonance spectroscopy as compared to traditional “hole burning”, which is solely due to a decrease in the population of the initial state |1〉. In particular, it has been shown that the resonance linewidth is determined by the magnitude of the contact shift and the amplitude of the drive field and does not depend on the static field gradient. The calculated line shape and width agree with the low-temperature electron-nuclear double-resonance spectra of two-dimensional atomic hydrogen.     

Absorption linewidth inversion with wavelength modulation spectroscopy

For absorption linewidth inversion with wavelength modulation spectroscopy(WMS), an optimized WMS spectral line fitting method was demonstrated to infer absorption linewidth effectively, and the analytical expressions for relationships between Lorentzian linewidth and the separations of first harmonic peak-to-valley and second harmonic zero-crossing were deduced. The transition of CO_2 centered at 4991.25 cm~(-1) was used to verify the optimized spectral fitting method and the analytical expressions. Results showed that the optimized spectra fitting method was able to infer absorption accurately and compute more than 10 times faster than the commonly used numerical fitting procedure. The second harmonic zero-crossing separation method calculated an even 6 orders faster than the spectra fitting without losing any accuracy for Lorentzian dominated cases. Additionally, linewidth calculated through second harmonic zero-crossing was preferred for much smaller error than the first harmonic peak-to-valley separation method. The presented analytical expressions can also be used in on-line optical sensing applications, electron paramagnetic resonance, and further theoretical characterization of absorption lineshape.     

Study of Survival Probability of Super Heavy Nuclei

The survival probability of super heavy nuclei produced in cold fusion reactions is studied by using the standard Fermi gas level density formula and analyzed with fission and neutron evaporation characteristics predicted in different theoretical models. The level density formula used in this letter suppresses the ratio of neutron emission width to fission width, Гn/Гf. The dependence of Гn/Гf on the saddle point level density parameter and excitation energy is also investigated.     

Probe field spectroscopy in three-level Λ systems under arbitrary collisional relaxation of low-frequency coherence

We investigate theoretically the spectrum of weak probe field absorption by three-level atoms with the Λ configuration of levels in the field of a strong electromagnetic wave acting on an adjacent transition and colliding with buffer gas atoms. Analysis is carried out for the general case of arbitrary collisional relaxation of low-frequency coherence at a transition between two lower levels. It is shown that, in the absence of collisional relaxation of low-frequency coherence, the probe field spectrum always exhibits clearly manifested anisotropy with respect to mutual orientation of wavevectors of the strong and probe radiation (even under small Doppler broadening). It is found that the probe field spectrum may acquire under certain conditions supernarrow resonances with a width proportional to the diffusion coefficient for atoms interacting with radiation. This fact may form the basis for a spectroscopic method for measuring transport frequencies of collisions between absorbing and buffer particles. A large-amplitude supernarrow resonance (with an amplitude much larger than the amplitude of the resonance near the line center), which is observed in the far wing of the absorption line, exhibits collisional narrowing (a nonlinear spectroscopic analog of the Dicke effect) at collision frequencies several orders of magnitude lower that the Doppler linewidth. Simple working equations proposed for describing the probe field spectrum are convenient for experimental data processing.     

Object dependent sweep width reduction with spectral-spatial EPR imaging

For spectral-spatial EPR imaging, prior knowledge about the spatial support of an imaged object can be exploited in two ways. We can shrink the spatial field of view (FOV) to closely wrap the object in a sphere or reduce the sweep width in a projection dependent fashion. Use of a smaller spatial FOV with the same number of samples enhances spatial resolution by reducing voxel volume at the expense of signal-to-noise and a consequent degraded line-width resolution. We have developed another approach to define sweep width that prunes away the portions of the projection sweep with no signal. This reduces data acquisition time for the continuous wave (CW) EPR image proportional to the sweep width reduction. This method also avoids voxel volume reduction. Using the reduced-sweep method, we decreased the data acquisition time by 20% maintaining spatial and linewidth resolution.     

The continuous wave electron paramagnetic resonance experiment revisited

When the modulation frequency used in continuous wave electron paramagnetic resonance (cw EPR) spectroscopy exceeds the linewidth, modulation sidebands appear in the spectrum. It is shown theoretically and experimentally that these sidebands are actually multiple photon transitions, sigma(+)+kxpi, where one microwave (mw) sigma(+) photon is absorbed from the mw radiation field and an arbitrary number k of radio frequency (rf) pi photons are absorbed from or emitted to the modulation rf field. Furthermore, it is demonstrated that both the derivative shape of the lines in standard cw EPR spectra and the distortions due to overmodulation are caused by the unresolved sideband pattern of these lines. The single-photon transition does not even give a contribution to the first-harmonic cw EPR signal. Multiple photon transitions are described semiclassically in a toggling frame and their existence is proven using second quantization. With the toggling frame approach and perturbation theory an effective Hamiltonian for an arbitrary sideband transition is derived. Based on the effective Hamiltonians an expression for the steady-state density operator in the singly rotating frame is derived, completely describing all sidebands in all modulation frequency harmonics of the cw EPR signal. The relative intensities of the sidebands are found to depend in a very sensitive way on the actual rf amplitude and the saturation of single sidebands is shown to depend strongly on the effective field amplitude of the multiple photon transitions. By comparison with the analogous solutions for frequency-modulation EPR it is shown that the field-modulation and the frequency-modulation technique are not equivalent. The experimental data fully verify the theoretical predictions with respect to intensities and lineshapes.     

Measurement of leptonic branching ratios of the Γ(9.46)

The electronic width Γ _ee and the muonic branching ratioB _μμ =Γ _μμ /Γ_tot of the Γ(9.46) have been measured as Γ _ee =(1.33±0.14) andB _μμ=(2.2±2.0)%. From these values a lower limit of Γ_tot<23keV for the total width of the Γ(9.46) is obtained.     

Effect of nitrogen dioxide on the EPR property of lithium octa-n-butoxy 2,3-naphthalocyanine (LiNc-BuO) microcrystals

Lithium octa-n-butoxy-naphthalocyanine (LiNc-BuO) is a stable free radical that can be detected by electron paramagnetic resonance (EPR) spectroscopy. Previously we have reported that microcrystals of LiNc-BuO exhibit a single sharp EPR peak, whose width varies linearly with the partial pressure of paramagnetic molecules such as oxygen and nitric oxide. In this report, we present the effect of nitrogen dioxide (NO2), which is also a paramagnetic molecule, on the EPR properties of LiNc-BuO. The gas-sensing property of LiNc-BuO is attributed to the open molecular framework of the crystal structure which is arranged with wide channels capable of accommodating large molecules such as NO2. The EPR linewidth of LiNc-BuO was highly sensitive to the partial pressure of NO2 in the gas mixture. The line-broadening was quick and reversible in the short-term for low concentration of NO2. However, the EPR signal intensity decreased with time of exposure, apparently due to a reaction of NO2 with LiNc-BuO crystals to give diamagnetic products. The results suggested that LiNc-BuO may be a useful probe for the determination of trace amounts of NO2 using EPR spectroscopy.     

Detection of undistorted continuous wave (CW) electron paramagnetic resonance (EPR) spectra with non-adiabatic rapid sweep (NARS) of the magnetic field

A continuous wave (CW) electron paramagnetic resonance (EPR) spectrum is typically displayed as the first harmonic response to the application of 100 kHz magnetic field modulation, which is used to enhance sensitivity by reducing the level of 1/f noise. However, magnetic field modulation of any amplitude causes spectral broadening and sacrifices EPR spectral intensity by at least a factor of two. In the work presented here, a CW rapid-scan spectroscopic technique that avoids these compromises and also provides a means of avoiding 1/f noise is developed. This technique, termed non-adiabatic rapid sweep (NARS) EPR, consists of repetitively sweeping the polarizing magnetic field in a linear manner over a spectral fragment with a small coil at a repetition rate that is sufficiently high that receiver noise, microwave phase noise, and environmental microphonics, each of which has 1/f characteristics, are overcome. Nevertheless, the rate of sweep is sufficiently slow that adiabatic responses are avoided and the spin system is always close to thermal equilibrium. The repetitively acquired spectra from the spectral fragment are averaged. Under these conditions, undistorted pure absorption spectra are obtained without broadening or loss of signal intensity. A digital filter such as a moving average is applied to remove high frequency noise, which is approximately equivalent in bandwidth to use of an integrating time constant in conventional field modulation with lock-in detection. Nitroxide spectra at L- and X-band are presented.     

激光器特性在痕量气体检测中的影响

研究了激光器扫描步长和线宽两种特性对可调谐半导体激光吸收光谱检测系统的影响,理论上推导出激光与气体吸收谱线的作用原理,分析出扫描信号(锯齿波)的台阶间隔和高度影响激光器中心波长的扫描原理.设定了仿真参数,仿真出锯齿波台阶数与最大扫描误差关系曲线,得出扫描信号的一个周期内具有4000个台阶时,半高全宽(FWHM)大于0.01 cm-1,误差小于1‰;仿真出激光器线宽与最大幅值、线宽误差关系曲线,给出线宽误差最大为1%,0.5%时激光器线宽对应的最小FWHM.在温度系数n取0.9,大气展宽系数γair取0.005的条件下,给出温度T,压强P与FWHM关系图,推出了适用的压强与温度范围.为指导选取激光器与气体吸收谱线、提高系统检测限提供了相关理论依据.     

Measurement of the wavelength modulation indices with selective reflection spectroscopy

The wavelength modulation indices are measured based on harmonic amplitude ratio of 4famp/6famp (4famp and 6famp are the 4- and 6-th harmonic central peak amplitudes correspondingly) with the Doppler-free selective reflection modulation spectroscopy. The experiments for the 6S1/2(F = 4) → 6P3/2(F' = 5) transition of cesium D2 line with 30-MHz linewidth were carried out. The 4f- and 6f-harmonic signals were detected with two digital lock-in amplifiers separately. The maximum error for modulation indices measurement was ±0.1 within the range of m from 3 to 6. The non-linear modulation behaviour of an external cavity diode laser induced by voltage tuning was studied with this method. The method for modulation indices measurement does not require a solid etalon as usual for measuring the wavelength modulation depth and the absorption linewidth correspondingly.     

EPR oximetry in three spatial dimensions using sparse spin distribution

A method is presented to use continuous wave electron paramagnetic resonance imaging for rapid measurement of oxygen partial pressure in three spatial dimensions. A particulate paramagnetic probe is employed to create a sparse distribution of spins in a volume of interest. Information encoding location and spectral linewidth is collected by varying the spatial orientation and strength of an applied magnetic gradient field. Data processing exploits the spatial sparseness of spins to detect voxels with nonzero spin and to estimate the spectral linewidth for those voxels. The parsimonious representation of spin locations and linewidths permits an order of magnitude reduction in data acquisition time, compared to four-dimensional tomographic reconstruction using traditional spectral-spatial imaging. The proposed oximetry method is experimentally demonstrated for a lithium octa-n-butoxy naphthalocyanine (LiNc–BuO) probe using an L-band EPR spectrometer.     

Measurement of J/ψ Resonance Parameters

The cross sections of e⁺e^－→hadrons,e⁺e^－,μ⁺μ^－have been measured in the vicinity of J/ψresonance at BES/BEPC.The fit of the observed cross sections gives the new results of J/ψ resonance parameters:the partial widths to hadrons,electrons and muous are Γh=74.1±8.1keV,Γe= 5.14±0.39keV and Γμ=5.13±0.52keV respectively;the total width Γ=84.4±8.9keV;the branching fractions Γh/Γ=(87.8±0.5)%,Γe/Γ=(6.09± 0.33)%,and Γμ/Γ=(6.08±0.33) %.     

Floating Potentials in the Vicinity of Biased Flush‐Mounted Probes

An array of surface‐mounted probe triplets in the Alcator C‐Mod divertor region [1, 2] demonstrates the influence of a biased probe tip on local plasma potential. For the experiments described here, each poloidally aligned triplet contains one probe which measures the local I—V characteristic with a bias sweep and two passive probes which sample the floating potential. The floating potential at the two passive tips varies as a function of the bias at the swept tip. This dependence is shown to vary according to the local plasma parameters. Variations in both the amplitude and width of the floating potential disturbance on electron temperature and density are resolved and compared with different mechanisms of cross field current transport.     

Time-dependent Rayleigh-Bénard convection and instrumental attenuation

We present new thermal data on time-dependent convection in a cylindrically confined layer of helium with aspect ratio Γ=7.87 (Γ≡layer radius/layer height). Experimental data and an analysis of attenuation effects indicate broadband spectral features obtained by a global probe tend to be independent of Γ for Γ?5.     

Reconstruction of the first-derivative EPR spectrum from multiple harmonics of the field-modulated continuous wave signal

Selection of the amplitude of magnetic field modulation for continuous wave electron paramagnetic resonance (EPR) often is a trade-off between sensitivity and resolution. Increasing the modulation amplitude improves the signal-to-noise ratio, S/N, at the expense of broadening the signal. Combining information from multiple harmonics of the field-modulated signal is proposed as a method to obtain the first derivative spectrum with minimal broadening and improved signal-to-noise. The harmonics are obtained by digital phase-sensitive detection of the signal at the modulation frequency and its integer multiples. Reconstruction of the first-derivative EPR line is done in the Fourier conjugate domain where each harmonic can be represented as the product of the Fourier transform of the 1st derivative signal with an analytical function. The analytical function for each harmonic can be viewed as a filter. The Fourier transform of the 1st derivative spectrum can be calculated from all available harmonics by solving an optimization problem with the goal of maximizing the S/N. Inverse Fourier transformation of the result produces the 1st derivative EPR line in the magnetic field domain. The use of modulation amplitude greater than linewidth improves the S/N, but does not broaden the reconstructed spectrum. The method works for an arbitrary EPR line shape, but is limited to the case when magnetization instantaneously follows the modulation field, which is known as the adiabatic approximation.