Exact solution of the CPMG pulse sequence with phase variation down the echo train: application to R₂ measurements

An implicit exact algebraic solution of CPMG experiments is presented and applied to fit experiments. Approximate solutions are also employed to explore oscillations and effective decay rates of CPMG experiments. The simplest algebraic approximate solution has illustrated that measured intensities will oscillate in the conventional CPMG experiments and that using even echoes can suppress errors of measurements of R? due to the imperfection of high-power pulses. To deal with low-power pulses with finite width, we adapt the effective field to calculate oscillations. An optimization model with the effective field approximation and dimensionless variables is proposed to quantify oscillations of measured intensities of CPMG experiments of different phases of the π pulses. We show, as was known using other methods, that repeating one group of four pulses with different phases in CPMG experiments, which we call phase variation, but others call phase alternation or phase cycling, can significantly smooth the dependence of measured intensities on frequency offset in the range of ±?γB?. In this paper, a second-order expression with respect to the ratio of frequency offset to π-pulse amplitude is developed to describe the effective R? of CPMG experiments when using a group phase variation scheme. Experiments demonstrate that (1) the exact calculation of CPMG experiments can remarkably eliminate systematic errors in measured R?s due to the effects of frequency offset, even in the absence of phase variation; (2) CPMG experiments with group phase variation can substantially remove oscillations and effects of the field inhomogeneity; (3) the second-order expression of the effective decay rate with phase variation is able to provide reliable estimates of R? when offsets are roughly within ±?γB?; and, most significantly, (4) the more sophisticated optimization model using an exact solution of the discretized CPMG experiment extends, to ±γB?, the range of offsets for which reliable estimates of R? can be obtained when using the preferred phase variation scheme.     

Precise measurement of the e~+e~- →π~+π~-(γ) crosssection with the initial state radiation method at BABAR

We present a precise BABAR measurement on the cross section of the process e+e-→π+π-(γ) from threshold to an energy of 3 GeV with the initial state radiation(ISR) technique,using 232 fb-1 of data collected with the BABAR detector at e+e-center-of-mass energies near 10.58 GeV.The ISR luminosity is determined from a study of the leptonic process e+e-→μ+μ-γ(γ).The leading-order hadronic contribution to the muon magnetic anomaly calculated using the ππ cross section measured from threshold to 1.8 GeV is(514.1±2.2(stat)±3.1(syst))×10-10.     

Observation of exclusive γγ production in pp¯ collisions at √s=1.96 TeV

We have observed exclusive γγ production in proton-antiproton collisions at √s=1.96 TeV, using data from 1.11±0.07 fb(-1) integrated luminosity taken by the Run II Collider Detector at Fermilab. We selected events with two electromagnetic showers, each with transverse energy E(T)>2.5 GeV and pseudorapidity |η|<1.0, with no other particles detected in -7.4<η<+7.4. The two showers have similar E(T) and azimuthal angle separation Δφ~π; 34 events have two charged particle tracks, consistent with the QED process ppˉ→p+e(+)e(-)+pˉ by two-photon exchange, while 43 events have no charged tracks. The number of these events that are exclusive π(0)π(0) is consistent with zero and is <15 at 95% C.L. The cross section for ppˉ→p+γγ+pˉ with |η(γ)|<1.0 and E(T)(γ)>2.5 GeV is 2.48(-0.35)(+0.40)(stat)(-0.51)(+0.40)(syst) pb.     

Application of optimal control to CPMG refocusing pulse design

We apply optimal control theory (OCT) to the design of refocusing pulses suitable for the CPMG sequence that are robust over a wide range of B(0) and B(1) offsets. We also introduce a model, based on recent progress in the analysis of unitary dynamics in the field of quantum information processing (QIP), that describes the multiple refocusing dynamics of the CPMG sequence as a dephasing Pauli channel. This model provides a compact characterization of the consequences and severity of residual pulse errors. We illustrate the methods by considering a specific example of designing and analyzing broadband OCT refocusing pulses of length 10t(180) that are constrained by the maximum instantaneous pulse power. We show that with this refocusing pulse, the CPMG sequence can refocus over 98% of magnetization for resonance offsets up to 3.2 times the maximum RF amplitude, even in the presence of ±10% RF inhomogeneity.     

半花菁衍生物分子第一超极化率频率色散效应的理论研究

采用含时耦合微扰(TDHF)和多态求和(SOS)方法计算了半花菁衍生物分子生色团4-N,N-dimethylami-no-4′-N′-methylstilbazolium(DAS)的第一超极化率频率色散效应。采用组态相关(INDO/CI)方法计算了分子的前线轨道性质。计算结果表明半花菁衍生物分子最大吸收波长约为480nm,与实验结果十分吻合;第一激发态对体系非线性光学性质起决定作用。在红外波段(800~2500nm),随着基频光频率的增大,二次谐波β(-2ω;ω,ω)和电光效应β(-ω;ω,0)都随之增大,但是β(-2ω;ω,ω)增加的幅度要大于β(-ω;ω,0)。在远红外区β(-2ω;ω,ω)的色散曲线变化比较平缓,到了近红外区(λ<1300nm)共振增强效应逐渐明显。基频光波长为1064nm时,β(-2ω;ω,ω)的含时耦合微扰计算值约为(380±5)×10-30esu。在较高频率时,采用多态求和方法计算应考虑其他态的贡献。此外,还讨论了基组效应对含时耦合微扰计算的影响。     

Comparison of T2 and LASER T2dagger image contrast in a rat model of acute cerebral ischemia

Previous studies have shown that T2(dagger)-weighted magnetic resonance images acquired using localization by adiabatic selective refocusing (LASER) can provide early tissue contrast following ischemia, possibly due to alterations in microscopic susceptibility within the tissue. The purpose of this study was to make a direct in vivo comparison of T2-, T2(dagger)- and diffusion-weighted image contrast during acute ischemia. Acute middle cerebral artery (MCA) occlusion was attempted in 14 rats using a modified Tamura approach incorporating electrocoagulation of the left MCA. T2(dagger)-weighted LASER images (Echo Time [TE]=108 ms), T2-weighted Carr-Purcell-Meiboom-Gill (CPMG) images (TE=110 ms) and diffusion-weighted images (b value=105 s/mm(2)) were acquired at 4 T within 1.5 h of ischemia onset. Tissue contrast in the MCA territory was quantified for histologically verified ischemic tissue (n=6) and in sham controls (n=4). T2(dagger)-weighted LASER images demonstrated greater contrast compared to the T2-weighted CPMG images, and more focal contrast compared to the diffusion-weighted images, suggesting different contrast mechanisms were involved.     

Absorption of a massless scalar wave from a Schwarzschild black hole surrounded by quintessence

By using the partial wave method,we investigate the absorption of a massless scalar wave from a Schwarzschild black hole surrounded by quintessence.We obtained the expression of absorption cross section σabs(ω)=π/ω2sum from l=0 to ∞(2l+1)|Tωl(ω)|2=π/ω2sum from l=0 to ∞(2l+1)Γωl(ω).Then we numerically carry out the absorption cross section and we find that the larger the angular momentum quantum number l is,the smaller the corresponding maximum value of the partial absorption cross section is,and that the total absorption cross section tends to the geometric-optical limit σ hf abs ≈πb 2 c.We also find that higher value of ω q(state parameter of quintessence) corresponds to the higher value of absorption cross section σ abs.     

Experimental Study of Resonance f2(1270) in the J/ψ Hadronic Decay

Based on the 2.5 million J/ψ's collected by the BES at BEPC,through the hadronic decay J/ψ→ωf₂(1270),f₂(1270)→π⁺π^－,ω→π⁺π^－π⁰,the properties of the resonance f₂(1270) are studied:its mass,width,and branching ratio.the angular distribution is fitted with maximum likelihood methood,determining its.J^PC=2⁺⁺ and giving in the first time the helicity amplitude ratios of this process as:x=0.99±0.29; y=－0.24±0.17; z₁=0.90±0.57;z₂=0.56±0.22.     

Electron-phonon coupling in high-temperature cuprate superconductors determined from electron relaxation rates

We determined electronic relaxation times via pump-probe optical spectroscopy using sub-15 fs pulses for the normal state of two different cuprate superconductors. We show that the primary relaxation process is the electron-phonon interaction and extract a measure of its strength, the second moment of the Eliashberg function λ[ω2] = 800 ± 200 meV2 for La(1.85)Sr(0.15)CuO4 and λ[ω2] = 400 ± 100 meV2 for YBa(2)Cu(3)O(6.5). These values suggest a possible fundamental role of the electron-phonon interaction in the superconducting pairing mechanism.     

News on PHOTOS Monte Carlo:γ*→π+π-(γ)and K±→π+π-e±ν(γ)

PHOTOS Monte Carlo is widely used for simulating QED effects in decay of intermediate particles and resonances.It can be easily connected to other main process generators.In this paper we consider decaying processes γ*→π+π-(γ)and K±→π+π-e±ν(γ)in the framework of Scalar QED.These two processes are interesting not only for the technical aspect of PHOTOS Monte Carlo,but also for precision measurement ofαQED(Mz),g-2,as well as ππ scattering lengths.     

Study of charmonium(-like) states via ISR at Belle

The cross sections for e+e-→π+π-J/ψ, π+π-ψ(2S), K+K-J/ψ, DD, D0D-π++c.c., D*D+c.c., and D*D-* are measured using data sample collected on or near the T(4S) resonance with the Belle detector at KEKB. A peak near 4.25 GeV/c2, corresponding to the so called Y(4260), is observed in π+π-J/ψ final state. In addition, there is another cluster of events at around 4.05 GeV/c2. Two resonant structures are observed in the π+π-J/ψ(2S) invariant mass distribution, one at 4361±9±9 MeV/c2 with a width of 74±15±10 MeV/c2, and another at 4664±11±5 MeV/c2 with a width of 48±15±3 MeV/c2. The rich structures observed in all these final states indicate that our understanding of the vector charmonium states above the open charm threshold is still poor, let alone the other possible dynamics such as charmonium hybrids or final state re-scattering and so on.     

An experimental study of ω neutral decays

The neutral branching ratios of the ω meson have been determined by measuring the c.m. momentum spectrum of single γ's from ω decay. The sample of 400 ω events after background subtraction yields an upper limit of (ω → ηγ)/(ω → neutrals) < 25% (90% confidence). The fit with ω → π⁰γ only cannot be excluded. However, the best fit is obtained with the ratios (ω →π⁰γ)/(ω → neutrals) = (78±7)% and (ω → π⁰π⁰γ)/(ω → neutrals) = (22 ± 7)%.     

Spin-lock techniques and CPMG imaging sequences: a critical appraisal of T1p contrast at 0.15 T

The addition of a spin-lock preparatory sequence to a Carr-Purcell-Meiboom-Gill (CPMG) imaging sequence provides a method which allows an accurate and simple comparison of T1p and T2 contrast. Sagittal and axial brain images, produced with the application of a three pulse preparatory spin-lock sequence prior to a sixteen-echo CPMG imaging sequence, are compared with images acquired without the spin-lock sequence. The CPMG sequence uses non-selective refocusing pulses. Therefore, observed echo signals accurately reflect T2 relaxation. This allows a convenient method for assessing the degree to which T1p and T2 contrast differ. The spin-lock CPMG (SL-CPMG) images were acquired with a spin-locking field amplitude of 0.4 G and resemble heavily T2-weighted images at 0.15 T. Quantitative analyses of signal intensities from edema and normal brain tissue confirm the qualitative observations. This in vivo method should prove useful for determining when the additional RF power deposition associated with spin-locking techniques will provide an alternate form of tissue contrast than that available from additional echo collection.     

Photoproduction of ω mesons from complex nuclei targets

Measurements are presented of the cross sections for omega meson photoproduction at a mean energy of 3.9 GeV from nuclear targets of D, Be, C, Al, Cu, Ag, Au. An optical and Glauber model analysis of the coherent cross sections has been performed to obtain the ω-nucleon cross section, σ_ωN, and the photon-omega coupling constant γ_ω²/4π. Our results are summarised in table 4. We find good agreement with the quark model prediction that σ_ωN = σ_?N, and with the value of γ_ω2/4π determined from the storage ring experiments and from an earlier complex nuclei measurement. However, we disagree with more recent complex nuclei measurements which found a high value of γ_ω²/4π.     

通过高斯加权的1H CPMG弛豫曲线测定橡胶交联密度

CPMG（Carr-Purcell-Meiboom-Gill）回波法是测量橡胶交联密度[常用交联点之间的分子量（M_c）表示]的一种常用核磁共振（NMR）技术,但实验发现通过该技术获得的M_c对于CPMG序列中脉冲间隔时间具有较强的依赖性,导致交联密度NMR测量值与橡胶材料硬度的相关性低.为了克服这一缺点,本文对不同脉冲间隔时间下CPMG实验测得的质子横向驰豫曲线进行高斯加权.通过对高斯加权求和后的质子横向驰豫曲线进行处理分析,实现了对橡胶交联密度更加准确地测量,大幅提升了天然橡胶交联密度NMR测量值与材料硬度的相关性.本文方案测量能获得与¹H DQ NMR方法相当,或比之更佳的交联密度-硬度相关性.同时,本文方案比¹H DQ NMR方法更为高效,整体测量时间缩短为¹H DQ NMR实验时间的1/10.     

Study of the process e+e-→π+π-π0π0 at energies √s< 1 GeV

In an experiment with the Spherical Neutral Detector at VEPP-2M collider the cross section of the process e+e-→π+π-π0π0 was measured. At energies √s < 920 MeV this cross section was measured for the first time. The energy dependence of the cross section is well discribed by the vector dominance model with contributions from ρ, ρ' ρ", mesons. The decay probability ρ→π+π-π0π0was found to be Bρ = (1.60±0.74±0.18)×10-5. The upper limit for the decay ω→π+π-π0π0 was improved by two orders of magnitude compared to the previous measurements and is Bω < 2 × 10-4 at 90% confidence level.     

Field gradient CPMG applied on postmortem muscles

As a new approach, Carr-Purcell-Meiboom-Gill (CPMG) experiments were performed in vitro on porcine muscles (n = 10) during the period from 15 min to 85 min postmortem and again at 24 h postmortem in the absence (G = 0) and the presence of an external field gradient (G = 0.5*10(-3) T/m), which was applied throughout the CPMG sequence. The experiments were performed on low-field nuclear magnetic resonance (NMR) equipment (0.47 T). Due to the inclusion of different pre-slaughter treatments (adrenaline treatment and pre-slaughter exercise/electrical stunning), the muscles could be divided into (I) a group (n = 5) characterized by a reduced decrease in pH postmortem and a high water-holding capacity and (II) a group (n = 5) characterized by an increased rate of pH decrease postmortem and a low water-holding capacity. Distributed analysis of the CPMG data revealed two major relaxation populations with relaxation times about 30-40 and 200-500 ms, respectively, and comparison of data obtained with G = 0 and G = 0.5*10(-3) T/m revealed effects of the external gradient on the relaxation time of both the two relaxation populations, which implies that both diffusion and relaxation contributes to the relaxation of the two populations. At 24 h postmortem the effect of the external field gradient on the relaxation time was significantly affected by muscle group (I vs. II), which reveals local differences in water diffusion in the two meat qualities. Finally, the discriminatory power with regard to muscle group (I vs. II) was investigated for data acquired with G = 0 and G = F = 0.5*10(-3) T/m, and both the two types of data were found highly suitable for separation of muscles according to meat quality.     

Comparison of electron spin relaxation times measured by Carr-Purcell-Meiboom-Gill and two-pulse spin-echo sequences

Electron spin relaxation times obtained by two-pulse spin-echo and Carr-Purcell-Meiboom-Gill (CPMG) experiments were compared for samples with: (i) low concentrations of nuclear spins, (ii) higher concentrations of nuclear spins and low concentrations of unpaired electrons, (iii) higher concentrations of nuclear spins and of electron spins, and (iv) dynamic averaging of inequivalent hyperfine couplings on the EPR timescale. In each case, the CPMG time constant decreased as the time between the refocusing pulses increased. For the samples with low concentrations of nuclear spins (the E' center in irradiated amorphous SiO2) the limiting value of the CPMG time constant at short interpulse spacings was similar to the Tm obtained by two-pulse spin echo at small turning angle. For the other samples, the time constants obtained by CPMG at short interpulse spacings were systematically longer than Tm obtained by two-pulse spin echo. For most of the samples, the CPMG time constant decreased with increasing electron spin concentration, which is consistent with the expectation that the CPMG sequence does not refocus dephasing due to electron-electron dipolar interaction between resonant spins. Dynamic processes that average inequivalent hyperfine couplings contributed less to the CPMG time constant than to the spin-echo decay time constant. The impact of nuclear echo envelope modulation on CPMG time constants also was examined. For a Nycomed trityl radical in glassy D2O:glycerol-d8 solution, the CPMG time constant was up to 20 times longer when the time between pulses was approximately equal to integer multiples of the reciprocal of the deuterium Larmor frequency than when the time between pulses was an odd multiple of half the reciprocal of the deuterium Larmor frequency.     

Experimental validation of a T2rho transverse relaxation model using LASER and CPMG acquisitions

The transverse relaxation rate (R2=1/T2) of many biological tissues are altered by endogenous magnetized particles (i.e., ferritin, deoxyhemoglobin), and may be sensitive to the pathological progression of neurodegenerative disorders associated with altered brain-iron stores. R2 measurements using Carr-Purcell-Meiboom-Gill (CPMG) acquisitions are sensitive to the refocusing pulse interval (2taucp), and have been modeled as a chemical exchange (CE) process, while R2 measurements using a localization by adiabatic selective refocusing (LASER) sequence have an additional relaxation rate contribution that has been modeled as a R2rho process. However, no direct comparison of the R2 measured using these two sequences has been described for a controlled phantom model of magnetized particles. The three main objectives of this study were: (1) to compare the accuracy of R2 relaxation rate predictions from the CE model with experimental data acquired using a conventional CPMG sequence, (2) to compare R2 estimates obtained using LASER and CPMG acquisitions, and (3) to determine whether the CE model, modified to account for R2rho relaxation, adequately describes the R2 measured by LASER for a full range of taucp values. In all cases, our analysis was confined to spherical magnetic particles that satisfied the weak field regime. Three phantoms were produced that contained spherical magnetic particles (10 microm diameter polyamide powders) suspended in Gd-DTPA (1.0, 1.5, and 2.0 mmol/L) doped gel. Mono-exponential R2 measurements were made at 4T as a function of refocusing pulse interval. CPMG measurements of R2 agreed with CE model predictions while significant differences in R2 estimates were observed between LASER and CPMG measurements for short taucp acquisitions. The discrepancy between R2 estimates is shown to be attributable to contrast enhancement in LASER due to T2rho relaxation.     

The modulation of coupled relaxation in porous media.

This work investigates the effects of modulation of the transverse and longitudinal relaxation of the surface-fluid/pore-fluid spin system in porous media. Important new NMR well logging applications identify pore fluids by varying the CPMG T(2) pulse spacing to discriminate on the basis of fluid diffusivities in applied and local static magnetic field gradients. However, anomalous laboratory CPMG T(2) results have been reported repeatedly over 25 years for various porous media filled with a single fluid. In relatively large pores, at near bulk conditions, the transverse relaxation of diffusing molecular spins should be proportional to the square of the CPMG pulse spacing tau, the susceptibility contrast at the pore wall and the applied gradient. Observed is a markedly linear tau dependence that saturates at a plateau for large tau. The effect is not quadratic in applied gradient or susceptibility. For large pores, the tau dependence and the saturation value are proportional to the surface-to-volume ratio of the pores. This is in distinct contrast to the behavior observed by Borgia, Brown and Fantazzini for systems with much smaller pores at higher magnetic fields. The large-pore anomalous behaviors can be explained as a modulation of the exchange between surface-fluid and pore-fluid spins, such as observed by Luz and Meiboom in 1963 for water enriched with quadrupolar 17O. Scalar coupling of the solid-surface spins to the fluid-surface spins was postulated by Kleinberg, Kenyon and Mitra as a dominant relaxation mechanism for the surface fluid. The CPMG tau effect can be described as the modulation of the exchange coupling by the CPMG pi pulses, which mix the magnetizations between the exchanging, strongly coupled spin systems of the pore-fluid and the surface-fluid, which is, in turn, weakly coupled by scalar or pseudo-scalar interactions to the fast-relaxing solid surface.