Massive Spectral Sum Rules for the Dirac Operator

a r X i v :h e p -p h /0205186v 1 17 M a y 2002Thermal QCD sum rules for mesonsS.MallikSaha Institute of Nuclear Physics,1/AF,Bidhannagar,Kolkata-700064,IndiaSourav SarkarVariable Energy Cyclotron Centre,1/AF,Bidhannagar,Kolkata-700064,IndiaA recently proposed scheme is used to saturate the spectral side of the QCD sum rules derivedfrom the thermal ,two-point correlation functions of the vector and the axial-vector currents.At lowtemperature,it constructs the spectral representation from all the one-loop Feynman diagrams forthe two-point functions.The old saturation scheme treats incorrectly some of these contributions.We end up with the familiar QCD sum rules obtained from the difference of the two correspondingvacuum correlation functions.The possibility of obtaining new sum rules in other media is discussed.I.INTRODUCTION In their original work extending the vacuum QCD sum rules [1]to those at finite temperature,Bochkarev and Shaposhnikov [2]recognised the importance of multiparticle (branch cuts)contributions in addition to those of single particles (poles)in constructing the spectral representation of thermal two-point functions.Thus for the vector current correlation function,they included not only the ρ-pole with temperature dependent residue and position,but also the ππcontinuum.In the same way the spectral representation for the nucleon current correlation function would consist of the nucleon pole with temperature dependent parameters and the πN continuum.Although such a saturation scheme is quite suggestive and had been extensively used in the past [3,4],it lacks a theoretical basis,leaving one to suspect if some equally important contributions are left out.A definitive saturation scheme emerged with the work of Leutwyler and Smilga [5],who calculated the nucleon current correlation function in chiral perturbation theory.Being interested in the shifts of the nucleon pole parameters at low temperature,they considered all the one-loop Feynman diagrams for the correlation function and evaluated them in the vicinity of the nucleon pole.Koike [6]examined the contributions of these diagrams in the context of QCD sum rules.He found a new contribution arising from the nucleon self-energy diagram to the sum rules,not required in the saturation scheme mentioned above.The one-loop Feynman diagrams for the nucleon correlation function were further analysed in Ref.[7].In this set of diagrams for the correlation function,one has not only diagrams with the (single particle)pole alone and the (two particle)branch point alone,but also other (one particle reducible)diagrams,appearing as product of factors with the pole and the branch cut.As an example,take the case of a vertex correction diagram having this product structure.It may be expressed as the sum of the pole term with constant residue and a remainder,regular at the pole.Clearly to find the pole parameters one may confine oneself to the pole term alone.But if one wishes to evaluate the diagram for large space-like momenta –the region of relevance for the QCD sum rules –both the pole and the remainder become of comparable magnitude.It is these remainder terms which are not included in the earlier saturation scheme.In this paper we write down the thermal QCD sum rules following from the vector current and the axial vector current correlation functions,constructing the spectral side from the set of all one-loop Feynman diagrams.At low temperature only the distribution function of the pions is significant in the heat bath.Thus,of the two particles in the loop,at least one must be a pion,the other being any one of the strongly interacting particles with appropriate quantum numbers in the low mass region.The vertices occurring in the diagrams are obtainable from the chiral perturbation theory [8,9]as well as from other formulations of the effective theory of QCD at low energy [10].But the former theory alone is based only on the chiral symmetry of QCD,the others assuming one or other unproven symmetries or relations.Thus the chiral perturbation theory is singled out to determine the vertices,if we claim the sum rules to follow from QCD.As with the nucleon sum rules [7],we subtract out the vacuum sum rules from the corresponding full sum rules at finite temperature,equating,in effect,terms of O (T 2)on both sides.All our calculations are done in the chiral symmetry limit,though we keep nonvanishing pion mass in intermediate steps.In Sec.II we collect some results to be used later.In Sec.III we analyse the one-loop Feynman diagrams to construct the spectral representation for the correlation functions.In Sec.IV we use the known results of Operator Product Expansion and write the sum rules.Finally our concluding remarks are contained in Sec.V.1II.PRELIMINARIESHere we review briefly the kinematics of the two point correlation functions of the vector and the axial-vector currents.Then we write the interaction vertices from the chiral perturbation theory and the results of calculation of a prototype loop integral.A.KinematicsConsider the two thermal correlation functions,T ab µν=i d 4x e iq ·x T r ̺T V a µ(x )V b ν(0),(2.1)and T ′ab µν=i d 4x e iq ·x T r ̺T A a µ(x )A b ν(0),(2.2)of the vector and axial vector currents,V a µ(x )=¯q (x )γµτa 2q (x ),generated by the SU (2)flavour symmetry group of the QCD Lagrangian.Here τa are the Pauli matrices and ̺=e −βH /T r e −βH is the thermal density matrix of QCD at temperature T =1/β.Note that in the limit of chiral symmetry,in which we shall work,the axial vector current is also conserved and the kinematics,in particular,the invariant decomposition is the same for both the correlation functions.The current conservation leads to the invariant decompositionT ab µν(q )=δab (P µνT t +Q µνT l ),(2.3)where the gauge invariant tensors are chosen asP µν=−g µν+q µq ν¯q 2˜u µ˜u ν,Q µν=q 4ω2−q 2,representing the time and space components of q µin the rest frame of the heatbath (u 0=1, u =0).The invariant amplitudes are functions of the scalar variables,say,q 2and ω.They can be conveniently extracted from the Feynman diagrams by forming the scalars,T 1=g µνT µν,T 2=u µu νT µν,(2.4)which are simply related to the invariant amplitudes.Having cast the kinematics in a Lorentz invariant form,we choose to do calculations in the rest frame of the heat bath.The kinematic decomposition (2.3)leads to a constraint on the invariant amplitudes which,in this frame reads asT t (q 0, q =0)=q 20T l (q 0, q =0).(2.5)Using this equation,the two sets of amplitudes,T l,t and T 1,2can be related for q =0asT l =13T 1.(2.6)Note also the symmetry of the imaginary parts of the amplitudes,ImT l,t (−q 0, q =0)=ImT l,t (q 0, q =0).(2.7)In the real time thermal field theory,we are going to use here,each of the above amplitudes stands for a 2×2matrix,whose components depend on a single analytic function [11].This function,in turn,is determined completely by the 11-component function itself:their real parts are equal and the imaginary part of the former equals π−1tanh (βq 0/2)times that of the latter.(The factor π−1is inserted for convenience.)To avoid further symbols,we henceforth redefine T to denote this analytic function.Its spectral representation at fixed q is given by,T l,t (q 20, q )=∞0dq ′20Im T l,t (q ′0, q )B.DynamicsAs we pointed out already,we must describe interaction among particles according to the chiral perturbation theory.The calculation of the two point functions in this theory is most conveniently carried out in the external field method [8],where the original QCD Lagrangian is extended by introducing external fields v a µ(x )and a a µ(x )coupled to the currents V a µ(x )and A a µ(x ),L QCD →L QCD +v a µ(x )V µa (x )+a a µ(x )A µa (x ).The resulting interaction vertices are obtained in Ref.[12,13]for the symmetry group SU (3)R ×SU (3)L .At low temperature the pions dominate the heat bath.We thus consider the reduced symmetry SU (2)R ×SU (2)L and write down the chiral couplings of pions with the external fields and the observed particles,to be encountered in the one-loop diagrams [14].We leave out the interaction among the pions themselves,as it would give rise to corrections of order higher than T 2.Their interaction with external fields are given byL int (π)=L v (π)+L a (π)(2.9)whereL v (π)=v µ·π×∂µπ+12F 2πa µ·a µ−F πa µ·∂µπ−12F π(π·π∂µπ·a µ−π·∂µππ·a µ),(2.10)the letters in bold face denoting isospin vectors.The third and the fourth terms in L a (π)represent corrections respectively to the first and the second term,when two of the pion fields without derivatives are contracted in them.Such a contraction can be worked out from the thermal pion propagator∆(π)11(k )=i(2π)3n (k 0)δ(k 2−m 2π)=δab T 22 1−T 212F 2π a µ·∂µπ.(2.13)Next we write the couplings of the isotriplets [ρ(770),a 1(1230)]and isosinglets [ω(782),f 1(1282)]of vector (1−−)and axial vector (1++)mesons respectively.Although we take their fields to transform according to SU (2)in constructing their interactions,we take the physical (zero temperature)masses of the multiplets of each of the SU (3)octets to be degenerate.Then the coupling linear in the vector meson fields are given byL (V )=F ρ12F 2π ∂µv ν·(∂µρν−∂νρµ)+1m V F 2π∂µρν·∂µπ×∂νπ−√m V F πǫµνλσωµ∂νπ·∂λv σ,(2.14)while those linear in the axial vector meson fields areL (A )=−F a 112F 2π∂µa ν·(∂µa 1ν−∂νa 1µ)+12H f 1Finally the quadratic couplings of the triplets with the singlets and between themselves are given by L(V,A)=−2ǫµνλσ g1Fπ∂µfν1aλ1·∂σπ +g3(2π)4fµν(q,k)∆(π)11(k)∆(X)11(q−k),(2.17)where the particle X can be a heavy(spin one)meson or the pion itself.The tensor fµνis given by the interactionvertices and any tensor structure in∆(X)11.Out of the interaction vertices we have isolated the coupling constants inc.Being gauge invariant,Fµνallows one to construct the invariant amplitudes F l,t in the same way as we did above for Tµν.As we shall see below,the one-particle irreducible diagrams consist only of loop integrals like(2.17),while the reducible ones are given by such integrals multiplied with a heavy particle pole(offirst or second order).In the former case we may evaluate directly the leading contribution of the integral and then Borel transform.In the latter case it is more systematic to use the exact spectral representation of the loop integral.We then Borel transform the resulting complete amplitude and extract its leading term.Until now we have considered full amplitudes,including the corresponding vacuum amplitudes.Our thermal sum rules need only their temperature dependent parts.So we evaluate only these(convergent)parts of the loop integrals, but continue to denote them by the same symbols as for the full amplitudes.Considerfirst the case where X is a heavy particle of mass m H.Let the full amplitude be given by just the loop integral(2.17).Going over to the invariant amplitudes,its thermal part is asF l,t(q)=−c d4k(q−k)2−m2H f l,t(q,k),(2.18) whose leading behaviour for large space-like momenta with q=0(q20=E2=−Q2<0)is given by(ωk=Q2+m2Hd3k n(k)ω2−m2πIII.SPECTRAL REPRESENTATIONHere we analyse the different one-loop Feynman diagrams for the correlation functions and extract the leading thermal contributions (to order T 2)to the spectral side of the sum rules.These diagrams are the same as those considered in [14]to find the shifts in the pole parameters of the ρand a 1mesons.The difference lies in the evaluation of the diagrams:While we evaluated them earlier in the neighbourhood of the respective poles,now we have to do so at large space-like momenta.The diagrams for the correlation functions can be grouped into three types,namely those with intermediate states,vertex corrections and self-energies.To write the Feynman amplitudes we anticipate the following gauge invariant tensors,A µν(q )=−g µν+q µq ν/q 2=P µν+Q µν/q 2,B µν(q,k )=q 2k µk ν−q ·k (q µk ν+k µq ν)+(q ·k )2g µν,C µν(q,k )=q 4k µk ν−q 2(q ·k )(q µk ν+k µq ν)+(q ·k )2q µq ν.(3.1)We now consider the diagrams separately for the correlation functions of the vector and the axial vector currents.Although we need only the T -dependent parts of the diagrams to order T 2,we shall write the pole amplitudes in full.A.Vector currentHere the pole and the one-loop diagrams are shown in Figs.1-4.ρπ(b)ρ(c)πρ(a)FIG.1.ρpole and constant vertex correction1,π,ω(b)ππ(a)FIG.2.Intermediate state diagramsπω,a ,πρ1(a)πρω,a ,π1(b)FIG.3.Vertex correction diagrams(a)πρρω,πa 1,(b)πρρFIG.4.Self-energy diagramsThe ρpole amplitude with its constant vertex corrections (Fig.1)is given byT (ρ)µν(q )=− F ρ6F 2πq 4(2π)4 (2k −q )µ(2k −q )ν∆(π)11(k )∆(π)11(q −k )−2ig µν∆(π)11(k ) ,(3.3)5whose thermal part isT(ππ)(q)=Aµν(−2q2) d4k(q−k)2−m2π→−T2µνm A 2(−Q2,Q4)6F2π(3.5) The(Borel transforms of the)amplitudes given by Eq.(3.2,3.4,3.5)constitute all of the contributions to the spectral side of the sum rules.In the rest of this subsection we verify that none of the remaining diagrams withπωintermediate state,vertex corrections and self-energies contribute to order T2to the sum rules.Clearly it suffices to show this behaviour for any one of the invariant amplitudes,say T l and we omit its subscript in the following.For theπωintermediate state,the amplitude is again given by Eq.(2.17)withc=−2(Hω/m V Fπ)2,fµν=q2k2Aµν+Bµν,f=−2| k|2/3,(3.6) where and below f stands for f l.Then Eq.(2.21)shows immediately that this amplitude is of order T4. Considering next the vertex corrections of Fig.3,each of the amplitudes is of the formFρq2−m2VΛµν,(3.7) whereΛµνis again a one-loop integral of the form of Eq.(2.17).Consider nowE2E′2−E2,which may be used to write the expression(3.8)asm2VΛ(m2V)(E′2−m2V)(E′2−E2),(3.9) separating the pole term from the one regular in the vicinity of the pole.On the other hand,if we go to large space-like E2=−Q2and take the Borel transform,it becomese−m2V/M2(E2−m2V) −m2V+E2e−(E2−m2V)/M2 ,(3.10) where M2is the Borel variable replacing Q2.Eqs.(3.9)and(3.10)allow us to compare how the same amplitude behaves near the pole and at large space-like momenta in the form of the Borel transform.Consider the vertex correction from theπωloop for which c=−(4√behaviour of the Borel transform(3.10).Because the branch point of the functionΛ(E2)also starts at E2=m2V,its leading term is given by1−m2V M2 dE2ImΛ(E),(3.11) which is of order T4.Thus to O(T2),the vertex correction diagram with theπωloop contributes neither to the pole parameters nor to the Borel transform to O(T2).Notice,however,that while near the pole the second term in Eq.(3.9)can be ignored,for large space-like momenta both the terms assume equal importance.Consider next theπa1loop withc=−(4F a1g3/m A F2π),fµν=q2q·kAµν+Bµν,f=E| k|.Again we see that at E2=m2V,the residueΛ(m2V)∼O(T4).Here the branch point ofΛ(E2)is is at E2=m2A.So the Borel transform is clearly of order T4.As shown in the Appendix,theππloop contribution is also at least of order T4to the pole residue and Borel transform.Finally the self-energy diagrams of Fig.4can be analysed in a similar way.Each of the diagrams contributes an amplitude of the form− Fρ(q2−m2V)2Πµν(q).(3.12)The self energyΠµνis again of the form of Eq.(2.17).Using the spectral representation for its invariant amplitudes, we getE4(E2−m2V)2 dE′2ImΠ(E′)E2−m2VdE′2(2E′2−m2V)ImΠ(E′)(E′2−m2V)2(E′2−E2),(3.13) which is the appropriate expression to study the neighbourhood of the meson pole.If we now go to space-like momenta and take the Borel transform,we get1E2−m2V 2+m2V E2−m2Ve−m2V/M2+ E2M2+E4B.Axial-vector currentHere the Feynman diagrams are shown in Figs.5-9.The new feature here is the existence of the pion pole in addition to the one for the axial vector meson a 1.(a)π(b)(c)ππ(d)(e)πππFIG.5.πpole and constant vertex corrections a 1a 1a 1(a)π(b)(c)πFIG.6.a 1pole and constant vertex corrections1π,ρFIG.7.Intermediate state diagrams a 1a 1f 1f 1π(a)π(b)ρρ,,FIG.8.Vertex correction diagramsa1a 1f 1ρ,πFIG.9.Self-energy diagramsThe π-pole with vertex corrections of Fig.5is given byT ′(π)µν=−F 2π 1−T 2m A 2 1−T 2q 2−m 2AA µν.(3.16)The contribution of the πρintermediate state of Fig.7to the invariant amplitudes T l,t are given byT ′(πρ)l,t = F ρ6F 2π(−Q 2,Q 4)currents.This piece turns out to be isospin scalar.The other four-quark operator arises from the Feynman diagram to second order in QCD perturbation expansion,where the large external momentumflows through the internal gluon line.In the medium there are additional operators,which are Lorentz non-scalars in the rest frame of the heat bath. They can,of course,be written as Lorentz scalars in a general frame by using the four-velocity vector uµ.Theyfirst appear as dimension four,which are¯q u/q,uµuνΘfµνand uµuνΘgµν,whereΘf,gµνare the energy momentum tensors of the quark and gluon respectively.More such operators arise at dimensionfive and six,but generally contain derivatives. In the process of subtracting out the vacuum sum rule to extract terms of order T2,the unit operator drops out.Also drops out m q¯q q in the chiral limit.The isospin scalar four-quark operator cannot have a temperature dependence in the chiral limit.The operator¯q u/q does not contribute,as we do not have non-zero chemical potential for the fermions.The thermal expectation value of GµνGµν,ΘfµνandΘgµνare all of order T4.Also the expectation values of other operators with derivative(s)are of higher order than T2,as each derivative gives rise to an additional power in pion momentum.Thus we are left with only the isospin non-scalar four quark operator as the relevant one for our sum rules.Their Wilson coefficients are known[1],i d4x e iq·x T V aµ(x)V bν(0) →δab −gµν+qµqν3Q4 O Ai d4x e iq·x T A aµ(x)A bν(0) →δab −gµν+qµqν3Q4 O V (4.1) whereO V=αs¯qγµτc2q¯qγµτc2qO A=αs¯qγµγ5τc2q¯qγµγ5τc2qandαs=g2s/4πis the strong interactionfine structure constant.The thermal average of any operator may be expanded asO = 0|O|0 + a d3k n(k)6F2π 0|O V−O A|0It is now simple to write the sum rules for a correlation function by equating the Borel transform of the spectral representation to the operator product expansion.It turns out that both the vector and the axial vector correlation functions give rise to the same sum rules[16],−F2ρe−m2V/M2+F2a1e−m2A/M2+F2π=−4π3M2 0|O V−O A|0 (4.3) It is interesting to observe that these sum rules are nothing but the vacuum sum rules derived from the difference of the correlation functions of the vector and the axial-vector currents,whose spectral side consists of the pole terms fromπ,ρand a1exchanges.Also as M2tends to infinity,we recover the well known sum rulesF2ρ−F2a1−F2π=0m2V F2ρ−m2A F2a1=0(4.4) originally derived by Weinberg[17]as superconvergence sum rules for the difference of the spectral functions.9V.CONCLUDING REMARKSIn this work we have obtained the sum rules following from the two point functions of the vector current and the axial vector current at finite temperature.For a reliable estimate,we calculate their spectral sides using the chiral perturbation theory.The resulting Feynman diagrams (to one loop)can be readily evaluated for their leading thermal contributions.Though there is a multitude of diagrams to begin with,only a few of these actually contribute to order T 2.This is due to the presence of derivatives on the pion fields in the interaction vertices derived from the chiral perturbation theory.Among the contributing ones,there is a one-particle reducible,self-energy diagram,whose contribution at space-like momenta is zero to order T 2.But the old saturation scheme would derive from this diagram a shift to this order in the residue of the meson pole.The older strategy of determining the temperature dependence of the pole parameters from such sum rules is not relevant anymore,as we have already included the diagrams responsible for this dependence in our calculation of the spectral functions.Our evaluation reproduces the sum rules which follow from the vacuum correlation functions themselves.The present saturation scheme has been used also for the nucleon correlation function at finite temperature,again reproducing the results obtainable from the corresponding vacuum correlation function [6,7].Thus we now have enough confirmation of the correctness of the QCD sum rules in a medium.Can we get new results from the sum rules in a medium?It would seem that we are merely reproducing the old results in a more complicated way:What one could have from single particle exchange diagrams in vacuum,are now derived from one loop diagrams at finite temperature.But we do not believe the situation to be so.Indeed,having been assured of the correct procedure to saturate the spectral side,we may apply the sum rule technique to other media,like the nuclear medium by introducing the nucleon chemical potential.There are no reliable estimates of higher dimension operators like the four-quark operators in such media.It is these quantities which should be readily available from such sum rules.APPENDIXSome care is necessary in constructing the spectral representation for the ππloop for q =0.The loop integral gives rise to cuts in the q 20plane for arbitrary q extending over 0<q 20<| q |2(short cut)and q 20>4(m 2π+|q |2)(unitary cut).As q →0the short cut shrinks to a point.But the spectral function can be singular in this limit,so that the part of the spectral representation due to this cut may be non-vanishing.Consider first the ππloop in the vertex diagram.It gives an amplitude of the form of Eq.(3.7),whereΛµν(q )=icd 4k 8(2π)2+1−1dx −q 2x 2/2−q 4/6 1+28(2π)2 ∞1dx−q 2x 2/2−q 4/6 1e β(| q |x +q 0)/2−1 ,q 2<0.(A.3)On the unitary cut the x -integrals are thus finite as q →0and because of q 2(q 4)in the integrands,their Borel transforms will have no contributions to O (T 2).But on the short cut the x -integrals diverge as q →0.Let us then consider the full Borel transformed amplitude with q =0,Λl Λt =1Defining new variablesλand u by q0=λ| q|and| q|x=u,it becomesΛlΛt =| q|2λ| q| 1eβ(u+λ| q|)/2−1→−2d eβu/2−1 ,(A.6)as| q|→0.Thus the short cut also cannot contribute for q=0.Theππloop in the self-energy correction is given by Eq.(3.12)whereΠµνis of the form of Eq.(A.1)with c= (2Gρ/m V F2π)2and fµν=Cµν.From the previous treatment it is clear that this amplitude again does not lead to any corrections of O(T2).ACKNOWLEDGEMENTOne of us(S.M.)acknowledges support of CSIR,Government of India.。

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Pass or fail conditions can initiate actions including document to local or networked files, e-mail the image of the failure, save waveforms, send a pulse out at the rear panel auxiliary BNC output, or (with the GPIB option) send a GPIB SRQ.Jitter and Timing Analysis Software Package (WRXi-JTA2)(Standard with MXi-A model oscilloscopes)•Jitter and timing parameters, with “Track”graphs of •Edge@lv parameter (counts edges)• Persistence histogram, persistence trace (mean, range, sigma)Software Options –Advanced Math and WaveShape AnalysisStatistics Package (WRXi-STAT)This package provides additional capability to statistically display measurement information and to analyze results:• Histograms expanded with 19 histogram parameters/up to 2 billion events.• Persistence Histogram• Persistence Trace (mean, range, sigma)Master Analysis Software Package (WRXi-XMAP)(Standard with MXi-A model oscilloscopes)This package provides maximum capability and flexibility, and includes all the functionality present in XMATH, XDEV, and JTA2.Advanced Math Software Package (WRXi-XMATH)(Standard with MXi-A model oscilloscopes)This package provides a comprehensive set of WaveShape Analysis tools providing insight into the wave shape of complex signals. Includes:•Parameter math – add, subtract, multiply, or divide two different parameters.Invert a parameter and rescale parameter values.•Histograms expanded with 19 histogram parameters/up to 2 billion events.•Trend (datalog) of up to 1 million events•Track graphs of any measurement parameter•FFT capability includes: power averaging, power density, real and imaginary components, frequency domain parameters, and FFT on up to 24 Mpts.•Narrow-band power measurements •Auto-correlation function •Sparse function• Cubic interpolation functionAdvanced Customization Software Package (WRXi-XDEV)(Standard with MXi-A model oscilloscopes)This package provides a set of tools to modify the scope and customize it to meet your unique needs. Additional capability provided by XDEV includes:•Creation of your own measurement parameter or math function, using third-party software packages, and display of the result in the scope. Supported third-party software packages include:– VBScript – MATLAB – Excel•CustomDSO – create your own user interface in a scope dialog box.• Addition of macro keys to run VBScript files •Support for plug-insValue Analysis Software Package (WRXi-XVAP)(Standard with MXi-A model oscilloscopes)Measurements:•Jitter and Timing parameters (period@level,width@level, edge@level,duty@level, time interval error@level, frequency@level, half period, setup, skew, Δ period@level, Δ width@level).Math:•Persistence histogram •Persistence trace (mean, sigma, range)•1 Mpts FFTs with power spectrum density, power averaging, real, imaginary, and real+imaginary settings)Statistical and Graphical Analysis•1 Mpts Trends and Histograms •19 histogram parameters •Track graphs of any measurement parameterIntermediate Math Software Package (WRXi-XWAV)Math:•1 Mpts FFTs with power spectrum density, power averaging, real, and imaginary componentsStatistical and Graphical Analysis •1 Mpts Trends and Histograms •19 histogram parameters•Track graphs of any measurement parameteramplitude area base cyclescustom (MATLAB,VBScript) –limited points delay Δdelay duration duty cyclefalltime (90–10%, 80–20%, @ level)firstfrequency lastlevel @ x maximum mean median minimumnumber of points +overshoot –overshoot peak-to-peak period phaserisetime (10–90%, 20–80%, @ level)rmsstd. deviation time @ level topΔ time @ levelΔ time @ level from triggerwidth (positive + negative)x@ max.x@ min.– Cycle-Cycle Jitter – N-Cycle– N-Cycle with start selection – Frequency– Period – Half Period – Width– Time Interval Error – Setup– Hold – Skew– Duty Cycle– Duty Cycle Error20WaveRunner WaveRunner WaveRunner WaveRunner WaveRunner 44Xi-A64Xi-A62Xi-A104Xi-A204Xi-AVertical System44MXi-A64MXi-A104MXi-A204MXi-ANominal Analog Bandwidth 400 MHz600 MHz600 MHz 1 GHz 2 GHz@ 50 Ω, 10 mV–1 V/divRise Time (Typical)875 ps500 ps500 ps300 ps180 psInput Channels44244Bandwidth Limiters20 MHz; 200 MHzInput Impedance 1 MΩ||16 pF or 50 Ω 1 MΩ||20 pF or 50 ΩInput Coupling50 Ω: DC, 1 MΩ: AC, DC, GNDMaximum Input Voltage50 Ω: 5 V rms, 1 MΩ: 400 V max.50 Ω: 5 V rms, 1 MΩ: 250 V max.(DC + Peak AC ≤ 5 kHz)(DC + Peak AC ≤ 10 kHz)Vertical Resolution8 bits; up to 11 with enhanced resolution (ERES)Sensitivity50 Ω: 2 mV/div–1 V/div fully variable; 1 MΩ: 2 mV–10 V/div fully variableDC Gain Accuracy±1.0% of full scale (typical); ±1.5% of full scale, ≥ 10 mV/div (warranted)Offset Range50 Ω: ±1 V @ 2–98 mV/div, ±10 V @ 100 mV/div–1 V/div; 50Ω:±400mV@2–4.95mV/div,±1V@5–99mv/div,1 M Ω: ±1 V @ 2–98 mV/div, ±10 V @ 100 mV/div–1 V/div,±10 V @ 100 mV–1 V/div±**********/div–10V/div 1 M Ω: ±400 mV @ 2–4.95 mV/div, ±1 V @5–99 mV/div, ±10 V @ 100 mV–1 V/div,±*********–10V/divInput Connector ProBus/BNCTimebase SystemTimebases Internal timebase common to all input channels; an external clock may be applied at the auxiliary inputTime/Division Range Real time: 200 ps/div–10 s/div, RIS mode: 200 ps/div to 10 ns/div, Roll mode: up to 1,000 s/divClock Accuracy≤ 5 ppm @ 25 °C (typical) (≤ 10 ppm @ 5–40 °C)Sample Rate and Delay Time Accuracy Equal to Clock AccuracyChannel to Channel Deskew Range±9 x time/div setting, 100 ms max., each channelExternal Sample Clock DC to 600 MHz; (DC to 1 GHz for 104Xi-A/104MXi-A and 204Xi-A/204MXi-A) 50 Ω, (limited BW in 1 MΩ),BNC input, limited to 2 Ch operation (1 Ch in 62Xi-A), (minimum rise time and amplitude requirements applyat low frequencies)Roll Mode User selectable at ≥ 500 ms/div and ≤100 kS/s44Xi-A64Xi-A62Xi-A104Xi-A204Xi-A Acquisition System44MXi-A64MXi-A104MXi-A204MXi-ASingle-Shot Sample Rate/Ch 5 GS/sInterleaved Sample Rate (2 Ch) 5 GS/s10 GS/s10 GS/s10 GS/s10 GS/sRandom Interleaved Sampling (RIS)200 GS/sRIS Mode User selectable from 200 ps/div to 10 ns/div User selectable from 100 ps/div to 10 ns/div Trigger Rate (Maximum) 1,250,000 waveforms/secondSequence Time Stamp Resolution 1 nsMinimum Time Between 800 nsSequential SegmentsAcquisition Memory Options Max. Acquisition Points (4 Ch/2 Ch, 2 Ch/1 Ch in 62Xi-A)Segments (Sequence Mode)Standard12.5M/25M10,00044Xi-A64Xi-A62Xi-A104Xi-A204Xi-A Acquisition Processing44MXi-A64MXi-A104MXi-A204MXi-ATime Resolution (min, Single-shot)200 ps (5 GS/s)100 ps (10 GS/s)100 ps (10 GS/s)100 ps (10 GS/s)100 ps (10 GS/s) Averaging Summed and continuous averaging to 1 million sweepsERES From 8.5 to 11 bits vertical resolutionEnvelope (Extrema)Envelope, floor, or roof for up to 1 million sweepsInterpolation Linear or (Sinx)/xTrigger SystemTrigger Modes Normal, Auto, Single, StopSources Any input channel, External, Ext/10, or Line; slope and level unique to each source, except LineTrigger Coupling DC, AC (typically 7.5 Hz), HF Reject, LF RejectPre-trigger Delay 0–100% of memory size (adjustable in 1% increments, or 100 ns)Post-trigger Delay Up to 10,000 divisions in real time mode, limited at slower time/div settings in roll modeHold-off 1 ns to 20 s or 1 to 1,000,000,000 events21WaveRunner WaveRunner WaveRunner WaveRunner WaveRunner 44Xi-A 64Xi-A 62Xi-A104Xi-A 204Xi-A Trigger System (cont’d)44MXi-A64MXi-A104MXi-A204MXi-AInternal Trigger Level Range ±4.1 div from center (typical)Trigger and Interpolator Jitter≤ 3 ps rms (typical)Trigger Sensitivity with Edge Trigger 2 div @ < 400 MHz 2 div @ < 600 MHz 2 div @ < 600 MHz 2 div @ < 1 GHz 2 div @ < 2 GHz (Ch 1–4 + external, DC, AC, and 1 div @ < 200 MHz 1 div @ < 200 MHz 1 div @ < 200 MHz 1 div @ < 200 MHz 1 div @ < 200 MHz LFrej coupling)Max. Trigger Frequency with400 MHz 600 MHz 600 MHz 1 GHz2 GHzSMART Trigger™ (Ch 1–4 + external)@ ≥ 10 mV@ ≥ 10 mV@ ≥ 10 mV@ ≥ 10 mV@ ≥ 10 mVExternal Trigger RangeEXT/10 ±4 V; EXT ±400 mVBasic TriggersEdgeTriggers when signal meets slope (positive, negative, either, or Window) and level conditionTV-Composite VideoT riggers NTSC or PAL with selectable line and field; HDTV (720p, 1080i, 1080p) with selectable frame rate (50 or 60 Hz)and Line; or CUSTOM with selectable Fields (1–8), Lines (up to 2000), Frame Rates (25, 30, 50, or 60 Hz), Interlacing (1:1, 2:1, 4:1, 8:1), or Synch Pulse Slope (Positive or Negative)SMART TriggersState or Edge Qualified Triggers on any input source only if a defined state or edge occurred on another input source.Delay between sources is selectable by time or eventsQualified First In Sequence acquisition mode, triggers repeatedly on event B only if a defined pattern, state, or edge (event A) is satisfied in the first segment of the acquisition. Delay between sources is selectable by time or events Dropout Triggers if signal drops out for longer than selected time between 1 ns and 20 s.PatternLogic combination (AND, NAND, OR, NOR) of 5 inputs (4 channels and external trigger input – 2 Ch+EXT on WaveRunner 62Xi-A). Each source can be high, low, or don’t care. The High and Low level can be selected independently. Triggers at start or end of the patternSMART Triggers with Exclusion TechnologyGlitch and Pulse Width Triggers on positive or negative glitches with widths selectable from 500 ps to 20 s or on intermittent faults (subject to bandwidth limit of oscilloscope)Signal or Pattern IntervalTriggers on intervals selectable between 1 ns and 20 sTimeout (State/Edge Qualified)Triggers on any source if a given state (or transition edge) has occurred on another source.Delay between sources is 1 ns to 20 s, or 1 to 99,999,999 eventsRuntTrigger on positive or negative runts defined by two voltage limits and two time limits. Select between 1 ns and 20 sSlew RateTrigger on edge rates. Select limits for dV, dt, and slope. Select edge limits between 1 ns and 20 s Exclusion TriggeringTrigger on intermittent faults by specifying the normal width or periodLeCroy WaveStream Fast Viewing ModeIntensity256 Intensity Levels, 1–100% adjustable via front panel control Number of Channels up to 4 simultaneouslyMax Sampling Rate5 GS/s (10 GS/s for WR 62Xi-A, 64Xi-A/64MXi-A,104Xi-A/104MXi-A, 204Xi-A/204MXi-A in interleaved mode)Waveforms/second (continuous)Up to 20,000 waveforms/secondOperationFront panel toggle between normal real-time mode and LeCroy WaveStream Fast Viewing modeAutomatic SetupAuto SetupAutomatically sets timebase, trigger, and sensitivity to display a wide range of repetitive signalsVertical Find ScaleAutomatically sets the vertical sensitivity and offset for the selected channels to display a waveform with maximum dynamic range44Xi-A 64Xi-A 62Xi-A104Xi-A 204Xi-A Probes44MXi-A 64MXi-A104MXi-A 204MXi-AProbesOne Passive probe per channel; Optional passive and active probes available Probe System; ProBus Automatically detects and supports a variety of compatible probes Scale FactorsAutomatically or manually selected, depending on probe usedColor Waveform DisplayTypeColor 10.4" flat-panel TFT-LCD with high resolution touch screenResolutionSVGA; 800 x 600 pixels; maximum external monitor output resolution of 2048 x 1536 pixelsNumber of Traces Display a maximum of 8 traces. Simultaneously display channel, zoom, memory, and math traces Grid StylesAuto, Single, Dual, Quad, Octal, XY , Single + XY , Dual + XY Waveform StylesSample dots joined or dots only in real-time mode22Zoom Expansion TracesDisplay up to 4 Zoom/Math traces with 16 bits/data pointInternal Waveform MemoryM1, M2, M3, M4 Internal Waveform Memory (store full-length waveform with 16 bits/data point) or store to any number of files limited only by data storage mediaSetup StorageFront Panel and Instrument StatusStore to the internal hard drive, over the network, or to a USB-connected peripheral deviceInterfaceRemote ControlVia Windows Automation, or via LeCroy Remote Command Set Network Communication Standard VXI-11 or VICP , LXI Class C Compliant GPIB Port (Accessory)Supports IEEE – 488.2Ethernet Port 10/100/1000Base-T Ethernet interface (RJ-45 connector)USB Ports5 USB 2.0 ports (one on front of instrument) supports Windows-compatible devices External Monitor Port Standard 15-pin D-Type SVGA-compatible DB-15; connect a second monitor to use extended desktop display mode with XGA resolution Serial PortDB-9 RS-232 port (not for remote oscilloscope control)44Xi-A 64Xi-A 62Xi-A104Xi-A 204Xi-A Auxiliary Input44MXi-A 64MXi-A104MXi-A 204MXi-ASignal Types Selected from External Trigger or External Clock input on front panel Coupling50 Ω: DC, 1 M Ω: AC, DC, GND Maximum Input Voltage50 Ω: 5 V rms , 1 M Ω: 400 V max.50 Ω: 5 V rms , 1 M Ω: 250 V max. (DC + Peak AC ≤ 5 kHz)(DC + Peak AC ≤ 10 kHz)Auxiliary OutputSignal TypeTrigger Enabled, Trigger Output. Pass/Fail, or Off Output Level TTL, ≈3.3 VConnector TypeBNC, located on rear panelGeneralAuto Calibration Ensures specified DC and timing accuracy is maintained for 1 year minimumCalibratorOutput available on front panel connector provides a variety of signals for probe calibration and compensationPower Requirements90–264 V rms at 50/60 Hz; 115 V rms (±10%) at 400 Hz, Automatic AC Voltage SelectionInstallation Category: 300 V CAT II; Max. Power Consumption: 340 VA/340 W; 290 VA/290 W for WaveRunner 62Xi-AEnvironmentalTemperature: Operating+5 °C to +40 °C Temperature: Non-Operating -20 °C to +60 °CHumidity: Operating Maximum relative humidity 80% for temperatures up to 31 °C decreasing linearly to 50% relative humidity at 40 °CHumidity: Non-Operating 5% to 95% RH (non-condensing) as tested per MIL-PRF-28800F Altitude: OperatingUp to 3,048 m (10,000 ft.) @ ≤ 25 °C Altitude: Non-OperatingUp to 12,190 m (40,000 ft.)PhysicalDimensions (HWD)260 mm x 340 mm x 152 mm Excluding accessories and projections (10.25" x 13.4" x 6")Net Weight7.26kg. (16.0lbs.)CertificationsCE Compliant, UL and cUL listed; Conforms to EN 61326, EN 61010-1, UL 61010-1 2nd Edition, and CSA C22.2 No. 61010-1-04Warranty and Service3-year warranty; calibration recommended annually. Optional service programs include extended warranty, upgrades, calibration, and customization services23Product DescriptionProduct CodeWaveRunner Xi-A Series Oscilloscopes2 GHz, 4 Ch, 5 GS/s, 12.5 Mpts/ChWaveRunner 204Xi-A(10 GS/s, 25 Mpts/Ch in interleaved mode)with 10.4" Color Touch Screen Display 1 GHz, 4 Ch, 5 GS/s, 12.5 Mpts/ChWaveRunner 104Xi-A(10 GS/s, 25 Mpts/Ch in interleaved mode)with 10.4" Color Touch Screen Display 600 MHz, 4 Ch, 5 GS/s, 12.5 Mpts/Ch WaveRunner 64Xi-A(10 GS/s, 25 Mpts/Ch in interleaved mode)with 10.4" Color Touch Screen Display 600 MHz, 2 Ch, 5 GS/s, 12.5 Mpts/Ch WaveRunner 62Xi-A(10 GS/s, 25 Mpts/Ch in interleaved mode)with 10.4" Color Touch Screen Display 400 MHz, 4 Ch, 5 GS/s, 12.5 Mpts/Ch WaveRunner 44Xi-A(25 Mpts/Ch in interleaved mode)with 10.4" Color Touch Screen DisplayWaveRunner MXi-A Series Oscilloscopes2 GHz, 4 Ch, 5 GS/s, 12.5 Mpts/ChWaveRunner 204MXi-A(10 GS/s, 25 Mpts/Ch in Interleaved Mode)with 10.4" Color Touch Screen Display 1 GHz, 4 Ch, 5 GS/s, 12.5 Mpts/ChWaveRunner 104MXi-A(10 GS/s, 25 Mpts/Ch in Interleaved Mode)with 10.4" Color Touch Screen Display 600 MHz, 4 Ch, 5 GS/s, 12.5 Mpts/Ch WaveRunner 64MXi-A(10 GS/s, 25 Mpts/Ch in Interleaved Mode)with 10.4" Color Touch Screen Display 400 MHz, 4 Ch, 5 GS/s, 12.5 Mpts/Ch WaveRunner 44MXi-A(25 Mpts/Ch in Interleaved Mode)with 10.4" Color Touch Screen DisplayIncluded with Standard Configuration÷10, 500 MHz, 10 M Ω Passive Probe (Total of 1 Per Channel)Standard Ports; 10/100/1000Base-T Ethernet, USB 2.0 (5), SVGA Video out, Audio in/out, RS-232Optical 3-button Wheel Mouse – USB 2.0Protective Front Cover Accessory PouchGetting Started Manual Quick Reference GuideAnti-virus Software (Trial Version)Commercial NIST Traceable Calibration with Certificate 3-year WarrantyGeneral Purpose Software OptionsStatistics Software Package WRXi-STAT Master Analysis Software Package WRXi-XMAP (Standard with MXi-A model oscilloscopes)Advanced Math Software Package WRXi-XMATH (Standard with MXi-A model oscilloscopes)Intermediate Math Software Package WRXi-XWAV (Standard with MXi-A model oscilloscopes)Value Analysis Software Package (Includes XWAV and JTA2) WRXi-XVAP (Standard with MXi-A model oscilloscopes)Advanced Customization Software Package WRXi-XDEV (Standard with MXi-A model oscilloscopes)Spectrum Analyzer and Advanced FFT Option WRXi-SPECTRUM Processing Web Editor Software Package WRXi-XWEBProduct Description Product CodeApplication Specific Software OptionsJitter and Timing Analysis Software Package WRXi-JTA2(Standard with MXi-A model oscilloscopes)Digital Filter Software PackageWRXi-DFP2Disk Drive Measurement Software Package WRXi-DDM2PowerMeasure Analysis Software Package WRXi-PMA2Serial Data Mask Software PackageWRXi-SDM QualiPHY Enabled Ethernet Software Option QPHY-ENET*QualiPHY Enabled USB 2.0 Software Option QPHY-USB †EMC Pulse Parameter Software Package WRXi-EMC Electrical Telecom Mask Test PackageET-PMT* TF-ENET-B required. †TF-USB-B required.Serial Data OptionsI 2C Trigger and Decode Option WRXi-I2Cbus TD SPI Trigger and Decode Option WRXi-SPIbus TD UART and RS-232 Trigger and Decode Option WRXi-UART-RS232bus TD LIN Trigger and Decode Option WRXi-LINbus TD CANbus TD Trigger and Decode Option CANbus TD CANbus TDM Trigger, Decode, and Measure/Graph Option CANbus TDM FlexRay Trigger and Decode Option WRXi-FlexRaybus TD FlexRay Trigger and Decode Physical Layer WRXi-FlexRaybus TDP Test OptionAudiobus Trigger and Decode Option WRXi-Audiobus TDfor I 2S , LJ, RJ, and TDMAudiobus Trigger, Decode, and Graph Option WRXi-Audiobus TDGfor I 2S LJ, RJ, and TDMMIL-STD-1553 Trigger and Decode Option WRXi-1553 TDA variety of Vehicle Bus Analyzers based on the WaveRunner Xi-A platform are available.These units are equipped with a Symbolic CAN trigger and decode.Mixed Signal Oscilloscope Options500 MHz, 18 Ch, 2 GS/s, 50 Mpts/Ch MS-500Mixed Signal Oscilloscope Option 250 MHz, 36 Ch, 1 GS/s, 25 Mpts/ChMS-500-36(500 MHz, 18 Ch, 2 GS/s, 50 Mpts/Ch Interleaved) Mixed Signal Oscilloscope Option 250 MHz, 18 Ch, 1 GS/s, 10 Mpts/Ch MS-250Mixed Signal Oscilloscope OptionProbes and Amplifiers*Set of 4 ZS1500, 1.5 GHz, 0.9 pF , 1 M ΩZS1500-QUADPAK High Impedance Active ProbeSet of 4 ZS1000, 1 GHz, 0.9 pF , 1 M ΩZS1000-QUADPAK High Impedance Active Probe 2.5 GHz, 0.7 pF Active Probe HFP25001 GHz Active Differential Probe (÷1, ÷10, ÷20)AP034500 MHz Active Differential Probe (x10, ÷1, ÷10, ÷100)AP03330 A; 100 MHz Current Probe – AC/DC; 30 A rms ; 50 A rms Pulse CP03130 A; 50 MHz Current Probe – AC/DC; 30 A rms ; 50 A rms Pulse CP03030 A; 50 MHz Current Probe – AC/DC; 30 A rms ; 50 A peak Pulse AP015150 A; 10 MHz Current Probe – AC/DC; 150 A rms ; 500 A peak Pulse CP150500 A; 2 MHz Current Probe – AC/DC; 500 A rms ; 700 A peak Pulse CP5001,400 V, 100 MHz High-Voltage Differential Probe ADP3051,400 V, 20 MHz High-Voltage Differential Probe ADP3001 Ch, 100 MHz Differential Amplifier DA1855A*A wide variety of other passive, active, and differential probes are also available.Consult LeCroy for more information.Product Description Product CodeHardware Accessories*10/100/1000Base-T Compliance Test Fixture TF-ENET-B †USB 2.0 Compliance Test Fixture TF-USB-B External GPIB Interface WS-GPIBSoft Carrying Case WRXi-SOFTCASE Hard Transit CaseWRXi-HARDCASE Mounting Stand – Desktop Clamp Style WRXi-MS-CLAMPRackmount Kit WRXi-RACK Mini KeyboardWRXi-KYBD Removable Hard Drive Package (Includes removeable WRXi-A-RHD hard drive kit and two hard drives)Additional Removable Hard DriveWRXi-A-RHD-02* A variety of local language front panel overlays are also available .† Includes ENET-2CAB-SMA018 and ENET-2ADA-BNCSMA.Customer ServiceLeCroy oscilloscopes and probes are designed, built, and tested to ensure high reliability. In the unlikely event you experience difficulties, our digital oscilloscopes are fully warranted for three years, and our probes are warranted for one year.This warranty includes:• No charge for return shipping • Long-term 7-year support• Upgrade to latest software at no chargeLocal sales offices are located throughout the world. Visit our website to find the most convenient location.© 2010 by LeCroy Corporation. All rights reserved. Specifications, prices, availability, and delivery subject to change without notice. Product or brand names are trademarks or requested trademarks of their respective holders.1-800-5-LeCroy WRXi-ADS-14Apr10PDF。

小学上册英语第3单元测验试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The _____ (绿色能源) movement promotes plant-based solutions.2.The _____ (cat/dog) is sleeping.3.The ______ (香味) of flowers can be very strong.4.What do we call a scientist who studies the properties of matter?A. ChemistB. PhysicistC. BiologistD. Geologist答案:A5.I want to _____ (see/watch) a movie tonight.6.What is the main language spoken in the USA?A. SpanishB. FrenchC. EnglishD. German答案:C7.The cake is ________ and sweet.8.We share ______ (秘密) with each other.9.I enjoy going ______ (远足) to enjoy the beauty of nature.10.The ______ teaches us about civic responsibilities.11.The chemical properties of an element depend on its ______ structure.12.The country famous for its tango is ________ (阿根廷).13.What is the opposite of 'fast'?A. QuickB. SlowC. SpeedyD. Rapid14.What is the capital of Tunisia?A. TunisB. SousseC. MonastirD. Bizerte答案:A15.What do you call a house made of ice?A. IglooB. CabinC. CastleD. Hut答案:A16._____ (当地植物) can adapt to specific environments.17.Chemical reactions often involve a change in ______.18.The __________ is the layer of skin that helps to protect against injury.19.I enjoy making memories with my toy ________ (玩具名称).20.I can ________ (manage) my time effectively.21.What do we call the opposite of ‘clean’?A. DirtyB. NeatC. TidyD. Clear22. A __________ is a sudden release of energy in the Earth's crust.23.My friend is a ______. He loves to collect stamps.24.My dad shows me how to be __________ (勇敢的) in difficult times.25.What is the largest country in the world?A. CanadaB. ChinaC. RussiaD. India26.The _______ (The Battle of Waterloo) marked the defeat of Napoleon.27.The ____ is a small creature that hides under leaves.28.What do we call the study of the universe?A. BiologyB. AstronomyC. GeologyD. Physics答案:B29.The _____ (果实) develops after a flower blooms.30. Wall of China was built to __________ (保护) the country from invasions. The Grea31.The ant carries food back to its ______ (巢).32.What is 4 + 5?A. 8B. 9C. 10D. 1133.The _____ (水果收成) happens in late summer.34.Many plants have a specific ______ period for blooming. (许多植物有特定的开花期。

THE MASS SPECTROMETERHow a mass spectrometer worksThe basic principleIf something is moving and you subject it to a sideways force, instead of moving in a straight line, it will move in a curve - deflected out of its original path by the sideways force.Suppose you had a cannonball travelling past you and you wanted to deflect it as it went by you. All you've got is a jet of water from a hose-pipe that you can squirt at it. Frankly, its not going to make a lot of difference! Because the cannonball is so heavy, it will hardly be deflected at all from its original course.But suppose instead, you tried to deflect a table tennis ball travelling at the same speed as the cannonball using the same jet of water. Because this ball is so light, you will get a huge deflection.The amount of deflection you will get for a given sideways force depends on the mass of the ball. If you knew the speed of the ball and the size of the force, you could calculate the mass of the ball if you knew what sort of curved path it was deflected through. The less the deflection, the heavier the ball.An outline of what happens in a mass spectrometerAtoms can be deflected by magnetic fields - provided the atom is first turned into an ion. Electrically charged particles are affected by a magnetic field although electrically neutral ones aren't.The sequence is :Stage 1: IonisationThe atom is ionised by knocking one or more electrons off to give a positive ion. This is true even for things which you would normally expect to form negative ions (chlorine, for example) or never form ions at all (argon, for example). Mass spectrometers always work with positive ions.Stage 2: AccelerationThe ions are accelerated so that they all have the same kinetic energy.Stage 3: DeflectionThe ions are then deflected by a magnetic field according to their masses. The lighter they are, the more they are deflected.The amount of deflection also depends on the number of positive charges on the ion - in other words, on how many electrons were knocked off in the first stage. The more the ion is charged, the more it gets deflected.Stage 4: DetectionThe beam of ions passing through the machine is detected electrically.A full diagram of a mass spectrometerUnderstanding what's going onThe need for a vacuumIt's important that the ions produced in the ionisation chamber have a free run through the machine without hitting air molecules.IonisationThe vaporised sample passes into the ionisation chamber. The electrically heated metal coil gives off electrons which are attracted to the electron trap which is a positively charged plate.The particles in the sample (atoms or molecules) are therefore bombarded with a stream of electrons, and some of the collisions are energetic enough to knock one or more electrons out of the sample particles to make positive ions.Most of the positive ions formed will carry a charge of +1 because it is much more difficult to remove further electrons from an already positive ion.These positive ions are persuaded out into the rest of the machine by the ion repeller which is another metal plate carrying a slight positive charge.AccelerationThe positive ions are repelled away from the very positive ionisation chamber and pass through three slits, the final one of which is at 0 volts. The middle slit carries some intermediate voltage. All the ions are accelerated into a finely focused beam.DeflectionDifferent ions are deflected by the magnetic field by different amounts. The amount of deflection depends on:∙the mass of the ion. Lighter ions are deflected more than heavier ones.∙the charge on the ion. Ions with 2 (or more) positive charges are deflected more than ones with only 1 positive charge.These two factors are combined into the mass/charge ratio. Mass/charge ratio is given the symbol m/z (or sometimes m/e).For example, if an ion had a mass of 28 and a charge of 1+, its mass/charge ratio would be 28. An ion with a mass of 56 and a charge of 2+ would also have a mass/charge ratio of 28.In the last diagram, ion stream A is most deflected - it will contain ions with the smallest mass/charge ratio. Ion stream C is the least deflected - it contains ions with the greatest mass/charge ratio.It makes it simpler to talk about this if we assume that the charge on all the ions is 1+. Most of the ions passing through the mass spectrometer will have a charge of 1+, so that the mass/charge ratio will be the same as the mass of the ion.Assuming 1+ ions, stream A has the lightest ions, stream B the next lightest and stream C the heaviest. Lighter ions are going to be more deflected than heavy ones.DetectionOnly ion stream B makes it right through the machine to the ion detector. The other ions collide with the walls where they will pick up electrons and be neutralised. Eventually, they get removed from the mass spectrometer by the vacuum pump.When an ion hits the metal box, its charge is neutralised by an electron jumping from the metal on to the ion (right hand diagram). That leaves a space amongst the electrons in the metal, and the electrons in the wire shuffle along to fill it.A flow of electrons in the wire is detected as an electric current which can be amplified and recorded. The more ions arriving, the greater the current.Detecting the other ionsHow might the other ions be detected - those in streams A and C which have been lost in the machine?Remember that stream A was most deflected - it has the smallest value of m/z (the lightest ions if the charge is 1+). To bring them on to the detector, you would need to deflect them less - by using a smaller magnetic field (a smaller sideways force).To bring those with a larger m/z value (the heavier ions if the charge is +1) on to the detector you would have to deflect them more by using a larger magnetic field.If you vary the magnetic field, you can bring each ion stream in turn on to the detector to produce a current which is proportional to the number of ions arriving. The mass of each ion being detected is related to the size of the magnetic field used to bring it on to the detector. The machine can be calibrated to record current (which is a measure of the number of ions) against m/z directly. The mass is measured on the 12C scale.THE MASS SPECTRA OF ELEMENTSThe mass spectrum for boronThe mass spectrum for zirconiumThe number of peaks in the mass spectrum shows the number of the isotopes for an element.The total mass of these 100 typical atoms would be(51.5 x 90) + (11.2 x 91) + (17.1 x 92) + (17.4 x 94) + (2.8 x 96) = 9131.8The average mass of these 100 atoms would be 9131.8 / 100 = 91.3 (to 3 significant figures).91.3 is the relative atomic mass of zirconium.Note: When you calculate the relative atomic mass for element, the total of % of abundance is 100%.。

Fatty Acid Metabolite Library of Standards Supplied by IROA Technologies, LLC. Catalog Number FAMLSStorage Temperature –20 ︒CProduct DescriptionFAMLS™ (Fatty Acid Metabolite Library of Standards) is a collection of high quality fatty acids that span a broad range of primary metabolism. These are high purity (>95%) compounds supplied in an economical, ready-to-use format.The library is most commonly used to provide retention times and spectra for key metabolic compounds, help optimize analytical mass spectrometry protocols, and qualify and quantify mass spectrometry sensitivity and limit of detection.FAMLS comes with MLSDiscovery™, a software tool to support the extraction, manipulation, and storage of the data generated when using the FAMLS. For further information on the software, to download, and for manual and video links please visit:/catalog/product/sigma/fam lsComponentsFAMLS contains 96 unique small molecule fatty acid metabolites, conveniently provided at 5 μg per well, enough for multiple injections, suitable for manual and automated workflow.Key primary metabolites and intermediates covering key metabolic pathways, including the following classes of fatty acids:•Short chain•Medium chain•Long chain•Very long chain•Saturated and unsaturated•BranchedThe library is intended to be used for mass spectrometry metabolomics applications and provides a broad representation of primary metabolism. Occasionally the plate map will change due to the availability of compounds. Although we try to make sure the compounds of each row have distinct molecular weights and can be multiplexed, users should refer to the plate map before proceeding.The plate map contains descriptors and represents information gathered from multiple databases. We try to ensure the accuracy of the data but it may contain errors. We suggest that the information provided is carefully reviewed. To help build a better database, please report any discrepancies.FAMLS includes:• 1 polypropylene plate in 96 well format• 5 μg (dried weight) of each metabolite •Polypropylene deepwell (1.2 mL, total volume per well) plates (MasterBlock®, Greiner #780215) incombination with seals (VIEWseal™, Greiner#676070)•Plate map•Alphanumeric assigned position•Descriptors:NameParent CIDKEGG ID where available or ChemSpider IDmolecular formulamolecular weightCASChEBIHMDB ID/YMDB IDPubChem Compound and Substance IDMetlin IDPrecautions and DisclaimerFor R&D use only. Not for drug, household, or other uses. Please consult the Safety Data Sheet for information regarding hazards and safe handling practices.2Preparation InstructionsThe following are suggestions and dependent on user chromatography and instrumentation.Rows A-C: Solubilize in high-quality chloroform. Pipette liquid up and down in the well 2-3 times to facilitate solubilization.Rows D-H: Solubilize in high-quality ethanol. Pipette liquid up and down in the well 2-3 times to facilitate solubilization.Pool compounds for multiplexing. Be sure to check the plate map to ensure one can adequately separate the compounds using the chromatographic system prior to pooling.Storage/StabilityStore the plates at –20 ︒C.Once the metabolites are dissolved, the plates should be resealed and kept at –20 ︒C or –80 ︒C for long-term storage and protected from light. Avoid repeated freeze/thaw cycles.ProcedureThe compounds of the FAMLS can either be used as standards and injected individually or mixed in such a way that the entire library may be examined with reasonable efficiency. Mixing compounds by row mixtures allows multiple compounds to be analyzed per injection. Be sure to check the plate map to ensure one can adequately separate the compounds using the chromatographic system prior to pooling.The following are only suggestions and depend on user chromatography and instrumentation.1. Individual Injections – As standards, each wellrepresents a single compound; thus the entirelibrary may be examined in great detail in96 injections for each of the unique compounds.(Total volumes for each well of 250 μL – 1 mL may be considered).2. Simple multiplex injections – If the rows of the plateare pooled, then the entire collection may beanalyzed with 8 injections of simple mixtures (Keep the total volume for each well to 500 μL or less toprevent loss due to dilution).Note: Be sure to check the individual massesacross plate rows to ensure these compounds can be separated with the chromatographic systememployed. References1. Wishart, D.S. et al., HMDB: the HumanMetabolome Database. Nucleic Acids Res. 2007Jan; 35 (Database issue):D521-6. 17202168.2. Wishart, D.S. et al., HMDB: a knowledgebase forthe human metabolome. Nucleic Acids Res., 200937 (Database issue):D603-610. 18953024.3. Wishart, D.S. et al., HMDB 3.0 — The HumanMetabolome Database in 2013. Nucleic Acids Res.2013. Jan 1;41 (D1):D801-7. 23161693.4. Jewison, T. et al., YMDB: The Yeast MetabolomeDatabase. Nucleic Acids Res. 2012 Jan;40(Database Issue): D815-20 PubMed: 22064855. 5. Hastings, J. et al., The ChEBI reference databaseand ontology for biologically relevant chemistry:enhancements for 2013. Nucleic Acids Res. 2013.Jan;41 (Database issue):D456-63. doi:10.1093/nar/gks1146. Epub 2012 Nov 24.6. CAS REGISTRY, Division of the AmericanChemical Society7. Kanehisa, M., and Goto, S., "KEGG: KyotoEncyclopedia of Genes and Genomes". NucleicAcids Res. 2000 28 (1): 27–30.doi:10.1093/nar/28.1.27. PMC 102409.PMID10592173.8. Tautenhahn, R. et al., An accelerated workflow foruntargeted metabolomics using the METLINdatabase. Nature Biotechnology 2012 30: 826–828.doi:10.1038/nbt.2348.9. Smith, C.A. et al., METLIN: a metabolite massspectral database. The Drug Monit 2005 27 (6):747–51. doi:10.1097/01.ftd.0000179845.53213.39.PMID 16404815.10. Kim, S. et al., PubChem Substance and Compounddatabases. Nucleic Acids Res. 2016 Jan 4;44(D1):D1202-13. Epub 2015 Sep 22 [PubMedPMID: 26400175] doi: 10.1093/nar/gkv951 [FreeFull Text at Oxford Journals]FAMLS and MLSDiscovery are trademarks of IROA Technologies, LLC.MasterBlock is a registered trademark and VIEWseal is a trademark of Greiner Bio-One GmbH.SS,AA,MAM 05/19-1©2019 Sigma-Aldrich Co. LLC. All rights reserved. SIGMA-ALDRICH is a trademark of Sigma-Aldrich Co. LLC, registered in the US and other countries. Sigma brand products are sold through Sigma-Aldrich, Inc. Purchaser must determine the suitability of the product(s) for their particular use. Additional terms and conditions may apply. Please see product information on the Sigma-Aldrich website at and/or on the reverse side of the invoice or packing slip.。

Interpretation of Mass SpectraBy Fred W. MclaffertyInterpretation of Mass Spectra Details:Mass spectral interpretation for chromatographersMass spectral interpretation for chromatographers This material is designed to helpGC/MS beginners who want to understand a few mass spectral interpretation basics. Interpretation of Mass Spectra Interpretation of Mass Spectra ...INTERPRETATION OF MASS and TANDEM MASS SPECTRA FOR STRUCTURE I. FRAGMENTATION OF GAS-PHASE IONS There are two main classes of fragmentation of radical cations in EIMS:Interpretation of Mass Spectra - Chemistry Courses: About ...Choose a reasonable structure Do the expected fragments agree w/ chosen structure YES NO Interpretation of Mass Spectra Is the structure unique? YESInterpretation of Mass Spectra Interpretation of Mass Spectra ...C. EXAMPLE CID OR PRODUCT-ION SPECTRA Figure 29. Product-ion spectrum of peptide found in proteomics experiment (sequence given in figure). Most of ions are y ions and singly chargedInterpretation of Mass Spectra - United States Home | AgilentCourse Outline Day One • GC-MS Data Structure • Chemistry Review • Data Acquisition Day Two • Introduction to Interpretation Goals • Structural InformationInterpretation of Mass Spectra Part 5 - UCO - BiologyPostulation of Molecular Structures • Put everything together using SIP • There are several major kinds of structural information available from the MSComputer-Assisted Interpretation of Mass SpectraJOHNS HOPKINS APL TECHNICAL DIGEST, VOLUME 20, NUMBER 3 (1999) 363 COMPUTER-ASSISTED INTERPRETATION OF MASS SPECTRA UComputer-Assisted Interpretation of Mass SpectraInterpretation of Mass Spectra Including those from ...Interpretation of Mass Spectra Including those from Electrospray and MALDI Presented by J. Throck Watson Professor, Biochemistry and ChemistryInterpretation of CID Mass SpectraInterpretation of CID Mass Spectra I. API BASICS FOR THE INTERPRETATION OF CID MASS SPECTRA 1. Interpretation Introduction and Isotopes. 2. Masses of Isotopes and Compound MW’S.Advanced Interpretation of Mass Spectra - United States Home ...Course Outline Day One • Performance Verification • QA and QC Measurements • Mass Resolution • Tuning • Review of Fundamental Principles • Element CompositionMass spectra interpretation system including spectra extraction( 1 of 1) United States Patent 5,453,613 Gray , et al. September 26, 1995 Mass spectra interpretation system including spectra extraction AbstractInterpretation of Infrared Spectra, A Practical Approachmass of sulfur, compared with oxygen, results in the characteristic group frequencies occurring at noticeably lower frequencies than the oxygen-containing analogs, ... INTERPRETATION OF INFRARED SPECTRA, A PRACTICAL APPROACH 23 REFERENCES 1.Interpretation of Organic Spectra - Research and Markets4.4.6 Examples of the interpretation of mass spectra from soft ionization 120 4.5 Interpretation of high resolution mass spectra 123 4.6 Interpretation of mass spectra from tandem mass spectrometry 126 References 127 5 Interpretation of infrared spectra 129Basic rules for the interpretation of atmospheric pressure ...step in the interpretation of mass spectra regardless of theioniza-tiontechniqueused.APItechniquesbelongtothegroupofso-called soft ionization techniques, so it is evident already from this name that the ionization process has a softer character in comparison toAutomated Interpretation of Mass Spectra by Incremental ...Rules ? Syntax of the applied fragmentation rules: IF (side1 AND side2) THEN (P(side1) AND P(side2)) where side1 and side2 represent subgraphs of the two possible fragments Interpretation of EI organometallics mass spectra LS in ...60 years of the Faculty of Chemical Technology and Engineering UT & LS in Bydgoszcz 246 • nr 4/2011 • tom 65 Interpretation of EI organometallics mass spectraIntroduction to Mass Spectral InterpretationIntroduction to Mass Spectral Interpretation by Robert Kobelski Each mass spectrum contains a wealth of information. With higher resolution instruments, faster computers, larger and betterOn de novo interpretation of tandem mass spectra for peptide ...On de novo interpretation of tandem mass spectra for peptide identi?cation Vineet Bafna Nathan Edwardsy ABSTRACT The correct interpretation of tandem mass spectra is a di -Mass Spectral Examples - University of AkronMass Spectral Examples We’ve introduced several simple tools to help in the interpretation of mass spectra. Now, lets put them to use and see how wellNovel Bioinformatics Tool: Interpretation of Glycan Mass ...Novel Bioinformatics Tool: Interpretation of Glycan Mass Spectra with Metal Adducts and Multiple Adduct Combinations Julian Saba1, Ningombam Sanjib Meitei 2 and Arun Apte2 Interpretation of Mass Spectral Data 1) The molecular ion1 Interpretation of Mass Spectral Data 1) The molecular ion The molecular ion in an E.I. spectrum may be identified using the following rules: 1) It must be the ion of highest m/z in the spectrum, apart from isotope peaks resulting from its molecularLecture I-1: MS Interpretation-1 - University of Colorado Boulder9 Lecture I-1: MS Interpretation-1 CU- Boulder CHEM 5181 Mass Spectrometry & Chromatography Prof. Jose-Luis Jimenez Fall 2007 Lecture based on an earlier version of notes from Dr. Dan CzizcoInterpretation of Tandem Mass Spectra Obtained from Cyclic ...Interpretation of Tandem Mass Spectra Obtained from Cyclic Nonribosomal PeptidesWei-Ting Liu, †Julio Ng, ‡Dario Meluzzi, Nuno Bandeira, Marcelino Gutierrez,§COMPARISON AND INTERPRETATION OF MASS SPECTRAL DATA OF ...Figure 2: TIC and mass spectrum of 2-bromodiphenyl ether The greater abundance of the doubly charged ion cluster (M-2Br) as compared to the absent orMS basics and spectra interpretationMS Basics What does a mass spectrometer do? A mass spectrometer produces charged particles (ions) from the chemical substances that are to be analyzed.An Introduction to Mass Spectrometry - Widener Universityinterpretation of mass spectra. It is only an introduction and interested readers are encouraged to consult more specialized books and journal articles for additional details. The articles and books referenced in this paper should be available at most college and university libraries.Mass Spectrometry InterpretationInterpretation of Mass Spectra Select a candidate peak for the molecular ion (M+) Examine spectrum for peak clusters of characteristic isotopic patternsIntroduction to Mass SpectroscopyMass Spectrometry: Interpretation of Spectra General Considerations The more stable a fragment (cation or cation radical), the more likely it will be observed in the mass interpretation of mass spectra. Furthermore, such correlations imply that mass spectrometry will provide an important tool for predicting and interpreting photo- chemical reactions. Pith3 and Nicholson4 have shown that the photo- (1) (a) ...Mass Spectrometry: Introduction - University of MinnesotaMass Spectrometry •NOT part of electromagnetic spectrum •What is measured are (typically) positively charged ions •Under certain circumstances negative ionsDownload Interpretation of Mass Spectra Full versionRead This First:We offer two ways that you can get this book for free, You can choose the way you like! You must provide us your shipping information after you complete the survey. All books will be shipped from Amazon US or Amazon UK depending on your region! Please share this free experience to your friends on your social network to prove that we really send free books!Tags:Interpretation of Mass Spectra,Interpretation of Mass Spectra By Fred W. 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