Charmed meson rescattering in the reaction pbar d to D Dbar N
a r X i v :0803.3752v 1 [h e p -p h ] 26 M a r 2008
EPJ manuscript No.
(will be inserted by the editor)
Charmed meson rescattering in the reaction ˉpd →ˉDDN
J.Haidenbauer 1,G.Krein 2,Ulf-G.Mei?ner 1,3,and A.Sibirtsev 1,3
1Forschungszentrum J¨u lich,Institut f¨u r Kernphysik,D-52425J¨u lich,Germany
2Instituto de F ′?sica Te′o rica,Universidade Estadual Paulista,Rua Pamplona,145-01405-900S?a o Paulo,SP,Brazil 3
Helmholtz-Institut f¨u r Strahlen-und Kernphysik (Theorie),Universit¨a t Bonn,Nu?allee 14-16,D-53115Bonn,Germany
Received:date /Revised version:date
Abstract.We examine the possibility to extract information about the DN and ˉDN
interactions from the ˉp d →D 0D ?
p reaction.We utilize the notion that the open-charm mesons are ?rst produced in the annihilation of the antiproton on one nucleon in the deuteron and subsequently rescatter on the other (the
spectator)nucleon.The latter process is then exploited for investigating the DN and ˉDN
interactions.We study di?erent methods for isolating the contributions from the D 0p and D ?p rescattering terms.PACS.13.60.Le Meson production –14.40.Lb Charmed mesons –25.10.+s Nuclear reactions involving few-nucleon systems –25.43.+t Antiproton-induced reactions
1Introduction
The distortion of charm in nuclear matter remains an heavily discussed issue since the ?rst proposals [1]to use charmonia and open charm as a probe of the early stage of
heavy-ion collisions,for a review see [2].It was expected [3]that charmed ?nal-state interactions (FSI)either at the partonic or the hadronic rescattering level would not dis-tort the spectra initially produced in heavy-ion collisions,because the cross sections for any such (elastic and inelas-tic)scattering processes are su?ciently small.Further-more,gluon radiation or bremsstrahlung [4–6],which distorts the original charm spectrum as well,becomes the dominant energy loss mechanism only if the heavy charmed quarks are ultra-relativistic.That is similar to the brems-strahlung losses of electrons passing through a hydrogen target [7,8].However,in the present experiments a large fraction of the heavy quarks are produced with momenta less than their mass and therefore the radiation losses might be negligible.In that case the heavy charmed quarks and antiquarks and,speci?cally,the ?nally detected D and ˉD
mesons are presumably not distorted in the nu-clear environment and thus can probe the initial stage of the interaction,possibly,the Quark Gluon Plasma.
On the other hand it was argued [8–11]that the two basic processes involved in the energy-loss mechanism of charmed particles moving in nuclear matter,namely gluon radiation and elastic scattering,might be equally impor-tant and non-negligible.Only recently the situation chan-ged due to the PHENIX and STAR experiments [12–15]at the Relativistic Heavy Ion Collider (RHIC).These new measurements indicate a substantial suppression of the production of open-charm mesons with transverse mo-menta above ?1GeV/c from central Au +Au collisions,as compared to that from d +Au collisions.This observa-tion could not be assigned to gluon radiation of charm and
thus indirectly points to an importance of distortions due to the FSI.
Apparently,the interactions of charmed quarks or an-tiquarks in nuclear matter are not the same as the inter-actions of open-charm mesons.However,it is clear that a reasonable understanding of elastic scattering involving particles with charm on a hadronic level is highly impor-tant.While one could not measure directly the interaction of the charmed and light quarks and antiquarks,the DN
and ˉDN
interactions can be studied experimentally.These could serve as a basis to construct phenomenologically the charmed FSI at the partonic rescattering level.
The basic problem is the complete lack of relevant ex-perimental data.This situation is expected to change with the operation of the Facility for Antiproton and Ion Re-search (FAIR)at Darmstadt (Germany).The Proton AN-tiproton at DArmstadt (PANDA)Collaboration [16]in-tends to investigate the distortion of open-charm mesons [17–19]in matter and in the vacuum .The matter mea-surements are based on D and ˉD meson production in an-tiproton annihilation on di?erent nuclei in order to study
the A -dependence.The vacuum measurements explore the production of open-charm mesons by annihilating antipro-tons on the deuteron and,through the rescattering of the
produced D and ˉD
mesons on the spectator nucleon,the interaction in the DN and ˉDN
systems.In the present paper we examine the possibility to extract information about the DN and ˉDN
interactions from the ˉp
d →D 0D ?p reaction.Th
e study is based on the notion that those open-charm mesons are ?rst produced by annihilating the antiproton on one o
f the nucleons in the deuteron and subsequently rescatter on the other (the
2J.Haidenbauer et al.:Charmed meson rescattering in the reactionˉpd→ˉDDN spectator)nucleon.The latter process is then exploited
for investigating the DN andˉDN interactions.
To explore the potential of pertinent experiments we perform concrete calculations taking into account the nu-cleon exchange Born diagram,corresponding to the ele-mentaryˉNN→ˉDD annihilation process,cf.Fig.1a), as well as rescattering diagrams involving the DN and theˉDN interactions,see Fig.1b).For those interactions we employ realisticˉDN→ˉDN[20]and DN→DN[21] scattering amplitudes.This is a substantial improvement as compared to previous studies[22–24]which relied on rather simple assumptions as far as the DN andˉDN scat-tering amplitudes were concerned.
The paper is structured in the following way:In the subsequent section we introduce brie?y the formalism used for calculating the reactionˉp d→D0D?p.The utilized in-teraction models in theˉDN and DN channels are intro-duced and discussed in Sect.3.In particular,we present results for total and di?erential cross sections for the var-ious charge channels.In Sect.4a short overview on our present knowledge on the elementaryˉNN→ˉDD reac-tion is given.Our results for the reactionˉp d→D0D?p are shown in Sect.5.Here the emphasis is put on the exploration of di?erent methods for detecting and isolat-ing the contributions from the D0p and D?p rescattering terms.For that purpose we consider the spectator mo-mentum distribution,Dalitz plots,the missing mass of the exchanged meson and correlations between properly de?ned scattering planes.The paper ends with a brief summary.As a test of our approach we also apply it to multipion production inˉp d annihilation and we compare our results with data available for theˉp d→π+2π?p and ˉp d→2π+3π?p reactions.Those results are included in an appendix.
2Formalism
In this section we introduce the formalism we use to in-vestigate the e?ects of the DN andˉDN interactions in antiproton annihilation on the deuteron.
Fig.1illustrates processes contributing to the reac-tionˉp d→DˉDN.The diagrams of interest are the nucleon exchange Born diagram,Fig.1a),and the meson rescat-tering diagram,Fig.1b).The corresponding amplitudes will be denoted below by T a and T b,respectively.
In what follows we assume for convenience that the spectator nucleon–the nucleon that does not enter the annihilation vertices–is the proton.The case of a neu-tron as spectator can be treated in a similar manner.The nucleon exchange Born diagram,Fig.1a),leads to the well-known reaction amplitude[25–27]
T a=ψd(p s)T A,(1) whereψd(p s)is the momentum-space deuteron wave func-tion,with p s being the proton spectator momentum,and T A is the amplitude for theˉp n→D?D0annihilation pro-cess.After summation over spin states the squared ampli-tude is given as
|T a|2=[u(p s)2+w(p s)2]|T A|2,
(2)Fig.1.Contributions to the reactionˉp d→DˉDN:a)The Born (nucelon exchange)diagram.T A denotes the annihilation am-plitude.b)Meson rescattering diagram.T M denotes the meson-nucleon scattering amplitude.Note that both DN andˉDN scatterings contribute to the reaction amplitude.
where u and w stand for the s-and d-wave components of the deuteron wave function.The overall size of the nucleon exchange contribution in Fig.1a)is determined by the annihilation amplitude T A,which depends on the meson channels produced in theˉp n annihilation.On the other hand,the spectator momentum distribution is gov-erned predominantly by the deuteron wave function,as indicated in Eq.(2),provided that T A is a slowly varying function of the energy.
Next we consider the rescattering diagram of Fig.1b) where one of the mesons produced at the annihilation vertex is scattered o?the spectator nucleon.In general, the intermediate meson in this diagram is not necessar-ily the same as the?nal rescattered meson.It could be an intermediate D?vector-meson,for example.Thus,in principle a sum over all possible intermediate states is re-quired.But in the following let us regard explicitly the features of the rescattering mechanism involving elastic Mp→Mp scattering only.Note that the formalism can be easily extended to other,non-diagonal transitions.We average over the spins in the annihilation and scattering vertices and take into account only the s-wave component u(p s)of the deuteron wave function.The d-wave compo-nent is expected to play a much less important role for the rescattering contribution[27,28]and,therefore,we ignore it here in this exploratory study.The integration for the rescattering diagram runs over the three momentum of the spectator proton in the loop and can be split into on-shell and o?-shell parts,which we denote by T on b and T off
b
.The on-shell part is de?ned by taking the intermediate proton to be on-shell and is given as[27,29–32]
T on b=?
i
E q
T M T A,(3)
J.Haidenbauer et al.:Charmed meson rescattering in the reactionˉpd→ˉDDN3 where T M is the meson-proton scattering amplitude,q is
the internal proton loop momentum,E q=(q2+m2p)1/2
with m p the proton mass,and p is the sum of the momenta
of the?nal proton and the rescattered meson.The limits
of the integral are given by[33]
q±=|p|
s1/2
Mp
p?,(4)
where E=E M+E p is the sum of the energies of the?nal
proton and the rescattered meson,while s1/2
Mp =(E2?p2)1/2
is their invariant energy and
p?2=
(s Mp?m2p?m2M)2?4m2p m2M
p?2+m2p,(5)
with m M the meson mass.The evaluation of T b requires the knowledge of both amplitudes T M and T A within the range of q?to q+allowed for the considered reaction.
The e?ect of the o?-shell part of the rescattering inte-gral was investigated in detail in Refs.[27,29–31,34,35]. In those studies it was found that the shape of the specta-tor momentum distribution,as given by the on-shell part, remains essentially unchanged when the o?-shell contri-bution is added.At the same time,the magnitude of the o?-shell contribution is signi?cant and can lead to modi?-cations of the on-shell results in the order of30%or more, but depends strongly on the speci?c o?-shell behaviour of the annihilation and scattering amplitudes.Explicitly,the o?-shell part of the amplitude can be written as[27,31, 34]
T off b =
1
E q
T M T A ×ln
E M+E p?E q?E?
4J.Haidenbauer et al.:Charmed meson rescattering in the reactionˉpd→ˉ
DDN
Fig. 2.Reaction cross section for(a)D?n→D?n(dashed
line),(b)D?p→D?p(solid line)and(c)D?p→ˉD0n(dash-
dotted line)as a function of theˉD-meson momentum(lower
axis)and the kinetic energy?in the center-of-mass system
(cms)(upper axis).
also recall that charged open-charm mesons are in gen-
eral reconstructed by the leptonic,semileptonic and ha-
dronic Kππand Kπππdecay https://www.wendangku.net/doc/8c14468067.html,ually the neutral
open-charm mesons can be well detected by their hadronic
D0→K?π+andˉD0→K+π?decays[7].For the full recon-
struction of the?nal state of theˉp d→D0D?p reaction it is
therefore important that both semileptonic and hadronic
modes are detected with high accuracy.This should be
kept in mind for the design of future experiments,e.g.,of
the PANDA experiment[16].High accuracy is crucial for
identi?cation of DN andˉDN rescattering e?ects,whose
absolute values and energy dependences could be very dif-
ferent,as indicated by several studies using di?erent mod-
els[22,40–44],and as will become clear from the present
work,too.The identi?cation of the di?erent e?ects might
be possible when a full reconstruction of the?nal state is
feasible.
3.1TheˉDN amplitude
For theˉDN scattering amplitude we use the results of
our recently published potential model[20].This model
for theˉDN interaction was constructed within the meson-
exchange framework,but supplemented with a short-distance
contribution from one-gluon-exchange.The model was de-
veloped in close analogy to the meson-exchange KN in-
teraction of the J¨u lich group[45,46]utilizing SU(4)sym-
metry constraints.The main ingredients of the interac-
tion are provided by vector meson(ρ,ω)exchange and
higher-order box diagrams involvingˉD?N,ˉD?,andˉD??
intermediate states.The short range part is supplemented
by additional contributions from genuine quark-gluon pro-
cesses[47,48].The reaction amplitude is obtained by solv-
ing a Lippmann-Schwinger type scattering equation for
the interaction potential.The features of theˉDN ampli-
tude based on this model are much more realistic than
the ones employed in previous studies[22–24].Indeed,
in the former studies the D?p cross section for instance
was assumed to be momentum independent and equal to
?20mb[22,24]or5mb[23].Moreover,the angular depen-
dence of the elastic scattering was assumed to be either
isotropic[22,24]or forward peaked[23],i.e.proportional
to exp(bt),where t is the four momentum transfer squared,
with a slope b=2GeV?2.The reason for such assumptions
was the lack of any microscopic calculations of theˉDN
scattering amplitude in those days.
To illustrate the di?erences between the previous cal-
culations[22–24]and the results of Ref.[20]we show in
Fig.2predictions for the D?n→D?n,D?p→D?p and
D?p→ˉD0n reaction cross sections as a function of theˉD-
meson momentum(lower axis)and the cm kinetic energy
?(upper axis).It is clear that the scattering cross sec-
tions for all channels depend signi?cantly on theˉD-meson
momentum.
Note that theˉDN scattering amplitudes for the dif-
ferent reaction channels shown in Fig.2are related to the
isospin basis used in Ref.[20]by
T M(D?n→D?n)=T M(ˉD0p→ˉD0p)=f1,(11)
T M(D?p→D?p)=T M(ˉD0n→ˉD0n)=
1
2
(f1?f0),(13)
where f0and f1are the isospin I=0and I=1amplitudes,
respectively.
Fig.3.Di?erential cross sections for the D?p→D?p reaction
in the cm system at di?erent momenta.
J.Haidenbauer et al.:Charmed meson rescattering in the reactionˉpd→ˉDDN5
Di?erential cross sections for D?p→D?p at di?erent momenta are presented in Fig.3.The distributions are almost isotropic for momenta below?500MeV/c,but be-come forward peaked at higher momenta.Note that there is no simple way to parametrize the angular dependence with functions like exp(bt)[23],unless the slope parameter b is taken to be momentum dependent.
For completeness,let us mention that other models of theˉDN interaction have been published in recent years [41,49].Those authors considered s-waves only.The cross sections predicted by these models at threshold are8.5mb (D?n→D?n),5.54mb(D?p→D?p),and0.03mb (D?p→ˉD0n)[41,43]and10.6mb,2.64mb,and2.64mb for model B of Ref.[49],respectively.
3.2The DN amplitude
The DN interaction[21]employed in the present study is also constructed in close analogy to the meson-exchange ˉKN model of the J¨u lich group[50]as well as by exploit-
ing the close connection between theˉDN and DN systems due to G-parity conservation.Speci?cally,the latter con-straint?xes the contributions to the direct DN interaction potential while the former one provides the transitions to and interactions in channels that can couple to the DN system.Accordingly,the DN interaction is likewise pro-vided by vector-meson(ρ,ω)exchange and higher-order box diagrams involving D?N,D?,and D??intermediate states.The short-ranged quark-gluon processes,however, are absent here because the quark-exchange mechanism cannot contribute to the DN interaction due to the dif-ferent quark structure of the D meson.As far as the cou-pling to other channels is concerned,we follow here the arguments of Ref.[50]and we take into account only the channelsπΛc(2285)andπΣc(2455).Furthermore,we re-strict ourselves to vector-meson exchange and we do not consider any higher-order diagrams in those channels.Pole diagrams due to theΛc(2285)andΣc(2455)intermediate states are,however,consistently included in all channels.
In this basic model all free parameters-the coupling constants and the cut-o?masses at the vertex form factors of the occurring meson-meson-meson and meson-baryon-baryon vertices,cf.[50]-are?xed by the assumed SU(4) symmetry and the connection with theˉKN model,re-spectively.When solving the coupled-channel Lippmann-Schwinger equation with this interaction model we observe that two states are generated dynamically below the DN threshold,one in the S01partial wave and the other one in the S11partial wave.(We use here the standard spectro-scopical nomenclature L I2J.)In view of the close analogy between our DN model and the correspondingˉKN inter-action[50]this is not too surprising,because also the lat-ter yields a quasi-bound state in the S01channel which is associated with theΛ(1405)resonance.The bound states in both theˉKN and DN are generated by the strongly attractive interaction due to the combined e?ect ofω,ρand scalar-meson exchanges,which add up coherently in speci?c channels.
It should be said that studies of theˉKN and DN inter-action within chiral unitary(and related)approaches like-wise generate theΛ(1405)resonance dynamically but also states in the DN system[41,44,51].In those approaches the strong attraction is also provided by vector-meson ex-change[41]or by the Weinberg-Tomazawa term[44,51]. In Refs.[42,44,49]the authors argued that the state oc-curing in the S01channel of the charm C=1sector should be identi?ed with the I=0resonanceΛc(2593). We adopt this viewpoint here too.Furthermore,we iden-tify the state we get in the S11channel with the I=1 resonanceΣc(2800)[7].
In order to make sure that the DN model we are going to apply in our study of the reactionˉp d→D0D?p incor-porates these features also quantitatively we?ne-tune the contributions of the scalar mesons to the DN interaction so that the position of those states generated by the model coincide with the values given in the list of the Particle Data Group.This can be achieved by a moderate change in the coupling constants of theσmeson(from1to2.6) and the a0meson(from?2.6to?4.6),cf.Table2in Ref.[20].
Interestingly,our model generates a further state,name-ly in the P01partial wave,which,after the above?ne-tuning,lies at2803MeV,i.e.just below the DN threshold. We are tempted to identfy this state with theΛc(2765)res-onance,whose quantum numbers are not yet established [7].Though we do not reproduce the resonance energy quantitatively,we believe that further re?nements in the DN model,speci?cally the inclusion of theΛcππchannel in terms of an e?ectiveσΛc channel,can provide su?cient additional attraction for obtaining also quantitative agree-ment.The mechanism could be the same as in case of the Roper(N?(1440))resonance,which is generated dynam-ically in the J¨u lichπN model[52,53].Here the
required Fig. 4.Reaction cross sections for(a)D0n→D0n(dashed line),(b)D0p→D0p(solid line)and(c)D0p→D+n(dash-dotted line)as a function of theˉD-meson momentum(lower axis)and the cms kinetic energy?(upper axis).
6
J.Haidenbauer et al.:Charmed meson rescattering in the reaction ˉpd →ˉ
DDN
Fig.5.Di?erential cross sections for the D 0p →D 0p reaction
in the cm system at di?erent momenta.
strong attraction is produced via the coupling of the πN p -wave (where the Roper occurs)to the s -wave in the σN system,facilitated by the di?erent parities of the πand σmesons.
Some results of our DN model are presented in Figs.4and 5.The DN scattering amplitude for the di?erent re-action channels shown in the Fig.4are related to those in the isospin basis by
T M (D 0n →D 0n )=T M (D +p →D +p )=f 1,
(14)
T M (D 0p →D 0p )=T M (D +n →D +n )=
1
2
(f 1?f 0),
(16)
where f 0and f 1are the isospin I =0and I =1amplitudes respectively.
Obviously,also the DN cross sections show a signi?-cant momentum dependence in all charge channels.Fur-thermore,the cross sections are substantially larger than
those we obtain for ˉDN
.Speci?cally,for the pure I =1channel D 0n the cross section amounts to almost 600mb at threshold.This is not too surprising in view of the near-by quasi-bound state.The latter is also re?ected in the s -wave scattering lengths,
a I =0DN =(?0.41+i 0.04)fm a I =1DN =(?2.07+i 0.57)fm ,
(17)
namely by the rather large value of the real part in the
I =1channel.For completeness,let us mention here that the scattering lengths of the DN interaction of Hofmann and Lutz [41],reported in [43],amount to about ?0.4fm for both isospin channels.In agreement with that work we
?nd that the imaginary part is negligibly small for I =0.
However,contrary to [43]in our DN model this is not the case for the I =1channel.
Angular distributions for the reaction D 0p →D 0p are shown in Fig.5.Obviously,there is a strong anisotropy al-ready at fairly low momenta.It is due to signi?cant contri-butions in the P 01partial wave in this momentum region induced by the near-threshold quasi-bound state produced by our model,as discussed above.For higher momenta the di?erential cross section becomes forward peaked,similar
to the predictions of our model for the ˉDN
system.Further details of our DN model will be reported in a forthcoming publication [21].
4ˉDD production in ˉpN annihilation
The total cross section for the reaction ˉp d →D 0D ?p de-pends crucially on the elementary ˉNN
→ˉDD annihila-tion amplitude T A .Unfortunately,so far there is no ex-perimental information about this reaction and even the-oretical studies are rather scarce [54–56].In Ref.[54]re-sults were given for the reaction ˉp p →D ?D +in a quark plus diquark model,where the elementary ?avour chang-ing process is due to diquark-antidiquark annihilation and subsequent creation of a quark-antiquark pair through one gluon.Kaidalov and Volkovitsky calculated the reaction
ˉp p →ˉDD
in the framework of a non-perturbative quark-gluon string model,based on secondary Regge pole ex-changes including absorptive corrections [55].The result of both works are summarized in Fig.6.The larger cross sections are predicted by the model of Ref.[54]with a maximal value of around 0.15μb at p lab =12GeV/c cor-responding to
√
J.Haidenbauer et al.:Charmed meson rescattering in the reactionˉpd→ˉDDN7
Fig.6.Predictions for theˉp p→ˉDD annhilation cross section taken from Refs.[54](solid line)and[55](dashed and dash-dotted lines).
the reaction amplitude,involving(DN orˉDN)charge-exchange rescattering,ˉp d→D?D+n→D?D0p and ˉp d→ˉD0D0n→D?D0p,requireˉp p→D?D+andˉp p→ˉD0D0,respectively,but here the relative phase between
the terms is not known.Thus,we are facing the problem that we either have to add all contributions incoherently and make additional assumptions about the isospin depen-dence ofˉNN→ˉDD or we consider only the amplitude involving elastic DN andˉDN rescattering.We prefer the latter option.In this case we can add the Born term and the DN andˉDN rescattering contributions coherently,be-cause they all involve the same elementaryˉp n→D?D0 annihilation amplitude,and we can include the resulting interference e?ects in the evaluation of the observables. However,absolute predictions are out of reach and all re-sults will be shown as number of events only.On the other hand we consider the energy dependence of the elementary ˉp n→D?D0annihilation amplitude in our calculation by adopting the results given in[55]forˉp p→ˉDD.But we should say that its in?uence on the observables shown in the present paper is practically negligible.
5Open charm production inˉpd annihilation
Now we present results for D0D?production in antiproton-deuteron annihilation utilizing the formalism and the ele-mentary DN andˉDN amplitudes described above,taking into account the Born diagram of Fig.1a)and the rescat-tering diagram of Fig.1b).For the latter we consider both D?p and D0p scattering in the?nal state.Theˉp n→DˉD threshold on a free nucleon corresponds to the antiproton momentum of roughly6.43GeV/c.The absolute thresh-old for theˉDD production in antiproton-deuteron anni-hilation is at the antiproton momentum of4.55GeV/c. Evidently,close to the reaction threshold the production rate will be strongly suppressed by the phase space.We choose for our calculation the antiproton momentum of 7GeV/c,corresponding to the region where the model calculation of[55]predicts the largest cross sections for the elementaryˉNN→ˉDD reaction.
5.1Spectator momentum distribution
In Fig.7we present our predictions for the spectator proton momentum distribution.Here the solid histogram indicates the full result that includes the Born and the rescattering diagrams while the dashed line is the result based on the nucleon-exchange Born diagram alone,both obtained with the deuteron wave function of the CD Bonn NN potential[37].Since the absolute normalization of the reaction cross section is quite uncertain we show the re-sults as number of generated events.
The dotted and dash-dotted curves are results for the Born term alone employing the deuteron wave functions of the Paris[38]and full Bonn[39]potentials,respectively. Obviously,there is some model dependence which becomes more pronounced for spectator proton momenta above300 MeV/c.But the rescattering mechanism is de?nitely by far the most dominant e?ect for momenta from around400 MeV/c upwards.Since rescattering occurs in both D?p and D0p systems one needs to apply speci?c methods to separate their contributions in a reliable way,as will be discussed below.
In comparison to the multipion production case,cf. Figs.11and12in the Appendix,the enhancement due to the rescattering processes sets in at noticably higher spec-tator momenta and is also less pronounced.It was argued [25,26]that the strong enhancement seen in the
proton Fig.7.Proton momentum spectrum for theˉp d→D0D?p re-action.The dashed(dotted,dash-dotted)line shows the result of a calculation for the nucleon exchange Born diagram only (Eq.(2))based on the s and d-wave parts of the deuteron wave function of the CD Bonn[37](Paris[38],full Bonn[39])NN potential.The solid histogram is the full calculation(for CD Bonn)that includes D0p and D?p rescattering.
8J.Haidenbauer et al.:Charmed meson rescattering in the reactionˉpd→ˉ
DDN
Fig.8.Dalitz plot for theˉp d→D D p reaction.Here,M(ˉDp)and M(DD)are the D p and D D invariant masses,re-spectively.The arrows points in the direction of decreasing intensity of the distribution.Each plot a)-d)is explained in the text.
momentum spectrum for the multipion reactions is to a
good part due to the excitation of the?(1232)resonance
in theπN rescattering processes.Though our DN scat-
tering amplitude is dominated likewise by poles,in several
partial waves,cf.the discussion above,their in?uence on
the momentum spectrum seems to be smaller,presumably
because they all lie below the DN elastic threshold.The
enhancement we get for theˉp d→D0D?p reaction seems to
be somewhat smaller than what was reported in an earlier
model calculation by Cassing et al.[23].But one has to
keep in mind that in the latter work the contribution of
the d-wave component to the Born(spectator)term was
neglected and,moreover,the results for the Born term
and the rescattering term are shown separately,while we
added them coherently in our calculation.
5.2Dalitz plot
A well-known method for the reconstruction of the re-
action dynamics is the Dalitz plot analysis of the?nal
state[33,58–61].For instance,for multi-pion production
fromˉp d annihilation the presence of rescattering e?ects
was demonstrated via the projection of the Dalitz plot on
the invariant mass spectrum of the?nalπp system[32,
62].An analysis in form of a partial wave decomposition
of the Dalitz plot was proposed[58–60]for the pp→pK+Λ
reaction,which?nally allowed to study and separate[61]
non-resonant and resonant contributions in the K+Λsub-
system.A similar technique could be applied in the anal-
ysis of theˉp d→D0D?p reaction.This method allows to
study all subsystems,D0p,D?p and D0D?,but obviously
requires high mass resolution and signi?cant statistics.
Fig.8presents the Dalitz plot evaluated for the reac-
tionˉp d→D0D?p at the antiproton momentum of7GeV/c.
The horizontal axes in the plot indicate the invariant mass
of the D0D?system,while the vertical axes indicate the
mass of the D?p system.Here panel a)shows the results
obtained with the nucleon-exchange Born diagram only,
b)those obtained with D?p rescattering alone,while c)
illustrates the results with D0p FSI alone.Finally,Fig.8d)
contains the full results,i.e.when all three contributions
are included coherently.The arrows in the?gures indi-
cate the direction of decreasing intensity of the distribu-
tion.Note that we implemented a cut on the spectator
proton momentum in the calculations in order to reduce
the contribution from the Born diagram.Speci?cally,we
considered only events involving spectator protons with
momenta above300MeV/c.
Evidently,the di?erences between the distributions re-
sulting from the di?erent diagrams are quite signi?cant.
The result based on the Born term alone indicates strong
correlations between the D0-and D?-meson invariant mass.
This is due to the fact that they are produced from the
same vertex,namely viaˉp n→D0D?.The invariant energy
of the D0D?system is essentially given by the energy of
the incoming antiproton,while the dispersion of the dis-
tribution is related to the square of the deuteron wave
function.Assuming the target neutron to be at rest,the
invariant mass of the D0D?system produced in the re-
actionˉp n→D0D?at antiproton momentum of7GeV/c
is equal to3.86GeV.The strong D0D?correlation pro-
duces also a kinematical re?ection,detectable in the D?p
system,namely in form of an enhancement in the high
mass D?p spectrum.However,this enhancement,being
purely kinematical,does not have any relevance for the
interpretation of the rescattering mechanism.
Results obtained for the rescattering diagrams alone
are shown in Figs.8b)and c).It is clear that there are no
strong correlations in the D0D?system anymore.Now
the spectrum is primarily distorted by the corresponding
rescattering terms.The D?p and D0p projections of the
J.Haidenbauer et al.:Charmed meson rescattering in the reaction ˉpd →ˉDDN
9
Fig.9.The missing mass distribution of P X given by Eq.(18)
for the ˉp d →D 0D ?p reaction.The dashed histogram shows re-sults obtained with the nucleon-exchange Born diagram and the D 0p FSI for spectator proton momenta above 300MeV/c.The solid histogram is the result for the D ?p rescattering di-agram based on Eq.(3).
Dalitz plot show the distribution produced by the relevant scattering amplitudes.
The ?nal distribution,shown in Fig.8d),corresponds to a calculation that includes the Born diagram plus both rescattering diagrams.It is fairly non-uniform and clearly indicates substructures resulting from the individual reac-tion mechanisms.
5.3Missing mass of the exchanged meson
A method [63]that could be useful for the separation of
the ˉDN
and DN rescattering contributions is based on the assumption that the dominant part of the rescattering amplitude comes from contributions where the particles in the intermediate state are on shell.We should emphasize that this method has no physical meaning when it comes to the o?-shell part of the rescattering diagrams because then the exchanged meson is virtual.
Under the assumption that the charmed meson and nucleon are on-shell before undergoing rescattering,one can reconstruct the four-momentum of the meson in the loop following the missing mass technique via
P 2X =(P s +P D ??P N )2,
(18)
where P s and P D ?are the four-momenta of the specta-tor proton and the ?nal D ?meson,and P N is the four-momentum of the nucleon in the loop (i.e.the one involved in the rescattering process),given by the loop momentum q and energy E q as in Eq.(3).Let us assume for the mo-ment that the scattering process takes place on a free nu-cleon at rest.Then we would get P 2
X =m 2D ,where m D is
the mass of the (incoming)D meson.However,since the
reaction does not take place on a free nucleon but on a nucleon from the initial deuteron,the interacting nucleon is not at rest and,therefore,one expects a distribution of the missing mass in Eq.(18)around the central value of m D re?ecting the Fermi motion of the nucleon in the deuteron.
It is clear that the Born term as well as D 0p scatter-ing would not lead to such a distribution because in this case there is no correlation between the four-momenta in Eq.(18).
In Fig.9we present results for the missing mass of the exchanged meson as given by Eq.(18),obtained for the antiproton momentum of 7GeV/c.In the corresponding calculations the Born diagram and the rescattering ampli-tudes according to Eq.(3)are taken into account.Then we evaluate Eq.(18)using the four-momenta of the ?nal spectator proton and of the ?nal D ?-meson,and assume that P N =(m p ,0).The dashed histogram in Fig.9includes contributions from the nucleon-exchange Born diagram for spectator momenta above 300MeV/c as well as from the D 0p FSI.The solid histogram is the result obtained for the D ?p rescattering term.
The results shown in the Fig.9look very promising with regard to the possibility for a separation of the re-action mechanisms.However,one should keep in mind that there are uncertainties due to the on-shell assump-tion made in the model calculation as well as in the eval-uation of the missing mass,which cannot be quanti?ed easily.Nonetheless,we want to mention that this method was actually used in Ref.[63]in the data evaluation and reconstruction of the hyperon production mechanisms in antiproton annihilation on xenon nuclei.Recently,this missing-mass method was also utilized for the analysis of K +K ?pair production from carbon [64].It is important to stress that the method cannot and should not be ap-plied for too high momenta of the spectator proton,where the reaction is dominated by o?-shell contributions and,therefore,the basic assumptions of the method are evi-dently no longer valid.
We have also performed calculations of the missing mass distribution for the corresponding case of a ?nal D 0meson where one can isolate the D 0p rescattering contri-butions.The results are qualitatively very similar to the D ?case and therefore we do not show them here.5.4Correlation between the scattering planes
Finally,we discuss the correlation between the two scat-tering planes [65].One plane is given by the momenta of the antiproton and of the spectator proton.The other one is ?xed by the momenta of the antiproton and of the produced charmed meson,the D ?meson,say.Then,due to the conservation of the transverse momenta in the D ?p →D ?p scattering process the azimuthal angle be-tween these planes is peaked around φ?180?.This cor-relation simply follows from the reaction kinematics.If the spectator proton is at rest before the scattering and the D ?-meson has no transverse momentum,then,after
10
J.Haidenbauer et al.:Charmed meson rescattering in the reaction ˉpd →ˉ
DDN
Fig.10.The distribution of the azimuthal angle between the scattering plane given by the momenta of the antiproton and spectator proton and the plane ?xed by the momenta of the an-tiproton and the D ?-meson.The results are for spectator pro-tons with momenta above 300MeV/c.The upper panel shows the result for the Born diagram alone,while in the lower panel calculations including the D ?p and D 0p rescattering diagrams are presented.Here the solid histogram shows the distribution obtained for rescattering of the D ?-meson,while the dashed histogram is the corresponding result for rescattering of the D 0-meson.
D ?p →D ?p scattering the transverse components of the momenta of the ?nal D ?-meson and proton must be ex-actly the same but aligned in opposite direction.However,both the Fermi motion in the deuteron and the ˉp n →D ?D 0annihilation allow for some variations in the transverse momenta of the spectator proton and of the D ?-meson.That is why in an actual experiment one would expect a distribution of the azimuthal angle around the value φ=180?.
Results of our model calculation for the distribution of the azimuthal angle are presented in Fig.10.They are obtained again by imposing a cut on the spectator pro-ton momentum so that only momenta above 300MeV/c contribute.The scattering plane is ?xed by the momenta of the antiproton and the D ?-meson.The upper panel of Fig.10shows predictions for the nucleon-exchange Born diagram while the lower panel contains results including the rescattering diagrams.Here the solid histogram corre-sponds to the contributions of the D ?p rescattering dia-gram and the dashed histogram to those from D 0p rescat-tering.From these results it seems feasible that the two rescattering contributions can be well isolated.
Also here we have considered the corresponding case for the D 0meson,where again the results turned out to be qualitatively similar.
6Summary
In this paper we examined the possibility to extract in-formation about the DN and ˉDN
interactions from the ˉp d →D 0D ?p reaction.We utilized the notion that those open-charm mesons are ?rst produced by annihilating an-tiprotons on the deuteron and subsequently rescatter on the remaining (spectator)nucleon.The latter process is
then exploited for investigating the DN and ˉDN
interac-tions.To explore the potential of a corresponding exper-iment we performed concrete model calculations taking into account the nucleon-exchange Born diagram as well as rescattering diagrams.
As a test of the approach we ?rst applied it to mul-tipion production in ˉp d annihilation and we compared our results with data available for the ˉp d →π+2π?p and ˉp d →2π+3π?p reactions.These data [66–68]show strong evidence for contributions from πN →πN rescattering,which can be seen in the spectra of the spectator proton and in-variant mass distribution of the ?nal pion and proton.We obtained very reasonable agreement with the data avail-able for the spectator proton distributions.In our investigation of the ˉp d →D 0D ?p reaction we
utilized realistic ˉDN
→ˉDN [20]and DN →DN [21]scat-tering amplitudes.This is a substantial improvement over
previous studies [22–24]which employed simplistic ˉDN
and DN scattering amplitudes based on somewhat ques-tionable assumptions.
We found that below spectator momenta of around 300MeV/c the reaction is dominated by the nucleon-exchange Born diagram.For higher spectator momenta there is a sizable contribution from the rescattering di-agrams.In particular,their contribution is signi?cantly larger than the uncertainties due variations in the high-momentum component of the deuteron wave function.Thus,selecting events with spectator momenta above 300or 400MeV/c,say,should allow to obtain a data sample that can be used for extracting information about the DN and ˉDN
interactions.Subsequently we explored di?erent methods for isolat-ing the contributions from the DN and ˉDN rescatter-ing terms.We showed that the missing mass technique
and the correlation between the planes given by the scat-tered meson and nucleon allow a reasonable reconstruction of the reaction dynamics and to separate the contribu-tions of ˉDN
rescattering from those of DN rescattering.Since these methods are based on the reaction kinematics we consider them as promising tools to extract informa-tion on the ˉDN
and DN interactions from the reaction ˉp d →D 0D ?p .
We appreciate discussions with A.Afanasev,W.Melnitchouk,W.Schweiger,S.Stepanyan,K.Tsushima and B.Wojtsekhowski.This work was ?nancially supported by the Deutsche Forschungs-gemeinschaft (Project no.444BRA-113/14and through funds provided by the SFB/TR 16“Subnuclear Structure of Matter”)and the Brazilian agencies CAPES,CNPq and F APESP.It was also supported in part by the Helmholtz Association through funds provided to the virtual institute “Spin and strong QCD”
J.Haidenbauer et al.:Charmed meson rescattering in the reactionˉpd→ˉDDN11
(VH-VI-231).This research is part of the EU Integrated In-frastructure Initiative Hadron Physics Project under contract number RII3-CT-2004-506078.A.S.acknowledges support by the JLab grant SURA-06-C0452and the COSY FFE grant No. 41760632(COSY-085).
A Multi-pion production inˉpd annihilation
To illustrate the applicability of the discussed formalism we consider experimental data available for the reactions ˉp d→2π+3π?p andˉp d→π+2π?p obtained at the Low En-ergy Antiproton Ring(LEAR)at CERN using annihila-tion at rest in a hydrogen gas[66,67]and at the Brookhaven National Laboratory(BNL)using the deuterium bubble chamber[68].
We calculate the proton spectator distribution by sum-ming the Born and rescattering amplitudes and integrat-ing over the6-body and4-body?nal states.The calcu-lations are done with the deuteron wave function of the CD-Bonn potential[37].Available data[69,70]on pion multiplicities forˉp p annihilation at rest and in?ight show practically no dependence on the antiproton momentum within the range up to?100MeV/c.Therefore,we as-sume the annihilation amplitude T A to be a constant.The spectator proton momentum distribution was measured in di?erent experiments[66–68]and the data were published with arbitrary normalization depending on the total num-ber of detected events.Therefore,we normalize our calcu-lation to the data but we also normalize the di?erent data sets to each other,as explained below.
For evaluating the contribution from pion-nucleon re-scattering we use the current solution of the GWU/CNS partial wave analysis[71,72].We account for isospin and topological factors following the prescription given in Refs.[30,31,35].The phase-space integration is done by the Monte-Carlo method based on event-by-event simu-lations.This allows us to apply kinematical cuts on the ?nal pion momenta similar to that discussed in Refs.[66, 67]in order to investigate discrepancies between the data at spectator proton momenta below250MeV/c.We will come back to this issue later.
Experimental results for the proton momentum distri-bution for the reactionˉp d→2π+3π?p are shown in Fig.11. The squares[66]and circles[67]are data from the LEAR facility while the triangles are from an experiment[68] at the Brookhaven National Laboratory(BNL)using the deuterium bubble chamber.
The basic di?culty in the counter measurements[66, 67]is the reconstruction of the low-momentum part of the spectator spectra.As mentioned in Ref.[66],for the di-rect proton detection at least transverse proton momenta of130MeV/c are required.The very low momentum pro-tons can be only reconstructed through exclusive measure-ments of the?nal pions and applying the missing momen-tum method.But such a reconstruction introduces addi-tional uncertainties in the low momentum spectator spec-tra.To avoid any ambiguity we normalized all data sets at momenta around400MeV/c,i.e.at values where the proton spectator momentum was measured directly.This normalization emphasizes that the shape of the measured spectrum from the di?erent experiments is almost iden-tical at higher spectator proton momenta.On the other hand,we see a substantial disagreement between the avail-able data[66–68]at momenta below?250MeV/c.
Experimental results for the reactionˉp d→π+2π?p are presented in Fig.12.Again,the squares are LEAR data[66] while the triangles are from the BNL[68].Both data sets are normalized at proton momenta around400MeV/c and in such a way that the scale is roughly the same as in Fig.11.This allows us to compare the shapes of the spec-tator proton distributions for the two reactions.There is clearly a di?erence between those shapes forˉp d→2π+3π?p andˉp d→π+2π?p.Indeed one expects that the shape of the spectator momentum distribution depends on the momen-tum carried by the scattering meson and,consequently, that reactions with di?erent?nal pion multiplicity would exhibit di?erent shapes of the proton spectra.The more energetic pions from theˉp d→π+2π?p reaction produce more energetic spectator protons in the rescattering.Qual-itatively this follows from the rescattering amplitude of Eq.(3).
Again,forˉp d→π+2π?p the experimental results are consistent at proton momenta above250MeV/c and dis-agree substantially at low momenta.As already indicated above,we applied kinematical cuts on the?nal pion mo-menta,similar to those discussed in Refs.[66,67],in the course of our investigation for the reactionˉp d→π+2π?p as well as forˉp d→2π+3π?p.But it turned out that those cuts do not resolve the disagreement between the data[66–68] at spectator proton momenta below250
MeV/c.
Fig.11.
action.
[68]
taking into account s-and d-wave parts of the deuteron wave function while the dotted line is based on the s-wave compo-nent alone.The solid histogram is the full calculation including the nucleon exchange Born diagram and rescattering diagrams using the GWU/CNSπN partial-wave amplitudes[71,72]for T M.
12
J.Haidenbauer et al.:Charmed meson rescattering in the reaction ˉpd →ˉ
DDN
Fig.12.Proton momentum spectrum for the ˉp d →π+2π?p
reaction.The data are from Ref.[66](squares)and [68](trian-gles).Same description of curves as in Fig.11.
Let us now come to the results of our model calculation and ?rst discuss the normalization,which is a somewhat delicate issue.From a theoretical point of view it should be done preferrably around the peak in the distribution at low momenta where the spectrum is dominated by the Born diagram and the s -wave component of the deuteron wave function.But this is exactly the region where the experimental uncertainty is very large.Thus,we decided to normalize our results also in the plateau region,i.e.around 400MeV/c.Note that the normalization is done for the full calculation.The relative size of the momen-tum distribution at the peak as compared to the plateau is ?xed by the ingredients of the model alone,i.e.the con-tributions of the Born diagram and from the rescattering diagram.There is no additional normalization constant involved here.
The dashed lines in Figs.11and 12correspond to the contribution from the nucleon-exchange Born diagram given by Eq.(2).Interestingly,our predictions for low mo-menta agree well with the data of [67](for ˉp d →2π+3π?p )and [66](for ˉp d →π+2π?p ).For proton momenta above 200MeV/c all data show a substantial enhancement with respect to the predictions based on the Born term alone.For illustration purposes we show here also results using only the s -wave part of the deuteron wave function (dot-ted line).There have been some speculations that the en-hancement at higher momenta could indicate an excitation of the short range component of the deuteron wave func-tion [73–77].But,in any case,a simple renormalization of the d -wave contribution would not reproduce the ob-served shape of the spectator proton distribution around the plateau,i.e.for p s ?400MeV/c.
The solid histograms in Figs.11and 12are the re-sults of our full calculation including the nucleon-exchange Born diagram and the rescattering diagram.But we should say that the o?-shell corrections of Eq.(6),not considered in the present investigation,are known to lead to varia-
tions of the order of 30%or more in the absolute value of the rescattering contribution,though they do not e?ect the shape of the spectator proton distribution [31].
Our results are in reasonable agreement with that of Ref.[31],but are in contradiction to the conclusions of Ref.[78],where the spectator proton momentum distri-bution is well reproduced by taking into account the Born diagram of Fig.1a)and pion absorption on the spectator nucleon.However,there is strong experimental evidence in favor of the rescattering mechanism:The invariant mass spectrum of the 2π+2π?system from the ˉp d →2π+3π?p reaction was measured [67]for di?erent cuts on the spec-tator proton momenta.If the ?nal pions do not undergo rescattering,such cuts should not change the invariant mass distribution.But in the experiment it turned out that the 2π+2π?invariant mass distribution depends sub-stantially on the proton momentum cut when taken below or above p s =200MeV/c.
References
1.T.Matsui and H.Satz,Phys.Lett.B 178,416(1986).
2.H.Satz,J.Phys.G 32,R25(2006)[arXiv:hep-ph/0512217].
3.S.Batsouli,S.Kelly,M.Gyulassy and J.L.Nagle,Phys.Lett.B 557,26(2003)[arXiv:nucl-th/0212068].
4.M.Djordjevic and M.Gyulassy,Phys.Lett.B 560,37(2003)[arXiv:nucl-th/0302069].
5.N.Armesto,C.A.Salgado and U.A.Wiedemann,Phys.Rev.D 69,114003(2004)[arXiv:hep-ph/0312106].
6.M.Djordjevic and M.Gyulassy,Nucl.Phys.A 733,265(2004)[arXiv:nucl-th/0310076].
7.W.-M.Yao et al.[Particle Data Group],J.Phys.G 33,1(2006)
8.G.D.Moore and D.Teaney,Phys.Rev.C 71,064904(2005)[arXiv:hep-ph/0412346].
9.H.van Hees and R.Rapp,Phys.Rev.C 71,034907(2005)[arXiv:nucl-th/0412015].
10.H.van Hees,V.Greco and R.Rapp,Phys.Rev.C 73,
034913(2006)[arXiv:nucl-th/0508055
11.S.Wicks,M.Djordjevic,C.Horowitz and M.Gyulassy,
Nucl.Phys.A 784,426(2007)[arXiv:nucl-th/0512076].12.S.S.Adler et al.[PHENIX Collaboration],Phys.Rev.Lett.
94,082301(2005)[arXiv:nucl-ex/0409028].
13.J.Bielcik et al.[STAR Collaboration],Nucl.Phys.A 774,
697(2006)[arXiv:nucl-ex/0511005].
14.Y.Zhang et al.[STAR Collaboration],J.Phys.G 32,S529
(2006)[arXiv:nucl-ex/0607011].
15. C.Zhong et al.[STAR Collaboration],J.Phys.G 34,S741
(2007)[arXiv:nucl-ex/0702014].
16.M.Kotulla et al.,Technical Progress Report for ˉP
ANDA,Strong Interaction Studies with Antiprotons ,Febru-ary 2005,http://www-panda.gsi.de/db/papersDB/PC19-050217
tpr.pdf.17.O.N.Hartmann et al.[PANDA Collaboration],Int.J.
Mod.Phys.A 22,578(2007).
18.K.T.Brinkmann,P.Gianotti,I.Lehmann [PANDA
Collaboration],Nucl.Phys.News 16,15(2006)[arXiv:physics/0701090].
19.W.Kuhn [PANDA Collaboration],Acta Phys.Polon.B
37,129(2006).
J.Haidenbauer et al.:Charmed meson rescattering in the reactionˉpd→ˉDDN13
20.J.Haidenbauer,G.Krein,Ulf-G.Mei?ner and A.Sibirtsev,
Eur.Phys.J.A33,107(2007)[arXiv:nucl-th/0704.3668].
21.J.Haidenbauer et al.,in preparation.
22. A.Sibirtsev,K.Tsushima and A.W.Thomas,Eur.Phys.
J.A6,351(1999)[arXiv:nucl-th/9904016].
23.W.Cassing,Y.S.Golubeva and L.A.Kondratyuk,Eur.
Phys.J.A7,279(2000)[arXiv:nucl-th/9911026].
24. A.Sibirtsev,Nucl.Phys.A680,274c(2001).
25. C.G.Fasano and M.P.Locher,Z.Phys.A336,469(1990).
26.V.M.Kolybasov,I.S.Shapiro and Yu.N.Sokolskikh,Phys.
Lett.B222,135(1989).
https://www.wendangku.net/doc/8c14468067.html,get,Phys.Rept.69,1(1981).
28. C.G.Fasano and M.P.Locher,Z.Phys.A338,197(1991).
https://www.wendangku.net/doc/8c14468067.html,get,Nucl.Phys.A296,388(1978).
30.M.P.Locher and B.S.Zou,Z.Phys.A340,187(1991).
31. C.G.Fasano,M.P.Locher and S.Nozawa,Z.Phys.A338,
95(1991).
32. D.V.Voronov and V.M.Kolybasov,JETP Lett.57,162
(1993).
33. E.Byckling and K.Kajantie,Particle Kinematics(Wiley
and Sons,New York,1973).
https://www.wendangku.net/doc/8c14468067.html,get,Phys.Rev.C73,044003(2006).
35.M.P.Locher and B.S.Zou,J.Phys.G19,463(1993).
https://www.wendangku.net/doc/8c14468067.html,get,Phys.Rev.C75,014002(2007)[arXiv:nucl-
th/0603009].
37.R.Machleidt,Phys.Rev.C63,024001(2001)[arXiv:nucl-
th/0006014].
https://www.wendangku.net/doc/8c14468067.html,combe,B.Loiseau,J.M.Richard,R.Vinh Mau,
J.Cote,P.Pires and R.De Tourreil,Phys.Rev.C21,861 (1980).
39.R.Machleidt,K.Holinde,and Ch.Elster,Phys.Rept.149,
1(1987).
40.Z.w.Lin,C.M.Ko and B.Zhang,Phys.Rev.C61,024904
(2000)[arXiv:nucl-th/9905003].
41.J.Hofmann and M.F.M.Lutz,Nucl.Phys.A763,90
(2005)[arXiv:hep-ph/0507071].
42.L.Tolos,J.Scha?ner-Bielich and A.Mishra,Phys.Rev.C
70,025203(2004)[arXiv:nucl-th/0404064].
43.M.F.M.Lutz and C.L.Korpa,Phys.Lett.B633,43
(2006)[arXiv:nucl-th/0510006].
44.T.Mizutani and A.Ramos,Phys.Rev.C74,065201
(2006)[arXiv:hep-ph/0607257].
45.R.B¨u ttgen,K.Holinde,A.M¨u ller–Groeling,J.Speth,and
P.Wyborny,Nucl.Phys.A506,586(1990).
46.M.Ho?mann,J.W.Durso,K.Holinde,B.C.Pearce,and
J.Speth,Nucl.Phys.A593,341(1995).
47. D.Hadjimichef,J.Haidenbauer and G.Krein,Phys.Rev.
C66,055214(2002)[arXiv:nucl-th/0209026].
48.J.Haidenbauer and G.Krein,Phys.Rev.C68,052201
(2003)[arXiv:hep-ph/0309243].
49.L.Tolos,A.Ramos and T.Mizutani,Phys.Rev.C77,
015207(2008)[arXiv:0710.2684[nucl-th]].
50. A.M¨u ller-Groehling,K.Holinde,and J.Speth,Nucl.Phys.
A513,557(1990).
51.M.F.M.Lutz and E.E.Kolomeitsev,Nucl.Phys.A730,
110(2004)[arXiv:hep-ph/0307233].
52.O.Krehl,C.Hanhart,S.Krewald and J.Speth,Phys.Rev.
C62,025207(2000)[arXiv:nucl-th/9911080].
53. A.M.Gasparyan,J.Haidenbauer, C.Hanhart and
J.Speth,Phys.Rev.C68,045207(2003)[arXiv:nucl-th/0307072].
54.P.Kroll,B.Quadder and W.Schweiger,Nucl.Phys.B
316,373(1989).55. A.B.Kaidalov and P.E.Volkovitsky,Z.Phys.C63,517
(1994).
56. B.Kerbikov and D.Kharzeev,Phys.Rev.D51,6103
(1995)[arXiv:hep-ph/9408378].
57.W.Schweiger,private communication.
58. C.Hanhart,Phys.Rept.397,155(2004)[arXiv:hep-
ph/0311341].
59. A.Sibirtsev,J.Haidenbauer,H.-W.Hammer and S.
Krewald,Eur.Phys.J.A27,269(2006)[arXiv:nucl-th/0512059].
60. A.Sibirtsev,J.Haidenbauer,U.-G.Mei?ner Phys.Rev.
Lett.98,039101(2007)[arXiv:hep-ph/0607212].
61.S.Abdel-Samad et al.[COSY-TOF Collaboration]Phys.
Lett.B632,27(2006).
62. A.Sibirtsev,K.Tsushima and A.Faessler,Z.Phys.A354,
215(1996)[arXiv:nucl-th/9511008].
63.V.V.Barmin et al.[DIANA Collaboration],Nucl.Phys.A
683,305(2001).
64.M.Hartmann,Yu.Kiselev et al.[ANKE Collaboration],
COSY Proposal147.
65.Y.S.Golubeva,W.Cassing,L.A.Kondratyuk,A.Sibirtsev
and M.B¨u scher,Eur.Phys.J.A7,(2000)[arXiv:nucl-th/9910028].
66.J.Riedlberger et al.,Phys.Rev.C40,2717(1989).
67.S.Ahmad et al.,IV th LEAR Workshop:Physics at LEAR
with Low-Energy Antiprotons,Villars-sur-Ollon,Switzer-land(1987),edited by C.Amsler et al.,Nucl.Sci.Res.
Conf.Ser.14,447(1988).
68.P.D.Zemany,Z.M.Ma and J.M.Mountz,Phys.Rev.Lett.
38,1443(1977).
69.J.Vandermeulen,Z.Phys.C37,563(1988).
70. C.Amsler,Rev.Mod.Phys.70,1293(1998)[arXiv:hep-
ex/9708025].
71.R.A.Arndt,I.I.Strakovsky and R.L.Workman Phys.Rev.
C52,2120(1995)[arXiv:nucl-th/9505040].
72.R.A.Arndt,W.J.Briscoe,I.I.Strakovsky and R.L.
Workman,Phys.Rev.C74,045205(2006)[arXiv:nucl-th/0605082].
73.P.Benz and P.S¨o ding,Phys.Lett.B52,367(1974).
74.P.J.Mulders and A.W.Thomas,Phys.Rev.Lett.52,1199
(1984).
75.Y.E.Kim and M.Orlowski,Phys.Rev.C29,2299(1984).
76.L.Ya.Glozman,Prog.Part.Nucl.Phys.34123(1995).
77.L.-C.Lu and T.-S.Cheng,Phys.Lett.B386,69(1996).
78. A.E.Kudryavtsev and V.E.Tarasov,Sov.J.Nucl.Phys.
54,36(1991).
The way常见用法
The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because
The way的用法及其含义(二)
The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中
(完整版)the的用法
定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...
“the way+从句”结构的意义及用法
“tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法
不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke.
way 用法
表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法
The way的用法及其含义(一)
The way的用法及其含义（一） 有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析： 一、the way作先行词，后接定语从句 以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started.
way 的用法
way 的用法 【语境展示】 1. Now I’ll show you how to do the experiment in a different way. 下面我来演示如何用一种不同的方法做这个实验。 2. The teacher had a strange way to make his classes lively and interesting. 这位老师有种奇怪的办法让他的课生动有趣。 3. Can you tell me the best way of working out this problem? 你能告诉我算出这道题的最好方法吗？ 4. I don’t know the way (that / in which) he helped her out. 我不知道他用什么方法帮助她摆脱困境的。 5. The way (that / which) he talked about to solve the problem was difficult to understand. 他所谈到的解决这个问题的方法难以理解。 6. I don’t like the way that / which is being widely used for saving water. 我不喜欢这种正在被广泛使用的节水方法。 7. They did not do it the way we do now. 他们以前的做法和我们现在不一样。 【归纳总结】 ●way作“方法，方式”讲时，如表示“以……方式”，前面常加介词in。如例1； ●way作“方法，方式”讲时，其后可接不定式to do sth.，也可接of doing sth. 作定语，表示做某事的方法。如例2，例3；
the-way-的用法讲解学习
t h e-w a y-的用法
The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮.
way的用法总结大全
way的用法总结大全 way的用法你知道多少，今天给大家带来way的用法，希望能够帮助到大家，下面就和大家分享，来欣赏一下吧。 way的用法总结大全 way的意思 n. 道路,方法,方向,某方面 adv. 远远地，大大地 way用法 way可以用作名词 way的基本意思是“路,道,街,径”,一般用来指具体的“路,道路”,也可指通向某地的“方向”“路线”或做某事所采用的手段,即“方式,方法”。way还可指“习俗,作风”“距离”“附近,周围”“某方面”等。 way作“方法,方式,手段”解时,前面常加介词in。如果way前有this, that等限定词,介词可省略,但如果放在句首,介词则不可省略。
way作“方式,方法”解时,其后可接of v -ing或to- v 作定语,也可接定语从句,引导从句的关系代词或关系副词常可省略。 way用作名词的用法例句 I am on my way to the grocery store.我正在去杂货店的路上。 We lost the way in the dark.我们在黑夜中迷路了。 He asked me the way to London.他问我去伦敦的路。 way可以用作副词 way用作副词时意思是“远远地,大大地”,通常指在程度或距离上有一定的差距。 way back表示“很久以前”。 way用作副词的用法例句 It seems like Im always way too busy with work.我工作总是太忙了。 His ideas were way ahead of his time.他的思想远远超越了他那个时代。 She finished the race way ahead of the other runners.她第一个跑到终点,远远领先于其他选手。 way用法例句
the_way的用法大全教案资料
t h e_w a y的用法大全
The way 在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或 in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了 另外，在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的
the way 的用法
The way 的用法 "the way+从句"结构在英语教科书中出现的频率较高, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 一.在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮.
the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms. 从那天起,其他同学是夹着书本来上课,而他们却带着"失败"的思想负担来上课.
The way的用法及其含义(三)
The way的用法及其含义（三） 三、the way的语义 1. the way=as（像） Please do it the way I’ve told you.请按照我告诉你的那样做。 I'm talking to you just the way I'd talk to a boy of my own.我和你说话就像和自己孩子说话一样。 Plant need water the way they need sun light. 植物需要水就像它们需要阳光一样。 2. the way=how（怎样，多么） No one can imagine the way he misses her.没人能够想象出他是多么想念她！ I want to find out the way a volcano has formed.我想弄清楚火山是怎样形成的。 He was filled with anger at the way he had been treated.他因遭受如此待遇而怒火满腔。That’s the way she speaks.她就是那样讲话的。 3. the way=according as （根据） The way you answer the questions, you must be an excellent student.从你回答问题来看，你一定是名优秀的学生。 The way most people look at you, you'd think a trash man was a monster.从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物。 The way I look at it, it’s not what you do that matters so much.依我看，重要的并不是你做什么。 I might have been his son the way he talked.根据他说话的样子，好像我是他的儿子一样。One would think these men owned the earth the way they behave.他们这样行动，人家竟会以为他们是地球的主人。
way的用法
一．Way：“方式”、“方法” 1.表示用某种方法或按某种方式 Do it (in) your own way. Please do not talk (in) that way. 2.表示做某事的方式或方法 It’s the best way of studying [to study] English.。 There are different ways to do [of doing] it. 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句 正：I don’t like the way he spoke. I don’t like the way that he spoke. I don’t like the way in which he spoke.误：I don’t like the way how he spoke. 4. the way 的从句 That’s the way (=how) he spoke. I know where you are from by the way you pronounce my name. That was the way minority nationalities were treated in old China. Nobody else loves you the way(=as) I do. He did not do it the way his friend did. 二．固定搭配 1. In a/one way：In a way he was right. 2. In the way /get in one’s way I'm afraid your car is in the way， If you are not going to help，at least don't get in the way. You'll have to move－you're in my way. 3. in no way Theory can in no way be separated from practice. 4. On the way (to……) Let’s wait a few moments. He is on the way Spring is on the way. Radio forecasts said a sixth-grade wind was on the way. She has two children with another one on the way. 5. By the way By the way，do you know where Mary lives? 6. By way of Learn English by way of watching US TV series. 8. under way 1. Elbow one’s way He elbowed his way to the front of the queue. 2. shoulder one’s way 3. feel one‘s way 摸索着向前走；We couldn’t see anything in the cave, so we had to feel our way out 4. fight/force one’s way 突破。。。而前进The surrounded soldiers fought their way out. 5.. push/thrust one‘s way（在人群中）挤出一条路He pushed his way through the crowd. 6. wind one’s way 蜿蜒前进 7. lead the way 带路，领路；示范 8. lose one‘s way 迷失方向 9. clear the way 排除障碍，开路迷路 10. make one’s way 前进，行进The team slowly made their way through the jungle.
the way的用法大全
在the way+从句中, the way 是先行词, 其后是定语从句.它有三种表达形式:1) the way+that 2)the way+ in which 3)the way + 从句(省略了that或in which),在通常情况下, 用in which 引导的定语从句最为正式,用that的次之,而省略了关系代词that 或in which 的, 反而显得更自然,最为常用.如下面三句话所示,其意义相同. I like the way in which he talks. I like the way that he talks. I like the way he talks. 如果怕弄混淆，下面的可以不看了 另外，在当代美国英语中,the way用作为副词的对格,"the way+从句"实际上相当于一个状语从句来修饰全句. the way=as 1)I'm talking to you just the way I'd talk to a boy of my own. 我和你说话就象和自己孩子说话一样. 2)He did not do it the way his friend did. 他没有象他朋友那样去做此事. 3)Most fruits are naturally sweet and we can eat them just the way they are ----all we have to do is clean or peel them . 大部分水果天然甜润,可以直接食用,我们只需要把他们清洗一下或去皮. the way=according to the way/judging from the way 4)The way you answer the qquestions, you must be an excellent student. 从你回答就知道,你是一个优秀的学生. 5)The way most people look at you, you'd think a trashman was a monster. 从大多数人看你的目光中,你就知道垃圾工在他们眼里是怪物. the way=how/how much 6)I know where you are from by the way you pronounce my name. 从你叫我名字的音调中,我知道你哪里人. 7)No one can imaine the way he misses her. 人们很想想象他是多么想念她. the way=because 8) No wonder that girls looks down upon me, the way you encourage her. 难怪那姑娘看不起我, 原来是你怂恿的 the way =while/when(表示对比) 9)From that day on, they walked into the classroom carrying defeat on their shoulders the way other students carried textbooks under their arms.
“the-way+从句”结构的意义及用法知识讲解
“the way+从句”结构的意义及用法 首先让我们来看下面这个句子： Read the following passage and talk about it with your classmates. Try to tell what you think of Tom and of the way the children treated him. 在这个句子中，the way是先行词，后面是省略了关系副词that 或in which的定语从句。 下面我们将叙述“the way+从句”结构的用法。 1．the way之后，引导定语从句的关系词是that而不是how,因此，<<现代英语惯用法词典>>中所给出的下面两个句子是错误的：This is the way how it happened. This is the way how he always treats me. 2. 在正式语体中，that可被in which所代替；在非正式语体中，that则往往省略。由此我们得到the way后接定语从句时的三种模式：1) the way +that-从句2) the way +in which-从句3) the way +从句 例如：The way(in which ,that) these comrades look at problems is wrong.这些同志看问题的方法不对。
The way(that ,in which)you’re doing it is completely crazy.你这么个干法，简直发疯。 We admired him for the way in which he faces difficulties. Wallace and Darwin greed on the way in which different forms of life had begun.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 This is the way (that) he did it. I liked the way (that) she organized the meeting. 3.the way(that)有时可以与how(作“如何”解)通用。例如： That’s the way (that) she spoke. = That’s how she spoke. I should like to know the way/how you learned to master the fundamental technique within so short a time. 4．the way的其它用法：以上我们讲的都是用作先行词的the way，下面我们将叙述它的一些用法。
定冠词the的12种用法
定冠词the的12种用法 定冠词the 的12 种用法，全知道?快来一起学习吧。下面就和大家分享，来欣赏一下吧。 定冠词the 的12 种用法，全知道? 定冠词the用在各种名词前面，目的是对这个名词做个记号，表示它的特指属性。所以在词汇表中，定冠词the 的词义是“这个，那个，这些，那些”，可见，the 即可以放在可数名词前，也可以修饰不可数名词，the 后面的名词可以是单数，也可以是复数。 定冠词的基本用法： (1) 表示对某人、某物进行特指，所谓的特指就是“不是别的，就是那个!”如： The girl with a red cap is Susan. 戴了个红帽子的女孩是苏珊。 (2) 一旦用到the，表示谈话的俩人都知道说的谁、说的啥。如：
The dog is sick. 狗狗病了。(双方都知道是哪一只狗) (3) 前面提到过的，后文又提到。如： There is a cat in the tree.Thecat is black. 树上有一只猫，猫是黑色的。 (4) 表示世界上唯一的事物。如： The Great Wall is a wonder.万里长城是个奇迹。(5) 方位名词前。如： thenorth of the Yangtze River 长江以北地区 (6) 在序数词和形容词最高级的前面。如： Who is the first?谁第一个? Sam is the tallest.山姆最高。 但是不能认为，最高级前必须加the，如： My best friend. 我最好的朋友。 (7) 在乐器前。如： play the flute 吹笛子
Way的用法
Way用法 A:I think you should phone Jenny and say sorry to her. B:_______. It was her fault. A. No way B. Not possible C. No chance D. Not at all 说明：正确答案是A. No way，意思是“别想！没门！决不！” 我认为你应该打电话给珍妮并向她道歉。 没门！这是她的错。 再看两个关于no way的例句： （1）Give up our tea break? NO way! 让我们放弃喝茶的休息时间？没门儿！ （2）No way will I go on working for that boss. 我决不再给那个老板干了。 way一词含义丰富，由它构成的短语用法也很灵活。为了便于同学们掌握和用好它，现结合实例将其用法归纳如下： 一、way的含义 1. 路线
He asked me the way to London. 他问我去伦敦的路。 We had to pick our way along the muddy track. 我们不得不在泥泞的小道上择路而行。 2. （沿某）方向 Look this way, please. 请往这边看。 Kindly step this way, ladies and gentlemen. 女士们、先生们，请这边走。 Look both ways before crossing the road. 过马路前向两边看一看。 Make sure that the sign is right way up. 一定要把符号的上下弄对。 3. 道、路、街，常用以构成复合词 a highway（公路），a waterway（水路），a railway（铁路），wayside（路边）
way与time的特殊用法
way/time的特殊用法 1、当先行词是way意思为”方式.方法”的时候,引导定语从句的关系词有下列3种形式： Way在从句中做宾语 The way that / which he explained to us is quite simple. Way在从句中做状语 The way t hat /in which he explained the sentence to us is quite simple. 2、当先行词是time时,若time表示次数时,应用关系代词that引导定语从句,that可以省略; 若time表示”一段时间”讲时,应用关系副词when或介词at/during + which引导定语从句 1.Is this factory _______ we visited last year? 2.Is this the factory-------we visited last year? A. where B in which C the one D which 3. This is the last time _________ I shall give you a lesson. A. when B that C which D in which 4.I don’t like the way ________ you laugh at her. A . that B on which C which D as 5.He didn’t understand the wa y ________ I worked out the problem. A which B in which C where D what 6.I could hardly remember how many times----I’ve failed. A that B which C in which D when 7.This is the second time--------the president has visited the country. A which B where C that D in which 8.This was at a time------there were no televisions, no computers or radios. A what B when C which D that