BREAK-UP of LIGHT NUCLEI BREAK-UP of LIGHT NUCLEI at INTERMEDIATE ENERGIESat INTERMEDIATE ENERGIES

Prof. Gabriela MartinskProf. Gabriela MartinskááFaculty of Science, University P.J. Šafárik, KošiceFaculty of Science, University P.J. Šafárik, Košice

Colloquium Prof. Dr. Hartmut Machner, Jülich, 26. Januar 2005

1. Introduction1. Introduction

2. Final State Interaction2. Final State Interaction

▪ ▪ isobaric excitationisobaric excitation

▪ ▪ rescattering and rescattering and ccoalescenceoalescence

3. Summary and outlook3. Summary and outlook

▪ ▪ summarysummary

▪ ▪ outlookoutlook

1. Introduction1. IntroductionAim of this talk:Aim of this talk: to present some selected experimental results on the light to present some selected experimental results on the light nuclei pionless break-up reactions, taken by 1m HBC LHE JINR nuclei pionless break-up reactions, taken by 1m HBC LHE JINR irradiated with beam ofirradiated with beam of light nuclei at different momenta. light nuclei at different momenta.

acceleration of light nuclei opened new possibilities for acceleration of light nuclei opened new possibilities for correlations studies using bubble chamber as correlations studies using bubble chamber as a detectora detector

the use of nuclear beams impinging on a fixed proton the use of nuclear beams impinging on a fixed proton target makes all the fragments of the incoming nuclei target makes all the fragments of the incoming nuclei fast and, thus, they can be detected, measured well and fast and, thus, they can be detected, measured well and identified practically without losesidentified practically without loses

these conditions allowed to study the reaction channels these conditions allowed to study the reaction channels containing not more than one neutral particle in containing not more than one neutral particle in exclusiveexclusive approach.approach.

I will discuss the results of different kind of FSI as: I will discuss the results of different kind of FSI as: isobaric excitation isobaric excitation rescattering with coalescence.rescattering with coalescence.

Intermediate inelastic mechanismsIntermediate inelastic mechanisms like like - isobar or pion - isobar or pion production and absorption were predicted many years ago in production and absorption were predicted many years ago in works of works of Watson K.M. (Phys. Rev., 88 (1952),1163) and Migdal A.B. Watson K.M. (Phys. Rev., 88 (1952),1163) and Migdal A.B.

ZhETF, 28 (1955)3ZhETF, 28 (1955)3 . .

Rescattering with coalescenceRescattering with coalescence was first time proposed in work was first time proposed in work Butler S.T., Pearson C.A. (Phys. Rev. Lett. 5,(1960) 276, ibid 7 (1962)69)Butler S.T., Pearson C.A. (Phys. Rev. Lett. 5,(1960) 276, ibid 7 (1962)69) to to explain the enhanced deuteron and tritium production from explain the enhanced deuteron and tritium production from high energy proton-nuclei collisions. high energy proton-nuclei collisions.

2. Final State Interaction2. Final State InteractionIsobaric excitationIsobaric excitation

It has been shown that :It has been shown that : simple models of the impulse approximation class (one simple models of the impulse approximation class (one

pole mechanism) reproduce well the spectatorpole mechanism) reproduce well the spectator momentum distribution at small momenta up to 100-momentum distribution at small momenta up to 100-300 MeV/c, depending on the nuclei.300 MeV/c, depending on the nuclei.

the slope of the differential cross section (four-the slope of the differential cross section (four-momentum transfer squared from the initial proton to momentum transfer squared from the initial proton to the fastest nucleon) for the studied reaction is of the the fastest nucleon) for the studied reaction is of the order of order of 5 (GeV/c)5 (GeV/c)–2–2 – close to that of NN elastic – close to that of NN elastic scattering also gives evidence in the favour of scattering also gives evidence in the favour of spectator mechanism. spectator mechanism.

in the high momentum tail of the slowest nucleonin the high momentum tail of the slowest nucleon spectra significant excess has been observed in spectra significant excess has been observed in the experimental data compared to the computed the experimental data compared to the computed ones, obtained in impulse approximation with ones, obtained in impulse approximation with different wave functions.different wave functions.

the momentum region over 200 MeV/c contains the momentum region over 200 MeV/c contains 16%16% respectively respectively 27%27% events in the charge retention and charge events in the charge retention and charge exchange channels, considerably higher than the exchange channels, considerably higher than the predictions with any wave function (e.g. in the case of predictions with any wave function (e.g. in the case of Gartenhaus-Moravcsik wave function Gartenhaus-Moravcsik wave function 8%8%).).

pd pd ->-> ppn at 1.67 GeV/c ppn at 1.67 GeV/c

––– ––– charge exchange channelcharge exchange channel

- - - charge retention channel- - - charge retention channel

Similar behaviour was observed for Similar behaviour was observed for 44Hep or Hep or 33Hep Hep interactions as in shown on the next picture. The interactions as in shown on the next picture. The curve represents Bassel- Wilkin wave functioncurve represents Bassel- Wilkin wave function

To explain this discrepansy we need some additional  mechanism To explain this discrepansy we need some additional  mechanism to produce high spectator momenta over the impulse to produce high spectator momenta over the impulse aproximation. This can be provided by aproximation. This can be provided by virtualvirtual - production- production. One . One of the first FSI theoretical calculation including of the first FSI theoretical calculation including production production was done by was done by Alberi G. and Baldracchini F.Alberi G. and Baldracchini F. in paper J.Phys. G: in paper J.Phys. G: Nucl. Phys. 4 (1978)665Nucl. Phys. 4 (1978)665. .

The spectator momentum forThe spectator momentum for

pd → ppn charge exchange pd → ppn charge exchange channel at 1.67 GeV/c. channel at 1.67 GeV/c.

- the dashed curve is the - the dashed curve is the spectator model with the Reid spectator model with the Reid wave function,wave function,

- the full curve is the complete - the full curve is the complete theory which involves theory which involves - - productionproduction..

Examples of some diagrams included Examples of some diagrams included are:are:

These diagrams illustrate These diagrams illustrate intermediate intermediate - production- production and consecutive absorption for and consecutive absorption for charge exchange and charge-retention channels.charge exchange and charge-retention channels.

Influence of intermediate Influence of intermediate production we also could see in proton ( ) production we also could see in proton ( ) and neutron ( ) invariant cross section for different production angles and neutron ( ) invariant cross section for different production angles in the backward hemisphere.in the backward hemisphere.

From an isospin analysis performed for the reaction From an isospin analysis performed for the reaction pd → ppnpd → ppn under under the assumption that it proceeds exclusively through the formation and the assumption that it proceeds exclusively through the formation and absorption of an absorption of an intermediate intermediate isobar isobar ,it was found that the ratio of ,it was found that the ratio of the yields of the slowest protons to neutrons is 5. the yields of the slowest protons to neutrons is 5. Kopeliovich V.B., Radomanov V.B., communication JINR P1-90-584, Dubna Kopeliovich V.B., Radomanov V.B., communication JINR P1-90-584, Dubna (1990); (1990);

Kopeliovich V.B., Phys.Report 139 (1986)51Kopeliovich V.B., Phys.Report 139 (1986)51

Similar effect was seeen in Similar effect was seeen in 44HepHep interactions studied at two momenta interactions studied at two momenta – 2.15 – 2.15 A GeV/c A GeV/c and and 3.4 A GeV/c3.4 A GeV/c. In the following figures inclusive invariant cross . In the following figures inclusive invariant cross sections are shown for protons and neutrons from pionless and pion sections are shown for protons and neutrons from pionless and pion containing channels at the two studied enegies.containing channels at the two studied enegies.

in pion containing channels (o) in pion containing channels (o) the spectra the spectra are approximately exponentialare approximately exponentialthe pionless channels cannot (x) be decribed by simple exponentional the pionless channels cannot (x) be decribed by simple exponentional functionfunction

the effect is again more pronounced for protons (a) than for the neutrons (b)the effect is again more pronounced for protons (a) than for the neutrons (b)

a - protonsa - protons

b - neutronsb - neutrons

at higher energies, beyond the at higher energies, beyond the -production maximum the -production maximum the structure in pionless channel becomes less visible (at higher structure in pionless channel becomes less visible (at higher energy - energy - 3.4 GeV/c3.4 GeV/c the the ++++ and and +-+- production cross section is production cross section is four time smaller than at lower energy - four time smaller than at lower energy - 2.15 GeV/c2.15 GeV/c).).

Rescattering and coalescenceRescattering and coalescence

In the frame of simple impulse approximation In the frame of simple impulse approximation we wait factorization for two vertices of we wait factorization for two vertices of quasielastic scattering diagram and isotropic quasielastic scattering diagram and isotropic Treiman-Yang angular distribution. But it is Treiman-Yang angular distribution. But it is valid only up to 50-70 MeV/c of Fermi motion valid only up to 50-70 MeV/c of Fermi motion momentum. More complete systematical momentum. More complete systematical investigations of the Treiman-Yang investigations of the Treiman-Yang asymmetry led to the observation of a strong asymmetry led to the observation of a strong angular dependence on the spectator angular dependence on the spectator momentum.momentum.

The kinematics of the deuteron break-up reaction The kinematics of the deuteron break-up reaction is presented in figis presented in figureure..

Here Here k k is momentum of the projectile is momentum of the projectile proton, proton, pp33 is momentum of the fastest is momentum of the fastest nucleon. The slowest nucleon is nucleon. The slowest nucleon is considered to be the spectator. The considered to be the spectator. The angle angle , between the spectator , between the spectator momentum momentum ppss and the three- and the three- momentummomentum q q transferred from the transferred from the incoming to the fastest nucleon, has incoming to the fastest nucleon, has been used in the theoretical description been used in the theoretical description of the final state interaction.of the final state interaction.

s

s

pq

pq

cos

To summarize the information on the angular distribution, we use an asymmetry parameter expressed in the following form To summarize the information on the angular distribution, we use an asymmetry parameter expressed in the following form

The asymmetry distribution for the The asymmetry distribution for the charge retentioncharge retention channel of the channel of the

dp dp →→ ppnppn reaction together with theoretical curves ( reaction together with theoretical curves (Ladygina N.B. et al.: Yad. Fiz. 59 (1996) 2207Ladygina N.B. et al.: Yad. Fiz. 59 (1996) 2207) are presented ) are presented in next in next figfigureure over a wide range of over a wide range of the spectator momenta for different intervals of the four-momentum transfer squared from the incident to the fastest nucleon. the spectator momenta for different intervals of the four-momentum transfer squared from the incident to the fastest nucleon.

)90()90(

)90()90(

NN

NNA

- - - impulse approximation without IKS- - - impulse approximation without IKS

––––––- impulse approximation with IKS- impulse approximation with IKS

The statistics in the The statistics in the 33HepHep and and 44HepHep are smaller are smaller than in the dp experiment, so the behaviour of the than in the dp experiment, so the behaviour of the asymmetry parameter only up to asymmetry parameter only up to 350 MeV/c350 MeV/c of the of the spectator momenta can be compared. This spectator momenta can be compared. This comparison is presented comparison is presented on followingon following figurefigure for for three different pionless reactions.three different pionless reactions.

The asymmetry The asymmetry dependence on dependence on spectator momenta spectator momenta shows similar tendency shows similar tendency for different initial light for different initial light nuclei.nuclei.

Analysis of pd and pHe Analysis of pd and pHe reactionreaction show that part of the non show that part of the non spectator nuclei like d,t, spectator nuclei like d,t, 33He was produced via coalescence He was produced via coalescence mechanism. In papers by mechanism. In papers by WatsonWatson, , ButlerButler and and PearsonPearson was was shown that light nuclei can be produced with high shown that light nuclei can be produced with high probability via coalescence from particles with small probability via coalescence from particles with small relative momenta. relative momenta.

Some possible diagrams for the FSI with coalescence are Some possible diagrams for the FSI with coalescence are displayed in the following figure.displayed in the following figure.

We can demonstrate the contribution of different mechanisms into e.g. deuteron We can demonstrate the contribution of different mechanisms into e.g. deuteron production production ((in in 44HHepep collisions at 8.6 GeV/c collisions at 8.6 GeV/c )) on their inclusive spectra in the forward on their inclusive spectra in the forward and backward and backward hhemispheres.emispheres.

From an exponential function fitted to the invariant differential cross sections of the From an exponential function fitted to the invariant differential cross sections of the deuterons in the backward direction one obtains the slope value deuterons in the backward direction one obtains the slope value B = 16.4 ± 0.2 B = 16.4 ± 0.2 (GeV/c)(GeV/c)-1-1 (χ (χ22/ndf= 1.4). For the forward direction a sum of the exponentials was /ndf= 1.4). For the forward direction a sum of the exponentials was fitted to the data with the following results fitted to the data with the following results B1 = 13.3 ± 0.2 (GeV/c)B1 = 13.3 ± 0.2 (GeV/c)--11, , B2 = 3.2 ± 0.1 B2 = 3.2 ± 0.1 (GeV/c)(GeV/c)-1-1 (χ (χ22/ndf= 1.3)/ndf= 1.3)

3. Summary and outlook3. Summary and outlookSummarySummary

Experimental investigation in the beams of accelerated light nuclei in Experimental investigation in the beams of accelerated light nuclei in the full solid angle geometry allowed to study different kinds of FSI. the full solid angle geometry allowed to study different kinds of FSI. It is shown that:It is shown that:

in addition to the predominant one-nucleon exchange mechanismin addition to the predominant one-nucleon exchange mechanism

FSI gives remarkable contribution to the angular asymmetry in theFSI gives remarkable contribution to the angular asymmetry in the dp → ppndp → ppn, , 33Hep → dppHep → dpp and and 44Hep → Hep → 33HepnHepn pionless reactions at pionless reactions at incoming energies of incoming energies of (1 – 4) GeV(1 – 4) GeV per nucleon. per nucleon.

FSI with coalescence weakly depends on the reaction energy and itFSI with coalescence weakly depends on the reaction energy and it is determined only by the relative energy of the produced particles.is determined only by the relative energy of the produced particles.

Inelastic intermediate excitations depends on the reaction energyInelastic intermediate excitations depends on the reaction energy

OutlookOutlook Based on experimental results from dp- interaction (statistics Based on experimental results from dp- interaction (statistics around 10around 1055 events) new experiments was proposed and events) new experiments was proposed and simulated:simulated:

““The estimation of the spin-dependent The estimation of the spin-dependent np → pnnp → pn amplitude amplitude from charge exchange reaction from charge exchange reaction dp → n(pp)dp → n(pp)””

Within the framework of impulse approximation simple Within the framework of impulse approximation simple connection between the cross sections of the connection between the cross sections of the dp → n(pp)dp → n(pp) charge exchange and the spin dependent part of the charge exchange and the spin dependent part of the elementary elementary np → pnnp → pn reactions, for the case of small four- reactions, for the case of small four-momentum transfer squared │t│≈0 gives momentum transfer squared │t│≈0 gives ((N.W.Dean, Phys. N.W.Dean, Phys. Rev. D5, (1972)461Rev. D5, (1972)461))

The proposed method is model dependent and the above equation is The proposed method is model dependent and the above equation is valid under the following assumptions:valid under the following assumptions:

small momentum transfer in quasielastic np scatteringsmall momentum transfer in quasielastic np scattering

(from initial proton to final neutron) and (from initial proton to final neutron) and small intrisic nucleons momenta in the deuteron.small intrisic nucleons momenta in the deuteron.

Both conditions can be fulfilled simultaneously, if one select events in Both conditions can be fulfilled simultaneously, if one select events in the laboratory frame containing two fast protons the laboratory frame containing two fast protons

at small production angles with respect to the incomingat small production angles with respect to the incoming

deuteron momenta and deuteron momenta and with momenta close to half that of the deuteron.with momenta close to half that of the deuteron.

The differential cross-section of the deuteron charge exchange The differential cross-section of the deuteron charge exchange reaction in the region of small │t│is shown in folowing figure reaction in the region of small │t│is shown in folowing figure together with the curve corresponding to a fit of together with the curve corresponding to a fit of dd/dt = d/dt = d/dt /dt (t=0)(t=0) exp(bt)exp(bt) . .

As a result the spin dependent part of elementary As a result the spin dependent part of elementary np np pn pn was was estimated as estimated as 0.94 ± 0.150.94 ± 0.15..

On the basis of these results new counter experiments have On the basis of these results new counter experiments have been realized. Experiment STRELA at the Nuclotron JINR been realized. Experiment STRELA at the Nuclotron JINR Dubna and the other on the ANKE using the inner beam of Dubna and the other on the ANKE using the inner beam of COSY Juelich. COSY Juelich.

Part of STRELA set-up is shown in the figure. The experiments Part of STRELA set-up is shown in the figure. The experiments is in progress.is in progress.

Thanks for your Thanks for your

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