BREAK-UP of LIGHT NUCLEI at INTERMEDIATE ENERGIES Prof. Gabriela Martinská Faculty of Science, University P.J. Šafárik, Košice Colloquium Prof. Dr. Hartmut Machner, Jülich, 26. Januar 2005

1. Introduction 2. Final State Interaction ▪ isobaric excitation ▪ isobaric excitation ▪ rescattering and coalescence ▪ rescattering and coalescence 3. Summary and outlook ▪ summary ▪ summary ▪ outlook ▪ outlook

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

acceleration of light nuclei opened new possibilities for correlations studies using bubble chamber as a detector acceleration of light nuclei opened new possibilities for correlations studies using bubble chamber as a detector the use of nuclear beams impinging on a fixed proton target makes all the fragments of the incoming nuclei fast and, thus, they can be detected, measured well and identified practically without loses the use of nuclear beams impinging on a fixed proton target makes all the fragments of the incoming nuclei fast and, thus, they can be detected, measured well and identified practically without loses these conditions allowed to study the reaction channels containing not more than one neutral particle in exclusive approach. these conditions allowed to study the reaction channels containing not more than one neutral particle in exclusive approach.

I will discuss the results of different kind of FSI as: isobaric excitation isobaric excitation rescattering with coalescence. rescattering with coalescence. Intermediate inelastic mechanisms like  - isobar or pion production and absorption were predicted many years ago in works of Watson K.M. (Phys. Rev., 88 (1952),1163) and Migdal A.B. ZhETF, 28 (1955)3. Rescattering with coalescence was first time proposed in work Butler S.T., Pearson C.A. (Phys. Rev. Lett. 5,(1960) 276, ibid 7 (1962)69) to explain the enhanced deuteron and tritium production from high energy proton-nuclei collisions.

2. Final State Interaction Isobaric excitation It has been shown that : It has been shown that : simple models of the impulse approximation class (one pole mechanism) reproduce well the spectator momentum distribution at small momenta up to MeV/c, depending on the nuclei. simple models of the impulse approximation class (one pole mechanism) reproduce well the spectator momentum distribution at small momenta up to MeV/c, depending on the nuclei. the slope of the differential cross section (four- momentum transfer squared from the initial proton to the fastest nucleon) for the studied reaction is of the order of 5 (GeV/c) –2 – close to that of NN elastic scattering also gives evidence in the favour of spectator mechanism. the slope of the differential cross section (four- momentum transfer squared from the initial proton to the fastest nucleon) for the studied reaction is of the order of 5 (GeV/c) –2 – close to that of NN elastic scattering also gives evidence in the favour of spectator mechanism.

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

the momentum region over 200 MeV/c contains 16% respectively 27% events in the charge retention and charge exchange channels, considerably higher than the predictions with any wave function (e.g. in the case of Gartenhaus-Moravcsik wave function  8%). the momentum region over 200 MeV/c contains 16% respectively 27% events in the charge retention and charge exchange channels, considerably higher than the predictions with any wave function (e.g. in the case of Gartenhaus-Moravcsik wave function  8%). pd -> ppn at 1.67 GeV/c ––– charge exchange channel charge retention channel

Similar behaviour was observed for 4 Hep or 3 Hep interactions as in shown on the next picture. The curve represents Bassel- Wilkin wave function

To explain this discrepansy we need some additional mechanism to produce high spectator momenta over the impulse aproximation. This can be provided by virtual  - production. One of the first FSI theoretical calculation including  production was done by Alberi G. and Baldracchini F. in paper J.Phys. G: Nucl. Phys. 4 (1978)665. To explain this discrepansy we need some additional mechanism to produce high spectator momenta over the impulse aproximation. This can be provided by virtual  - production. One of the first FSI theoretical calculation including  production was done by Alberi G. and Baldracchini F. in paper J.Phys. G: Nucl. Phys. 4 (1978)665. The spectator momentum for pd → ppn charge exchange channel at 1.67 GeV/c. - the dashed curve is the spectator model with the Reid wave function, - the full curve is the complete theory which involves  - production.

Examples of some diagrams included are: Examples of some diagrams included are: These diagrams illustrate intermediate  - production and consecutive absorption for charge exchange and charge-retention channels.

Influence of intermediate  production we also could see in proton ( ) and neutron ( ) invariant cross section for different production angles in the backward hemisphere. From an isospin analysis performed for the reaction pd → ppn under the assumption that it proceeds exclusively through the formation and absorption of an intermediate  isobar,it was found that the ratio of the yields of the slowest protons to neutrons is 5. Kopeliovich V.B., Radomanov V.B., communication JINR P , Dubna (1990); Kopeliovich V.B., Phys.Report 139 (1986)51

Similar effect was seeen in 4 Hep interactions studied at two momenta – 2.15 A GeV/c and 3.4 A GeV/c. In the following figures inclusive invariant cross sections are shown for protons and neutrons from pionless and pion containing channels at the two studied enegies. Similar effect was seeen in 4 Hep interactions studied at two momenta – 2.15 A GeV/c and 3.4 A GeV/c. In the following figures inclusive invariant cross sections are shown for protons and neutrons from pionless and pion containing channels at the two studied enegies. in pion containing channels (o) the spectra are approximately exponential in pion containing channels (o) the spectra are approximately exponential the pionless channels cannot (x) be decribed by simple exponentional function the pionless channels cannot (x) be decribed by simple exponentional function 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 - protons b - neutrons

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

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

The kinematics of the deuteron break-up reaction is presented in figure. The kinematics of the deuteron break-up reaction is presented in figure. Here k is momentum of the projectile proton, p 3 is momentum of the fastest nucleon. The slowest nucleon is considered to be the spectator. The angle , between the spectator momentum p s and the three- momentum q transferred from the incoming to the fastest nucleon, has been used in the theoretical description of the final state interaction.

To summarize the information on the angular distribution, we use an asymmetry parameter expressed in the following form The asymmetry distribution for the charge retention channel of the dp → ppn reaction together with theoretical curves (Ladygina N.B. et al.: Yad. Fiz. 59 (1996) 2207) are presented in next figure over a wide range of the spectator momenta for different intervals of the four- momentum transfer squared from the incident to the fastest nucleon.

- - - impulse approximation without IKS –––- impulse approximation with IKS

The statistics in the 3 Hep and 4 Hep are smaller than in the dp experiment, so the behaviour of the asymmetry parameter only up to 350 MeV/c of the spectator momenta can be compared. This comparison is presented on following figure for three different pionless reactions. The asymmetry dependence on spectator momenta shows similar tendency for different initial light nuclei.

Analysis of pd and pHe reaction show that part of the non spectator nuclei like d,t, 3 He was produced via coalescence mechanism. In papers by Watson, Butler and Pearson was shown that light nuclei can be produced with high probability via coalescence from particles with small relative momenta. Analysis of pd and pHe reaction show that part of the non spectator nuclei like d,t, 3 He was produced via coalescence mechanism. In papers by Watson, Butler and Pearson was shown that light nuclei can be produced with high probability via coalescence from particles with small relative momenta. Some possible diagrams for the FSI with coalescence are displayed in the following figure. Some possible diagrams for the FSI with coalescence are displayed in the following figure.

We can demonstrate the contribution of different mechanisms into e.g. deuteron production (in 4 Hep collisions at 8.6 GeV/c ) on their inclusive spectra in the forward and backward hemispheres. We can demonstrate the contribution of different mechanisms into e.g. deuteron production (in 4 Hep collisions at 8.6 GeV/c ) on their inclusive spectra in the forward and backward hemispheres. From an exponential function fitted to the invariant differential cross sections of the deuterons in the backward direction one obtains the slope value B = 16.4 ± 0.2 (GeV/c) -1 (χ 2 /ndf= 1.4). For the forward direction a sum of the exponentials was fitted to the data with the following results B1 = 13.3 ± 0.2 (GeV/c) -1, B2 = 3.2 ± 0.1 (GeV/c) -1 (χ 2 /ndf= 1.3) From an exponential function fitted to the invariant differential cross sections of the deuterons in the backward direction one obtains the slope value B = 16.4 ± 0.2 (GeV/c) -1 (χ 2 /ndf= 1.4). For the forward direction a sum of the exponentials was fitted to the data with the following results B1 = 13.3 ± 0.2 (GeV/c) -1, B2 = 3.2 ± 0.1 (GeV/c) -1 (χ 2 /ndf= 1.3)

3. Summary and outlook Summary 3. Summary and outlook Summary Experimental investigation in the beams of accelerated light nuclei in the full solid angle geometry allowed to study different kinds of FSI. It is shown that: in addition to the predominant one-nucleon exchange mechanism in addition to the predominant one-nucleon exchange mechanism FSI gives remarkable contribution to the angular asymmetry in the FSI gives remarkable contribution to the angular asymmetry in the dp → ppn, 3 Hep → dpp and 4 Hep → 3 Hepn pionless reactions at dp → ppn, 3 Hep → dpp and 4 Hep → 3 Hepn pionless reactions at incoming energies of (1 – 4) GeV per nucleon. incoming energies of (1 – 4) GeV per nucleon. FSI with coalescence weakly depends on the reaction energy and it FSI 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 energy Inelastic intermediate excitations depends on the reaction energy

Outlook Based on experimental results from dp- interaction (statistics around 10 5 events) new experiments was proposed and simulated: “The estimation of the spin-dependent np → pn amplitude from charge exchange reaction dp → n(pp)” Within the framework of impulse approximation simple connection between the cross sections of the dp → n(pp) charge exchange and the spin dependent part of the elementary np → pn reactions, for the case of small four-momentum transfer squared │ t │ ≈0 gives (N.W.Dean, Phys. Rev. D5, (1972)461)

The proposed method is model dependent and the above equation is valid under the following assumptions: small momentum transfer in quasielastic np scattering small 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 the laboratory frame containing two fast protons at small production angles with respect to the incoming at 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 reaction in the region of small │ t │ is shown in folowing figure together with the curve corresponding to a fit of d  /dt = d  /dt (t=0) exp(bt). As a result the spin dependent part of elementary np  pn was estimated as 0.94 ± 0.15.

On the basis of these results new counter experiments have been realized. Experiment STRELA at the Nuclotron JINR Dubna and the other on the ANKE using the inner beam of COSY Juelich. Part of STRELA set-up is shown in the figure. The experiments is in progress.

Thanks for your Thanks for your  attention 