Study of Neutron Emission in Nuclear System Decay For

Study of neutron emission in nuclear system decay for

1H, 2H, 4He, and 12C - Pb collisions at 1-2 AGeV

V.I. Yurevich1, R.M. Yakovlev2, V.G. Lyapin2

1 JINR, Laboratory of high energies, Dubna, Russia

2 V.G. Khlopin Radium institute, St. Petersburg, Russia

Neutron production double differential cross sections for the interactions of 2-GeV p and d, 4-GeV 4He, and 24-GeV 12C ions with Pb nuclei were measured by the TOF method in angular range 30o-150o. The four-component Moving Source Model was applied for the neutron data analyses. The temperature and velocity parameters of the sources corresponding to the decay of highly excited nuclear system are in a good agreement with the results obtained in charged fragment emission studies. The freeze-out temperature for the thermal decay by fragmentation was estimated as Tf = 4.70.3 MeV. The mean neutron multiplicities and beam energy fraction coming to the neutron emission are discussed.

1. Introduction

Neutron emission in intermediate-energy hadron-nucleus and nucleus-nucleus collisions plays an important role in reaction dynamics and energy balance. A motivation to study neutrons is

• the neutrons are emitted at all stages of the nuclear system evolution in decay processes;
• the neutron spectra bring the most direct information about excited nuclear matter properties which is not distorted by the Coulomb interaction as it has place for the charged fragment emission.

Thus, one can expect that by analysis of the neutron production double differential cross sections some unique information on the collision dynamics and reaction mechanisms can be obtained. A basic principle of such experimental data analysis is a selection of main reaction stages with essential contributions to the neutron emission. For this purpose overall picture of nuclear system evolution based on results of experiments and theory can be used.

Traditionally, two mechanisms of neutron production, the pre-equilibrium emission and the evaporation, are considered for low- and medium-energy reactions and next mechanism, the intra-nuclear cascade, is added at higher energies. Such approach was used in [1] for development of three-component Moving Source Model (MSM) and it was applied for fitting of the double differential cross sections of neutron production in the proton-nucleus interactions at intermediate energies up to 3 GeV [2]. A contribution of the elastic and quasi-elastic nucleon-nucleon collisions is important at small angles and it is taken into account by additional Gaussian-like term.

On the other hand, already more than 25 years the MSM is successfully used for analysis of results on charged particle and fragment emission in the hadron-nucleus and nucleus-nucleus collisions at energies from hundred MeV to about 10 GeV per nucleon [3,4]. Basic approach in this analysis is selection of the emission from the participant nucleon region and from the target and projectile spectators. The collisions of GeV protons and light nuclei with heavy nuclei are effective method to prepare equilibrium highly excited nuclear system with small excitation of collective modes. Information obtained in these experiments is extensively used in theoretical studies of the reaction dynamics and it supports the idea about existence of liquid-gas phase transition in the fragmentation process.

Two stages of the hot nuclear system decay were observed in [5-9]. At the earlier stage the moving non-equilibrium hot source is formed in the central interactions following the first collisions in the participant region. The temperature and lifetime of this source are estimated as 18-20 MeV [8] and 25-30 fm/c [7,9] respectively. The energetic low-mass fragments are emitted at this non-equilibrium stage. Further expansion and thermalization up to thermal break-up of the nuclear system takes additional ~40 fm/c [6,9,10]. According to the statistical multifragmentation model [11] remnant with excitation energy ~2-3 MeV/nucleon continues expansion, gets thermal equilibrium and then decays on nucleons and fragments at a moment characterized by the freeze-out temperature Tf . Experimental study of the charged fragment emission gave estimation of the Tf  4-5.5 MeV [5-8,12-15]. Multiplicity and masses of the nuclear fragments depend on the initial excitation, and in a limit of very high excitation the decay to many IMFs occurs (thermal multifragmentation).

It is naturally to expect that both the hot non-equilibrium source and the thermal fragmentation of the excited remnant give an essential contribution to the neutron emission. These sources have to be included to the MSM for the neutron data analysis in accordance with the new experimental and theoretical results. It was a motivation for our attempt to modify the MSM. Certainly, one has to expect that the source parameters found in the analysis of the neutron emission won’t be in contradiction with the values obtained in the studies of charged fragment emission.

Main aim of our investigation is study of the neutron emission mechanisms in the interactions of 2-GeV p and d, 4-GeV 4He, and 24-GeV 12C with Pb nucleus. For this purpose a new approach in the MSM framework was developed. First of all our efforts were focused on search and study of the neutron components corresponding to disintegration of the hot nuclear system by the non-equilibrium and thermal fragmentation decays.

1. Experiment

The measurements of the neutron production double differential cross sections were carried out by the TOF method in the target fragmentation region between 30o and 150o with the relativistic ion beams of the Dubna synchrophasotron. The experimental setup is schematically shown in Fig. 1.

Fig.1. A scheme of the TOF spectrometer: C1-C3 – the scintillation beam counters; T – the Pb target; VC – the scintillation veto counters; D – the neutron detectors.

The neutrons were registered with three types of detectors based on stylben crystals and large volume plastic scintillators. The detector efficiencies were mainly studied in special experiments in wide energy range from 100 keV up to hundreds MeV. The gamma-quanta were rejected by the TOF and pulse-shape discrimination (for the stylben detectors). The charged particles were vetoed by the thin plastic scintillation counters VC placed in front of the neutron detectors. The system of beam counters C1-C3 with thin plastic scintillators was applied for beam monitoring and event triggering. Event selection was produced by trigger used a fast coincidence of pulses from 1) the upstream counters C1and C2 for p and 4He beams and 2) the upstream counters and the veto downstream counter C3 for d and 12C beams. In the last case the veto-signal produced by the downstream counter discriminated interactions with any charged particles for the deuteron beam and with fragment charge Zf > 5 for the carbon beam at angles less 2o to the beam axis. Taking into account the trigger selection of the events the effective reaction cross sections 1.695, 1.77, 2.44, and 3.0 b were used for determination of the mean neutron multiplicities for the reactions p, d, 4He, and 12C + Pb respectively. Detail information about the experiment can be found in [16,17].

1. Development of the Moving Source Model

The modified MSM bases on a picture of the collision dynamics shown in Fig.2 corresponding to our knowledge about this phenomenon. Assumption that the pre-equilibrium emission before the last evaporation stage is the second orderprocess and gives smaller contribution in comparison with other main sources included in the model and shown in the figure is used.

Fig.2. A scheme of the nuclear system decay modes in central and peripheral collisions of GeV hadrons and light nuclei with heavy nuclei used as a base for modification of the MSM.

The source 1 reflects the first nucleon-nucleon interactions as initial stage of the collision. The hot source 2 is formed in the interactions with the dense core of target nucleus in the central collisions. Further nuclear system evolution depends on the excitation energy value. At low, medium and high excitations the formation of excited remnant, the fragmentation to heavy fragment plus some light fragments and nucleons, and the multifragmentation to some IMFs are realized respectively. The excited remnant, heavy fragment, and fission fragments produced in the peripheral and central collisions decay by the evaporation process, and they are joined to the source 4 due to the common decay process and small velocity in the lab. frame. The ejection of neutrons in the fragmentation and multifragmentation processes is reproduced by the source 3. Maximum contribution of the third source (fragmentation) is expected in a neutron energy range between 5 and 20 MeV taking into account the freeze-out temperature Tf ~ 5 MeV found in the charged fragment emission studies.

The MSM is based on the traditional assumption that in a source frame the neutron emission is isotropic with invariant cross section described by the formula

, (1)

where E and – the neutron kinetic energy (MeV) in the lab. frame and the source frame respectively, the neutron momentum p is calculated as – the solid angle, T – the temperature parameter (MeV). The Lorenz transformation to the lab. frame gives the following expression for the four-source model

(2)

where θ – the angle of emitted neutron in the lab. frame. There are three parameters for each the source: the amplitude Ai, the temperature Ti and the velocity i=Vi/c. In accordance with the picture of the decay processes (Fig.2), relations T1T2T3T4 and 1234 between the temperature and velocity parameters of the different sources are expected.

1. Application of the MSM for neutron emission analyses

The developed MSM was applied for analyses of the neutron production double differential cross sections obtained at large angles (θ30o) in our measurement and some other available experiments for p+Pb reaction [18-25]. For this purpose the expression (2) was used for fitting of the data. The fitting procedure consisted of two steps. At the first step the source 3 was excluded from the fitting process. Here we tried to get a good description of the neutron spectra in ranges above 30 MeV by the terms 1 and 2 and below 5 MeV by the term 4. It was found that the best fits corresponded to some underestimation between 5 and 30 MeV. The next step was the fitting with the term 3 stating from the parameters obtained at the step 1. Finally, a perfect agreement in all energy range and for any angle above 30o was reached. The two examples of the fitting for reactions 4-GeV 4He+Pb and 24-GeV 12C+Pb are shown in Fig.3 and Fig.4.

Fig.3. Contributions of the different sources to the neutron production double differential cross sections measured for 4-GeV 4He+Pb at 30о (■) и 60о (○) (a) and for 24-GeV 12C+Pb at 53о(b). The curve numbers correspond to the source numbers.

Fig.4. The fitting of the experimental data on neutron production double differential cross sections measured for the reactions 4-GeV 4He+Pb (a) and 24-GeV 12C+Pb (b) at various angles. The points – the experimental data, the curves – the result of the fitting.

The contributions of the sources 2 and 3 to the neutron production cross section increases with energy and mass of the projectile. In the energy range of incident protons above about 0.5 GeV the temperature parameter values become universal and do not depend on energy. Our measurements with heavier projectiles gave the same results and showed their independence on projectile type as it is presented in Fig. 5.

Fig.5. Energy dependence of the source temperatures found for our data with different projectiles p (○), 2H (∆), 4He () and 12C (□) and for some available data for the reaction p+Pb:  [18],  [19-23], [24], [25].

The obtained temperature and velocity parameters for the sources 2 and 3 have to be compared with the corresponding values found for the non-equilibrium hot source and the thermal equilibrium source in the charged fragment emission studied for similar collisions. The temperature 212 MeV for the hot source 2 obtained in the neutron emission analysis is practically reproduces the result [8] for the reaction 4.8-GeV 3He+Au. In the same work the hot source velocity was measured as ~0.03-0.045 (for Li fragments) that agrees with value 0.04 found for the neutron source 2 for the reaction 4-GeV 4He+Pb.

Study of the neutron emission the thermal fragmentation via the liquid-gas phase transition (the source 3) gives a possibility to estimate the freeze-out temperature Tf. The found value 4.70.3 MeV is perfectly reproduces the results 4.70.4 MeV of the EOS collaboration [6] and 5.00.5 MeV of the ISiS collaboration [8] obtained as the isotope ratio temperature THeDT for the reactions 1-AGeV Au+C and 4.8-GeV 3He+Au respectively. The slope temperature parameters corresponding to the volume emission of fragments with Z=2 in the reactions p+Au and 3He+Au at 2 GeV were estimated in [7] as 4.50.3 MeV and 4.60.5 MeV respectively that also supports the neutron result.The neutron source velocity changes from 0.0025 for protons to 0.007 for carbon projectiles and agrees with the value 0.0060.001 obtained for the thermal equilibrium source of the IMFs formed in the 8.1-GeV p+Au collisions [26]. The similar results were obtained in [5] for the reaction p+Xe in a range of proton energies 1-19 GeV and in [8].

There were many theoretical and experimental attempts to estimate the critical temperature Tc for the nuclear liquid-gas phase transition. The extracted values of Tc for collisions with Au are from 7.6 MeV [27,28] to 17 MeV [29] and lie between the found temperatures for the thermal and hot sources.

The made comparison leads us to the apparent conclusion about the same origin of the hot non-equilibrium and thermal sources for neutrons and charged fragments and shows that the developed MSM gives adequate fit to the neutron experimental data. Here it is important to note that physics of the hot source is not clearly understood yet.

The last de-excitation stage by the neutron evaporation described with the source 4 is characterized by the temperature 1.60.2 MeV that is approximately 50 % higher of the values observed in nuclear reactions at low energies.

1. Mean neutron multiplicity

The mean neutron multiplicity is important characteristic of the neutron emission process is the mean neutron multiplicity in a reaction. For our measurements the neutron production cross sections were calculated by integration of the expression (2) with found parameters over the neutron energy and solid angle. The mean neutron multiplicities shown in Table 1 were derived by division of these values by the effective reaction cross sections given in Section 2. Also, the relative contributions of the sources 2 and 3 are given there.

Table 1. The mean neutron multiplicities and the contributions of the sources 2 and 3 for the studied reactions.

Reaction / Mn
(n/interaction) / Source 2
contribution
(%) / Source 3
contribution
(%)
p+Pb / 21.8±3.4 / 16 / 22
d+Pb / 17.1±3.4 / 14 / 20
4He+Pb / 22.5±3.5 / 19 / 23
12C+Pb / 29.1±4.5 / 16 / 26

The mean neutron multiplicity a bit grows coming from protons to helium and then to carbon ions. The deuterons give the smaller value than the same energy protons but it is needed to note that the difference lies inside the experimental errors. The contributions of the sources 2 and 3 are essential 14-19 % and 20-26 % respectively. Also, one can obtain contributions of these two modes for the neutron emission in central collisions assuming that such collisions take about a half of the reaction cross sections. A simple calculation shows that about 80 % of the emitted neutrons in the central collisions come from these two sources. Here one has to keep in mind that the neutron production at small angles in the elastic, quasi-elastic and projectile fragmentation processes is not taken into account.

Energy dependence of the mean neutron multiplicity was studied on a base of some available results of TOF [19-25,30] and integral measurements [31-33] for the reaction p+Pb in a range from 0.1 to 3 GeV. The TOF data were integrated over the neutron energy and solid angle where for determination of the total mean neutron multiplicity some extrapolations of he experimental results to low- and high-energy ranges were made. The data [31] obtained by the moderation technique were corrected on high-energy neutron leakage. The fitting to these data gave the following expression for the mean neutron multiplicity in the reaction p+Pb and energy range 0.1-3 GeV

, (3)

where Ep is the proton energy in GeV. This dependence together with the experimental results are shown in Fig. 6. The curve (3) is close to the curve produced by the formula from [34] recommended for incident protons with energy up to 2 GeV. These two dependences are extrapolated to higher energy range for a comparison with our data found for the reactions He+Pb and C+Pb. Adding of the neutron production in the elastic, quasi-elastic and projectile fragmentation processes will raise the points corresponding to our results for the reactions He+Pb and C+Pb, and agreement with the extrapolated dependences will become much better.

Fig. 6. A dependence of the mean neutron multiplicities on the beam energy for the reactions with Pb: ○, ∆,, □ – our results for p, d, He, and C beams respectively; and the results of other experiments with proton beam: ■ [19-23],  [24], ▲ [25], ● [30], [31] (corrected on high-energy neutron leakage), [32,33], the solid curve – our fit (3), the dashed curve – the Cugnon’s formula [34].

1. Energy coming to neutron emission

The neutron emission takes an essential part of the projectile energy in the reactions. Estimation of the kinetic energy of the emitted neutrons was performed using the experimental results [19-24,30] for the reaction p+Pb. It was found that the kinetic energy of the neutrons takes on average about 31 % of the incident proton energy in GeV range as it is shown in Fig. 7. The main contribution ~27% is given by the high-energy neutrons with energies above 20 MeV. Estimation of the mean energy coming to the neutron production in the reaction is obtained by adding of the neutron separation energy ~7 MeV and it gives about 40% of the incident proton energy.