Light Particle Multiplicities Research Articles

Investigation of the nuclear liquid-gas phase transition in the static AMD

Nuclear liquid-gas phase transitions are investigated in the framework of static antisymmetrized molecular dynamics (static AMD) model under either a constant volume or a constant pressure. A deuteron quadrupole momentum fluctuation thermometer is applied to extract the temperature of fragmenting systems of 36Ar and 100Sn. A plateau structure of caloric curves is observed under a constant volume for those system with a density ρ ⩽ 0.03 fm−3. A clear backbending in the caloric curves, which indicates a first order phase transition, is observed under a constant pressure with all pressures studied. The similar behavior of caloric curves of 36Ar and 100Sn systems indicates that there is no strong system size effect under a constant volume or a constant pressure. Both the mass distributions and the light particle multiplicities show a strong α clusterization at low excitation energies in the static AMD simulations. The liquid-gas phase transition measures of the multiplicity derivative (dM/dT) and the normalized variance of Z max (NVZ) are applied. The experimental caloric curves are also compared with those of 100Sn of the static AMD simulations under both the constant volume and the constant pressure conditions. Discussions are presented with the available experimental results and those from the static AMD simulations. Large errors in the experimental temperature measurements and those in the reconstruction technique for the primary fragmenting source hinder to draw a conclusion whether the phase transition occurs under either a constant volume or a constant pressure. This study suggests that different measures for the liquid-gas phase transitions should be examined besides the caloric curves in order to draw a conclusion.

Backstreaming effects on probing postsaddle dissipation with light particle multiplicity

Nuclear dissipation retards fission. Using the stochastic Langevin model, we study pre- and post-saddle emitted neutrons, protons and α particles of heavy 245Cf nuclei as a function of the postsaddle dissipation strength (β) in the absence and presence of backstreaming around the saddle point. It is shown that the backstreaming effects (BEs) cause the fissioning system to return back inside saddle, which increases presaddle light particles but decreases postsaddle emission. Moreover, the BEs on pre- and post-saddle evaporation are found to become greater with increasing β and excitation energy. These findings demonstrate a significant role of BEs in tightly constraining the postsaddle dissipation strength with light particle multiplicity. Furthermore, we analyze the measured prescission neutron number in the reaction 16O (Elab=104 MeV) +232Th ⟶248Cf, and find that, after accounting for the BEs, the best-fit value of the β required to satisfactorily describe the experimental data changes from 9.6 ×1021 s−1 to 6×1021 s−1, showing a strong influence of backstreaming on accurately probing the postsaddle dissipation strength.

Probing postsaddle dissipation with light-particle multiplicity of hot heavy nuclear systems

Probing postsaddle dissipation with light-particle multiplicity of hot heavy nuclear systems

Exploring postsaddle nuclear dissipation with light-particle multiplicity at high energy

Exploring postsaddle nuclear dissipation with light-particle multiplicity at high energy

The role of isospin in fusion evaporation reactions

The isospin dependence of the level density, both through the level density parameter and the symmetry energy contribution has been evaluated. The effects on the most relevant observables in fusion evaporation reactions have been estimated by using the statistical model. We present here the results for the 134Sn +4 He reaction, whose measurement will be possible with the second generation RIB facilities SPES and SPIRAL2. Sizeable effects are predicted on the light particle energy spectra and multiplicities and evaporation residue distribution. In particular, the measure of evaporation residue yields and light particle multiplicities are expected to unfold the two effects. In addition, the same calculations have been carried out for reactions induced by stable beams, in order to search for clues of isospin effects. In this case, the direct comparison of the experimental light charged particle energy spectra for the two reactions 7Li+58,64Ni at the same excitation energy and angular momentum, is proposed as a good approach to observe isospin effects.

THE SYMMETRY ENERGY IN NUCLEAR REACTIONS

New results for the strength of the symmetry energy are presented which illustrate the complementary aspects encountered in reactions probing nuclear densities below and above saturation. A systematic study of isotopic effects in spectator fragmentation was performed at the ALADIN spectrometer with 124 Sn primary and 107 Sn and 124 La secondary beams of 600 MeV/nucleon incident energy. The analysis within the Statistical Fragmentation Model shows that the symmetry-term coefficient entering the liquid-drop description of the emerging fragments decreases significantly as the multiplicity of fragments and light particles from the disintegration of the produced spectator systems increases. Higher densities were probed in the FOPI/LAND study of nucleon and light-particle flows in central and mid-peripheral collisions of 197 Au +197 Au nuclei at 400 MeV/nucleon incident energy. From the comparison of the measured neutron and hydrogen squeeze-out ratios with predictions of the UrQMD model a moderately soft symmetry term with a density dependence of the potential term proportional to (ρ/ρ0)γ with γ = 0.9 ± 0.3 is favored.

The canonical partition function for relativistic hadron gases

Particle production in high-energy collisions is often addressed within the framework of the thermal (statistical) model. We present a method to calculate the canonical partition function for the hadron resonance gas with exact conservation of the baryon number, strangeness, electric charge, charmness and bottomness. We derive an analytical expression for the partition function which is represented as series of Bessel functions. Our results can be used directly to analyze particle production yields in elementary and in heavy ion collisions. We also quantify the importance of quantum statistics in the calculations of the light particle multiplicities in the canonical thermal model of the hadron resonance gas.

Examination of isospin effects in multi-dimensional Langevin fission dynamics

One-dimensional and three-dimensional dynamical fission calculations based on Langevin equations are performed for the compound nuclei 194Pb, 200Pb, 206Pb, 182Hg, and 204Hg to investigate the influence of the compound nucleus isospin on the prescission particle multiplicities and on the fission fragment mass–energy distribution. It is found that the prescission neutron, proton, and alpha particle multiplicities have approximately the same sensitivity to the dissipation strength for a given nucleus. This is at variance with conclusions of recent papers. The sensitivity of the calculated prescission particle multiplicities to the dissipation strength becomes higher with decreasing isospin of fissioning compound nucleus, and the increase of prescission particle multiplicities could reach 200%, when the reduction coefficient of one-body viscosity ks increases from 0.1 to 1, for the most neutron deficient nuclei considered. The variances of fission fragment mass and kinetic energy distributions are less sensitive to the change of dissipation strength than the prescission light particle multiplicities. A comparison to experimental data concerning 200Pb nucleus is also presented.

Correlations between reaction product yields as a tool for probing heavy-ion reaction scenarios

Experimental multidimensional joint distributions of neutrons and charged reaction products were analyzed for 136 Xe + 209 Bi reactions at E/A = 28, 40, and 62 MeV and were found to exhibit several different types of prominent correlation patterns. Some of these correlations have a simple explanation in terms of the system excitation energy and pose little challenge to most statistical decay theories. However, several other types of correlation patterns are difficult to reconcile with some, but not other, possible reaction scenarios. In this respect, correlations between the average atomic numbers of intermediate-mass fragments, on the one hand, and light particle multiplicities, on the other, are notable. This kind of multiparticle correlation provides a useful tool for probing reaction scenarios, which is different from the traditional approach of interpreting inclusive yields of individual reaction products.

Centrality dependence of the thermal excitation-energy deposition in 8–15 GeV/chadron-Au reactions

The excitation energy per residue nucleon (${E}^{*}/A$) and fast and thermal light particle multiplicities are studied as a function of centrality defined as the number of grey tracks emitted ${N}_{\mathrm{grey}}$ and by the mean number of primary hadron-nucleon scatterings ($\ensuremath{\langle}\ensuremath{\nu}\ensuremath{\rangle}$) and the mean impact parameter ($\ensuremath{\langle}b\ensuremath{\rangle}$) extracted from it. The value of ${E}^{*}/A$ and the multiplicities show an increase with centrality for all systems, 14.6 GeV p-Au and 8.0 GeV \ensuremath{\pi}-Au and $\overline{\mathrm{p}}$-Au collisions, and the excitation energy per residue nucleon exhibits a uniform dependence on ${N}_{\mathrm{grey}}$.

Application of a two-step dynamical model to calculating properties of fusion-fission reactions

The two-step model of fusion-fission reactions that was proposed previously by the present authors is extended in such a way as to describe the multiplicity of light particles emitted from nuclearfission fragments. Calculations are performed for the reaction induced by 48Ca + 244Pu collisions. The mass distribution of fragments, their mass-energy distribution, and the total multiplicity of neutrons and gamma rays are obtained for Elab = 230, 238, 249, and 255 MeV. It is shown that the model reproduces qualitatively relevant experimental data. In order to attain quantitative agreement, it is necessary to take into account the angular momentum carried away by particles from the nucleus undergoing fission and various types of gamma rays emitted by the nucleus and its fission fragments.

The effect of curvature and compressibility energies on the multiplicity of a prescission light particle

The aim of this paper is to study the effect of curvature and compressibility energies on the deexcitation process of hot nuclei within a modified version of the combined dynamical statistical model. The prescission light particle multiplicities are chosen as the probe. The calculation results show that the multiplicity calculated with the modified model is closer to the data compared with the original one, especially for the neutron-deficient systems. Our results also show that the multiplicity decreases as the coordinate dependence of the employed level-density parameter strengthens. Therefore, this coordinate dependence is taken into consideration in investigating the deformation dependence of nuclear friction. With a physically reasonable correction factor for the emission barrier, better agreement with data can be acquired for the light charged particle multiplicities. The physics of the compressibility energy considered in this work is discussed.

Threshold effects in relativistic gases

Particle multiplicities and ratios in the micro-canonical ensemble of relativistic gases near production thresholds are studied. It is shown that the ratio of heavy to light particle multiplicity may be enhanced in comparison to its thermodynamic limit.

Influence of excitation energy and angular momentum on the isospin dependence of particle emission

The isospin dependences of the light-particle emission for fissioning isobaric sources 202Fr, 202Po, 202Tl and for isotopic sources 189,202,212Po as functions of excitation energy and angular momentum are studied by the Smoluchowski equation. Calculations show that different excitation energies and angular momenta do not change the dependence of particle emission on the isospin of the system. It is also shown that increasing the excitation energy and/or decreasing the angular momentum can greatly enhance the sensitivity of the emission of pre-scission particles to the nuclear viscosity coefficient. In particular, this sensitivity also depends on the isospin, indicating an important role of isospin in an accurate extraction of the viscosity coefficient by means of light-particle multiplicity.

Effects of Isospin on Pre-scission Particle Multiplicity of Heavy Systems and Its Excitation Energy Dependence**The project supported in part by the Teaching & Researching Foundation for Outstanding Teachers of Southeast University

Isospin effects on particle emission of fissioning isobaric sources and isotopic sources , and its dependence on the excitation energy are studied via Smoluchowski equations. It is shown that with increasing the isospin of fissioning systems, charged-particle emission is not sensitive to the strength of nuclear dissipation. In addition, we have found that increasing the excitation energy not only increases the influence of nuclear dissipation on particle emission but also greatly enhances the sensitivity of the emission of pre-scission neutrons or charged particles to the isospin of the system. Therefore, in order to extract dissipation strength more accurately by taking light particle multiplicities it is important to choose both a highly excited compound nucleus and a proper kind of particles for systems with different isospins.

Neutron-skin effect in the nuclear reactionsNi58+Sn122andNi64+Sn116around6MeV∕nucleon

The use of two proton-magic nuclei for both the projectile $(Z=28)$ and the target $(Z=50)$ in the ``mirror'' reaction types $^{58}\mathrm{Ni}+^{122}\mathrm{Sn}$ and $^{64}\mathrm{Ni}+^{116}\mathrm{Sn}$, leading to the same $^{180}\mathrm{Pt}$ compound nucleus, allows isolation of possible neutron-skin effects from both the target and the projectile. In these reactions, we studied the influence of neutron effects on the competition between fusion-fission, fusion-evaporation, and light-particle emission at equal compound-nucleus excitation energies and similar angular momentum distribution. The comparison of the experimental data, cross sections, and light-particle multiplicities, with the dynamical model HICOL and the statistical model GEMINI incorporating simple aspects of the dynamics, provides insights to the mechanisms of the studied reactions. Our study confirms that, at energy about $6\phantom{\rule{0.3em}{0ex}}\text{MeV}∕\text{nucleon}$, there is no influence of the entrance channel on the formation and on the decay of the compound nucleus produced by these reactions.

Temperature andn−pasymmetry dependencies of the level-density parameter in Ni+Mo fusion reactions

Properties of evaporation residues and the accompanying light particles have been measured in ${}^{60}\mathrm{Ni}{+}^{92,100}\mathrm{Mo}$ fusion reactions at bombarding energies from $E/A=5$ to 9 MeV. The data indicate that these reactions are essentially complete-fusion reactions with only a small amount of nonequilibrium emission at the highest bombarding energy studied. The measured kinetic-energy spectra of evaporated n, p, d, t, ${}^{3}\mathrm{He},$ and $\ensuremath{\alpha}$ particles are compared to statistical-model predictions. It is found that a constant excitation-energy independent level-density parameter is not able to reproduce these spectra over the compound-nucleus excitation-energy range from 90 to 250 MeV. The kinetic-energy spectra for all particles were fit using the level-density parametrization $a=A/(7+1.3\ifmmode\times\else\texttimes\fi{}U/A){\mathrm{MeV}}^{\ensuremath{-}1},$ where U is the thermal excitation energy. The Coulomb barriers for charged-particle emission were reduced from the standard values to reproduce the peak energy and multiplicity for $\ensuremath{\alpha}$ particles. Using these ingredients, the measured mass, velocity, and angular distributions of evaporation residues are also reproduced. The average Z and N of the evaporation residues deduced from the light-particle multiplicities are in agreement with the predicted location of the evaporation attractor line. A neutron-proton asymmetry dependence of the level-density parameter is shown to have potentially important consequences for the neutron or proton richness of the evaporation residues. However, no evidence for such an effect is found in the measured data; and from the experimental multiplicity ratio of ${t/}^{3}\mathrm{He}$ it was deduced that any such dependence in the excitation-energy regime $100<{E}^{*}<250\mathrm{MeV}$ is very small.

Thermal excitation and decay of nuclei from antiproton-nucleus interactions at 1.22 GeV

The formation and subsequent decay of nuclei excited via the annihilation of 1.22-GeV antiprotons have been investigated at the low energy antiproton ring (LEAR). Both neutrons and charged products, from protons up to fission fragments and heavy residues, were detected over a solid angle of $4\ensuremath{\pi}$ by means of the Berlin neutron ball (BNB) and the Berlin silicon ball (BSiB), respectively. All events associated with an inelasticity greater than 10 MeV were recorded, a condition fulfilled for 100% of the annihilation events. The distributions of excitation energy ${(E}^{*})$ of the transient hot nuclei have been investigated for a large range of target nuclei, ${E}^{*}$ being determined event by event from the total multiplicity of light particles. The average excitation energies are about twice as large as for annihilations at rest, and range from 2.5 MeV/nucleon for the Cu target to 1.5 MeV/nucleon for the U target, in good agreement with the predictions of an intranuclear-cascade model. The distributions extend to ${E}^{*}>8$ MeV/nucleon for Cu and ${E}^{*}>5$ MeV/nucleon for Au, with cross sections exceeding 1% of ${\ensuremath{\sigma}}_{\mathrm{reac}}.$ Thanks to the capability of determining ${E}^{*}$ for all events, largely irrespective of their mass partitions, the probabilities of the different decay channels at play could be estimated as a function of ${E}^{*}.$ The data show the prevalence of fission and evaporation up to ${E}^{*}=4--5$ MeV/nucleon for Au and U. The fission probability ${P}_{\mathrm{fis}}$ was measured for the first time over the full range of ${E}^{*}.$ The reproduction of the data by statistical models is reasonable, provided that the ratio ${a}_{f}{/a}_{n}$ is adjusted for the different targets and a transient time shorter than $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}21}$ s is considered. The experiment has allowed the fission probability to be investigated as functions of the associated neutron and light-charged particle multiplicities. The intermediate-mass fragment multiplicities rise smoothly with ${E}^{*}$ up to about 1 unit at ${E}^{*}=1$ GeV for Au and U, with no indication of significant contribution from another process than evaporation. Heavy residues have been measured quite abundantly at the highest ${E}^{*},$ with most of their kinetic energy arising from the recoil effects in the evaporation stage. Overall, the data allow a coherent picture to be established, consistent with the hot nucleus retaining conventional decay properties.

Prompt light particle emission in the 36Ar + 58Ni reaction at 95 MeV/nucleon

The prompt component at intermediate velocity of light charged particles is investigated. An improved coalescence model coupled to the intra-nuclear cascade code ISABEL is used to obtain light complex particle energy spectra and multiplicities as a function of impact parameter. The results are compared with experimental data from the 36Ar + 58Ni experiment at 95 MeV/nucleon, performed with the INDRA 4π detection system. The calculated prompt component is found to rather well reproduce proton spectra. For complex light charged particles the calculated components well populate the high energy part of spectra. Prompt emission can therefore explain the large transverse energies experimentally observed at mid-rapidity.

Isospin influences on particle emission and critical phenomena in nuclear dissociation

Features of particle emission and critical point behavior are investigated as functions of the isospin of disassembling sources and temperature at a moderate freeze-out density for medium-size Xe isotopes in the framework of isospin dependent lattice gas model. Multiplicities of emitted light particles, isotopic and isobaric ratios of light particles show the strong dependence on the isospin of the dissociation source, but double ratios of light isotope pairs and the critical temperature determined by the extreme values of some critical observables are insensitive to the isospin of the systems. Values of the power law parameter of cluster mass distribution, mean multiplicity of intermediate mass fragments ($IMF$), information entropy ($H$) and Campi's second moment ($S_2$) also show a minor dependence on the isospin of Xe isotopes at the critical point. In addition, the slopes of the average multiplicites of the neutrons ($N_n$), protons ($N_p$), charged particles ($N_{CP}$), and IMFs ($N_{imf}$), slopes of the largest fragment mass number ($A_{max}$), and the excitation energy per nucleon of the disassembling source ($E^*/A$) to temperature are investigated as well as variances of the distributions of $N_n$, $N_p$, $N_{CP}$, $N_{IMF}$, $A_{max}$ and $E^*/A$. It is found that they can be taken as additional judgements to the critical phenomena.