Fragmentation reactions induced on light target nuclei by protons and light nuclei of energies around 1 GeV/nucleon and below are studied with the latest Los Alamos Monte Carlo transport code MCNP6 and with its cascade-exciton model (CEM) and Los Alamos version of the quark-gluon string model (LAQGSM) event generators, version 03.03, used as stand-alone codes. Such reactions are involved in different applications, like cosmic-ray-induced single event upsets (SEU's), radiation protection, and cancer therapy with proton and ion beams, among others; therefore, it is important that MCNP6 simulates them as well as possible. CEM and LAQGSM assume that intermediate-energy fragmentation reactions on light nuclei occur generally in two stages. The first stage is the intranuclear cascade (INC), followed by the second, Fermi breakup disintegration of light excited residual nuclei produced after INC. Both CEM and LAQGSM account also for coalescence of light fragments (complex particles) up to He4 from energetic nucleons emitted during INC. We investigate the validity and performance of MCNP6, CEM, and LAQGSM in simulating fragmentation reactions at intermediate energies and discuss possible ways of further improving these codes.
The process of nuclear multifragmentation has been implemented, together with evaporation and fission channels of the disintegration of excited remnants in nucleus-nucleus collisions using percolation theory and the intranuclear cascade model. Colliding nuclei are treated as face--centered--cubic lattices with nucleons occupying the nodes of the lattice. The site--bond percolation model is used. The code can be applied for calculation of the fragmentation of nuclei in spallation and multifragmentation reactions.
A novel mechanism of prompt nuclear fragmentation is proposed. Assuming micro-canonical or canonical equilibrium, it is shown that a strong enhancement of the accessible phase space volume, due to the diffuceness of the nuclear surface, leads to dynamical instabilities of hot nuclei and to prompt fragmentation. Equations are derived for the transition temperature T_T, for which the thermodynamical surface tension vanishes, as well as for the thermodynamical fissility parameter chi_td.
Fragmentation reactions induced on light and medium nuclei by protons and light nuclei of energies around 1 GeV/nucleon and below are studied with the Los Alamos transport code MCNP6 and with its CEM03.03 and LAQGSM03.03 event generators. CEM and LAQGSM assume that intermediate-energy fragmentation reactions on light nuclei occur generally in two stages. The first stage is the intranuclear cascade (INC), followed by the second, Fermi breakup disintegration of light excited residual nuclei produced after the INC. CEM and LAQGSM account also for coalescence of light fragments (complex particles)…
A remarkably simple dependence of fragmentation cross-section on average binding energy has been established in experimental data. This dependence was empirically parametrised leading to a very useful formula for extrapolation. We find that the canonical thermodynamic model, which has been used in the past for successful computations of many observables resulting from multifragmentation, reproduces the salient fetures of fragmentation cross-sections of very neutron rich nuclei very well. This helps towards a theoretical understanding of the observed data.
We investigate the contributions of various reaction channels to the interaction, reaction, charge-changing and neutron-changing cross sections. The goal is to investigate the relation between microscopic interactions and the symmetry energy component of the equation of state (EoS) of interest for the structure of neutron stars. We have made a comparison of the neutron skins extracted from diverse experimental techniques with those obtained with Hartree-Fock-Bogoliubov calculations with 23 Skyrme and with 8 density-dependent interactions used in the relativistic mean field method. We have show…
We use a binary sequential decay model in order to describe the fragmentation of a nucleus induced by the high energy collisions of protons with Au nuclei. Overall agreement between measured and calculated physical observables is obtained. We evaluate and analyse the decay times obtained with two different parametrisations of the decay rates and discuss the applicability of the model to high energy fragmentation.
We report here an empirical formalism for predicting the cross-sections of neutron-rich nuclei produced in fragmentation of relativistic \b{eta}-unstable neutron-rich projectiles in the mid-mass region. The formalism is based on the abrasion-ablation picture of the projectile fragmentation reaction. It has been shown that the formalism can accurately reproduce the experimental cross-section data for nuclei produced in the fragmentation of 132Sn. The formalism, it is shown, can also reproduce the experimental cross-sections of neutron-rich nuclei produced in the fragmentation of 129Xe fairly ac…
Directed and elliptic flow of light nuclei and hypernuclei in Au+Au collisions at $\sqrt{s_\mathrm{NN}}=3$ GeV: Coalescence vs. Statistical Fragmentation
Starting from a Skyrme interaction with tensor terms, the $β$-decay rates of $^{52}$Ca have been studied within a microscopic model including the $2p-2h$ configuration effects. We observe a redistribution of the strength of Gamow-Teller transitions due to the $2p-2h$ fragmentation. Taking into account this effect results in a satisfactory description of the neutron emission probability of the $β$-decay in $^{52}$Ca.
We present a simple time dependent model for the excitation of a nucleon from a bound state to a continuum resonant state in a neutron-core complex potential which acts as a final state interaction. The final state is described by an optical model S-matrix so that both resonant and non resonant states of any continuum energy can be studied as well as deeply bound initial states. It is shown that, due to the coupling between the initial and final states, the neutron-core free particle phase shifts are modified, in the exit channel, by an additional phase. The effect of the additional phase on t…
We present a complete systematically theoretical study of multifragmentation for asymmetric colliding nuclei for heavy-ion reactions in the energy range between 50 MeV/nucleon and 600 MeV/nucleon by using soft and hard equations of state. This study is performed within an isospindependent quantum molecular dynamics model. To see the effect of mass asymmetry, simulations are carried out in the absence of Coulomb interactions. Coulomb interactions enhances the production of fragments by about 20%. We envision an interesting outcome for large asymmetric colliding nuclei. Although nearly symmetric…
Quark-quark double scattering in eA DIS and its contribution to quark and anti-quark fragmentation functions are investigated with the generalized factorization of the relevant twist-four processes in pQCD. It is shown that the resulting modifications to quark and anti-quark fragmentation functions are different. While the numerical size of these effects cannot be determined from pQCD, the structure of our result leads to a number of qualitative predictions for the relative size of the effect for different hadrons. These qualitative predictions agree with the multiplicity ratios for positive a…
Motivated by recent experiments on colloidal systems with competing attractive and repulsive interactions, we simulate a two-dimensional system of colloids with competing interactions that can undergo fragmentation. In the absence of any other confining potential, the colloids can form stable clusters depending on the strength of the short range attractive term. By suddenly changing the strength of one of the interaction terms we find a rich variety of fragmentation behavior which is affected by the existence of "magic" cluster numbers. Such soft matter systems can be used to construct artific…
A new empirical parametrization for the estimation of cross-sections of projectile fragments has been prescribed for studying the advantages and limitations of high energy RI beams for the production of new exotic nuclei. The parametrization reproduces the experimental data for the production of fragments from neutron rich projectiles accurately in contrast to the existing parametrization which tends to overestimate the cross-section of neutron rich fragments in most cases. The modified formalism has been used to compute the cross-sections of neutron-rich species produced by fragmentation of r…
Within the framework of generalized factorization of higher-twist contributions, including modification to splitting functions of both quark and gluon, we get and numerically resolve the medium-modified DGLAP (mDGLAP) evolution equations. With Woods-Saxon nuclear geometry and Hirano 3D ideal hydrodynamic simulations of hot medium, we study the medium modified fragmentation functions (mFF) in DIS and Au+Au collisions in RHIC. Our calculation imply that the parton density in hot medium produced in RHIC is about 30 times larger than cold nucleon.
Transverse momentum spectra of pions, protons and antiprotons in Au+Au collisions at intermediate RHIC energy of $\sqrt{s_{NN}}=62$ GeV are studied in a model that includes both quark coalescence from the dense partonic matter and fragmentation of the quenched perturbative minijet partons. The resulting baryon to meson ratio at intermediate transverse momenta is predicted to be larger than that seen in experiments at higher center of mass energies.
We test the influence of the Coulomb interaction on the thermodynamic and cluster generation properties of a system of classical particles described by different lattice models. Numerical simulations show that the Coulomb interaction produces essentially a shift in temperature of quantities like the specific heat but not qualitative changes. We also consider a cellular model. The thermodynamic properties of the system are qualitatively unaltered.
Heavy nuclei bombarded with protons and deuterons in the 1 GeV range have a large probability of undergoing a process of evaporation and fission; less frequently, the prompt emission of few intermediate-mass fragments can also be observed. We employ a recently developed microscopic approach, based on the Boltzmann-Langevin transport equation, to investigate the role of mean-field dynamics and phase-space fluctuations in these reactions. We find that the formation of few IMF's can be confused with asymmetric fission when relying on yield observables, but it can not be assimilated to the statist…
Fissioning nuclei and fission fragments, nuclear fragments emerging from energetic collisions, or nuclei probed with various external fields can emit one or more pre-equilibrium neutrons, protons, and potentially other heavier nuclear fragments. I describe a formalism which can be used to evaluate the pre-equilibrium neutron emission probabilities and the excitation energies of the remnant fragments.
We call "projectile fragmentation" of neutron halo nuclei the elastic breakup (diffraction) reaction, when the observable studied is the neutron-core relative energy spectrum. This observable has been measured in relation to the Coulomb breakup on heavy target and recently also on light targets. Such data enlighten the effect of the neutron final state interaction with the core of origin. Projectile fragmentation is studied here by a time dependent model for the excitation of a nucleon from a bound state to a continuum resonant state in a neutron-core complex potential which acts as a final st…
Characteristic signatures of statistical Coulomb fragmentation of highly excited nuclear systems were analyzed. It was found that in some important aspects, they coincide with perceived signatures of phase transitions in confined hypothetical pseudo-microcanonical systems, thus potentially giving rise to a false interpretation of experimental observations in terms of phase transitions. It is demonstrated that the heat capacity as derived based on experimental observations may show domains of faux negative heat capacity for the same fundamental reason a faux negative heat capacity appears in co…
Multiple scattering, induced radiative energy loss and modified fragmentation functions of a heavy quark in nuclear matter are studied within the framework of generalized factorization in perturbative QCD. Modified heavy quark fragmentation functions and energy loss are derived in detail with illustration of the mass dependencies of the Landau-Pomeranchuk-Migdal interference effects and heavy quark energy loss. Due to the quark mass dependence of the gluon formation time, the nuclear size dependencies of nuclear modification of the heavy quark fragmentation function and heavy quark energy loss…
The properties of excited nuclear matter and the quest for a phase transition which is expected to exist in this system are the subject of intensive investigations. High energy nuclear collisions between finite nuclei which lead to matter fragmentation are used to investigate these properties. The present report covers effective work done on the subject over the two last decades. The analysis of experimental data is confronted with two major problems, the setting up of thermodynamic equilibrium in a time-dependent fragmentation process and the finite size of nuclei. The present status concerni…
We report fragmentation cross sections measured at 0 deg for beams of 14-N, 16-O, 20-Ne, and 24-Mg ions, at energies ranging from 290 MeV/nucleon to 1000 MeV/nucleon. Beams were incident on targets of C, CH2, Al, Cu, Sn, and Pb, with the C and CH2 target data used to obtain hydrogen-target cross sections. Using methods established in earlier work, cross sections obtained with both large-acceptance and small-acceptance detectors are extracted from the data and when necessary corrected for acceptance effects. The large-acceptance data yield cross sections for fragments with charges approximately…
To understand the role of isospin effects on fragmentation due to the collisions of charge asymmetric nuclei, we have performed a complete systematical study using isospin dependent quantum molecular dynamics model. Here simulations have been carried out for $^{124}X_{n}+ ^{124}X_{n}$, where n varies from 47 to 59 and for $^{40}Y_{m}+ ^{40}Y_{m}$, where m varies from 14 to 23. Our study shows that isospin dependent cross-section shows its influence on fragmentation in the collision of neutron rich nuclei.
We studied the influence of a momentum dependent interaction in the context of isopspin effects on fragmentation and dissipation in intermediate energy heavy ion collisions by using an isospin dependent quantum molecular dynamics model. It is shown that the nuclear stopping, the number of nucleons emitted ,and the multiplicity of intermediate mass fragments are larger with a momentum dependent interaction than without. In particular, the differences for these observables, when using an isospin dependent in-medium nucleon nucleon cross section versus an isospin independent one, are also larger …
Nuclear energy released by splitting Uranium and Thorium isotopes into two, three, four, up to eight fragments with nearly equal size are studied. We found that the energy released come from equally splitting the $^{235,238}$U and $^{230,232}$Th nuclei into to three fragments is largest. The statistical multifragmentation model is employed to calculate the probability of different breakup channels for the excited nuclei. Weighing the the probability distributions of fragments multiplicity at different excitation energies for the $^{238}$U nucleus, we found that an excitation energy between 1.2…
We extract values for the free symmetry energy as a function of the fragment size (the proton number Z) from antisymmetrized molecular dynamics (AMD) calculations of calcium collisions. Simple statistical physics describe well the distribution of hot nuclei at breakup, provided the surface symmetry term in the free energy is much smaller at high excitation than in ground state nuclei. This result may reflect the condition of low density and finite temperature when these systems disassemble.
We present results of a phase space coalescence approach within the UrQMD transport and -hybrid model for a very wide range of beam energies from SIS to LHC. The coalescence model is able to qualitatively describe the whole range of experimental data with a fixed set of parameters. Some systematic deviations are observed for very low beam energies where the role of feed down from heavier nuclei and multi-fragmentation becomes relevant. The coalescence results are mostly very close to the thermal model fits. However, both the coalescence approach as well as thermal fits are struggling to simult…
Multiple parton scattering and induced parton energy loss is studied in deeply inelastic scattering (DIS) off nuclei. The effect of multiple scattering of a highly off-shell quark and the induced parton energy loss is expressed in terms of the modification to the quark fragmentation functions. We derive such modified quark fragmentation functions and their QCD evolution equations in DIS using generalized factorization of higher twist parton distributions. We consider double-hard, hard-soft parton scattering as well as their interferences in the same framework. The final result, which depends o…
The LAQGSM code has been recently developed at Los Alamos National Laboratory to simulate nuclear reactions for proton radiography applications. We have benchmarked our code against most available measured data both for proton-nucleus and nucleus-nucleus interactions at incident energies from 10 MeV to 800 GeV and have compared our results with predictions of other current models used by the nuclear community. Here, we present a brief description of our code and show illustrative results obtained with LAQGSM for neutron spectra measured recently by Nakamura's groups for reactions induced by li…
We use the McLerran-Venugopalan model of the glasma energy-momentum tensor to compute the rapidity loss and excitation energy of the colliding nuclei in the fragmentation regions followed by a space-time picture to obtain their energy and baryon densities. At the top RHIC energy we find baryon densities up to 3 baryons/fm$^3$, which is 20 times that of atomic nuclei. Assuming the formation of quark-gluon plasma, we find initial temperatures of 200 to 300 MeV and baryon chemical potentials of order 1 GeV. Assuming a roughly adiabatic expansion it would imply trajectories in the $T-μ$ plane whic…
Theoretical calculations are performed to investigate the angular momentum and Coulomb effects on fragmentation and multifragmentation in peripheral heavy-ion collisions at Fermi energies. Inhomogeneous distributions of hot fragments in the freeze-out volume are taken into account by microcanonical Markov chain calculations within the Statistical Multifragmentation Model (SMM). Including an angular momentum and a long-range Coulomb interaction between projectile and target residues leads to new features in the statistical fragmentation picture. In this case, one can obtain specific correlation…
We present our recent results on the fragmentation by varying the mass asymmetry of the reaction between 0.2 and 0.7 at an incident energy of 250 MeV/nucleon. For the present study, the total mass of the system is kept constant (ATOT = 152) and mass asymmetry of the reaction is defined by the asymmetry parameter (? = | (AT - AP)/(AT + AP) |). The measured distributions are shown as a function of the total charge of all projectile fragments, Zbound. We see an interesting outcome for rise and fall in the production of intermediate mass fragments (IMFs) for large asymmetric colliding nuclei. This…
Collective-flow signatures of bubble nuclei in intermediate-energy projectile fragmentation reactions
Henan Normal University（河南师范大学）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；Institute of Nuclear Science and Technology, Henan Academy of Sciences（河南省科学院核科学技术的研究所）；Shanghai Research Center for Theoretical Nuclear Physics, NSFC and Fudan University（国家自然科学基金委与复旦大学理论物理上海研究中心）；Shanghai Institute of Applied Physics, Chinese Academy of Sciences（中国科学院上海应用物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Phenomenological and theoretical aspects of fragmentation for elementary particles (resp. nuclei) are discussed. It is shown that some concepts of classical fragmentation remain relevant in a microscopic framework, exhibiting non-trivial properties of quantum relativistic field theory (resp. lattice percolation). Email contact: pesch@amoco.saclay.cea.fr
Recent LHC results indicate a suppression of jet fragmentation functions in Pb-Pb collisions at intermediate values of $ξ=\ln(1/z)$. This seems to contradict the picture of energy loss based on the induced QCD radiation that is expected to lead to the enhancement of in-medium fragmentation functions. We use an effective 1+1 dimensional quasi-Abelian model to describe the dynamical modification of jet fragmentation in the medium. We find that this approach describes the data, and argue that there is no contradiction between the LHC results and the picture of QCD radiation induced by the in-medi…
The fragmentation of projectile and spectator matter is studied at different incident energies using an isospin-dependent QMD model with reduced isospin dependent cross-section. The sensitivity of the production of fragments is analyzed using different parametrizations of density dependence of symmetry energy. We shall also highlight the collective response of the momentum dependent interactions(MDI) and symmetry energy towards the fragmentation of colliding nuclei at intermediate energies.
The giant monopole, dipole and quadrupole responses in $^{40}$Ca, $^{90}$Zr, $^{120}$Sn and $^{208}$Pb are investigated using linear response treatment based on a stochastic one-body transport theory. Effects of the coupling to low-lying surface modes (coherent mechanism) and the incoherent mechanism due to nucleon-nucleon collisions are included beyond the usual mean-field description. We emphasize the importance of both mechanism in the fragmentation and damping of giant resonance. Calculated spectra are compared with experiment in terms of percentage of Energy-Weighted Sum-Rules in various …
On the basis of systematic measurements of fragmentation reactions, which provide a detailed overview on the velocity distributions of residual nuclei, an improved description of the kinematical properties of the fragmentation residues is established. This work is dedicated to the fluctuations of their momentum distributions. In contrast to previous investigations, limited to close-to-projectile fragments, we extended our study to the entire production range, down to the lightest observed fragments. In this context, beside the contribution of abrasion and evaporation processes, we considered t…
The isobaric yield ratios of the fragments produced in the neutron-rich 48Ca and 64Ni projectile fragmentation are analyzed in the framework of a modified Fisher model. The correlations between the isobaric yield ratios (R) and the energy coefficients in the Weiszäcker-Beth semiclassical mass formula (the symmetry-energy term asym, the Coulomb-energy term ac, and the pairing-energy term ap) and the difference between the chemical potentials of the neutron and proton (μn-μp) are investigated. Simple correlations between (μn-μp)/T, ac/T, asym/T, and ap/T (where T is the temperature), and lnR are…
Antiproton scattering off $^3\He$ and $^4\He$ targets is considered at beam energies below 300 MeV within the Glauber-Sitenko approach, utilizing the $\bar N N$ amplitudes of the Jülich model as input. A good agreement with available data on differential $\bar p ^4\He$ cross sections and on $\bar p ^3\He$ and $\pbar ^4\He$ reaction cross sections is obtained. Predictions for polarized total $\bar p ^3$He cross sections are presented, calculated within the single-scattering approximation and including Coulomb-nuclear interference effects. The kinetics of the polarization buildup is discussed.
Spectroscopic properties of nuclei are accessible with projectile fragmentation reactions, but approximations made in the reaction theory can limit the accuracy of the determinations. We examine here two models that have rather different approximations for the nucleon wave function, the target interaction, and the treatment of the finite duration of the reaction. The nucleon-target interaction is treated differently in the eikonal and the transfer-to-continuum model, but the differences are more significant for light targets. We propose a new parameterization with that in mind. We also propose…
A systematic analysis of giant quadrupole resonances is performed for several nuclei, from $^{30}$Si to $^{208}$Pb, within the subtracted second random--phase--approximation (SSRPA) model in the framework of the energy--density--functional theory. Centroid energies and widths of the isoscalar giant quadrupole resonances are compared with the corresponding random--phase--approximation (RPA) values. We find lower SSRPA centroid energies compared to the RPA values leading, in general, to a better agreement with the experimental data. As far as the widths are concerned, we observe for both SSRPA a…
We have investigated the Gamow-Teller transitions from ${}^{22}\textrm{Ne}$ to ${}^{22}\textrm{Na}$ by applying the isospin projected antisymmetrized molecular dynamics combined with generator coordinate method. We have found that the GT strength from $^AZ(J^πT)={}^{22}\textrm{Ne}(0_1^+1)$ is fragmented into two final states ${}^{22}\textrm{Na}(1_{1,2}^+0)$, which belong to $K=0$ and $K=1$ bands constructed by a prolately deformed $^{20}$Ne core with a $S=1$ proton-neutron ($pn$) pair. Coupling of the intrinsic-spin of the $pn$ pair with the core deformation play an important role in the GT fr…
We investigate neutrino-nucleus collisions at intermediate energies incorporating quasielastic scattering and Delta(1232) excitation as elementary processes, together with Fermi motion, Pauli blocking and mean-field potentials in the nuclear medium. A full coupled-channel treatment of final state interactions is achieved with a semiclassical BUU transport model. Results for inclusive reactions and nucleon knockout are presented.
Modifications to quark and antiquark fragmentation functions due to quark-quark (antiquark) double scattering in nuclear medium are studied systematically up to order \cal{O}(α_{s}^2)$ in deeply inelastic scattering (DIS) off nuclear targets. At the order $\cal{O}(α_s^2)$, twist-four contributions from quark-quark (antiquark) rescattering also exhibit the Landau-Pomeranchuck-Midgal (LPM) interference feature similar to gluon bremsstrahlung induced by multiple parton scattering. Compared to quark-gluon scattering, the modification, which is dominated by $t$-channel quark-quark (antiquark) scatt…
Low-energy multinucleon transfer reactions are shown to be very effective tool for the production and spectroscopic study of light exotic nuclei. The corresponding cross sections are found to be significantly larger as compared with high energy fragmentation reactions. Several optimal reactions for the production of extremely neutron rich isotopes of elements with Z=6-14 are proposed.
A general analytical expression for the double differential cross section of inclusive deuteron stripping reaction on nuclei at intermediate energies of incident particles was obtained in the diffraction approximation. Nucleon-nucleus phases were calculated in the framework of Glauber formalism and making use of the double-folding potential. The exact wave function of deuteron with correct asymptotics at short and long distances between nucleons was used. The calculated angular dependencies of cross sections are in good agreement with corresponding experimental data.
We investigate the thermodynamical content of a cellular model which describes nuclear fragmentation as a process taking place in an excited disordered system. The model which reproduces very well the size distribution of fragments does not show the existence of a first order phase transition.
We investigate nuclear fragmentation in the central proton-nucleus and nucleus - nucleus collisions at the energies of LHC. We argue that within the semi-classical approximation because of fast increase with energy of cross sections of soft and hard interactions each nucleon is stripped in the average process off ``soft'' partons and fragments into a collection of leading quarks and gluons with large $p_t$. Valence quarks and gluons are streaming in the opposite directions when viewed in the c.m. of the produced system. The resulting pattern of the fragmentation of the colliding nuclei leads t…
Properties of intermediate mass nuclei have been investigated within the framework of the alpha-cluster model in combination with systematic double-folding potentials. Previously, this alpha-cluster model has been widely applied to light nuclei, in particular to 8Be = alpha \otimes alpha, 20Ne = 16O \otimes alpha, and 44Ti = 40Ca \otimes alpha, and to heavy nuclei, in particular to 212Po = 208Pb \otimes alpha. In the present work a wide range of nuclei is investigated with the magic neutron number N = 50 in the mass range around A \approx 80 - 100: (A+4,N=52) = (A,N=50) \otimes alpha. It is fo…
We investigate the Coulomb excitation of low-lying states of unstable nuclei in intermediate energy collisions ($E_{lab}\sim10-500$ MeV/nucleon). It is shown that the cross sections for the $E1$ and $E2$ transitions are larger at lower energies, much less than 10 MeV/nucleon. Retardation effects and Coulomb distortion are found to be both relevant for energies as low as 10 MeV/nucleon and as high as 500 MeV/nucleon. Implications for studies at radioactive beam facilities are discussed.
Optical potentials for elastic p-d scattering and the coupled processes p+$^3$He $\rightarrow$ p+$^3$He and p+$^3$He $\rightarrow$ d+d are derived in the Faddeev-Yakubovsky framework with special emphasis on leading order terms, which are expected to be valid at intermediate energies. In addition, equations for the fragmentations $^3$He(p,ppp)n and $^3$He(p,pp)d are derived within the same framework. Again leading order terms for intermediate energies are considered.
A study of multifragmentation of gold nuclei is reported at incident energies of 400, 600 and 1000 MeV/nucleon using microscopic theory. The present calculations are done within the framework of quantum molecular dynamics (QMD) model. The clusterization is performed with advanced sophisticated algorithm namely \emph{simulated annealing clusterization algorithm} (SACA) along with conventional spatial correlation method. A quantitative comparison of mean multiplicity of intermediate mass fragments with experimental findings of ALADiN group gives excellent agreement showing the ability of SACA me…
