New scalings in nuclear fragmentation

Fragment partitions of fragmenting hot nuclei produced in central and semiperipheral collisions have been compared in the excitation energy region 4-10?MeV per nucleon where radial collective expansion takes place. It is shown that, for a given total excitation energy per nucleon, the amount of radial collective energy fixes the mean fragment multiplicity. It is also shown that, at a given total excitation energy per nucleon, the different properties of fragment partitions are completely determined by the reduced fragment multiplicity (i.e., normalized to the source size). Freeze-out volumes seem to play a role in the scalings observed.     

Multi three-cluster coupling model of nuclear reactions

Two alternative versions of practicable connected kernel theories of nuclear reactions are proposed. The basic assumption is that the state of a many-body system can be approximated by a superposition of two- and three-cluster states corresponding to various possible reaction processes. The approach is based on the concept of transitions due to particle exchange as in the AmadoLovelace (AL) formalism. All important three-cluster partitions can be incorporated via multichannel couplings in two-cluster subsystems. The simpler of two models, which is called the multi three-cluster coupling (MTCC) model, is a direct extension of the AL formalism. Using the separable representation of two-cluster potentials, the AL type coupled equations among reaction amplitudes are postulated. The MTCC equation is shown to be reduced to the equation with the same structure as the Faddeev equation. Thus, while the MTCC model can treat a much wider class of nuclear reactions than the Faddeev approach, the calculation is no more complicated than that. The basic assumption in this model, as well as in the AL and AGS theories, is shown to contain some degree of inconsistency regarding the treatment of bound state pole parts of interacting pairs. This is remedied in the other model, which we call the multi two- and three-cluster coupling (MTTC) model. This is the most extended MTCC model that is possible within the two- and three-cluster coupling model. In the MTTC treatment, it is shown that sequential (multi-step) transfers can also be accommodated in addition to all various processes that are possible in the MTCC approach.     

Emission time of the intermediate mass fragments in collisions of relativistic deuterons with the gold target

The relative velocity correlation function of pairs of intermediate mass fragments has been studied for d + Au collisions at 4.4 GeV. Experimental correlation functions are compared to that obtained by multi-body Coulomb trajectory calculations under the assumption of various decay times of the fragmenting system. The combined approach with the empirically modified intranuclear cascade code followed by the statistical multifragmentation model was used to generate the starting conditions for these calculations. The fragment emission time is found to be less than 40 fm c ⁻¹.     

Nuclear interactions of 21 GeV/c protons and 50 GeV/c negative pions in emulsions exposed in a strong magnetic field

Incoherent nuclear interactions of 21 GeV/c protons and 50 GeV/cπ ^?-mesons in emulsions exposed in a strong (180 kG) magnetic field have been investigated. The following topics are covered: the multiplicity of various types of charges secondaries, general features of one-particle rapidity and transverse momentum distributions, energy partitions among secondaries, characteristics of the leading particles and relativistic recoil protons, correlation relations. The experimental data are compared with predictions of current models of nuclear production.     

反对称分子动力学模型中的冻结概念（英文）

给出了反对称分子动力学模型(AMD)计算的50 Me V/nucleon112Sn+112Sn反应的分析结果。该研究是反对称分子动力学模型中统计冻结概念的部分研究结果。利用自洽法结合修正的Fisher模型,提取了发射源的温度和密度分别为T=(6.1±0.2)Me V,ρ/ρ0=0.69±0.03。通过与AMD模型计算的系统在时间演化过程中的最大密度比较,得出碎片发射源的密度远小于系统的最大密度。利用自洽法提取的温度和密度与35 Me V/nucleon的40Ca+40Ca反应系统及40 Me V/nucleon的64Zn+112Sn反应系统所提取的温度和密度非常接近。该结果表明反对称分子动力学模型中,系统在中等质量碎片形成时刻处于统计冻结体积。     

Fluctuations of fragment observables

This contribution presents a review of our present theoretical as well as experimental knowledge of different fluctuation observables relevant to nuclear multifragmentation. The possible connection between the presence of a fluctuation peak and the occurrence of a phase transition or a critical phenomenon is critically analyzed. Many different phenomena can lead both to the creation and to the suppression of a fluctuation peak. In particular, the role of constraints due to conservation laws and to data sorting is shown to be essential. From the experimental point of view, a comparison of the available fragmentation data reveals that there is a good agreement between different data sets of basic fluctuation observables, if the fragmenting source is of comparable size. This compatibility suggests that the fragmentation process is largely independent of the reaction mechanism (central vs. peripheral collisions, symmetric vs. asymmetric systems, light ions vs. heavy-ion-induced reactions). Configurational energy fluctuations, that may give important information on the heat capacity of the fragmenting system at the freeze-out stage, are not fully compatible among different data sets and require further analysis to properly account for Coulomb effects and secondary decays. Some basic theoretical questions, concerning the interplay between the dynamics of the collision and the fragmentation process, and the cluster definition in dense and hot media, are still open and are addressed at the end of the paper. A comparison with realistic models and/or a quantitative analysis of the fluctuation properties will be needed to clarify in the next future the nature of the transition observed from compound nucleus evaporation to multi-fragment production.     

Nuclear Reactions in Micro/Nano-Scale Metal Particles

Low-energy nuclear reactions in micro/nano-scale metal particles are described based on the theory of Bose–Einstein condensation nuclear fusion (BECNF). The BECNF theory is based on a single basic assumption capable of explaining the observed LENR phenomena; deuterons in metals undergo Bose–Einstein condensation. The BECNF theory is also a quantitative predictive physical theory. Experimental tests of the basic assumption and theoretical predictions are proposed. Potential application to energy generation by ignition at low temperatures is described. Generalized theory of BECNF is used to carry out theoretical analyses of recently reported experimental results for hydrogen–nickel system.     

On azimuthal anisotropy in fragmentation of a classical relativistic string

A fragmenting relativistic string is widely used for modeling particle production via quark–gluon strings formed in hadronic and nuclear inelastic interactions at high energies. In this note we focus on motion and fragmentation of a relativistic string with non-zero transverse separation of its ends and study this scenario as a possible mechanism for bringing anisotropy into the azimuthal angle distribution of produced particles in inelastic interactions of hadrons.     

Some Properties of π Meson in Nuclear Matter with Finite Density

In the GCM we study some properties of π meson as the Goldstone bosons in a nuclear matter with finite density.Using the effective action in a nuclear matter,we calculate the decay constant and π mass as functions of the chemical potential.The relation between the chemical potential and the density of a nuclear matter is firstly given here.We find that fπ and mπ monotonously decrease as nuclear matter density increases.The result is consistent with the usual assumption that the chiral symmetry is gradually restored as the density of a nuclear matter increases.     

Critical behaviour in Au fragmentation at 10.7A GeV

The complete charge distribution of products from Au nuclei fragmenting in nuclear emulsion at 10.7A GeV has been measured. Multiplicities of produced particles and particles associated with the target source are used to select peripheral and central events. A statistical analysis, based on event-by-event charge distributions, show that a population of subcritical, critical and supercritical events, i.e. a phase transition like behaviour, is observed among peripheral collisions. Received: 23 September 1997     

Probing string fragmentation in nuclear matter: Lepton-nucleus scattering

We introduce a new model for the fragmentation of strings in a “medium” of hadronic objects. These objects may be hadrons, resonances, or string pieces from the fragmentation of other strings. As a first application we treat the fragmentation of a string inside a nuclear medium, taking into account interactions of the fragmenting string with spectator nucleons (spectators of the hard process which created the string in the first place). We compare with neutrino-neon data.     

Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions

In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kähler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers. The D6/D2/D0 partition functions in different chambers were obtained by applying the wall crossing formula. On the other hand, the pyramid partitions describe T ³ fixed points of the moduli space of a quiver quantum mechanics. This quiver arises after we apply Seiberg dualities to the D6/D2/D0 system on the conifold and choose a particular set of FI parameters. The arrow structure of the dual quiver is confirmed by computation of the Ext group between the sheaves. We show that the superpotential and the stability condition of the dual quiver with this choice of the FI parameters give rise to the rules specifying pyramid partitions with length n ERC.     

Statistical multifragmentation of nuclei: (II). Application of the model to finite nuclei disassembly

The fragmentation of a hot nuclear system is studied in a statistical model. The partitions of the system are calculated by means of a Monte Carlo technique. The resulting mass spectra, multiplicity distributions, average values of temperature, entropy, heat capacity and break-up density are presented and discussed. It is found that the fragmentation process begins rather suddenly at a crack temperature $\text{T}{}^1\text{?5–6}\text{MeV}$. The occurrence at a higher temperature of a transition to a gaseous-like phase in finite systems is investigated and compared with infinite-matter calculations.     

Onset of multifragmentation dominance at 1 GeV proton-induced nuclear reaction for target nuclei with A 160

The onset of the multifragmentation regime is studied by means of 1 GeV proton-induced nuclear reactions at various target nuclei. Analysing the measured longitudinal momentum transferred to the fragmenting nucleus it is found that the multifragmentation process seems to dominate over the induced fission in the mass region A 160. The qualitative behaviour of the experimental findings is reproduced by considering a simple model.     

中能原子核多重碎裂中的方位角关联

在发射源静止系碎片各向同性发射的假设条件下，考虑到碎片之间的电磁作用，研究了中能原子核多重碎裂中碎片间的方位角关联，计算结果与５００─９８０ＡＭｅＶ能区的实验数据一致．     

Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.     

Method for solving the many-body bound state nuclear problem

We present a method based on hyperspherical harmonics to solve the nuclear many-body problem. It is an extension of accurate methods used for studying few-body systems to many bodies and is based on the assumption that nucleons in nuclei interact mainly via pairwise forces. This leads to a two-variable integro-differential equation which is easy to solve. Unlike methods that utilize effective interactions, the present one employs directly nucleon-nucleon potentials and therefore nuclear correlations are included in an unambiguous way. Three body forces can also be included in the formalism. Details on how to obtain the various ingredients entering into the equation for the A-body system are given. Employing our formalism we calculated the binding energies for closed and open shell nuclei with central forces where the bound states are defined by a single hyperspherical harmonic. The results found are in agreement with those obtained by other methods.     

An approach to comparing Kolmogorov-Sinai and permutation entropy

In this paper we discuss the relationship between permutation entropy and Kolmogorov-Sinai entropy in the one-dimensional case. For this, we consider partitions of the state space of a dynamical system using ordinal patterns of order (d + n? 1) on the one hand, and using n-letter words of ordinal patterns of order d on the other hand. The answer to the question of how different these partitions are provides an approach to comparing the entropies.     

Some Properties of πr Meson in Nuclear Matter with Finite Density

In the GCM we study some properties of π meson as the Goldstone bosons in a nuclear matter with finitedensity. Using the effective action in a nuclear matter, we calculate the decay constant and π mass as functions of thechemical potential. The relation between the chemical potential and the density of a nuclear matter is firstly given here.We find that fπ and mπ monotonously decrease as nuclear matter density increases. The result is consistent with theusual assumption that the chiral symmetry is gradually restored as the density of a nuclear matter increases.     

Many-fragment correlations and possible signature of spinodal fragmentation

Abnormal production of events with almost equal-sized fragments was theoretically proposed as a signature of spinodal instabilities responsible for nuclear multifragmentation. Many-fragment correlations can be used to enlighten any extra production of events with specific fragment partitions. The high sensitivity of such correlation methods makes it particularly appropriate to look for small numbers of events as those expected to have kept a memory of spinodal decomposition properties and to reveal the dynamics of a first-order phase transition for nuclear matter and nuclei. This paper summarizes results obtained so far for both experimental and dynamical simulations data.