International Journal of Modern Physics E

Embedded random matrix ensembles generated by random interactions (of low body rank and usually two-body) in the presence of a one-body mean field, introduced in nuclear structure physics, are now established to be indispensable in describing statistical properties of a large number of isolated finite quantum many-particle systems. Lie algebra symmetries of the interactions, as identified from nuclear shell model and the interacting boson model, led to the introduction of a variety of embedded ensembles (EEs). These ensembles with a mean field and chaos generating two-body interaction generate in three different stages, delocalization of wave functions in the Fock space of the mean-field basis states. The last stage corresponds to what one may call thermalization and complex nuclei, as seen from many shell model calculations, lie in this region. Besides briefly describing them, their recent applications to nuclear structure are presented and they are (i) nuclear level densities with interactions; (ii) orbit occupancies; (iii) neutrinoless double beta decay nuclear transition matrix elements as transition strengths. In addition, their applications are also presented briefly that go beyond nuclear structure and they are (i) fidelity, decoherence, entanglement and thermalization in isolated finite quantum systems with interactions; (ii) quantum transport in disordered networks connected by many-body interactions with centrosymmetry; (iii) semicircle to Gaussian transition in eigenvalue densities with $k$-body random interactions and its relation to the Sachdev–Ye–Kitaev (SYK) model for majorana fermions.

The low-energy sector of the mesonic spectrum exhibits some features which may be understood in terms of the SO(4) symmetry contained in the QCD-Hamiltonian written in the Coulomb Gauge. In our previous work, we have shown that this is indeed the case when the Instantaneous Color-Charge Interaction (ICCI) is treated by means of nonperturbative many-body techniques. Continuing along this line of description, in this work we calculate the width of meson states belonging to the low portion of the spectrum ($E<1$ GeV). In spite of the rather simple structure of the Hamiltonian used to calculate the spectra of pseudoscalar and vector mesons, the results for the width of these states follow the pattern of the data.

Simple expression for the temperature dependence of the width of fission-fragment mass yields is obtained for high excitation energies. The width depends on the number of nucleons in nuclei, the volume and surface terms of the energy level density parameter, the temperature and the stiffness parameter of the potential related to mass-asymmetric degree of freedom. The contribution of the surface term of the energy level density parameter into the width is important at temperatures $\gtrsim 1$MeV.

Based on theoretical models and experimental evidences of a soft phase transition, with significant, but not abrupt changes in pairing gap of nuclei, a modified pairing gap function was suggested and examined for some of nuclei in our previous publications. Now, we propose a new method to extract the parameters, which exist in the modified pairing gap function. This method is based on phenomenological models, which consider the small size of nuclei and the effect of thermal fluctuations, at the vicinity of the critical temperature. The obtained pairing gap function by this method is easily applicable in the microscopic model calculations within an entire temperature range, from zero to temperatures above the critical point.

Entropy, dimensions and other multifractal characteristics of multiplicity distributions of relativistic charged hadrons produced in ion–ion collisions at SPS energies are investigated. The analysis of the experimental data is carried out in terms of phase space bin-size dependence of multiplicity distributions following the Takagi’s approach. Yet another method is also followed to study the multifractality which, is not related to the bin-width and (or) the detector resolution, rather involves multiplicity distribution of charged particles in full phase space in terms of information entropy and its generalization, Rényi’s order-$q$ information entropy. The findings reveal the presence of multifractal structure — a remarkable property of the fluctuations. Nearly constant values of multifractal specific heat “$c$” estimated by the two different methods of analysis followed indicate that the parameter “$c$” may be used as a universal characteristic of the particle production in high energy collisions. The results obtained from the analysis of the experimental data agree well with the predictions of Monte Carlo model AMPT.

The half-lives of the cluster decay (CD) from the isotopes having the known experimental values, the half-lives of the $\alpha$-decay (AD) of same nuclei and also the branching ratios are obtained, within the framework of two-potential approach with cosh potential including with and without the isospin effects. Using two-potential approach and taking into account the isospin effects in the calculations decrease the rms values and they improve the results. The obtained branching ratios are in good agreement with the experimental ones for some isotopes. It is obtained that the isospin-dependent potentials have an influence on the half-lives of the cluster decays of nuclei. Present calculations would be important for predicting the experimental half-lives and branching ratios for the cluster decays of different types of isotopes.

We study the strange quark mass effect on the phase diagram of strong interaction and the structure of compact stars with a thermodynamically enhanced perturbative QCD model by matching quark matter onto nuclear matter using the Gibbs conditions. It is found that the mass effect of strange quark matter can obviously stiffen the equation of state of mixed phases and result in more massive hybrid stars (HSs), while that usually lowers the maximum mass of pure quark stars. Given reasonable model parameters, the maximum mass of HSs can reach two times the solar mass and the stars always have mixed-phase core in a considerably wide range of model parameters.

In this work we present some results of the interaction of high-energy muons with emulsion nuclei. The interaction results in emission of a number of fragments as a consequence of electromagnetic dissociation of the excited target nuclei. This excitation is attributed to absorption of photons by the target nuclei due to the intense electric field of the very fast incident muon particles. The interactions take place at impact parameters that allow ultra-peripheral collisions to take place, leading to giant resonances and hence multifragmentation of emulsion targets. Charge identification, range, energy spectra, angular distribution and topological cross-section of the produced fragments are measured and evaluated.

We argue that $p_T$ distribution data from the LHC on the invariant differential yield of the charged primary particles in $pp$ collisions at $\sqrt{s}=0.9\mathrm{\text{TeV}},2.76\mathrm{\text{TeV}},7\mathrm{\text{TeV}}$ and in Pb–Pb collisions at $\sqrt{s_{NN}}=2.76$TeV with six centrality bins contains several $p_T$ regions with special properties. These distributions were analyzed by fitting the data with exponential functions. We conclude that the regions reflect features of fragmentation and hadronization of partons through the string dynamics. The nuclear transparency results in negligible influence of the medium in the III region ($p_T>17-20\mathrm{\text{GeV/c}}$), which has highest $p_T$ values. The effects and changes by the medium start to appear weakly in the II region ($4-6\mathrm{\text{GeV/c}}<p_T<17-20\mathrm{\text{GeV/c}}$) and become stronger in the I region ($p_T<4-6\mathrm{\text{GeV/c}}$). It seems that the II region has highest number of strings. The increase in string density in this region could lead to fusion of strings, appearance of a new string and collective behavior of the partons in the most central collisions. These phenomena can explain anomalous behavior of the Nuclear Modification Factor in the II region. We propose the II region as a possible area of Quark Gluon Plasma formation through string fusion. The first $p_T$ regions are the ones with the maximum number of hadrons and minimum number of strings due to direct hadronization of the low energy strings into two quark systems–mesons.

A continuous wavelet analysis is performed for pattern recognition of the pseudorapidity density profile of singly charged particles produced in ${}^{16}$O+Ag/Br and ${}^{32}$S+Ag/Br interactions, each at an incident energy of $200$ GeV per nucleon in the laboratory system. The experiments are compared with a model prediction based on the ultra-relativistic quantum molecular dynamics (UrQMD). To eliminate the contribution coming from known source(s) of particle cluster formation like Bose–Einstein correlation (BEC), the UrQMD output is modified by “an algorithm that mimics the BEC as an after burner.” We observe that for both interactions particle clusters are found at same pseudorapidity locations at all scales. However, the cluster locations in the ${}^{16}$O+Ag/Br interaction are different from those found in the ${}^{32}$S+Ag/Br interaction. Significant differences between experiments and simulations are revealed in the wavelet pseudorapidity spectra that can be interpreted as the preferred pseudorapidity values and/or scales of the pseudorapidity interval at which clusters of particles are formed. The observed discrepancy between experiment and corresponding simulation should therefore be interpreted in terms of some kind of nontrivial dynamics of multiparticle production.