Nuclear level density and related physics

Condensed Matter

In this work, we investigate the collective role of thermal and quantum fluctuations on non-equilibrium thermodynamics of a quantum system, specifically, the quantum-thermodynamic description of spin-1 nuclei based on the concepts of quantum and statistical mechanics. We explore the dynamical response of the system when driven out of equilibrium by a work parameter and compute analytically the full distribution of the work generated by the process. Considering work performed on the system as a random variable, we collect data for a large number of repeated cyclic processes of finite time. These data of finite time non-equilibrium processes will permit us to derive equilibrium values in quantities such as the free energy difference between the final and initial states of the system. Various properties of the system’s work distribution are explored.

Physical Review C, 2016

The knowledge of the nuclear level density is necessary for understanding various reactions including those in the stellar environment. Usually the combinatorics of Fermi-gas plus pairing is used for finding the level density. Recently a practical algorithm avoiding diagonalization of huge matrices was developed for calculating the density of many-body nuclear energy levels with certain quantum numbers for a full shell-model Hamiltonian. The underlying physics is that of quantum chaos and intrinsic thermalization in a closed system of interacting particles. We briefly explain this algorithm and, when possible, demonstrate the agreement of the results with those derived from exact diagonalization. The resulting level density is much smoother than that coming from the conventional mean-field combinatorics. We study the role of various components of residual interactions in the process of thermalization, stressing the influence of incoherent collision-like processes. The shell-model results for the traditionally used parameters are also compared with standard phenomenological approaches.

A general overview is given on the phenomenological methods used to describe the level densities in nuclei. Two well-known two-parameter formulas of level densities, the Back-Shifted Fermi Gas (BSFG) model and the Constant Temperature (CT) model, were used. A common ingredient of both is the spin distribution function, which contains in Ericsons's parametrization the spin-cutoff parameter σ. A realistic description of the parameters of both spin distribution function and the two level density models has been obtained by fitting the experimental data of 310 nuclei between 18 F and 251 Cf, consisting of the complete level schemes at low excitation energies and the s-wave neutron resonance spacings at the neutron binding energy. We determine a simple formula for the spin-cutoff parameter as a function of mass number and excitation energy. Also, an even-odd spin staggering in the spin distribution of the even-even nuclei was observed, and described with a simple formula. Using this newly defined spin distribution function, an empirical set of parameters of the BSFG and CT models was determined by fitting both the low-energy levels and the neutron resonance spacings. For these parameters, simple formulas were proposed that involve only quantities available from the mass tables, and allow reasonable estimations of the level density parameters for nuclei far from stability. Both the BSFG and CT models describe equally well the level densities at energies up to at least the neutron binding energy. Finally, we discuss recent experimental evidence that the CT model is the more correct description of the nuclei in the low-excitation energy (pairing) regime.

Physics Letters B, 2005

Physical review, 2015

The effect of temperature (T) and angular momentum (J) on the inverse level density parameter (k) has been studied by populating the compound nucleus 97 Tc in the reaction 4 He + 93 Nb at four incident beam energies of 28, 35, 42 and 50 MeV. For all the four energies, the value of k decreases with increasing J. The T dependence of k has been compared for two angular momentum windows with different theoretical predictions as well as with FTBCS1 calculation which takes into account the quasiparticle-number fluctuations in the pairing field. Interestingly, the experimental data are in good agreement with the theoretical calculations at higher J but deviate from all the calculations at lower J.

Physical Review C, 2002

The properties of the pairing interaction in the shell model framework are considered with the aid of the exact numerical solution utilizing the quasispin symmetry. We emphasize the features which are out of reach for the usual approximate techniques based on the BCS approach supplemented by the random phase approximation treatment of pair vibrations, especially in the region of weak pairing where the BCS+RPA theory fails. For the first time chaotic aspects of the mixing generated by the pairing interaction are studied. The level repulsion and large information entropy of the eigenstates coexist with the absence of thermalization of single-particle motion. The full spectrum of pair vibration in average displays the spin dependence similar to that for a rigid rotor.

Physics reports, 1996

Atomic nuclei analyzed in the framework of the shell model provide a good example of a many-body quantum system with strong interactions between its constituents. As excitation energy and level density increase, the system evolves in the direction of very complicated ...

Nuclear Physics A, 1991

We develop a general model with which the statistical properties of nuclear systems can be addressed. Within a semi-classical treatment, using a new finite-range effective nucleon-nucleon interaction depending on both momentum and density, we derive expressions for the free energy as a functional of the specified spatial density distribution, at a given temperature. We explore a family of interactions that all yield the same reasonable properties of nuclear systems at zero temperature, but differ with regard to the effective mass of the nucleon. In order to make contact with other approaches, we calculate the equation of state for uniform isosymmetric matter and the associated phase diagram; the limiting temperature is 12-13 MeV, while the critical temperature is around 16 MeV. The response of uniform matter to density ripples is studied for a range of temperatures and densities and the calculated critical wave length is found to be sensitive to the new parameter governing the effective mass.

Arxiv preprint nucl-th/0107074, 2001

Journal of Physics: Conference Series, 2015

Shell-model calculations with realistic empirical interactions constitute an excellent tool to study statistical properties of nuclei. Using large-scale shell-model calculations in pfshell nuclei, we study how the onset of chaos depends on different properties of the nuclear interaction and on excitation energy. We make use of classical random matrix theory and other theoretical developments based on information theory and time series analysis. We show that besides energy-level statistics, other statistical properties like the complexity of wave functions are fundamental for a proper determination of the dynamical regime of nuclei. Important deviations from GOE are observed in level fluctuations and in the complexity of wave functions.