C. Özen

Crossover from vibrational to rotational collectivity in heavy nuclei in the shell-model Monte Carlo approach.

Heavy nuclei exhibit a crossover from vibrational to rotational collectivity as the number of neutrons or protons increases from shell closure towards midshell, but the microscopic description of this crossover has been a major challenge. We apply the shell model Monte Carlo approach to families of even-even samarium and neodymium isotopes and identify a microscopic signature of the crossover from vibrational to rotational collectivity in the low-temperature behavior of ⟨J(2)⟩(T), where J is the total spin and T is the temperature. This signature agrees well with its values extracted from experimental data. We also calculate the state densities of these nuclei and find them to be in very good agreement with experimental data. Finally, we define a collective enhancement factor from the ratio of the total state density to the intrinsic state density as calculated in the finite-temperature Hartree-Fock-Bogoliubov approximation. The decay of this enhancement factor with excitation energy is found to correlate with the pairing and shape phase transitions in these nuclei.

Shell-model Monte Carlo simulations of the BCS-BEC crossover in few-fermion systems

Frankfurt Institute for Advanced Studies, D-60438 Frankfurt, Germany(Dated: July 23, 2009)We study a trapped system of fermions with a zero-range two-body interaction using the shell-model Monte Carlo method, providing ab initio results for the low particle number limit wheremean-field theory is not applicable. We present results for the N-body energies as function ofinteraction strength, particle number, and temperature. The subtle question of renormalization ina finite model space is addressed and the convergence of our method and its applicability acrossthe BCS-BEC crossover is discussed. Our findings indicate that very good quantitative results canbe obtained on the BCS side, whereas at unitarity and in the BEC regime the convergence is lessclear. Comparison to N = 2 analytics at zero and finite temperature, and to other calculations inthe literature for N > 2 show very good agreement.

Parity-projected shell model Monte Carlo level densities for fp-shell nuclei

We calculate parity-dependent level densities for the even-even isotopes 58,62,66Fe and 58Ni and the odd-A nuclei 59Ni and 65Fe using the Shell Model Monte Carlo method. We perform these calculations in the complete fp-gds shell-model space using a pairing+quadrupole residual interaction. We find that, due to pairing of identical nucleons, the low-energy spectrum is dominated by positive parity states. Although these pairs break at around the same excitation energy in all nuclei, the energy dependence of the ratio of negative-to-positive parity level densities depends strongly on the particular nucleus of interest. We find equilibration of both parities at noticeably lower excitation energies for the odd-A nuclei 59Ni and 65Fe than for the neighboring even-even nuclei 58Ni and 66Fe.

Mapping the two-component atomic Fermi gas to the nuclear shell-model

The physics of a two-component cold Fermi gas is now frequently addressed in laboratories. Usually this is done for large samples of tens to hundreds of thousands of particles. However, it is now possible to produce few-body systems (1–100 particles) in very tight traps where the shell structure of the external potential becomes important. A system of two-species fermionic cold atoms with an attractive zero-range interaction is analogous to a simple model of nucleus in which neutrons and protons interact only through a residual pairing interaction. In this article, we discuss how the problem of a two-component atomic Fermi gas in a tight external trap can be mapped to the nuclear shell-model so that readily available many-body techniques in nuclear physics, such as the Shell-Model Monte Carlo (SMMC) method, can be directly applied to the study of these systems. We demonstrate an application of the SMMC method by estimating the pairing correlations in a small two-component Fermi system with moderate-to-strong short-range two-body interactions in a three-dimensional harmonic external trapping potential.

Turkey's nuclear energy policy: towards a sustainable energy mix?

To originate new sustainable development policies is a prerequisite for achieving a higher level of worldwide economic and social development. The efficiency of a sustainable development policy could, and should, be measured by a multi-dimensional analysis that comprises all social, economic and environmental factors. Acknowledging the requirement to have a sustainable energy mix, net energy importer Turkey has initiated its nuclear energy programme. However, this move by Turkey also brings forth certain environmental, social and economic issues that have been a matter of ongoing debate. This study aims not only to contribute to the debate by providing a balanced enquiry of nuclear energys pros and cons, but also to determine the pre-conditions for it to prompt Turkey to reach a sustainable energy future. The nuclear option has a significant potential to drive Turkeys transition to sustainable energy as long as several environmental, social and economic risk factors are minimised.

Shell model Monte Carlo method in the pn-formalism and applications to the Zr and Mo isotopes

We report the development of a new shell model Monte Carlo algorithm, which uses the proton-neutron formalism. Shell model Monte Carlo methods, within the isospin formulation, have been successfully used in large-scale shell model calculations. Motivation for this work is to extend the feasibility of these methods to shell model studies involving nonidentical proton and neutron valence spaces. We show the feasibility of the new approach with some test results. Finally, we use a realistic nucleon-nucleon interaction in the model space described by (1p{sub 1/2},0g{sub 9/2}) proton and (1d{sub 5/2},2s{sub 1/2},1d{sub 3/2},0g{sub 7/2},0h{sub 11/2}) neutron orbitals above the {sup 88}Sr core to calculate ground-state energies, binding energies, B(E2) strengths, and to study pairing properties of the even-even {sup 90-104}Zr and {sup 92-106}Mo isotope chains.

Collectivity in Heavy Nuclei in the Shell Model Monte Carlo Approach

The microscopic description of collectivity in heavy nuclei in the framework of the configuration-interaction shell model has been a major challenge. The size of the model space required for the description of heavy nuclei prohibits the use of conventional diagonalization methods. We have overcome this difficulty by using the shell model Monte Carlo (SMMC) method, which can treat model spaces that are many orders of magnitude larger than those that can be treated by conventional methods. We identify a thermal observable that can distinguish between vibrational and rotational collectivity and use it to describe the crossover from vibrational to rotational collectivity in families of even-even rare-earth isotopes. We calculate the state densities in these nuclei and find them to be in close agreement with experimental data. We also calculate the collective enhancement factors of the corresponding level densities and find that their decay with excitation energy is correlated with the pairing and shape phase transitions.

Recent developments in the shell model Monte Carlo approach to nuclei

The shell model Monte Carlo (SMMC) approach provides a powerful method for the microscopic calculation of statistical and collective nuclear properties in model spaces that are many orders of magnitude larger than those that can be treated by conventional methods. We discuss recent applications of the method to describe the emergence of collectivity in the framework of the configuration-interaction shell model and the crossover from vibrational to rotational collectivity in families of rare-earth nuclei. We have calculated state densities of these rare-earth nuclei and find their collective enhancement factors to be correlated with the pairing and shape phase transitions. We also discuss an accurate method to calculate the ground-state energy of odd-even and odd-odd nuclei, circumventing the sign problem that originates in the projection on an odd number of particles. We have applied this method to calculate pairing gaps in families of isotopes in the iron region.

Nuclear Level Density of 161Dy in the Shell Model Monte Carlo Method

We extend the shell-model Monte Carlo applications to the rare-earth region to include the odd-even nucleus 161 Dy. The projection on an odd number of particles leads to a sign problem at low temperatures making it impractical to extract the ground-state energy in direct calculations. We use level counting data at low energies and neutron resonance data to extract the shell model ground-state energy to good precision. We then calculate the level density of 161 Dy and find it in very good agreement with the level density extracted from experimental data.

Recent Advances in the Application of the Shell Model Monte Carlo Approach to Nuclei

The shell model Monte Carlo (SMMC) method is a powerful technique for calculating the statistical and collective properties of nuclei in the presence of correlations in model spaces that are many orders of magnitude larger than those that can be treated by conventional diagonalization methods. We review recent advances in the development and application of SMMC to mid-mass and heavy nuclei.