We introduce spin projection methods in the shell model Monte Carlo approach and apply them to calculate the spin distribution of level densities for iron-region nuclei using the complete (pf + g9/2) shell. We compare the calculated distributions with the spin-cutoff model and extract an energy-dependent moment of inertia. For even-even nuclei and at low excitation energies, we observe a significant suppression of the moment of inertia and odd-even staggering in the spin dependence of level densities.

The heat capacity of iron isotopes is calculated within the interacting shell model using the complete $(pf+0g_{9/2})$-shell. We identify a signature of the pairing transition in the heat capacity that is correlated with the suppression of the number of spin-zero neutron pairs as the temperature increases. Our results are obtained by a novel method that significantly reduces the statistical errors in the heat capacity calculated by the shell model Monte Carlo approach. The Monte Carlo results are compared with finite-temperature Fermi gas and BCS calculations.Comment: 14 pages, 4 eps figures included, RevTe

A simple formula for the ratio of the number of odd- and even-parity states as a function of temperature is derived. This formula is used to calculate the ratio of level densities of opposite parities as a function of excitation energy. We test the formula with quantum Monte Carlo shell model calculations in the (pf+g(9/2)) shell. The formula describes well the transition from low excitation energies where a single parity dominates to high excitations where the two densities are equal.

We introduce a particle-number reprojection method in the shell model Monte Carlo that enables the calculation of observables for a series of nuclei using a Monte Carlo sampling for a single nucleus. The method is applied to calculate nuclear level densities in the complete ͑ pf 1 g 9͞2 ͒-shell using a good-sign Hamiltonian. Level densities of odd-A and odd-odd nuclei are reliably extracted despite an additional sign problem. Both the mass and the T z dependence of the experimental level densities are well described without any adjustable parameters. The odd-even staggering observed in the calculated backshift parameter follows the experimental data more closely than do empirical formulas. PACS numbers: 21.10.Ma, 21.60.Cs, 21.60.Ka, 27.40. + z The interacting shell model has successfully described a variety of nuclear properties. However, the size of the model space increases rapidly with the number of valence nucleons and/or orbits, and exact diagonalization of the nuclear Hamiltonian in a full major shell is limited to nuclei with A & 50 [1,2]. The development of quantum Monte Carlo methods for the nuclear shell model allowed realistic calculations of finite-and zero-temperature observables in model spaces that are much larger than those treated by conventional diagonalization techniques [3,4].The Monte Carlo method was successfully adapted to the microscopic calculation of nuclear level densities [5]. Accurate level densities are needed for estimating nuclear reaction rates, e.g., neutron and proton capture rates. The nucleosynthesis of many of the heavy elements proceeds by radiative capture of neutrons (s and r processes) or protons (rp process) in competition with beta decay [6,7]. Theoretical approaches to level densities are often based on the Fermi gas model, i.e., the Bethe formula [8], which describes the many-particle level density in terms of the single-particle level density parameter a. Shell corrections and two-body correlations are taken into account empirically by defining a fictitious ground state energy. In the backshifted Bethe formula (BBF) the ground state energy is shifted by an amount D. This formula describes well the experimental level densities of many nuclei if both a and D are fitted for each individual nucleus [9]. While these parameters have been discussed in terms of their global systematics, it is difficult to predict their values for particular nuclei. The nuclear shell model offers an attractive framework for calculating level densities, but the model space required to calculate level densities at excitation energies in the neutron resonance regime is usually too large for conventional diagonalization methods. We have recently developed a method [5] to calculate exact level densities using the shell model Monte Carlo (SMMC) approach, and applied it to calculate the level densities of even-even nuclei from iron to germanium [10]. Fermionic Monte Carlo methods are usually hampered by the so-called sign problem, which causes a breakdown of the method at low temperatures. A prac...

Nuclear level densities are crucial for estimating statistical nuclear reaction rates. The shell model Monte Carlo method is a powerful approach for microscopic calculation of state densities in very large model spaces. However, these state densities include the spin degeneracy of each energy level, whereas experiments often measure level densities, in which each level is counted just once. To enable the direct comparison of theory with experiments, we introduce a method to calculate directly the level density in the shell model Monte Carlo approach. The method employs a projection on the minimal absolute value of the magnetic quantum number. We apply the method to nuclei in the iron region and to the strongly deformed rare-earth nucleus 162 Dy. We find very good agreement with experimental data and methods, including level counting at low energies, charged particle spectra and Oslo method data at intermediate energies, neutron and proton resonance data, and Ericson's fluctuation analysis at higher excitation energies. We also extract a thermal moment of inertia from the ratio between the state density and the level density, and observe that in even-even nuclei it exhibits a signature of a phase transition to a superconducting phase below a certain excitation energy. Introduction. The level density is among the most important statistical properties of atomic nuclei. It appears explicitly in Fermi's golden rule for transition rates and in the Hauser-Feshbach theory [1] of statistical nuclear reactions. Yet its microscopic calculation presents a major theoretical challenge. In particular, correlations have important effects on nuclear level densities but are difficult to include quantitatively beyond the mean-field approximation. The configuration-interaction (CI) shell model is a suitable framework, in which both shell effects and correlations are included. However, the dimension of the required model space increases combinatorially with the number of single-particle states and/or the number of nucleons, and conventional shell model calculations become intractable in medium-mass and heavy nuclei. This difficulty has been overcome using the shell model Monte Carlo (SMMC) approach [2][3][4][5]. The SMMC has proved to be a powerful method to calculate microscopically nuclear state densities [6][7][8][9][10][11].The SMMC method is based on a thermodynamic approach, in which observables such as the thermal energy are calculated by tracing over the complete many-particle Hilbert space at fixed number of protons and neutrons. Thus, the calculated density is the state density, which takes into account the magnetic degeneracy of the nuclear levels, i.e., each level of spin J is counted 2J + 1 times.However, experiments often measure the level density, in which each level is counted exactly once, irrespective of its spin degeneracy [12][13][14]. To make direct comparison of theory with experiments, it would be necessary to calculate the level density within the SMMC approach. A spin-projection method, introduced in Ref. 10...