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...

We apply a spin-projection method to calculate microscopically the level densities of a family of nickel isotopes 59−64 Ni using the shell model Monte Carlo approach in the complete pf g 9/2 shell. Accurate ground-state energies of the odd-mass nickel isotopes, required for the determination of excitation energies, are determined using the Green's function method recently introduced to circumvent the odd particle-number sign problem. Our results are in excellent agreement with recent measurements based on proton evaporation spectra and with level counting data at low excitation energies. We also compare our results with neutron resonance data, assuming equilibration of parity and a spin-cutoff model for the spin distribution at the neutron binding energy, and find good agreement with the exception of 63 Ni.Introduction. Nuclear level densities play an important role in determining the elemental abundances in stellar nucleosynthesis [1,2]. However, the microscopic calculation of level densities from underlying effective interactions has been a major theoretical challenge [3].The configuration-interaction (CI) shell model approach [4] offers an attractive framework for reliable calculation of nuclear level densities. In this approach, both shell effects and correlations are included a priori; thereby eliminating the need for a posteriori parameter fitting as is done, for example, in empirical approaches based on the back-shifted Bethe formula (BBF) [5][6][7].However, the conventional shell model approach, which is based on direct diagonalization of the Hamiltonian in a truncated CI shell model space, becomes prohibitively difficult in medium-mass and heavy nuclei because of the combinatorial increase of the dimensionality of the manybody Hilbert space. An alternative is provided by the shell model Monte Carlo (SMMC) approach [8][9][10][11][12]. The SMMC can be used to calculate thermodynamic observables within the CI shell model framework. In particular, it has been shown to provide accurate estimates of nuclear state densities [13][14][15][16][17][18][19]. The computational resources required for SMMC calculations scale gently with the size of the single-particle space, enabling calculations in very large many-particle model spaces.A variety of methods are used to extract level densities from experimental data: direct level counting at very low excitation energies, neutron or proton resonance data at the neutron or proton binding energy, and Ericson's fluctuation analysis [20] at higher excitation energies (E x 15 MeV in medium-mass nuclei). Level densities at intermediate energies can be extracted from charged particle reactions [21], and using the Oslo method [22] in nuclei for which both level counting and neutron resonance data are available. More recently, neutron and proton evaporation spectra have been used to determine level densities at intermediate energies independently of the neutron resonance data [23]. In particular, the level densities of a family of nickel isotopes ( 59−64 Ni) were extracted from p...

The B(E2) excitation strength of the first excited 2 + state in even-even nuclei should directly correlate to the size of the valence space and maximize at mid-shell. A previously found saturation of B(E2) strengths in well-deformed rotors at mid-shell is tested through high-precision measurements of the lifetimes of the lowest-lying 2 + states of the 168 Hf and 174 W rare earth isotopes. Measurements were performed using fast LaBr3 scintillation detectors. Combined with the recently re-measured B(E2; 2

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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.