Shell Model Monte Carlo Methods

We review quantum Monte Carlo methods for dealing with large shell model problems. These methods reduce the imaginary-time many-body evolution operator to a coherent superposition of one-body evolutions in fluctuating one-body fields; the resultant path integral is evaluated stochastically. We first discuss the motivation, formalism, and implementation of such Shell Model Monte Carlo (SMMC) methods. There then follows a sampler of results and insights obtained from a number of applications. These include the ground state and thermal properties of {\it pf}-shell nuclei, the thermal and rotational behavior of rare-earth and $\gamma$-soft nuclei, and the calculation of double beta-decay matrix elements. Finally, prospects for further progress in such calculations are discussed

^7Be(p,γ)^8B cross section and the properties of ^7Be

We study the nonresonant part of the ^7Be(p,γ)^8B reaction using a three-cluster resonating group model that is variationally converged and virtually complete in ^4He+^3He+p model space. The importance of using adequate nucleon-nucleon interaction is demonstrated. We find that the low-energy astrophysical S factor is linearly correlated with the quadrupole moment of ^7Be. A range of parameters is found where the most important ^8B, ^7Be, and ^7Li properties are reproduced simultaneously; the corresponding S factor at E_(c.m.)=20 keV is 24.6–26.1 eV b

New Physics at the International Facility for Antiproton and Ion Research (FAIR) Next to GSI

The project of the international Facility for Antiproton and Ion Research (FAIR), co-located to the GSI facility in Darmstadt, has been officially started on November 7, 2007. The current plans of the facility and the planned research program will be described. An investment of about 1 billion euro will permit new physics programs in the areas of low and medium energy antiproton research, heavy ion physics complementary to LHC, as well as in nuclear structure and astrophysics. The facility will comprise about a dozen accelerators and storage rings, which will enable simultaneous operations of up to four different beams.Comment: 7 pages, 1 figure. Invited Talk presented at the "Fourth International Conference on Fission and Properties of Neutron-Rich nuclei", held at Sanibel Island, Florida, November 11-17, 200

Shell-Model Monte Carlo Simulations of BCS-BEC Crossover in Few-Fermion Systems

We study a trapped system of fermions with a zero-range two-body interaction using the shell-model Monte Carlo method, providing {\em ab initio} results for the low particle number limit where mean-field theory is not applicable. We present results for the $N$-body energies as function of interaction strength, particle number, and temperature. The subtle question of renormalization in a finite model space is addressed and the convergence of our method and its applicability across the BCS-BEC crossover is discussed. Our findings indicate that very good quantitative results can be obtained on the BCS side, whereas at unitarity and in the BEC regime the convergence is less clear. Comparison to N=2 analytics at zero and finite temperature, and to other calculations in the literature for $N>2$ show very good agreement.Comment: 6 pages, 5 figures, Revtex4, final versio

Structure of matter in strong magnetic fields

We give a detailed presentation of Hartree-Fock calculations of atoms and molecular chains in 10^12 G magnetic fields, as are supposed to exist on the surface of neutron stars. These calculations are the first self-consistent ones treating exchange properly for atoms heavier than helium in high fields. We find that the isolated atom is energetically favored over molecular chains for Z>2 at fields greater than 1×10^12G and for Z>4 at fields greater than 5×10^12 G. These results indicate that matter on the surface of neutron stars is bound very weakly, if at all

On the temperature dependence of the symmetry energy

We perform large-scale shell model Monte Carlo (SMMC) calculations for many nuclei in the mass range A=56-65 in the complete pfg_{9/2}d_{5/2} model space using an effective quadrupole-quadrupole+pairing residual interaction. Our calculations are performed at finite temperatures between T=0.33-2 MeV. Our main focus is the temperature dependence of the symmetry energy which we determine from the energy differences between various isobaric pairs with the same pairing structure and at different temperatures. Our SMMC studies are consistent with an increase of the symmetry energy with temperature. We also investigate possible consequences for core-collapse supernovae events

Resonant tunneling in a schematic model

Tunneling of an harmonically bound two-body system through an external Gaussian barrier is studied in a schematic model which allows for a better understanding of intricate quantum phenomena. The role of finite size and internal structure is investigated in a consistent treatment. The excitation of internal degrees of freedom gives rise to a peaked structure in the penetration factor. The model results indicate that for soft systems the adiabatic limit is not necessarily reached although often assumed in fusion of nuclei and in electron screening effects at astrophysical energies.Comment: 7 pages, 7 figure