Estimating Parameter Uncertainty in Binding-Energy Models by the Frequency-Domain Bootstrap.

We propose using the frequency-domain bootstrap (FDB) to estimate errors of modeling parameters when the modeling error is itself a major source of uncertainty. Unlike the usual bootstrap or the simple χ^{2} analysis, the FDB can take into account correlations between errors. It is also very fast compared to the Gaussian process Bayesian estimate as often implemented for computer model calibration. The method is illustrated with a simple example, the liquid drop model of nuclear binding energies. We find that the FDB gives a more conservative estimate of the uncertainty in liquid drop parameters than the χ^{2} method, and is in fair accord with more empirical estimates. For the nuclear physics application, there are no apparent obstacles to apply the method to the more accurate and detailed models based on density-functional theory.

Exit-Channel Suppression in Statistical Reaction Theory.

Statistical reaction theories such as the Hauser-Feshbach theory assume that branching ratios follow Bohr's compound nucleus hypothesis by factorizing into independent probabilities for different channels. Corrections to the factorization hypothesis are known in both nuclear theory and quantum transport theory, particularly an enhanced memory of the entrance channel. We apply the Gaussian orthogonal ensemble to study a complementary suppression of exit channel branching ratios. The combined effect of the width fluctuation and the limitation on the transmission coefficient can provide a lower bound on the number of exit channels. The bound is demonstrated for the branching ratio in neutron-induced reactions on a ^{235}U target.

Nuclear Matrix Elements for Tests of Local Lorentz Invariance Violation.

The nuclear matrix elements for the spin operator and the momentum quadrupole operator are important for the interpretation of precision atomic physics experiments that search for violations of local Lorentz and CPT symmetry and for new spin-dependent forces. We use the configuration-interaction nuclear shell model and self-consistent mean-field theory to calculate the momentum matrix elements for ^{21}Ne, ^{23}Na, ^{133}Cs, ^{173}Yb, and ^{201}Hg. We show that these momentum matrix are strongly suppressed by the many-body correlations, in contrast to the well-known enhancement of the spatial quadrupole nuclear matrix elements.

Nuclear deformation at finite temperature.

Deformation, a key concept in our understanding of heavy nuclei, is based on a mean-field description that breaks the rotational invariance of the nuclear many-body Hamiltonian. We present a method to analyze nuclear deformations at finite temperature in a framework that preserves rotational invariance. The auxiliary-field Monte Carlo method is used to generate a statistical ensemble and calculate the probability distribution associated with the quadrupole operator. Applying the technique to nuclei in the rare-earth region, we identify model-independent signatures of deformation and find that deformation effects persist to temperatures higher than the spherical-to-deformed shape phase-transition temperature of mean-field theory.

Nuclear correlations and the r process.

We show that long-range correlations for nuclear masses have a significant effect on the synthesis of heavy elements by the r process. As calculated by Delaroche et al. [Phys. Rev. C 81, 014303 (2010)], these correlations suppress magic number effects associated with minor shells. This impacts the calculated abundances before the third r-process peak (at mass number A≈195), where the abundances are low and form a trough. This trough and the position of the third abundance peak are strongly affected by the masses of nuclei in the transition region between deformed and spherical. Based on different astrophysical environments, our results demonstrate that a microscopic theory of nuclear masses including correlations naturally smoothens the separation energies, thus reducing the trough and improving the agreement with observed solar system abundances.

Symmetry restoration in Hartree-Fock-Bogoliubov based theories.

We present a Pfaffian formula for projection and symmetry restoration for wave functions of the general Bogoliubov form, including quasiparticle excited states and linear combinations of them. This solves a long-standing problem in calculating states of good symmetry, arising from the sign ambiguity of the commonly used determinant formula. A simple example is given of projecting a good particle number and angular momentum from a Bogoliubov wave function in the Fock space of a single j-shell.

Nonadiabatic generation of coherent phonons.

The time-dependent density functional theory (TDDFT) is the leading computationally feasible theory to treat excitations by strong electromagnetic fields. Here the theory is applied to coherent optical phonon generation produced by intense laser pulses. We examine the process in the crystalline semimetal antimony (Sb), where nonadiabatic coupling is very important. This material is of particular interest because it exhibits strong phonon coupling and optical phonons of different symmetries can be observed. The TDDFT is able to account for a number of qualitative features of the observed coherent phonons, despite its unsatisfactory performance on reproducing the observed dielectric functions of Sb. A simple dielectric model for nonadiabatic coherent phonon generation is also examined and compared with the TDDFT calculations.

Mixed-spin pairing condensates in heavy nuclei.

We show that the Bogoliubov-de Gennes equations for nuclear ground-state wave functions support solutions in which the condensate has a mixture of spin-singlet and spin-triplet pairing. We find that such mixed-spin condensates do not occur when there are equal numbers of neutrons and protons, but only when there is an isospin imbalance. Using a phenomenological Hamiltonian, we predict that such nuclei may occur in the physical region within the proton dripline. We also solve the Bogoliubov-de Gennes equations with variable constraints on the spin-singlet and spin-triplet pairing amplitudes. For nuclei that exhibit this new pairing behavior, the resulting energy surface can be rather soft, suggesting that there may be low-lying excitations associated with the spin mixing.

Magnetic circular dichroism in real-time time-dependent density functional theory.

We apply the adiabatic time-dependent density functional theory to magnetic circular dichroism (MCD) spectra using the real-space, real-time computational method. The standard formulas for the MCD response and its A and B terms are derived from the observables in the time-dependent wave function. We find real-time method is well suited for calculating the overall spectrum, particularly at higher excitation energies where individual excited states are numerous and overlapping. The MCD sum rules are derived and intepreted in the real-time formalism; we find that they are very useful for normalization purposes and assessing the accuracy of the theory. The method is applied to MCD spectrum of C(60) using the adiabatic energy functional from the local density approximation. The theory correctly predicts the signs of the A and B terms for the lowest allowed excitations. However, the magnitudes of the terms only show qualitative agreement with experiment.

Porter-Thomas fluctuations in complex quantum systems.

The Gaussian orthogonal ensemble (GOE) of random matrices has been widely employed to describe diverse phenomena in strongly coupled quantum systems. In particular, it has often been invoked to explain the fluctuations in decay rates that follow the χ-squared distribution for one degree of freedom, as originally proposed by Brink and by Porter and Thomas. However, we find that the coupling to the decay channels can change the effective number of degrees of freedom from one to two. Our conclusions are based on a configuration-interaction Hamiltonian originally constructed to test the validity of transition-state theory, also known as the Rice-Ramsperger-Kassel-Marcus theory in chemistry. The internal Hamiltonian consists of two sets of GOE reservoirs connected by an internal channel. We find that the effective number of degrees of freedom depends on the control parameter ρΓ, where ρ is the level density in the first reservoir and Γ is the level decay width. The distribution for two degrees of freedom is a well-known property of the Gaussian unitary ensemble (GUE); our model demonstrates that the GUE fluctuations can be present under much milder conditions. Our treatment of the model permits an analytic derivation for ρΓ≳1.

Effective 3-body interaction for mean-field and density-functional theory.

Density functionals for nuclei usually include an effective 3-body interaction that depends on a fractional power of the density. Using insights from the many-body theory of the low-density two-component Fermi gas, we consider a new, nonlocal, form for the energy functional that is consistent with the Fock-space representation of interaction operators. In particular, there is a unique spatially nonlocal generalization of the contact form of the interaction that preserves the ρ(7/3) density dependence required by the many-body theory. We calculate the ground-state energies for particles in a harmonic trap by using the nonlocal induced 3-body interaction and compare them to numerically accurate Green's function Monte Carlo calculations. Using no free parameters, we find that a nonlocality in the space domain provides a better description of the weak-coupling regime than the local-density approximation.

First-principles description for coherent phonon generation in diamond.

We report a first-principles description for coherent phonon generation in diamond based on the time-dependent density functional theory. The time-dependent Kohn-Sham equation is solved in real time in order to calculate the electron dynamics in periodic solid exposed to an ultrashort laser pulse. We find that the calculated forces acting on ions are consistent with measurements as regards the selection rule and the dependence on the laser intensity.

New effective interaction for the trapped fermi gas.

We apply the configuration-interaction method to calculate the spectra of two-component Fermi systems in a harmonic trap, studying the convergence of energies at the unitary interaction limit. We find that for a fixed regularization of the two-body interaction the convergence is exponential or better in the truncation parameter of the many-body space. However, the conventional regularization is found to have poor convergence in the regularization parameter, with an error that scales as a low negative power of this parameter. We propose a new regularization of the two-body interaction that produces exponential convergence for systems of three and four particles. We estimate the ground-state energy of the four-particle system to be (5.045 +/- 0.003) variant Planck's constant over 2 pi omega.

Systematics of the first 2+ excitation with the Gogny interaction.

We report the first comprehensive calculations of 2(+) excitations with a microscopic theory applicable to over 90% of the known nuclei. The theory uses a quantal collective Hamiltonian in five dimensions. The only parameters in theory are those of the finite-range, density-dependent Gogny D1S interaction. The following properties of the lowest 2(+) excitations are calculated: excitation energy, reduced transition probability, and spectroscopic quadrupole moment. We find that the theory is very reliable to classify the nuclei by shape. For deformed nuclei, average excitation energies and transition quadrupole moments are within 5% of the experimental values, and the dispersion about the averages are roughly 20% and 10%, respectively. Including all nuclei in the performance evaluation, the average transition quadrupole moment is 11% too high and the average energy is 13% too high.

Systematics of quadrupolar correlation energies.

We calculate correlation energies associated with the quadrupole shape degrees of freedom with a view to improving the self-consistent mean-field theory of nuclear binding energies. Systematic results are presented for 605 even-even nuclei from mass number 16 to the heaviest whose mass has been measured, using the Skyrme SLy4 interaction and the generator coordinate method. Correlation energies range from 0.5 to 6.0 MeV, and their inclusion improves two qualitative deficiencies of the mean-field theory, namely, the exaggerated shell effect at neutron magic numbers and the failure of mean-field theory to describe mutually enhanced magicity. For the mass table as a whole, the quadrupolar correlations improve binding energies, separation energies, and separation energy differences by 20%30%.

Reconciling coulomb dissociation and radiative capture measurements.

We calculate the energy spectrum for 8B dissociation on a Pb target to all orders in the Coulomb and nuclear fields, and show that the slope of S17(E) obtained in previous analyses of Coulomb dissociation data is too steep, due to deficiencies in the conventional first-order analysis that was used. With a more complete theory that avoids the far-field approximation and includes E2, nuclear and dynamical projectile polarization, the disagreement between indirect and direct methods for determining the S17(E) slope and the extrapolated S17(0) values is reduced significantly.