Ab initioderivation of model energy density functionals
I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results.
Hartree-Fock-Bogoliubov theory of polarized Fermi systems
Condensed Fermi systems with an odd number of particles can be described by means of polarizing external fields having a time-odd character. We illustrate how this works for Fermi gases and atomic nuclei treated by density functional theory or Hartree-Fock-Bogoliubov (HFB) theory. We discuss the method based on introducing two chemical potentials for different superfluid components, whereby one may change the particle-number parity of the underlying quasiparticle vacuum. Formally, this method is a variant of non-collective cranking, and the procedure is equivalent to the so-called blocking. We present and exemplify relations between the two-chemical-potential method and the cranking approxi…
Simple regularization scheme for multi-reference density functional theories
Background: Extensions of single-reference (SR) energy-density-functionals (EDFs) to multi-reference (MR) applications involve using the generalized Wick theorem (GWT), which leads to singular energy kernels that cannot be properly integrated to restore symmetries, unless the EDFs are generated by true interactions. Purpose: We propose a new method to regularize the MR EDFs, which is based on using auxiliary quantities obtained by multiplying the kernels with appropriate powers of overlaps. Methods: Regularized matrix elements of two-body interactions are obtained by integrating the auxiliary quantities and then solving simple linear equations. Results: We implement the new regularization m…
Correlating Schiff Moments in the Light Actinides with Octupole Moments
We show that the measured intrinsic octupole moments of $^{220}$Rn, $^{224}$Ra, and $^{226}$Ra constrain the intrinsic Schiff moments of $^{225}$Ra$^{221}$Rn, $^{223}$Rn, $^{223}$Fr, $^{225}$Ra, and $^{229}$Pa. The result is a dramatically reduced uncertainty in intrinsic Schiff moments. Direct measurements of octupole moments in odd nuclei will reduce the uncertainty even more. The only significant source of nuclear-physics error in the laboratory Schiff moments will then be the intrinsic matrix elements of the time-reversal non-invariant interaction produced by CP-violating fundamental physics. Those matrix elements are also correlated with octupole moments, but with a larger systematic u…
Energy-density-functional calculations including the proton-neutron mixing
We present results of calculations based on the Skyrme energy density functional including the arbitrary mixing between protons and neutrons. In this framework, single-particle states are superpositions of proton and neutron components and the energy density functional is fully invariant with respect to three-dimensional rotations in the isospin space. The isospin of the system is controlled by means of the isocranking method, which carries over the standard cranking approach to the isospin space. We show numerical results of the isocranking calculations performed for isobaric analogue states in the A=14 and $A=40-56$ nuclei. We also present such results obtained for high-isospin states in …
Nuclear structure of lowestTh229states and time-dependent fundamental constants
The electromagnetic transition between the almost degenerate $5/{2}^{+}$ and $3/{2}^{+}$ states in $^{229}\mathrm{Th}$ is deemed to be very sensitive to potential changes in the fine structure constant $\ensuremath{\alpha}$. State of the art Hartree-Fock and Hartree-Fock-Bogoliubov calculations are performed to compute the difference in Coulomb energies of the two states that determines the sensitivity of the transition frequency \ensuremath{\nu} on variations in $\ensuremath{\alpha}$. The kinetic energies are also calculated that reflect a possible variation in the nucleon or quark masses. As the two states differ mainly in the orbit occupied by the last unpaired neutron the Coulomb energy…
Spatial symmetries of the local densities
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial cases are considered.
Error Estimates of Theoretical Models: a Guide
This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical error estimates, strategies to assess systematic errors, and show how to uncover inter-dependencies by correlation analysis. The basic concepts are illustrated through simple examples. By providing theoretical error bars on predicted quantities and using statistical methods to study correlations between observables, theory can significantly enhance the feedback between experiment and nuclear modeling.
Global nuclear structure aspects of tensor interaction
A direct fit of the isoscalar spin-orbit and both isoscalar and isovector tensor coupling constants to the f5/2-f7/2 SO splittings in 40Ca, 56Ni, and 48Ca requires: (i) a significant reduction of the standard isoscalar spin-orbit strength and (ii) strong attractive tensor coupling constants. The aim of this paper is to address the consequences of these strong attractive tensor and weak spin-orbit fields on total binding energies, two-neutron separation energies and nuclear deformability.
In-beam spectroscopic study of $^{244}$Cf
The ground-state rotational band of the neutron-deficient californium ( Z = 98 ) isotope 244 Cf was identified for the first time and measured up to a tentative spin and parity of I π = 20 + . The observation of the rotational band indicates that the nucleus is deformed. The kinematic and dynamic moments of inertia were deduced from the measured γ -ray transition energies. The behavior of the dynamic moment of inertia revealed an up-bend due to a possible alignment of coupled nucleons in high- j orbitals starting at a rotational frequency of about ℏ ω = 0.20 MeV . The results were compared with the systematic behavior of the even-even N = 146 isotones as well as with available theoretical c…
Isospin Mixing Within the Symmetry Restored Density Functional Theory and Beyond
We present results of systematic calculations of the isospin-symmetry-breaking corrections to the superallowed I=$0+,T=1 --> I=0+,T=1 beta-decays, based on the self-consistent isospin- and angular-momentum-projected nuclear density functional theory (DFT). We discuss theoretical uncertainties of the formalism related to the basis truncation, parametrization of the underlying energy density functional, and ambiguities related to determination of Slater determinants in odd-odd nuclei. A generalization of the double-projected DFT model towards a no core shell-model-like configuration-mixing approach is formulated and implemented. We also discuss new opportunities in charge-symmetry- and cha…
Fully self-consistent calculations of nuclear Schiff moments
We calculate the Schiff moments of the nuclei 199Hg and 211Ra in completely self-consistent odd-nucleus mean-field theory by modifying the Hartree-Fock-Bogoliubov code HFODD. We allow for arbitrary shape deformation, and include the effects of nucleon dipole moments alongside those of a CP-violating pion-exchange nucleon-nucleon interaction. The results for 199Hg differ significantly from those of previous calculations when the CP-violating interaction is of isovector character.