W. Satula

Odd-even staggering of binding energies as a consequence of pairing and mean-field effects

Odd-even staggering of binding energies is studied in finite fermion systems with pairing correlations. We discuss contributions of the pairing and mean field to the staggering, and we construct the binding-energy indicators which measure the magnitude of pairing correlations and the effective single-particle spacings in a given system. The analysis is based on studying several exactly solvable many-body Hamiltonians as well as on the analytical formulas that can be applied in the weak and strong pairing limits.

Extended mean field description of deformed states in neutron deficient Cd- and Sn-nuclei

Extensions to the standard total routhian surface calculations are presented. The particle number symmetry is approximately restored using the Lipkin-Nogami method to avoid the well known problems of sharp pairing phase transitions, that are predicted by mean-field calculations in the vicinity of closed shells or in the high-spin regime. Secondly, the quadrupole pairing interaction is added to the standard seniority pairing to account for an improved treatment of particle-particle correlations. The method is applied to the analysis of collective rotational bands found in neutron deficient Cd, In, Sn, Sb and Te isotopes.

Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VI) hfodd (v2.40h): A new version of the program ✩

We describe the new version (v2.38j) of the code hfodd which solves the nuclear SkyrmeHartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for statedependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the D T transformations and rotations of wave functions, (ix) quasiparticle blocking for the HFB solutions in odd and odd-odd nuclei, (x) the Broyden method to accelerate the convergence, (xi) the Lipkin-Nogami method to treat pairing correlations, (xii) the exact Coulomb exchange term, (xiii) several utility options, and we have corrected two insignificant errors.

Additivity of Quadrupole Moments in Superdeformed Bands: Single-Particle Motion at Extreme Conditions

Quadrupole and hexadecapole moments of superdeformed bands in the A�150 mass region have been analyzed in the cranking Skyrme-Hartree-Fock model. It is demonstrated that, independently of the intrinsic configuration and of the proton and neutron numbers, the charge moments calculated with respect to the doubly-magic superdeformed core of 152 Dy can be expressed very precisely in terms of independent contributions from the individual hole and particle orbitals. This result, together with earlier studies of the moments of inertia distributions, suggests that many features of the superdeformed bands in the A�150 mass region can be very well understood in terms of an almost undisturbed single-particle motion.

Empirical Proton-Neutron Interactions and Nuclear Density Functional Theory : Global, Regional, and Local Comparisons

Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals.

Isospin-breaking corrections to superallowed Fermi beta-decay in isospin- and angular-momentum-projected nuclear Density Functional Theory

Background: The superallowed �-decay rates provide stringent constraints on physics beyond the Standard Model of particle physics. To extract crucial information about the electroweak force, small isospin-breaking corrections to the Fermi matrix element of superallowed transitions must be applied. Purpose: We perform systematic calculations of isospin-breaking corrections to superallowed �-decays and estimate theoretical uncertainties related to the basis truncation, time-odd polarization effects related to the intrinsic symmetry of the underlying Slater determinants, and to the functional parametrization. Methods: We use the self-consistent isospin- and angular-momentum-projected nuclear density functional theory employing two density functionals derived from the density independent Skyrme interaction. Pairing correlations are ignored. Our framework can simultaneously describe various effects that impact matrix elements of the Fermi decay: symmetry breaking, configuration mixing, and long-range Coulomb polarization. Results: The isospin-breaking corrections to the I = 0 + ,T = 1 → I = 0 + ,T = 1 pure Fermi transitions are computed for nuclei from A=10 to A=98 and, for the first time, to the Fermi branch of the I,T = 1/2 → I,T = 1/2 transitions in mirror nuclei from A=11 to A=49. We carefully analyze various model assumptions impacting theoretical uncertainties of our calculations and provide theoretical error bars on our predictions. Conclusions: The overall agreement with empirical isospin-breaking corrections is very satisfactory. Using computed isospin-breaking corrections we show that the unitarity of the CKM matrix is satisfied with a precision better than 0.1%.

Symmetry energy in nuclear density functional theory

The nuclear symmetry energy represents a response to the neutron-proton asymmetry. In this paper we discuss various aspects of symmetry energy in the framework of nuclear density functional theory, considering both non-relativistic and relativistic self-consistent mean-field realizations side by side. Key observables pertaining to bulk nucleonic matter and finite nuclei are reviewed. Constraints on the symmetry energy and correlations between observables and symmetry energy parameters, using statistical covariance analysis, are investigated. Perspectives for future work are outlined in the context of ongoing experimental efforts.

Exact Solution of the Spin-Isospin Proton-Neutron Pairing Hamiltonian

The exact solution of the proton-neutron isoscalar-isovector (T=0,1) pairing Hamiltonian with nondegenerate single-particle orbits and equal pairing strengths is presented for the first time. The Hamiltonian is a particular case of a family of integrable SO(8) Richardson-Gaudin models. The exact solution of the T=0,1 pairing Hamiltonian is reduced to a problem of 4 sets of coupled nonlinear equations that determine the spectral parameters of the complete set of eigenstates. The microscopic structure of individual eigenstates is analyzed in terms of evolution of the spectral parameters in the complex plane for a system of A=80 nucleons. The spectroscopic trends of the exact solutions are discussed in terms of generalized rotations in isospace.

Neutron orbitals above the N = 74 shell gap at large deformation: spectroscopy in the superdeformed minimum of 133Ce

Abstract High-spin states in 133 Ce were populated via the 116 Cd( 22 Ne,5n) reaction at 120 MeV. Analysis of these data has revealed three new superdeformed bands in 133 Ce, two of which have transitions which are identical to those observed in the yrast bands of 132 Ce and 136 Nd. These bands have been interpreted as signature partners of the [530] 1 2 − orbital coupled to the 132 Ce yrast superdeformed core. The third band is believed to be built upon a π5 4 ν6 3 configuration at high rotational frequency and to show the effects resulting from an alignment of a pair of f 7 2 neutrons at ℏgω ⋍ 0.7 MeV. It is tentatively suggested that the sharp rise in the dynamic moment of inertia of this band at low rotational frequency may result from an admixture of the π5 4 ν6 1 configuration.

Isospin mixing within the symmetry restored density functional theory and beyond

We present results of systematic calculations of the isospin-symmetrybreaking corrections to the superallowed I=0 + ;T =1 ! I=0 + ;T =1 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 conguration-mixi ng approach is formulated and implemented. We also discuss new opportunities in charge-symmetry- and charge-independencebreaking studies oered by the newly developed DFT formalism involving proton-neutron mixing in the particle-hole channel.