M. Rafalski

Microscopic Calculations of Isospin-Breaking Corrections to Superallowed Beta Decay

The superallowed β-decay rates that provide stringent constraints on physics beyond the standard model of particle physics are affected by nuclear structure effects through isospin-breaking corrections. The self-consistent isospin- and angular-momentum-projected nuclear density functional theory is used for the first time to compute those corrections for a number of Fermi transitions in nuclei from A=10 to A=74. The resulting leading element of the Cabibbo-Kobayashi-Maskawa matrix, |V(ud)|=0.97447(23), agrees well with the recent result of Towner and Hardy [Phys. Rev. C 77, 025501 (2008)].

Global properties of the Skyrme-force-induced nuclear symmetry energy

A novel concept for the nuclear symmetry energy (NSE) is corroborated by large scale calculations. The paper firmly demonstrates that within the local density approximation, the value of the NSE co ...

Isospin Mixing in Nuclei around N similar or equal to Z and the Superallowed beta-decay

Theoretical approaches that use one-body densities as dynamical variables, such as Hartree-Fock or the density functional theory (DFT), break isospin symmetry both explicitly, by virtue of charge-dependent interactions, and spontaneously. To restore the spontaneously broken isospin symmetry, we implemented the isospin-projection scheme on top of the Skyrme-DFT approach. This development allows for consistent treatment of isospin mixing in both ground and exited nuclear states. In this study, we apply this method to evaluate the isospin impurities in ground states of even-even and odd-odd N similar or equal to Z nuclei. By including simultaneous isospin and angular-momentum projection, we compute the isospin-breaking corrections to the 0(+) -> 0(+) superallowed beta-decay.

Isospin-Symmetry Restoration Within the Nuclear Density Functional Theory: Formalism and Applications

Isospin symmetry of atomic nuclei is explicitly broken by the charge-dependent interactions, primarily the Coulomb force. Within the nuclear density functional theory, isospin is also broken spontaneously. We propose a projection scheme rooted in a Hartree-Fock theory that allows the consistent treatment of isospin-breaking in both ground and excited nuclear states. We demonstrate that this scheme is free from spurious divergences plaguing particle-number and angular-momentum restoration approaches. Applications of the new technique include excited high-spin states in medium-mass N=Z nuclei, such as super-deformed bands and many-particle, many-hole terminating states. Owing to the large spin polarization and/or high seniority of these states, pairing correlations have been ignored.

ISOSPIN MIXING IN THE VICINITY OF THE N = Z LINE

We present the isospin- and angular-momentum-projected nuclear density functional theory (DFT) and its applications to the isospin-breaking corrections to the superallowed β-decay rates in the vicinity of the N = Z line. A preliminary value obtained for the Cabibbo–Kobayashi–Maskawa matrix element, |Vud| = 0.97463(24), agrees well with the recent estimate by Towner and Hardy [Phys. Rev.C77, 025501 (2008)]. We also discuss new opportunities to study the symmetry energy by using the isospin-projected DFT.

Shell structure fingerprints of tensor interaction

We address the consequences of strong tensor terms in the local energy density functional, resulting from fits to the f5/2 -f7/2 splittings in 40Ca , 48Ca , and 56Ni . In this study, we focus on the tensor contribution to the nuclear binding energy. In particular, we show that it exhibits an interesting topological feature closely resembling that of the shell correction. We demonstrate that in the extreme single-particle scenario at spherical shape, the tensor contribution shows tensorial magic numbers equal to N(Z) = 14 , 32, 56, and 90, and that this structure is smeared out due to configuration mixing caused by pairing correlations and migration of proton/neutron sub-shells with neutron/proton shell filling. Based on a specific Skyrme-type functional SLy4T, we show that the proton tensorial magic numbers shift with increasing neutron excess to Z = 14 , 28, and 50.

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 f(5/2) - f(7/2) SO splittings in Ca-40, Ni-56, and Ca-48 requires (i) a significant reduct ...

ISOSPIN MIXING OF ISOSPIN-PROJECTED SLATER DETERMINANTS: FORMALISM AND PRELIMINARY APPLICATIONS

We report on the development of a new theoretical tool that allows for isospin projection of Slater determinants and we present its first applications. In particular, we determine the isospin mixing in ground states of N = Z nuclei and discuss its dependence on the size of the harmonic-oscillator basis used in the calculations. We also discuss the unphysical contribution to the isospin mixing caused by the spurious isospin-symmetry breaking inherent to the mean-field approach. We show that these contributions may be as large as 30% of the value of the isospin-mixing parameter.

MASS NUMBER DEPENDENCE OF THE SKYRME-FORCE-INDUCED NUCLEAR SYMMETRY ENERGY

The global mass dependence of the nuclear symmetry energy and its two basic ingredients due to the mean-level spacing and effective strength of the isovector mean-potential is studied within the Skyrme-Hartree-Fock model. In particular, our study determines the ratio of the surface-to-volume contributions to the nuclear symmetry energy to be ~1.6 and reveals that contributions due to mean-level spacing and effective strength of the isovector mean-potential are almost equal after removing momentum-dependent effects by rescaling them with isoscalar and isovector effective masses, respectively.