An improved calculation of the isospin-symmetry-breaking corrections to superallowed Fermi beta decay

We report new shell-model calculations of the isospin-symmetry-breaking correction to superallowed nuclear beta decay. The most important improvement is the inclusion of core orbitals, which are demonstrated to have a significant impact on the mismatch in the radial wave functions of the parent and daughter states. We determine which core orbitals are important to include from an examination of measured spectroscopic factors in single-nucleon pick-up reactions. We also examine the new radiative-correction calculation by Marciano and Sirlin and, by a simple reorganization, show that it is possible to preserve the conventional separation into a nucleus-independent inner radiative term and a nucleus-dependent outer term. We tabulate new values for the three theoretical corrections for twenty superallowed transitions, including the thirteen well-studied cases. With these new correction terms the corrected Ft values for the thirteen cases are statistically consistent with one another and the anomalousness of the 46V result disappears. These new calculations lead to a lower average Ft value and a higher value of Vud. The sum of squares of the top-row elements of the CKM matrix now agrees exactly with unitarity.Comment: 15 pages, 2 postscript figures, revtex

A new analysis of 14O beta decay: branching ratios and CVC consistency

The ground-state Gamow-Teller transition in the decay of 14O is strongly hindered and the electron spectrum deviates markedly from the allowed shape. A reanalysis of the only available data on this spectrum changes the branching ratio assigned to this transition by seven standard deviations: our new result is (0.54 \pm 0.02)%. The Kurie plot data from two earlier publications are also examined and a revision to their published branching ratios is recommended. The required nuclear matrix elements are calculated with the shell model and, for the first time, consistency is obtained between the M1 matrix element deduced from the analog gamma transition in 14N and that deduced from the slope of the shape-correction function in the beta transition, a requirement of the conserved vector current hypothesis. This consistency is only obtained, however, if renormalized rather than free-nucleon operators are used in the shell-model calculations. In the mirror decay of 14C a similar situation occurs. Consistency between the 14C lifetime, the slope of the shape-correction function and the M1 matrix element from gamma decay can only be achieved with renormalized operators in the shell-model calculation.Comment: 9 pages; revtex4; one figur

Time-odd triaxial relativistic mean field approach for nuclear magnetic moments

The time-odd triaxial relativistic mean field approach is developed and applied to the investigation of the ground-state properties of light odd-mass nuclei near the double-closed shells. The nuclear magnetic moments including the isoscalar and isovector ones are calculated and good agreement with Schmidt values is obtained. Taking $^{17}$F as an example, the splitting of the single particle levels (around $~0.7$ MeV near the Fermi level), the nuclear current, the core polarizations, and the nuclear magnetic potential, i.e., the spatial part of the vector potential, due to the violation of the time reversal invariance are investigated in detail.Comment: 26 pages, 8 figures. PHYSICAL REVIEW C (accepted

New 32^{32}Cl(p,γ\gamma)33^{33}Ar reaction rate for astrophysical rp-process calculations

The $^{32}$Cl(p,$\gamma$)$^{33}$Ar reaction rate is of potential importance in the rp-process powering type I X-ray bursts. Recently Clement et al. \cite{CBB04} presented new data on excitation energies for low lying proton unbound states in $^{33}$Ar obtained with a new method developed at the National Superconducting Cyclotron Laboratory. We use their data, together with a direct capture model and a USD shell model calculation to derive a new reaction rate for use in astrophysical model calculations. In particular, we take into account capture on the first excited state in $^{32}$Cl, and also present a realistic estimate of the remaining uncertainties. We find that the $^{32}$Cl(p,$\gamma$)$^{33}$Ar reaction rate is dominated entirely by capture on the first excited state in $^{32}$Cl over the whole temperature range relevant in X-ray bursts. In the temperature range from 0.2 to 1 GK the rate is up to a factor of 70 larger than the previously recommended rate based on shell model calculations only. The uncertainty is now reduced from up to a factor of 1000 to a factor of 3 at 0.3-0.7 GK and a factor of 6 at 1.5 GK.Comment: To be published in Phys. Rev.

Shell-model calculations for the energy levels of the N=50 isotones with A=80–87

The detailed features of the calculated energy-level schemes and of the single-particle, orbit-occupancy properties of the low-lying levels of the N=50 isotones 80Zn, 81Ga, 82Ge, 83As, 84Se, 85Br, 86Kr, and 87Rb are presented and discussed. These results are obtained with a new effective Hamiltonian operator obtained empirically from an iterative fit to experimental energies taken from all experimentally studied (A=82–96) N=50 nuclei. The model space for the calculations consists of active 0f5/2, 1p3/2, 1p1/2, and 0g9/2 proton orbits relative to a nominal 78Ni core. This space is truncated internally by restricting the number of particles excited from the negative-parity orbits into the g9/2 orbit to be no greater than four. The typical structures predicted for these lighter N=50 isotones are found to be dominated by well-mixed combinations of fp-orbit configurations, with the g9/2 orbit playing a minor role in all but a few special cases. The model energy-level spectra are compared with existing experimental information, as are calculated spectroscopic factors for single-proton stripping and pickup reactions

Gamow-Teller transitions from 24Mg and its impact on the electron capture rates in the O + Ne + Mg cores of stars

Electron captures on nuclei play an important role in the collapse of stellar core in the stages leading to a type-II supernova. Recent observations of subluminous Type II-P supernovae (e.g. 2005cs, 2003gd, 1999br) were able to rekindle the interest in 8 - 10 which develop O+Ne+Mg cores. We used the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory to calculate the B(GT) strength for 24Mg \rightarrow 24Na and its associated electron capture rates for incorporation in simulation calculations. The calculated rates, in this letter, have differences with the earlier reported shell model and Fuller, Fowler, Newman (hereafter F2N) rates. We compared Gamow-Teller strength distribution functions and found fairly good agreement with experiment and shell model. However, the GT centroid and the total GT strength, which are useful in the calculation of electron capture rates in the core of massive pre-supernova stars, lead to the enhancement of our rate up to a factor of four compared to the shell model rates at high temperatures and densities.Comment: 13 pages, 3 figure

Shell-model study of the N=82 isotonic chain with a realistic effective hamiltonian

We have performed shell-model calculations for the even- and odd-mass N=82 isotones, focusing attention on low-energy states. The single-particle energies and effective two-body interaction have been both determined within the framework of the time-dependent degenerate linked-diagram perturbation theory, starting from a low-momentum interaction derived from the CD-Bonn nucleon-nucleon potential. In this way, no phenomenological input enters our effective Hamiltonian, whose reliability is evidenced by the good agreement between theory and experiment.Comment: 7 pages, 11 figures, 3 tables, to be published in Physical Review

On the Strength of Spin-Isospin Transitions in A=28 Nuclei

The relations between the strengths of spin-isospin transition operators extracted from direct nuclear reactions, magnetic scattering of electrons and processes of semi-leptonic weak interactions are discussed.Comment: LaTeX, 8 pages, 1Postscript with figur

Beta-decay properties of 25^{25}Si and 26^{26}P

The $\beta$-decay properties of the neutron-deficient nuclei $^{25}$Si and $^{26}$P have been investigated at the GANIL/LISE3 facility by means of charged-particle and $\gamma$-ray spectroscopy. The decay schemes obtained and the Gamow-Teller strength distributions are compared to shell-model calculations based on the USD interaction. B(GT) values derived from the absolute measurement of the $\beta$-decay branching ratios give rise to a quenching factor of the Gamow-Teller strength of 0.6. A precise half-life of 43.7 (6) ms was determined for $^{26}$P, the $\beta$- (2)p decay mode of which is described