Neutrino-Nucleus Reactions and Muon Capture in 12C

The neutrino-nucleus cross section and the muon capture rate are discussed within a simple formalism which facilitates the nuclear structure calculations. The corresponding formulae only depend on four types of nuclear matrix elements, which are currently used in the nuclear beta decay. We have also considered the non-locality effects arising from the velocity-dependent terms in the hadronic current. We show that for both observables in 12C the higher order relativistic corrections are of the order of ~5 only, and therefore do not play a significant role. As nuclear model framework we use the projected QRPA (PQRPA) and show that the number projection plays a crucial role in removing the degeneracy between the proton-neutron two quasiparticle states at the level of the mean field. Comparison is done with both the experimental data and the previous shell model calculations. Possible consequences of the present study on the determination of the $\nu_\mu ->\nu_e$ neutrino oscillation probability are briefly addressed.Comment: 29 pages, 6 figures, Revtex4. Several changes were made to the previous manuscript, the results and final conclusions remain unalterable. It has been accepted for publication as a Regular Article in Physical Review

Nuclear Magnetic Resonance and Hyperfine Structure

Contains reports on five research projects

Isoscalar g Factors of Even-Even and Odd-Odd Nuclei

We consider T=0 states in even-even and odd-odd N=Z nuclei. The g factors that emerge are isoscalar. We find that the single j shell model gives simple expressions for these g factors which for even-even nuclei are suprisingly close to the collective values for K=0 bands. The g factors of many 2+ in even-even nuclei and 1+ and 3+ states in odd-odd nuclei have g factors close to 0.5

Isospin-mixing corrections for fp-shell Fermi transitions

Isospin-mixing corrections for superallowed Fermi transitions in {\it fp}-shell nuclei are computed within the framework of the shell model. The study includes three nuclei that are part of the set of nine accurately measured transitions as well as five cases that are expected to be measured in the future at radioactive-beam facilities. We also include some new calculations for $^{10}$C. With the isospin-mixing corrections applied to the nine accurately measured $ft$ values, the conserved-vector-current hypothesis and the unitarity condition of the Cabbibo-Kobayashi-Maskawa (CKM) matrix are tested.Comment: 13 pages plus five tables. revtex macro

Time Reversal Invariance Violating and Parity Conserving effects in Neutron Deuteron Scattering

Time reversal invariance violating parity conserving effects for low energy elastic neutron deuteron scattering are calculated for meson exchange and EFT-type of potentials in a Distorted Wave Born Approximation, using realistic hadronic wave functions, obtained by solving three-body Faddeev equations in configuration space.Comment: There was a technical mistake in calculations due to singular behavior of Yukawa functions at short range. We corrected the integration algorithm. There were some typos which are corrected. arXiv admin note: text overlap with arXiv:1104.305

Large-basis shell-model calculation of 10C->10B Fermi matrix element

We use a $4\hbar\Omega$ shell-model calculation with a two-body effective interaction derived microscopically from the Reid93 potential to calculate the isospin-mixing correction for the 10C->10B superallowed Fermi transition. The effective interaction takes into account the Coulomb potential as well as the charge dependence of T=1 partial waves. Our results suggest the isospin- mixing correction $\delta_{C}\approx 0.1$, which is compatible with previous calculations. The correction obtained in those calculations, performed in a $0\hbar\Omega$ space, was dominated by deviation from unity of the radial overlap between the converted proton and the corresponding neutron. In the present calculation this effect is accommodated by the large model space. The obtained $\delta_{C}$ correction is about a factor of four too small to obtain unitarity of the Cabibbo-Kobayashi-Maskawa matrix with the present experimental data.Comment: 14 pages. REVTEX. 3 PostScript figure

Magnetic moments of 33^{33}Mg in time-odd relativistic mean field approach

The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground-state properties of $^{33}$Mg with effective interaction PK1. The ground state of $^{33}$Mg has been found to be prolate deformed, $\beta_2=0.23$, with the odd neutron in $1/2[330]$ orbital and the energy -251.85 MeV which is close to the data -252.06 MeV. The magnetic moment $- 0.9134 \mu_\mathrm{N}$ is obtained with the effective electromagnetic current which well reproduces the data $- 0.7456 \mu_\mathrm{N}$ self-consistently without introducing any parameter. The energy splittings of time reversal conjugate states, the neutron current, the energy contribution from the nuclear magnetic potential, and the effect of core polarization are discussed in detail.Comment: 13 pages, 4 figure

Parity nonconservation effects in the photodesintegration of polarized deuterons

P-odd correlations in the deuteron photodesintegration are considered. The $\pi$-meson exchange is not operative in the case of unpolarized deuterons. For polarized deuterons a P-odd correlation due to the $\pi$-meson exchange is about $3 \times 10^{-9}$. Short-distance P-odd contributions exceed essentially than the contribution of the $\pi$-meson exchange.Comment: 12 pages, Latex, 3 figure

The Effect of the Pairing Interaction on the Energies of Isobar Analog Resonances in 112−124^{112-124}Sb and Isospin Admixture in 100−124^{100-124}Sn Isotopes

In the present study, the effect of the pairing interaction and the isovector correlation between nucleons on the properties of the isobar analog resonances (IAR) in $^{112-124}$Sb isotopes and the isospin admixture in $^{100-124}$Sn isotopes is investigated within the framework of the quasiparticle random phase approximation (QRPA). The form of the interaction strength parameter is related to the shell model potential by restoring the isotopic invariance of the nuclear part of the total Hamiltonian. In this respect, the isospin admixtures in the $^{100-124}$Sn isotopes are calculated, and the dependence of the differential cross section and the volume integral $J_{F}$ for the Sn($^{3}$He,t)Sb reactions at E($^{3}$He)$=200$ MeV occurring by the excitation of IAR on mass number A is examined. Our results show that the calculated value for the isospin mixing in the $^{100}$Sn isotope is in good agreement with Colo et al.'s estimates $(4-5$, and the obtained values for the volume integral change within the error range of the value reported by Fujiwara et al. (53$\pm$5 MeV fm$^{3}$). Moreover, it is concluded that although the differential cross section of the isobar analog resonance for the ($^{3}$He,t) reactions is not sensitive to pairing correlations between nucleons, a considerable effect on the isospin admixtures in $N\approx Z$ isotopes can be seen with the presence of these correlations.Comment: 16 pages, 5 EPS figures and 2 tables, Late

Parity Mixed Doublets in A = 36 Nuclei

The $\gamma$-circular polarizations ($P_{\gamma}$) and asymmetries ($A_{\gamma}$) of the parity forbidden M1 + E2 $\gamma$-decays: $^{36}Cl^{\ast} (J^{\pi} = 2^{-}; T = 1; E_{x} = 1.95$ MeV) $\rightarrow$ $^{36}Cl (J^{\pi} = 2^{+}; T = 1; g.s.)$ and $^{36}Ar^{\ast} (J^{\pi} = 2^{-}; T = 0; E_{x} = 4.97$ MeV) $\rightarrow$ $^{36}Ar^{\ast} (J^{\pi} = 2^{+}; T = 0; E_{x} = 1.97$ MeV) are investigated theoretically. We use the recently proposed Warburton-Becker-Brown shell-model interaction. For the weak forces we discuss comparatively different weak interaction models based on different assumptions for evaluating the weak meson-hadron coupling constants. The results determine a range of $P_{\gamma}$ values from which we find the most probable values: $P_{\gamma}$ = $1.1 \cdot 10^{-4}$ for $^{36}Cl$ and $P_{\gamma}$ = $3.5 \cdot 10^{-4}$ for $^{36}Ar$.Comment: RevTeX, 17 pages; to appear in Phys. Rev.