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Register a new userImpact of clustering on the $^8$Li $beta$ decay and recoil form factors
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We place unprecedented constraints on recoil corrections in the $beta$ decay of $^8$Li, by identifying a strong correlation between them and the $^8$Li ground state quadrupole moment in large-scale ab initio calculations. The results are essential for improving the sensitivity of high-precision experiments that probe the weak interaction theory and test physics beyond the Standard Model. In addition, our calculations predict a $2^+$ state of the $alpha+alpha$ system that is energetically accessible to $beta$ decay but has not been observed in the experimental $^8$Be energy spectrum, and has an important effect on the recoil corrections and $beta$ decay for the $A=8$ systems. This state and an associated $0^+$ state are notoriously difficult to model due to their cluster structure and collective correlations, but become feasible for calculations in the ab initio symmetry-adapted no-core shell-model framework.
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Effect of the tensor force on $beta$?-decay is studied in the framework of the proton-neutron random-phase-approximation (RPA) with the Skyrme force. The investigation is performed for even-even semi-magic and magic nuclei, $^{34}$Si, $^{68}$, $^{78}$Ni and $^{132}$Sn. The tensor correlation induces strong impact on low-lying Gamow-Teller state. In particular, it improves the ?$beta$-decay half-lives. $Q$ and $ft$ values are also investigated and compared with experimental data.
The $^8$Li($n,gamma$)$^9$Li reaction plays an important role in several astrophysics scenarios. It cannot be measured directly and indirect experiments have so far provided only cross section limits. Theoretical predictions differ by an order of magnitude. In this work we study the properties of $^9$Li bound states and low-lying resonances and calculate the $^8$Li($n,gamma$)$^9$Li cross section within the no-core shell model with continuum (NCSMC) with chiral nucleon-nucleon and three-nucleon interactions as the only input. The NCSMC is an ab initio method applicable to light nuclei that provides a unified description of bound and scattering states well suited to calculate low-energy nuclear scattering and reactions. Our calculations reproduce the experimentally known bound states as well as the lowest $5/2^-$ resonance of $^9$Li. We predict a $3/2^-$ spin-parity assignment for the resonance observed at 5.38 MeV. In addition to the a very narrow $7/2^-$ resonance corresponding presumably to the experimental 6.43 MeV state, we find several other broad low-lying resonances. Our calculated $^8$Li($n,gamma$)$^9$Li cross section is within the limits derived from the 1998 National Superconducting Cyclotron Laboratory Coulomb-dissociation experiment [Phys. Rev. C {bf 57}, 959 (1998)]. However, it is higher than cross sections obtained in recent phenomenological studies. It is dominated by a direct E1 capture to the ground state with a resonant contribution at $sim0.2$ MeV due to E2/M1 radiation enhanced by the $5/2^-$ resonance.
The neutron-rich $^{11}$Li halo nucleus is unique among nuclei with known separation energies by its ability to emit a proton and a neutron in a $beta$ decay process. The branching ratio towards this rare decay mode is evaluated within a three-body model for the initial bound state and with Coulomb three-body final scattering states. The branching ratio should be comprised between two extreme cases, i.e. a lower bound $6 times 10^{-12}$ obtained with a pure Coulomb wave and an upper bound $5 times 10^{-10}$ obtained with a plane wave. A simple model with modified Coulomb waves provides plausible values between between $0.8 times 10^{-10}$ and $2.2 times 10^{-10}$ with most probable total energies of the proton and neutron between 0.15 and 0.3 MeV.
The roles played by mesons in the electromagnetic form factors of the nucleon are explored using as a basis a model containing vector mesons with coupling to the continuum together with the asymptotic $Q^2$ behavior of perturbative QCD. Specifically, the vector dominance model (GKex) developed by Lomon is employed, as it is known to be very successful in representing the existing high-quality data published to date. An analysis is made of the experimental uncertainties present when the differences between the GKex model and the data are expanded in orthonormal basis functions. A main motivation for the present study is to provide insight into how the various ingredients in this model yield the measured behavior, including discussions of when dipole form factors are to be expected or not, of which mesons are the major contributors, for instance, at low-$Q^2$ or large distances, and of what effects are predicted from coupling to the continuum. Such insights are first discussed in momentum space, followed by an analysis of how different and potentially useful information emerges when both the experimental and theoretical electric form factors are Fourier transformed to coordinate space. While these Fourier transforms should not be interpreted as charge distributions, nevertheless the roles played by the various mesons, especially which are dominant at large or small distance scales, can be explored via such experiment--theory comparisons.
Pioneering study of Gamow-Teller (GT) and Fermi matrix elements (MEs) using no-core-configuration-interaction formalism rooted in multi-reference density functional theory is presented. After successful test performed for 6He -> 6Li beta-decay, the model is applied to compute MEs in the sd- and pf-shell T=1/2 mirror nuclei. The calculated GT MEs and the isospin-symmetry-breaking corrections to the Fermi branch are found to be in a very good agreement with shell-model predictions in spite of fundamental differences between these models concerning model space, treatment of correlations or inclusion of a core. This result indirectly supports the two-body current based scenarios behind the quenching of axial-vector coupling constant.
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