Session Y7: Nuclear Theory II

Study of nuclear clustering using the modern shell model approach

Nuclear clustering, alpha decays, and multi-particle correlations are important components of nuclear dynamics. In this work we use the modern configuration-interaction approach with most advanced realistic shell-model Hamiltonians to study these questions. We utilize the algebraic many-nucleon structures and the corresponding fractional parentage coefficients to build the translationally invariant wave functions of the alpha-cluster channels. We explore the alpha spectroscopic factors, study the distribution of clustering strength, and discuss the structure of an effective 4-body operator describing the in-medium alpha dynamics in the multi-shell valence configuration space. Sensitivity of alpha clustering to the components of an effective Hamiltonian, which includes its collective and many-body components, as well as isospin symmetry breaking terms, are of interest. We offer effective techniques for evaluation of the cluster spectroscopic factors satisfying the orthogonality conditions of the respective cluster channels. We present a study of clustering phenomena, single-particle dynamics, and electromagnetic transitions for a number of nuclei in p-sd shells and compare our results with the experimentally available data.   

Application of shell model with non-orthogonal basis to nuclear clustering

Our goal is to study nuclear structure and reactions from ab initio principles. To do so we use a no-core shell model with non-orthogonal basis and apply the framework of the Resonating Group Method. In this presentation we discuss the overlap norm kernel and study the role of the orthogonality condition for channel wavefunctions. Some simple examples will be used to illustrate the techniques and the physics behind our approach.   

Emergence of rotational bands in \textit{ab initio} no-core configuration interaction calculations of light nuclei

The emergence of rotational bands has recently been observed in no-core configuration interaction (NCCI) calculations for $p$-shell nuclei, as evidenced by rotational patterns for excitation energies, electromagnetic moments, and electromagnetic transitions. Yrast and low-lying excited bands are found. The results demonstrate the possibility of well-developed rotational structure in NCCI calculations, using realistic nucleon-nucleon interactions, and within finite, computationally-accessible configuration spaces. This talk will focus on results for rotation in both the even-mass and odd-mass Be isotopes ($7\leq A \leq 12$).   

Sp(3,$R$) decomposition of the SU(3) no-core shell model basis

Numerical evidence shows an important role of the symplectic Sp(3,$R$) symmetry in the ab initio no-core shell model results for light nuclei. Therefore, the construction of symplectic states from SU(3) states is necessary, as a prerequisite and crucial step of understanding the symplectic symmetry for those nuclei. This presentation will provide an introduction to our numerical calculation that decomposes the basis states of Sp(3,$R$) irreducible representations in terms of SU(3) nuclear basis. We use the null space of the Sp(3,$R$) generator $B^{(02)}$ to find the extremal states, and then ladder them with the generator $A^{(20)}$ to build the entire irreps.   

Operator evolution in the three-body space via the similarity renormalization group

Performing quantitative calculations of nuclear observables in terms of nucleons interacting through two- and three-nucleon forces is a guiding principle of \textit{ab initio} nuclear theory. Computationally, this is complicated by the large model spaces needed to reach convergence in many-body approaches, such as the no-core shell model (NCSM). In recent years, the similarity renormalization group (SRG) has provided a powerful tool to soften interactions for \textit{ab initio} structure calculations, thus leading to convergence within smaller model spaces. SRG has been very successful when applied to the Hamiltonian of the nuclear system. However, when computing observables other than spectra, one must evolve the relevant operators using the same transformation that was applied to the Hamiltonian. Here we compute the root mean square (RMS) radius of $^3$H to show that evolving the $\hat{r}^2$ operator in the three-body space, thus including two- and three-body SRG induced terms, will yield an exactly unitary transformation. We then extend our calculations to $^4$He and compute the RMS radius and total strength of the dipole transition using operators evolved in the three-body space.   

Nuclear landscape and drip lines in covariant density functional theory

Neutron and proton drip lines represent the limits of nuclear landscape. While proton drip line is measured experimentally, the location of neutron drip line for absolute majority of elements is based on theoretical predictions which involve extreme extrapolations. The first ever systematic investigation of the location of the proton and neutron drip lines in the relativitic Hartree-Bogoliubov (RHB) approach has been performed by us employing the set of modern covariant density functional parametrizations. Separable pairing is used in particle-particle channel of the RHB. This study covers all even-even nuclei with $Z\leq 120$ between proton and neutron drip lines. The accuracy of the description of ground state (masses, two-particle separation energies, deformations, radii etc) properties of known nuclei and its dependence on parametrization have been analysed.Statistical errors in the predictions of neutron-drip line are established within the RHB. The comparison with the results of non-relativistic approaches (Skyrme density functional theory, macroscopic+microscopic approach) allows to define systematic errors in the predictions of neutron-drip line. * This work has been supported by the U.S. DOE under the grant DE-FG02-07ER41459 and by an allocation of advanced