Nuclear clustering using a modern shell model approach

Nuclear clustering, alpha decays, and multiparticle correlations are important components of nuclear dynamics. In this work we put forward the cluster-nucleon configuration interaction model. We use the modern configuration interaction approach with advanced realistic shell-model Hamiltonians in order to study clustering phenomena; the study is facilitated by the algebraic properties of many-nucleon configurations in the harmonic oscillator basis. Using a translationally invariant formalism we built cluster channels that satisfy the Pauli exclusion principle as well as orthogonality and normalization conditions. We formally justify the formalism and demonstrate that, within the new method, clustering strengths satisfy sum rules that are consistent with the statistical properties of nuclear reactions with composite particles. Using properly renormalized cluster form factors our approach appears to resolve long-standing problems related to absolute normalization of the alpha clustering spectroscopic factors and their behavior in $sd$-shell nuclei. Our methods are demonstrated in studies of $\alpha$ spectroscopic factors in $sd$-shell nuclei and in ${}^{16}\mathrm{O}$ treated in $p-sd$ shells. Comparison with experimental data supports the validity of the approach.

Figure 1

Spectrum of ${}^{16}\mathrm{O}$ is shown: experimentally observed spectrum is on the left and calculated shell model spectrum is in the middle. Selected states are labeled with spin, parity, and with a number in subscript indicating their position ordered by excitation energy. On the right side, using the same vertical excitation energy scale, the distribution of spectroscopic factors $S_{\ell }^{\left(\mathrm{new}\right)}$ is shown. The SFs are given for channels involving $\alpha$ and the ground state of ${}^{12}\mathrm{C}$; different colors are used to differentiate spins and parities.