Theory of Angular Momentum Projection for Excited Bands from Hatree-Fock-Bogoliubov Intrinsic States

Nazakat Ullah

G. F. Bertsch, Luis Miguel Robledo

We present a Pfaffian formula for projection and symmetry restoration for wave functions of the general Bogoliubov form, including quasiparticle excited states and linear combinations of them. This solves a long-standing problem in calculating states of good symmetry, arising from the sign ambiguity of the commonly used determinant formula. A simple example is given of projecting a good particle number and angular momentum from a Bogoliubov wave function in the Fock space of a single j-shell.

Long-Jun Wang, Fangqi Chen, T. Mizusaki +2 more

In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasiparticles (qp's). The problem can be solved by employing the Pfaffian algorithm generally applicable to calculations of matrix elements for Hartree-Fock-Bogoliubov states with any number of qp's. This breakthrough in many-body techniques enables studies of high-spin states in a shell-model framework. As the first application of the Pfaffian algorithm, the configuration space of the projected shell model is expanded to include 6-qp states for both positive and negative parities. Taking $^{166}\mathrm{Hf}$ as an example, we show that 6-qp states become the main configuration of the yrast band beyond spin $I\ensuremath{\approx}34\ensuremath{\hbar}$, which explains the observed third back-bending in moment of inertia. Structures of multi-qp high-$K$ isomers in $^{176}\mathrm{Hf}$ are analyzed as another example.

D. Janssen

Naeem Ullah, K.K. Gupta

Alejandro López‐Castillo