Normal-ordered $k$-body approximation in particle-number-breaking theories

Understand

The reach of ab initio many-body theories is rapidly extending over the nuclear chart.

• However, dealing fully with three-nucleon, possibly four-nucleon, interactions makes the solving of the A-body Schr\"odinger equation particularly cumbersome, if not impossible beyond a certain nuclear mass.
• Consequently, ab initio calculations of mid-mass nuclei are typically performed on the basis of the normal-ordered two-body (NO2B) approximation that captures dominant effects of three-nucleon forces while effectively working with two-nucleon operators.
• A powerful idea currently employed to extend ab initio calculations to open-shell nuclei consists of expanding the exact solution of the A-body Schr\"odinger equation while authorizing the approximate solution to break symmetries of the Hamiltonian.