Unmixing Symmetries.

Area of Science:

• Nuclear physics
• Quantum mechanics
• Symmetry in physics

Background:

• Atomic nuclei exhibit behaviors like rotational bands, often described by symmetry groups (e.g., spatial SU(3)).
• Dynamical symmetry implies a Hamiltonian commutes with symmetry group operators, leading to block-diagonal structures.
• Microscopic calculations reveal that these symmetries are often mixed, with wave functions fragmented across irreducible representations (irreps).

Purpose of the Study:

• To numerically construct unitary transformations that convert quasidynamical symmetries into dynamical symmetries.
• To address limitations of the standard similarity renormalization group (SRG) in achieving desired dynamical symmetries.
• To develop an improved SRG method for unmixing symmetries in nuclear Hamiltonians.

Main Methods:

• Adapting the similarity renormalization group (SRG) to transform Hamiltonians.
• Utilizing spectral distribution theory to analyze and rederive the standard SRG.
• Developing and applying a new form of SRG to transform quasidynamical symmetries.

Main Results:

• Standard SRG methods produce unsatisfactory results, often dominated by high-weight irreps.
• The new SRG method successfully transforms quasidynamical symmetries into dynamical symmetries.
• The developed method unmixes symmetries, leading to more intuitively appealing results.

Conclusions:

• A novel SRG approach effectively converts quasidynamical symmetries into dynamical symmetries in atomic nuclei.
• This method overcomes the limitations of standard SRG, offering better control over symmetry transformations.
• The findings provide a more accurate and intuitive understanding of nuclear structure and symmetries.