Nonunitary bogoliubov transformations and extension of Wick’s theorem

The overlap of the excited states in quasiparticle random-phase approximation (QRPA) is calculated to simulate the overlap of the intermediate nuclear states of the double-β decay. Our basic idea is to use the like-particle QRPA with the aid of the closure approximation and calculate the overlap as rigorously as possible by making use of the explicit equation of the QRPA ground state. The formulation is shown in detail, and the mathematical properties of the overlap matrix are investigated. Two test calculations are performed for relatively light nuclei with the Skyrme and volume δ-pairing energy functionals. The validity of the truncations used in the calculation is examined and confirmed.

Section: Formulation Of Overlap Of Intermediate Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Overlap of quasiparticle random-phase approximation states based on ground states of different nuclei: Mathematical properties and test calculations

Terasaki

2013

“…and the exponential term e −tr[Y]/2 = (det T 22 ) 1/2 follows from the Balian-Brézin decomposition [19] of the operator e (1/2)η † Rη . pf denotes the Pfaffian of a matrix.…”

mentioning

confidence: 99%

Projection after variation in the finite-temperature Hartree-Fock-Bogoliubov approximation

Fanto

2017

The finite-temperature Hartree-Fock-Bogoliubov (HFB) approximation often breaks symmetries of the underlying many-body Hamiltonian. Restricting the calculation of the HFB partition function to a subspace with good quantum numbers through projection after variation restores some of the correlations lost in breaking these symmetries, although effects of the broken symmetries such as sharp kinks at phase transitions remain. However, the most general projection after variation formula in the finite-temperature HFB approximation is limited by a sign ambiguity. Here, we extend the Pfaffian formula for the many-body traces of HFB density operators introduced by L. M. Robledo in Ref.[1] to eliminate this sign ambiguity and evaluate the more complicated many-body traces required in projection after variation in the most general HFB case. We validate our method through a proof-of-principle calculation of the particle-number-projected HFB thermal energy in a simple model.Introduction.-The Hartree-Fock-Bogoliubov (HFB) approximation is an important mean-field method for studying many-fermion systems in which pairing correlations are important. When extended to finite temperature [2], this method provides an efficient way to calculate statistical observables. The finite-temperature HFB approximation has been widely applied to study the deformation and pairing properties of nuclei [3,4] and is also useful for the study of atomic Fermi gases [5]. However, the finite-temperature HFB approximation often breaks symmetries of the underlying many-body Hamiltonian. In particular, the HFB approximation explicitly violates particle-number conservation if the pairing field is nonzero and can also violate rotational invariance when the mean-field solution is deformed. Breaking these symmetries reduces the accuracy of HFB predictions of statistical properties such as nuclear level densities [6].

“…The equation of the QRPA ground state has been known for decades, e.g., Ref. [24]. To the best of our knowledge, however, this is the first time that a numerical calculation has been carried out rigorously.…”

mentioning

confidence: 99%

Overlap of quasiparticle random-phase approximation states for nuclear matrix elements of the neutrino-less double-βdecay

Terasaki

2012

Quasiparticle random-phase approximation (QRPA) is applied to two nuclei, and the overlap of the QRPA excited states based on the different nuclei is calculated. The aim is to calculate the overlap of intermediate nuclear states of the double-β decay. We use the like-particle QRPA after the closure approximation is applied to the nuclear matrix elements. The overlap is calculated rigorously by making use of the explicit equation of the QRPA ground state. The formulation of the overlap is shown, and a test calculation is performed. The effectiveness of the truncations used is shown.