Related papers: A new and practical formulation for overlaps of Bo…
Pfaffian formulas used to compute overlaps necessary to carry out generator coordinate method calculations using a set of Hartree- Fock- Bogoliubov wave functions, is generalized to the case where each of the HFB states are expanded in…
Several technical aspects concerning the evaluation of the overlap between two mean field wave functions of the Hartree Fock Bogoliubov type, are discussed. The limit when several orbitals become fully occupied is derived as well as the…
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…
Overlap between Hartree-Fock-Bogoliubov(HFB) vacua is very important in the beyond mean-field calculations. However, in the HFB transformation, the $U,V$ matrices are sometimes singular due to the exact emptiness ($v_i=0$) or full…
We derive an expression that allows for the unambiguous evaluation of the overlap between two arbitrary quasiparticle vacua, including its sign. Our expression is based on the Pfaffian of a skew-symmetric matrix, extending the formula…
Numerical difficulties associated with computing matrix elements of operators between Hartree-Fock-Bogoliubov (HFB) wavefunctions have plagued the development of HFB-based many-body theories for decades. The problem arises from divisions by…
A formula to calculate a norm overlap between Hartree-Fock-Bogoliubov (HFB) states with the odd number parity (one quasi-particle excited states) is derived with help of the Grassmann numbers and the Fermion coherent states. The final form…
We propose a new method to solve the Hartree-Fock-Bogoliubov equations for weakly bound nuclei, which works for both spherical and axially deformed cases. In this approach, the quasiparticle wave functions are expanded in a complete set of…
We present an overview of the Hartree-Fock-Bogoliubov (HFB) theory of nucleonic superfluidity for finite nuclei. After introducing basic concepts related to pairing correlations, we show how the correlated pairs are incorporated into the…
A new formula is presented for the calculation of matrix elements between multi-quasiparticle Hartree-Fock-Bogoliubov (HFB) states. The formula is expressed in terms of the Pfaffian, and is derived by using the Fermion coherent states with…
State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation…
In reactions the wave packets of the emerging products typically are not eigenstates of particle number operators or any other conserved quantities and their properties are entangled. I describe a particle projection technique in parts of…
The numerical solution of the recently formulated number-projected Hartree-Fock-Bogoliubov equations is studied in an exactly soluble cranked-deformed shell model Hamiltonian. It is found that the solution of these number-projected…
The existing formalism used to compute the operator overlaps necessary to carry out generator coordinate method calculations using a set of Hartree- Fock- Bogoliubov wave functions, is generalized to the case where each of the HFB states…
Reliable predictions of the static and dynamic properties of a nucleus require a fully microscopic description of both ground and excited states of this complicated many-body quantum system. Predictive calculations are key to understanding…
We present the first set of results of solving the Hartree-Fock-Bogoliubov equations, which describe the self-consistent mean field theory with pairing interaction. Calculations for even-even nuclei are carried out on a two-dimensional…
We apply a formalism recently developed to carry out Generator Coordinate Method calculations using a set of Hartree- Fock- Bogoliubov wave functions, where each of the members of the set can be expanded in an arbitrary basis. In this paper…
We introduce a new framework for the low-energy nuclear structure calculations, which describes the single-particle wave function as a superposition of localized Gaussians. It is a hybrid of the Hartree-Fock and antisymmetrized molecular…
We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This…
The Hartree-Fock-Bogoliubov approximation is very useful for treating both long- and short-range correlations in finite quantum fermion systems, but it must be extended in order to describe detailed spectroscopic properties. One problem is…