arXiv subjects
Publications and source records attributed to Giovanni Puddu.
We apply the Hybrid-Multi-Determinant method using the recent chiral two-body interactions of Entem-Machleidt-Nosyk (EMN) without renormalization to few nuclei up to A=48. Mostly we use the bare fifth order NN interaction N4LO-450. For ${}^{24}Mg$ and ${}^{48}Cr$ the excitation energies of the $2^+_1$ states are far larger than the corresponding experimental values.
We use the recently introduced single-particle states obtained from localized Deuteron wave-functions as a basis for nuclear many-body calculations. We show that energies can be substantially lowered if the natural orbits obtained from this basis are used. We use this modified basis for ${}^{10}B$, ${}^{16}O$ and ${}^{24}Mg$ employing the bare $NNLO_{opt}$ Nucleon-Nucleon interaction. The lowering of the energies increases with the mass. Although in principle natural orbits require a full scale preliminary many-body calculation, we found that an approximate preliminary many-body calculation, with a marginal increase in the computational cost, is sufficient. The use of natural orbits based on an harmonic oscillator basis leads to a much smaller lowering of the energies for a comparable computational cost.
Predominantly, harmonic oscillator single-particle wave functions are the choice as a basis in ab-initio nuclear many-body calculations. These wave-functions, although very convenient in order to evaluate the matrix elements of the interaction in the laboratory frame, have a too fast fall-off at large distances. In the past, in alternative to the harmonic oscillator, other single-particle wave functions have been proposed. In this work we propose a new single-particle basis, directly linked to the nucleon-nucleon interaction. This new basis is orthonormal and complete, has the proper asymptotic behavior at large distances and does not contain the continuum which would pose severe convergence problems in nuclear many body calculations. We consider the newly proposed NNLO-opt nucleon-nucleon interaction, without any renormalization. We show that unlike other basis, this single-particle representation has a computational cost similar to the harmonic oscillator basis with the same space truncation and it gives lower energies for ${}^6He$ and ${}^6Li$.
Using the Argonne V18 interaction, renormalized with the Lee-Suzuki method, we study nuclei around the $N=20$ island of inversion. We include 5 major oscillator shells, in a no-core approach, using the Hybrid Multi-Determinant method reaching up to few hundreds Slater determinants. Although qualitatively in agreement with the experimental levels, the calculated BE2 do not show the same amount of collectivity seen experimentally.
We extend the recently proposed Time-Dependent Multi-Determinant approach (ref.[1]) to the description of fermionic propagators. The method hinges on equations of motions obtained using variational principles of Dirac type. In particular we focus on traces of imaginary time propagators, i.e. the partition function. The method is equally applicable with or without projectors to good quantum numbers.
We study a multi-determinant approach to the time evolution of the nuclear wave functions (TDMD). We employ the Dirac variational principle and use as anzatz for the nuclear wave-function a linear combination of Slater determinants and derive the equations of motion. We demonstrate explicitly that the norm of the wave function and the energy are conserved during the time evolution. This approach is a direct generalization of the time dependent Hartree-Fock method. We apply this approach to a case study of ${}^6Li$ using the N3LO interaction renormalized to 4 major harmonic oscillator shells. We solve the TDMD equations of motion using Krylov subspace methods of Lanczos type. We discuss as an application the isoscalar monopole strength function.
We propose a simple, easy to implement, variant of the EXCITED method for variational many-body calculations for excited states. We apply this method to the Hybrid Multideterminant method(HMD). We test this method with relatively few Slater determinants by comparing the results with exact shell model calculations for ${}^{56}Ni$ using the $fpd6$ interaction. We obtain very good agreement with the exact results.
The Thermal Hartree-Fock-Bogoliubov approximation with reprojection to good quantum numbers is analyzed in a canonical ensemble. Simple recipes are given for the evaluation of traces, gradients and expectation values in the canonical ensemble.
We perform calculations for the binding energies and low-lying levels of ${}^{10,11,12,13,14,15,16,17,18,19,20,21,22}C$ nuclei starting from the chiral $N3LO$ nucleon-nucleon potential within the framework of the Hybrid Multideterminant scheme. The calculations are restricted to 4 major harmonic oscillator shells, via the Lee-Suzuki renormalization scheme. The results are compared with the experimental data.
We perform an ab-initio calculation for the binding energy of ${}^6Li$ using the CD-Bonn 2000 NN potential renormalized with the Lee-Suzuki method. The many-body approach to the problem is the Hybrid Multideterminant method. The results indicate a binding energy of about $31 MeV$, within a few hundreds KeV uncertainty. The center of mass diagnostics are also discussed.