HAL : in2p3-00740410, version 1
 arXiv : 1205.3230
 Convergence properties of {\itshape ab initio} calculations of light nuclei in a harmonic oscillator basis
 (2012)
 We study recently proposed ultraviolet and infrared momentum regulators of the model spaces formed by construction of a variational trial wavefunction which uses a complete set of many-body basis states based upon three-dimensional harmonic oscillator (HO) functions. These model spaces are defined by a truncation of the expansion characterized by a counting number ($\mathcal{N}$) and by the intrinsic scale ($\hbar\omega$) of the HO basis; in short by the ordered pair ($\mathcal{N},\hbar\omega$). In this study we choose for $\mathcal{N}$ the truncation parameter $N_{max}$ related to the maximum number of oscillator quanta, above the minimum configuration, kept in the model space. The ultraviolet (uv) momentum cutoff of the continuum is readily mapped onto a defined uv cutoff in this finite model space, but there are two proposed definitions of the infrared (ir) momentum cutoff inherent in a finite-dimensional HO basis. One definition is based upon the lowest momentum difference given by $\hbar\omega$ itself and the other upon the infrared momentum which corresponds to the maximal radial extent used to encompass the many-body system in coordinate space. Extending both the uv cutoff to infinity and the ir cutoff to zero is prescribed for a converged calculation. We calculate the ground state energy of light nuclei with "bare" and "soft" $NN$ interactions. By doing so, we investigate the behaviors of the uv and ir regulators of model spaces used to describe $^2$H, $^3$H, $^4$He and $^6$He with $NN$ potentials Idaho N$^3$LO and JISP16. We establish practical procedures which utilize these regulators to obtain the extrapolated result from sequences of calculations with model spaces characterized by ($\mathcal{N},\hbar\omega$).
 Thème(s) : Physique/Physique Nucléaire Théorique
 Lien vers le texte intégral : http://fr.arXiv.org/abs/1205.3230
 in2p3-00740410, version 1 http://hal.in2p3.fr/in2p3-00740410 oai:hal.in2p3.fr:in2p3-00740410 Contributeur : Sophie Heurteau <> Soumis le : Mercredi 10 Octobre 2012, 10:35:34 Dernière modification le : Mercredi 10 Octobre 2012, 13:44:09