Convergence properties of {\itshape ab initio} calculations of light nuclei in a harmonic oscillator basis - IN2P3 - Institut national de physique nucléaire et de physique des particules Access content directly
Journal Articles Physical Review C Year : 2012

Convergence properties of {\itshape ab initio} calculations of light nuclei in a harmonic oscillator basis

S. A. Coon
  • Function : Author
M. I. Avetian
  • Function : Author
M. K. G. Kruse
  • Function : Author
P. Maris
  • Function : Author
J. P. Vary
  • Function : Author

Abstract

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 ($\mathcal{N},\hbar\omega$).

Dates and versions

in2p3-00740410 , version 1 (10-10-2012)

Identifiers

Cite

S. A. Coon, M. I. Avetian, M. K. G. Kruse, U. van Kolck, P. Maris, et al.. Convergence properties of {\itshape ab initio} calculations of light nuclei in a harmonic oscillator basis. Physical Review C, 2012, 86 (5), pp.054002. ⟨10.1103/PhysRevC.86.054002⟩. ⟨in2p3-00740410⟩
25 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More