Speaker
Description
An extrapolation of ab initio results to get more accurate observables became a trend in nuclear physics [1-4]. We consider calculations of binding energies in oscillator basis, which depend on two
basis parameters, the oscillator frequency, $\hbar\Omega$, and the oscillator quanta, $N$. We study general convergence patterns of these calculations. We use the SS-HORSE (single-state harmonic-oscillator representation of scattering equations) approach [5], extended to the case of bound states. Within this method, we extract the $S$-matrix from the results obtained in oscillator basis, and locate $S$-matrix poles associated with bound states. The respective binding energies improve the variational results obtained by the pure diagonalization in oscillator basis [6]. In this way we can extrapolate binding energies to the infinite basis and eliminate the dependence on basis parameters. By calculating the $S$-matrix pole, we can also calculate the asymptotic normalization constant. Till now we use a two-particle model problem with known exact solution to verify our method with an idea to apply it later to many-body shell-model afterwards. We compare also our method with approaches of Ref. [1-3].
References
[1] P. Maris, J. P. Vary, A. M. Shirokov, Phys. Rev. C. 79, 014308 (2009)
[2] S. A. Coon, M. I. Avetian, M. K. G. Kruse, U. van Kolck, P. Maris, and J. P. Vary, Phys. Rev. C. 86, 054002 (2012)
[3] R. J. Furnstahl, G. Hagen and T. Papenbrock, Phys. Rev. C. 86, 031301(R) (2012)
[4] G. A. Negoita et al, arXiv:1803.03215 [physics.comp-ph], (2018)
[5] A. M. Shirokov, A. I. Mazur, I. A. Mazur and J. P. Vary,
Phys. Rev. C 94, 064320 (2016).
[6] Yu. A. Lurie, A. M. Shirokov, Ann. Phys. (NY), 312, 284 (2004)
