LXXI International conference "NUCLEUS – 2021. Nuclear physics and elementary particle physics. Nuclear physics technologies"

Convergence of calculations in oscillator basis

22 Sept 2021, 13:55

25m

Oral report Section 1. Experimental and theoretical studies of the properties of atomic nuclei. Section 1. Experimental and theoretical studies of the properties of atomic nuclei

Speaker

Vasily Kulikov (Lomonosov Moscow State University)

Description

We study general convergence trends of binding energy calculations in oscillator basis depending on two basis parameters, the oscillator frequency, $\hbar\Omega$, and maximal oscillator quanta, $N$. We propose and test a new method which suggests extending the Hamiltonian matrix by the kinetic energy matrix elements. We study also convergence of calculations with smoothed potential matrix elements [1].

We use the SS-HORSE (single-state harmonic-oscillator representation of scattering equations) approach [2] extended to the case of bound states [3]. Within this method, we extract the $S$ matrix from the results of variational calculations with oscillator basis and locate the $S$-matrix poles associated with bound states. The respective binding energies improve the variational results and provide an extrapolation of the variational binding energies to the infinite basis space. A great advantage of our approach as compared with other extrapolation techniques suggested in current literature [4–6] is that it makes possible to calculate also asymptotic normalization constants.

References:

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2. A. M. Shirokov, A. I. Mazur, I. A. Mazur and J. P. Vary, Phys. Rev. C 94, 064320 (2016).
3. A. M. Shirokov, V. A. Kulikov and A. I. Mazur, Phys. At. Nucl. 82, 285 (2019).
4. Yu. A. Lurie and A. M. Shirokov, Ann. Phys. (NY), 312, 284 (2004).
5. P. Maris, J. P. Vary and A. M. Shirokov, Phys. Rev. C. 79, 014308 (2009).
6. 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).
7. R. J. Furnstahl, G. Hagen and T. Papenbrock, Phys. Rev. C. 86, 031301(R) (2012).