Improving harmonic oscillator basis in covariant density functional theory
ORAL
Abstract
Covariant density functional theory (CDFT) describes the nucleus as a system of A nucleons (fermions) which
interact via the exchange of different mesons. It is very successful in the description of phenomena related to
nuclear structure, nuclear reactions and nuclear astrophysics [1]. The basis set expansion (BSE) based on harmonic
oscillator (HO) wave functions is used in the majority of the CDFT applications [2]. This theory represents a rare
example of two interconnected subsystems (i.e. mesonic (bosonic) and fermionic) the wave functions in which are
described by BSEs. It is well known that in the BSEs the wave functions are precisely
described only in the case of infinite basis. However, numerical calculations in such bases are impossible and the fermionic
and bosonic BSE are truncated at full NF fermionic and full NB bosonic shells, respectively. It is
only recently that the accuracy of such truncations was tested with respect of extrapolated solutions corresponding
to infinite bases [3]. It turns out that the calculations with NB=40 reproduce the solutions corresponding to infinite
basis with accuracy of few keV across the nuclear chart. The situation with fermionic basis is much more difficult
since the transition from NF=20 to NF=40 increases the computational time by two orders of magnitude and leads
to drastic increase of memory. However, the global optimization of the HO basis carried in [4] leads to a drastic
reduction of the global difference between the results obtained with NF=20 and NF=40.
interact via the exchange of different mesons. It is very successful in the description of phenomena related to
nuclear structure, nuclear reactions and nuclear astrophysics [1]. The basis set expansion (BSE) based on harmonic
oscillator (HO) wave functions is used in the majority of the CDFT applications [2]. This theory represents a rare
example of two interconnected subsystems (i.e. mesonic (bosonic) and fermionic) the wave functions in which are
described by BSEs. It is well known that in the BSEs the wave functions are precisely
described only in the case of infinite basis. However, numerical calculations in such bases are impossible and the fermionic
and bosonic BSE are truncated at full NF fermionic and full NB bosonic shells, respectively. It is
only recently that the accuracy of such truncations was tested with respect of extrapolated solutions corresponding
to infinite bases [3]. It turns out that the calculations with NB=40 reproduce the solutions corresponding to infinite
basis with accuracy of few keV across the nuclear chart. The situation with fermionic basis is much more difficult
since the transition from NF=20 to NF=40 increases the computational time by two orders of magnitude and leads
to drastic increase of memory. However, the global optimization of the HO basis carried in [4] leads to a drastic
reduction of the global difference between the results obtained with NF=20 and NF=40.
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Publication: [1] D. Vretenar, A. V. Afanasjev, G. A. Lalazissis, and P. Ring, Phys. Rep. 409, 101 (2005).<br>[2] A. Taninah, B. Osier, A.V. Afanasjev, U.C. Perera and S. Teeti, Phys. Rev. C 109, 024321 (2024)<br>[3] B. Osei, A. V. Afanasjev, A. Taninah, A. Dalbah, U. C. Perera, V. A. Dzuba, and V. V. Flambaum, <br> submitted to Phys. Rev. C<br>[4] B. Osei, A. V. Afanasjev and A. Dalbah, in preparation
Presenters
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Bernard Osei
Mississippi State University
Authors
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Bernard Osei
Mississippi State University
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Anatoli Afanasjev
Mississippi State University
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Ali Dalbah
Mississippi State University