Universal Coordinate Gaussian Basis for Calculations of the Bound States of a Few-Particle System
DOI:
https://doi.org/10.15407/ujpe68.9.587Keywords:
a few-body system, variational method, variational basisAbstract
A new simple basis is proposed for variational calculations of the bound states of a few-particle system. For an N-particle system with pairwise interactions, the matrix elements of the Hamiltonian are found in an explicit form. A modified version of the basis invariant with respect to spatial translations is considered as well. As an example, the 12C nucleus is considered as a system consisting of three α-particles, and the convergence of the method is briefly discussed.
References
Yu.A. Lashko, G.F. Filippov, V.S. Vasilevsky. Dynamics of two-cluster systems in phase space. Nucl. Phys. A 941, 121 (2015).
https://doi.org/10.1016/j.nuclphysa.2015.06.006
O.M. Povoroznyk, V.S. Vasilevsky. Spectrum of resonance states in 6He. Experimental and theoretical analyses. Ukr. J. Phys. 60, No. 3, 201 (2015).
https://doi.org/10.15407/ujpe60.03.0201
V.S. Vasilevsky, Yu.A. Lashko, G.F. Filippov. Two- and three-cluster decays of light nuclei within a hyperspherical harmonics approach. Phys. Rev. C 97, 064605 (2018).
https://doi.org/10.1103/PhysRevC.97.064605
G.F. Filippov, I.P. Okhrimenko. On the possibility of using the oscillatory basis for solving continuous spectrum problems. Sov. J. Nucl. Phys. 32 (4), 480 (1980).
G.F. Filippov. On the account of correct asymptotics in the expansions in the oscillatory basis. Sov. J. Nucl. Phys. 33 (4), 488 (1981).
V.I. Kukulin, V.M. Krasnopol'sky. A stochastic variational method for Few-Body Systems. J. Phys. G Nucl. Phys. 3, No. 6, 795 (1977).
https://doi.org/10.1088/0305-4616/3/6/011
Y. Suzuki, K. Varga. Stochastic Variational Approach to Quantum Mechanical Few-Body Problems (Springer-Verlag, Berlin, Heidelberg, 1998) [ISBN: 978-3-540-65152-9].
B.E. Grinyuk, I.V. Simenog. Structure of the 6He nucleus in the three-particle model. Physics of Atomic Nuclei 72, No. 1, 6 (2009).
https://doi.org/10.1134/S1063778809010025
B.E. Grinyuk, I.V. Simenog. Three-particle structure of the halo nucleus 6Li. Nucl. Phys. Atomic Energy 10, No. 9, 9 (2009).
https://doi.org/10.1134/S1063778809010025
B.E. Grinyuk, M.V. Kuzmenko, I.V. Simenog. Precise study of the Efimov three-particle spectrum and structure functions within variational approach. Ukr. J. Phys. 48, No. 10, 1014 (2003).
B.E. Grinyuk, D.V. Piatnytskyi, I.V. Simenog. Structure characteristics of a 4He nucleus within the microscopic approach. Ukr. J. Phys. 52, No. 5, 424 (2007).
B.E. Grinyuk, I.V. Simenog. Structure characteristics of light cluster nuclei with two extra nucleons. Ukr. J. Phys. 56, No. 7, 635 (2011).
https://doi.org/10.15407/ujpe56.7.635
B.E. Grinyuk, I.V. Simenog. Structural properties of the 10Be and 10C four-cluster nuclei. Physics of Atomic Nuclei 77, No. 4, 415 (2014).
https://doi.org/10.1134/S1063778814030090
B.E. Grinyuk, D.V. Piatnytskyi. Structure of 14C and 14O nuclei calculated in the variational approach. Ukr. J. Phys. 61, No. 8, 674 (2016).
https://doi.org/10.15407/ujpe61.08.0674
B.E. Grinyuk, D.V. Piatnytskyi. Structure of 14N nucleus within a five-cluster model. Ukr. J. Phys. 62, No. 10, 835 (2017).
https://doi.org/10.15407/ujpe62.10.0835
B.E. Grinyuk, D.V. Piatnytskyi, V.S. Vasilevsky. The lowest excited states of 14C and 14O nuclei within a five-cluster model. Nucl. Phys. A 1030, 122588 (2023).
https://doi.org/10.1016/j.nuclphysa.2022.122588
A.G. Donchev, S.A. Kalachev, N.N. Kolesnikov, V.I. Tarasov. Carcass functions in variational calculations for few-body systems. Physics of Atomic Nuclei 67, No. 12, 2154 (2004).
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