Abstract
For variational calculations of molecular and nuclear systems involving a few particles, it is proposed to use carcass basis functions that generalize exponential and Gaussian trial functions. It is shown that the matrix elements of the Hamiltonian are expressed in a closed form for a Coulomb potential, as well as for other popular particle-interaction potentials. The use of such carcass functions in two-center Coulomb problems reduces, in relation to other methods, the number of terms in a variational expansion by a few orders of magnitude at a commensurate or even higher accuracy. The efficiency of the method is illustrated by calculations of the three-particle Coulomb systems μμe, ppe, dde, and tte and the fourparticle molecular systems H2 and HeH+ of various isotopic composition. By considering the example of the 9Λ Be hypernucleus, it is shown that the proposed method can be used in calculating nuclear systems as well.
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References
N. N. Kolesnikov and V. I. Tarasov, Yad. Fiz. 35, 609 (1982) [Sov. J. Nucl. Phys. 35, 354 (1982)].
N. N. Kolesnikov, V. I. Tarasov, and M. I. Starosotnikov, Available from VINITI, No. 3832-80 (1980).
E. A. Hylleraas, Z. Phys. 54, 347 (1929).
A. G. Donchev, N. N. Kolesnikov, and V. I. Tarasov, Preprint No. 8/2002, MGU (Moscow State University, Moscow, 2002).
J. Zs. Mezei, J. Mitroy, R. G. Loves, and K. Varga, Phys. Rev. A 64, 032501 (2001).
D. B. Kinghorn and I. Adomicz, Phys. Rev. Lett. 83, 2541 (1999).
T. K. Rebane and O. N. Yusupov, Zh. Éksp. Teor. Fiz. 98, 1870 (1990) [Sov. Phys. JETP 71, 1050 (1990)].
A. M. Frolov, Phys. Rev. A 57, 2436 (1998); A. M. Frolov and V. H. Smith, Jr., J. Phys. B 8, L449 (1995).
A. K. Bhatia, Phys. Rev. A 58, 2787 (1998).
M. Born and J. R. Oppenheimer, Ann. Phys. 84, 457 (1927).
B. Gremaud, D. Dominique, and N. Billy, J. Phys. B 31, 383 (1998).
S. I. Vinitsky and L. I. Ponomarev, Fiz. Élem. Chastits At. Yadra 13, 1336 (1982).
P. P. Zakharov, N. N. Kolesnikov, and V. I. Tarasov, Vestn. Mos. Gos. Univ., Ser. 3: Fiz., Astron., No. 24, 34 (1983).
V. I. Kukulin, Izv. Akad. Nauk SSSR, Ser. Fiz. 39, 535 (1975).
A. G. Donchev, N. N. Kolesnikov, and V. I. Tarasov, Yad. Fiz. 63, 419 (2000) [Phys. At. Nucl. 63, 353 (2000)].
I. N. Filikhin and S. L. Yakovlev, Yad. Fiz. 63, 409 (2000) [Phys. At. Nucl. 63, 343 (2000)].
S. Ali and A. R. Bodmer, Nucl. Phys. 80, 99 (1966).
N. N. Kolesnikov and V. A. Kopylov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 5, 36 (1983); N. N. Kolesnikov and V. I. Tarasov, Izv. Vyssh. Uchebn. Zaved., Fiz. 40 (10), 19 (1997).
W. A. Chupka and M. E. Rassel, J. Chem. Phys. 49, 5426 (1968).
D. van Pijkeren, J. van Eok, and A. Niehaus, Chem. Phys. Lett. 96, 20 (1984).
A. A. Evett, J. Chem. Phys. 24, 150 (1956).
L. Wolnievicz, J. Chem. Phys. 43, 1087 (1965).
J. D. Stuart and F. A. Motsen, J. Chem. Phys. 41, 1646 (1964).
A. G. Donchev, N. N. Kolesnikov, and V. I. Tarasov, Izv. Akad. Nauk, Ser. Fiz. 66, 1519 (2002).
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Translated from Yadernaya Fizika, Vol. 67, No. 12, 2004, pp. 2178–2189.
Original Russian Text Copyright © 2004 by Donchev, Kalachev, Kolesnikov, Tarasov.
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Donchev, A.G., Kalachev, S.A., Kolesnikov, N.N. et al. Carcass functions in variational calculations for few-body systems. Phys. Atom. Nuclei 67, 2154–2165 (2004). https://doi.org/10.1134/1.1842294
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DOI: https://doi.org/10.1134/1.1842294