Abstract
It is assumed that the total potential of proton interaction with a hydrogen atom is the sum of the short-range nuclear soft-core Reid potential and the long-range Thomas-Fermi potential. A quantum mechanical analysis of low-energy features of the phase shift and cross section for elastic proton scattering on a hydrogen atom is given for the case of zero total angular momentum. The calculations performed in the present study within a nonlinear version of the variable-phase approach ultimately revealed that, because of a long-range character of the asymptotic behavior of the Thomas-Fermi potential, the respective cross section at low energies oscillates but has a finite number of zeros.
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References
O. Chuluunbaatar, A. A. Gusev, V. L. Derbov, et al., Phys. At. Nucl. 72, 768 (2009).
O. Chuluunbaatar, A. A. Gusev, V. L. Derbov, et al., Phys. At. Nucl. 71, 844 (2008).
O. Chuluunbaatar, A. A. Gusev, S. I. Vinitsky, et al., Phys. Rev. A 77, 034702–1 (2008).
O. Chuluunbaatar, A. A. Gusev, V. P. Gerdt, et al., Comput. Phys. Commun. 178, 301 (2008).
S. I. Vinitsky, A. A. Gusev, and O. Chuluunbaatar, Vestn. SPb. Univ., Ser. Fiz. Khim., No. 3, 111 (2010).
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory (Nauka, Moscow, 1989, 4th ed.; Pergamon, New York, 1977, 3rd ed.).
I. E. Tamm, Foundations of Electricity Theory (Nauka, Moscow, 1976) [in Russian].
L. D. Faddeev and S. P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Kluwer, Dordrecht, 1993; Nauka, Moscow, 1985).
V. V. Babikov, Variable-Phase Approach in QuantumMechanics (Nauka, Moscow, 1976) [inRussian]
G. F. Drukarev, Collisions of Electrons with Atoms and Molecules (Nauka, Moscow, 1978; Plenum Press, New York, 1987).
J. E. Braun and A. D. Jackson, Nucleon-Nucleon Interactions (North-Holland, Amsterdam, 1976; Atomizdat, Moscow, 1979).
S. Pashkovskii, Computational Applications of Chebyshev Polynomials and Series (Nauka, Moscow, 1983) [in Russian].
V. I. Krylov, V. V. Bobkov, and P. I. Monastyrnyi, Numerical Methods (Nauka, Moscow, 1977), vol. 2 [in Russian].
Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Methods of Spline-Functions (Nauka, Moscow, 1980) [in Russian].
R. V. Reid, Jr., Ann. Phys. (N.Y.) 50, 411 (1968).
L. H. Thomas, Proc. Cambridge Philos. Soc. 23, 542 (1927).
E. Fermi, Z. Phys. 48, 73 (1928).
E. Fermi, Scientific Works, Ed. by B. Pontekorvo (Nauka, Moscow, 1971), vol. 1 [in Russian].
V. Bush and S. H. Caldwell, Phys. Rev. 38, 1898 (1931).
J. C. Mason, Proc. Phys. Soc. London 84, 357 (1964).
H. Krutter, J. Comput. Phys. 47, 308 (1982).
N. Anderson and A. M. Arthurs, Q. Appl. Math. 39, 127 (1981).
B. L. Burrows and P. W. Core, Q. Appl. Math. 42, 73 (1984).
A. J. MacLeod, Comput. Phys. Commun. 67, 389 (1992).
J. W. Mooney, Comput. Phys. Commun. 76, 51 (1993).
V. V. Pupyshev and O. P. Solovtsova, Phys. Lett. B 354, 1 (1995).
V. V. Pupyshev and O. P. Solovtsova, Phys. At. Nucl. 59, 1745 (1996).
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Original Russian Text © V. V. Pupyshev, 2013, published in Yadernaya Fizika, 2013, Vol. 76, No. 2, pp. 184–198.
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Pupyshev, V.V. Proton scattering by a hydrogen atom in an effectively two-body model. Phys. Atom. Nuclei 76, 155–170 (2013). https://doi.org/10.1134/S1063778813010092
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DOI: https://doi.org/10.1134/S1063778813010092