Abstract.
The one-body and two-body density matrices in coordinate space and their Fourier transforms in momentum space are studied for a nucleus (a nonrelativistic, self-bound finite system). Unlike the usual procedure, suitable for infinite or externally bound systems, they are determined as expectation values of appropriate intrinsic operators, dependent on the relative coordinates and momenta (Jacobi variables) and acting on intrinsic wave functions of nuclear states. Thus, translational invariance (TI) is respected. When handling such intrinsic quantities, we use an algebraic technique based upon the Cartesian representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators \( \hat{{\vec{a}}}^{{{\dagger}}}_{{}}\) and \( \hat{{\vec{a}}}\) for oscillator quanta. Each of the relevant multiplicative operators can then be reduced to the form: one exponential of the set {\( \hat{{\vec{a}}}^{{{\dagger}}}_{{}}\)} times another exponential of the set {\( \hat{{\vec{a}}}\)}. In the course of such a normal-ordering procedure we offer a fresh look at the appearance of “Tassie-Barker” factors, and point out other model-independent results. The intrinsic wave function of the nucleus in its ground state is constructed from a nontranslationally-invariant (nTI) one via existing projection techniques. As an illustration, the one-body and two-body momentum distributions (MDs) for the 4He nucleus are calculated with the Slater determinant of the harmonic-oscillator model as the trial, nTI wave function. We find that the TI introduces quite important effects in the MDs.
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References
P.O. Löwdin, Phys. Rev. 97, 1474 (1955).
O. Benhar, A. Fabrocini (Editors), Proceedings of the Workshop on Two-Nucleon Emission Reactions, Elba International Physics Center, Italy, 1989 (ETS Edition, Pisa 1990).
A. Braghieri, C. Giusti, P. Grabmayr (Editors), Proceedings of the 6th Workshop on Electromagnetically Induced Two-Hadron Emission, Pavia, Italy September 24-27, 2003.
T. Walcher, Prog. Part. Nucl. Phys. 50, 503 (2003).
R.A. Niyazov, Phys. Rev. Lett. 92, 052303 (2004).
A.V. Stavinsky (CLAS Collaboration), Phys. Rev. Lett. 93, 192301 (2004).
P. Papakonstantinou, E. Mavrommatis, T.S. Kosmas, Nucl. Phys. A 673, 171 (2000).
Ch. Moustakidis, P. Papakonstantinou, E. Mavrommatis, arXiv: nucl-th/0511056.
G. Orlandini, L. Sarra, Proceedings of the 2nd Workshop on Electromagnetically Induced Two-Nucleon Emission, Gent, May 17-20, 1995 (University of Gent, 1995) p. 1.
S.S. Dimitrova, D.N. Kadrev, A.N. Antonov, M.V. Stoitsov, Eur. Phys. J. A 7, 335 (2000).
P. Papakonstantinou, E. Mavrommatis, T.S. Kosmas, Nucl. Phys. A 713, 81 (2003).
J.P. Elliot, T.H. Skyrme, Proc. R. Soc. London, Ser. A 232, 561 (1955).
A.E.L. Dieperink, T. de Forest, Phys. Rev. C 10, 543 (1974).
T. de Forest, Phys. Rev. C 22, 2222 (1980).
L.J. Tassie, C.F. Barker, Phys. Rev. 111, 940 (1958).
S. Gartenhaus, C. Schwartz, Phys. Rev. 108, 482 (1957).
R. Peierls, J. Yoccoz, Proc. Phys. Soc. A 70, 381 (1957).
D.J. Ernst, C.M. Shakin, R.M. Thaler, Phys. Rev. C 7, 925 (1973).
D.J. Ernst, C.M. Shakin, R.M. Thaler, Phys. Rev. C 7, 1340 (1973).
C.M. Vincent, Phys. Rev. C 8, 929 (1973).
A.V. Shebeko, N.N. Goncharov, Sov. J. Nucl. Phys. 18, 532 (1974).
S. Dementiji, V. Ogurtzov, A. Shebeko, N.G. Afanasiev, Sov. J. Nucl. Phys. 22, 6 (1976).
J.L. Friar, Nucl. Phys. A 173, 257 (1971).
K.W. Schmid, F. Grümmer, Z. Phys. A 336, 5 (1990).
K.W. Schmid, F. Grümmer, Z. Phys. A 337, 267 (1990).
K.W. Schmid, Eur. Phys. J. A 12, 29 (2001)
R.R. Rodriguez-Guzman, K.W. Schmid, Eur. Phys. J. A 19, 45
B. Mihaila, J.H. Heisenberg, Phys. Rev. C 60, 054303 (1999).
M. Grypeos, C. Koutroulos, A. Shebeko, K. Ypsilantis, Part. Nucl. Lett. 2, 111 (2002).
D. Van Neck, M. Waroquier, Phys. Rev. C 58, 3359 (1998).
P. Papakonstantinou, PhD Thesis, University of Athens, 2004.
M. Dal Ri, S. Stringari, O. Bohigas, Nucl. Phys. A 376, 81 (1982).
M.L. Goldberger, K.M. Watson, Collision Theory (John Wiley and Sons, 1964).
A. Bohr, B.R. Mottelson, Nucleal Structure I (A. Benjamin, New York, 1969).
V. Neudachin, Yu. Smirnov, Nucleon Clusters in Light Nuclei (Nauka, Moscow, 1964).
N.H. March, W.H. Young, S. Sampanthar, The Many-Body Problem in Quantum Mechanics (Cambridge University Press, London, 1967).
A. Antonov, P.E. Hodgson, I.Zh. Petkov, Nucleon Momentum and Density Distributions in Nuclei (Clarendon Press, Oxford, 1988).
A. Antonov, P.E. Hodgson, I.Zh. Petkov, Nucleon Correlations in Nuclei (Springer-Verlag, Berlin-Heidelberg-New York, 1993).
A.Yu. Korchin, A.V. Shebeko, Z. Phys. A 321, 687 (1985) and references therein.
C. Ciofi degli Atti, E. Pace, G. Salme, Phys. Lett. B 141, 14 (1984).
A.Yu. Korchin, A.V. Shebeko, Ukr. J. Phys. 22, 1646 (1977)
R.E. Peierls, D.J. Thouless, Nucl. Phys. 38, 154 (1962).
T.S. Kosmas, J.D. Vergados, Nucl. Phys. A 536, 72 (1992).
C. Ciofi degli Atti, Prog. Part. Nucl. Phys. 3, 163 (1980).
S.V. Dementij, J. Phys. Soc. Jpn. 57, 2988 (1988).
A.V. Shebeko, Lectures on Selected Topics of Nuclear Theory, Aristotle University of Thessaloniki, 2000.
H. de Vries, C.W. de Jager, C. de Vries, At. Data Nucl. Data Tables 36, 495 (1987).
A.V. Shebeko, M.I. Shirokov, Prog. Part. Nucl. Phys. 44, 75 (2000)
B. Hamme, W. Glöckle, Few-Body Syst. 13, 1 (1992).
D.H. Lu, A.W. Thomas, A.G. Williams, Phys. Rev. C 57, 2628 (1998).
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Shebeko, A., Papakonstantinou , P. & Mavrommatis, E. The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆ . Eur. Phys. J. A 27, 143–155 (2006). https://doi.org/10.1140/epja/i2005-10247-3
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DOI: https://doi.org/10.1140/epja/i2005-10247-3