Eur. Phys. J. A (2006) 27: 143-155
https://doi.org/10.1140/epja/i2005-10247-3

Nuclear Structure and Reactions

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion^⋆

¹ “Kharkov Institute of Physics and Technology”, NCS, Academicheskaya Str. 1, 61108, Kharkov, Ukraine
² Institute of Nuclear Physics, T.U. Darmstadt, Schlossgartenstr. 9, D-64289, Darmstadt, Germany
³ Physics Department, Nuclear and Particle Physics Division, University of Athens, GR-157 71, Athens, Greece

Received: 17 July 2005
Accepted: 7 February 2006
Published online: 30 March 2006

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 and for oscillator quanta. Each of the relevant multiplicative operators can then be reduced to the form: one exponential of the set {} times another exponential of the set {}. 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.