2 research outputs found
The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion
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
wavefunctions 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 a^+ and a for oscillator quanta. Each of the relevant multiplicative
operators can then be reduced to the form: one exponential of the set {a^+}
times other exponential of the set {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 wavefunction 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 wavefunction. We find that the TI
introduces important effects in the MDs.Comment: 13 pages, incl. 3 figures - to appear in Eur. Phys. J.
Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included
Relying upon our previous treatment of the density matrices for nuclei (in
general, nonrelativistic self-bound finite systems) we are studying a combined
effect of center-of-mass motion and short-range nucleon-nucleon correlations on
the nucleon density and momentum distributions in light nuclei ( and
). Their intrinsic ground-state wave functions are constructed in the
so-called fixed center-of-mass approximation, starting with mean-field Slater
determinants modified by some correlator (e.g., after Jastrow or Villars). We
develop the formalism based upon the Cartesian or boson representation, in
which the coordinate and momentum operators are linear combinations of the
creation and annihilation operators for oscillatory quanta in the three
different space directions, and get the own "Tassie-Barker" factors for each
distribution and point out other model-independent results. After this
separation of the center-of-mass motion effects we propose additional analytic
means in order to simplify the subsequent calculations (e.g., within the
Jastrow approach or the unitary correlation operator method). The charge form
factors, densities and momentum distributions of and
evaluated by using the well known cluster expansions are compared with data,
our exact (numerical) results and microscopic calculations.Comment: 19 pages, 6 figure