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

Abstract

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 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 operatorsâ + andâ for oscillator quanta. Each of the relevant multiplicative operators can then be reduced to the form: one exponential of the set {â + } times other exponential of the set {â}. 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 4 He 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.PACS. 21.60.-n Nuclear structure models and methods -21.45.+v Nuclear few-body systems -24.10.-i Nuclear reaction models and methods

The effect of short-range correlations on the generalized momentum distribution in finite nuclei

“…One should start along the lines of references [44,45] for the case of N = Z, l-closed nuclei. Starting from these nuclei, one must also consider to include in the calculations of n( p, Q) state-dependent correlations.…”

“…Following the notation of Ref. [44] we write the relevant operator in the form (hats denote operators)…”

Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

“…Therefore, the corresponding theoretical approaches are needed in certain refinements to bringing a reliable information on the distributions in question from experimental data. Neglecting these complexities one has to deal [3], [14], [15] with the two structure quantities, viz., the intrinsic density distribution (DD) or simply the intrinsic density ρ int (r) and the intrinsic MD η int (p). They are expectation values in the translationally invariant (intrinsic) g.s.…”

“…[15]) while the not intrinsic DM n(k) has been corrected (without any good reasons) via the renormalization…”

“…An alternative evaluation [3]- [5], [15] of the intrinsic FF's, densities and momentum distributions, put forward in [3] to overcome some obstacles in describing the elastic and inclusive electron scattering off the 4 He nucleus, has brought a fresh look at the CM correction of these quantities. In particular, it turns out that ρ int (r) and η int (p) are shrunk (from the periphery of each of them to its central part) compared to ρ(r) and η(p).…”