Background: It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from ab initio no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available.Purpose: Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities.Results: A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of 4 He, 6 Li, 12 C, and 16 O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space. Conclusions:We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms. PACS numbers: 21.60De,27.20.+n arXiv:1711.07080v1 [nucl-th] 19 Nov 2017where R nl (r) is the radial component of the single-particle harmonic oscillator wave function (defined in Appendix A). Using Eq. (7), the matrix elements of ρ sf ( r, r ) can be expressed as a sum over all tensors ρ ll K (r, r ), ρ sf ( r, r ) = Kll (−1) J −M J K J −M 0 M Y * l l K0 (r,r )ρ ll K (r, r ),separating out the radial and angular components of the nonlocal density.

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Background: Calculating microscopic optical potentials for elastic nucleon-nucleus scattering has already led to large body of work in the past. For folding first-order calculations the nucleon-nucleon (NN) interaction and the one-body density of the nucleus were taken as input to rigorous calculations in a spectator expansion of the multiple scattering series.Purpose: Based on the Watson expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calculation of the effective (optical) potential for nucleon-nucleus scattering for light nuclei.Methods: The first order effective (optical) folding potential is computed by integrating over the nonlocal, translationally invariant NCSM one-body density and the off-shell Wolfenstein amplitudes A and C. The resulting nonlocal potential serves as input for a momentum-space Lippmann-Schwinger equation, whose solutions are summed to obtain the nucleon-nucleus scattering observables. Results:We calculate scattering observables, such as total, reaction, and differential cross sections as well as the analyzing power and the spin-rotation parameter, for elastic scattering of protons and neutrons from 4 He, 6 He, 12 C, and 16 O, in the energy regime between 100 and 200 MeV projectile kinetic energy, and compare to available data.Conclusions: Our calculations show that the effective nucleon-nucleus potential obtained from the first-order term in the spectator expansion of the multiple scattering expansion describes experiments very well to about 60 degrees in the center-of-mass frame, which coincides roughly with the validity of the NNLO chiral interaction used to calculate both the NN amplitudes and the one-body nuclear density.

The pseudo-SU͑3͒ model is used to describe the low-energy spectra and electromagnetic transition strengths in 156 Gd, 158 Gd, and 160 Gd. The Hamiltonian includes spherical single-particle energies, the quadrupolequadrupole interaction, proton and neutron pairing interactions, plus four rotorlike terms. The quadrupolequadrupole and pairing interaction strengths are assigned the values ϭ23A Ϫ5/3 and G ϭ21/A, G ϭ17/A, respectively. The single-particle energies were taken from experiment but scaled to yield an overall best fit. For the other four rotorlike terms, which do not mix SU͑3͒ representations and induce only small changes in the spectra, a consistent set of parameters is given. The basis states are built as linear combinations of SU͑3͒ states which are the direct product of SU͑3͒ proton and neutron states with pseudospin zero. The results are in good agreement with experimental data, demonstrating the suitability of the model to describe heavy deformed nuclei.

An empirical investigation of the trends in the properties of the nonyrast K =2 ␥ + and K =0 2 + bandhead configurations in nuclei that are related to one another through the addition or removal of ␣-particle-like structures, reveals their complex and changing behavior in contrast to the smooth behavior of the yrast states. A systematic application of the pseudo-SU(3) model for such a sequence of deformed nuclei from the rare earth region leads to an accurate and unified description of not only yrast, but nonyrast collective bands. The onset of deformation as manifested through the position of the excited bandheads in the spectra is understood and interpreted by using a realistic model Hamiltonian in conjunction with a microscopic distribution of the eigenstates across allowed proton and neutron strong-coupled SU (3) configurations.