An investigation of the basement complex aquifer system in Lofa county, Liberia, for the purpose of siting boreholes

Liberia is recovering from a 14 year civil war and only 51% of the rural population has access to safe drinking water. Little hydrogeological knowledge survives in Liberia, increasing the difficulty in successfully siting new boreholes. An understanding of the local hydrogeological environment is therefore needed to improve borehole site selection and increase success rates. This research provides a semi-quantitative characterization of the hydrogeological environment of the basement aquifer in Lofa county, Liberia. Based on literature review and analysis of borehole logs, the study has developed a conceptual hydrogeological model for the local conditions, which is further characterized using 2D geoelectrical sections. Groundwater is predominantly obtained from the saprolite and underlying fractured bedrock, but specific capacities (median 281 l h-1 m-1; 25th and 75th percentile of 179 and 490 l h-1 m-1, respectively) are constrained by the limited thickness of the saturated saprolite. This study has shown that the groundwater resources in the crystalline basement in this part of Liberia conform to the general conceptual model, allowing standard techniques used elsewhere for siting and developing groundwater to be used

Modern NN Force Predictions for the Total ND Cross Section up to 300 MeV

For several modern nucleon-nucleon potentials state-of-the-art Faddeev calculations are carried out for the $nd$ total cross section between 10 and 300 MeV projectile energy and compared to new high precision measurements. The agreement between theory and data is rather good, with exception at the higher energies where a 10% discrepancy builds up. In addition the convergence of the multiple scattering series incorporated in the Faddeev scheme is studied numerically with the result, that rescattering corrections remain important. Based on this multiple scattering series the high energy limit of the total $nd$ cross section is also investigated analytically. In contrast to the naive expectation that the total $nd$ cross section is the sum of the $np$ and $nn$ total cross sections we find additional effects resulting from the rescattering processes, which have different signs and different behavior as function of the energy. A shadowing effect in the high energy limit only occurs for energies higher than 300 MeV. The expressions in the high energy limit have qualitatively a similar behavior as the exactly calculated expressions, but can be expected to be valid quantitatively only at much higher energies.Comment: 22 pages, 5 figure

Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory

[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it 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.Comment: 13 pages, 11 Figure

Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves

We extend our subtractive-renormalization method in order to evaluate the 1S0 and 3S1-3D1 NN scattering phase shifts up to next-to-next-to-leading order (NNLO) in chiral effective theory. We show that, if energy-dependent contact terms are employed in the NN potential, the 1S0 phase shift can be obtained by carrying out two subtractions on the Lippmann-Schwinger equation. These subtractions use knowledge of the the scattering length and the 1S0 phase shift at a specific energy to eliminate the low-energy constants in the contact interaction from the scattering equation. For the J=1 coupled channel, a similar renormalization can be achieved by three subtractions that employ knowledge of the 3S1 scattering length, the 3S1 phase shift at a specific energy and the 3S1-3D1 generalized scattering length. In both channels a similar method can be applied to a potential with momentum-dependent contact terms, except that in that case one of the subtractions must be replaced by a fit to one piece of experimental data. This method allows the use of arbitrarily high cutoffs in the Lippmann-Schwinger equation. We examine the NNLO S-wave phase shifts for cutoffs as large as 5 GeV and show that the presence of linear energy dependence in the NN potential creates spurious poles in the scattering amplitude. In consequence the results are in conflict with empirical data over appreciable portions of the considered cutoff range. We also identify problems with the use of cutoffs greater than 1 GeV when momentum-dependent contact interactions are employed. These problems are ameliorated, but not eliminated, by the use of spectral-function regularization for the two-pion exchange part of the NN potentialComment: 40 pages, 21 figure

Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory

The leading-order nucleon-nucleon (NN) potential derived from chiral perturbation theory consists of one-pion exchange plus a short-distance contact interaction. We show that in the 1S0 and 3S1-3D1 channels renormalization of the Lippmann-Schwinger equation for this potential can be achieved by performing one subtraction. This subtraction requires as its only input knowledge of the NN scattering lengths. This procedure leads to a set of integral equations for the partial-wave NN t-matrix which give cutoff-independent results for the corresponding NN phase shifts. This reformulation of the NN scattering equation offers practical advantages, because only observable quantities appear in the integral equation. The scattering equation may then be analytically continued to negative energies, where information on bound-state energies and wave functions can be extracted.Comment: 16 pages, 11 figure

Ab initio Folding Potentials for Nucleon-Nucleus Scattering based on NCSM One-Body Densities

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. 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. 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. 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.Comment: 10 pages, 14 figures, 1 tabl