We report microscopic calculations of the equation of state for dense nuclear and neutron matter. The calculations are performed for five Hamiltonians: the Argonne u && and Urbana v &4 two-nucleon potentials, both alone and with the Urbana VII three-nucleon potential, and the density-dependent Urbana u&4 plus three-nucleon interaction model of Lagaris, Friedman, and Pandharipande. The beta-stable equation of state and neutron star structure are also calculated for three of the models. The models with the three-nucleon potential bracket the density-dependent model and are significantly stiffer than those with an unmodified two-nucleon potential only. The Argonne u&4 plus Urbana VII Hamiltonian produces a softening in the neutron matter equation of state localized around twice nuclear matter density which may indicate a neutral pion condensate.

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The cross section for inclusive electron scattering by nuclear matter is calculated at high momentum transfers using a microscopic spectral function, and compared with that extrapolated from data on laboratory nuclei. It is found that the cross section obtained with the plane-wave impulse approximation is close to the observed data at large values of the energy loss, but too small at low values. In this regime final-state interactions are important; after including their effects theory and data are in fair agreement.It is necessary to treat nucleon-nucleon correlations consistently in estimating the final-state interactions. The effects of possible time dependence of the nucleon-nucleon cross section, giving rise to nuclear transparency, are also investigated. The y scaling of the response function is discussed to further elucidate the role of final-state interactions. the response, due to the momentum distribution in the initial state, is proportional to~q~, as it is in the case of strongly interacting quantum liquids. If the width of the folding function is finite, then it can be argued that, at large enough values of~q~, FSI can be neglected, and, as a consequence, the response will exhibit y scaling. In con-2328 1991 The American Physical Society SCATTERING OF GeV ELECTRONS BY NUCLEAR MATTER 2329 trast, in the case of the nuclear medium at high q, one has to use relativistic kinematics and therefore the width of the response due to the momentum distribution of particles in the initial state is roughly constant -k~. It then follows that FSI eA'ects can be neglected only if the folding width goes to zero at large q. The folding width is of the order of the imaginary part of the optical potential which is -60 MeV -kF/4 for several hundreds MeV nucleons. Therefore, FSI are not obviously negligible in scattering of multi-GeV electrons by nuclei.Ideally, one should start from a realistic relativistically covariant theory of nuclei; however, such a theory is not yet practicable due to difFiculties in treating pionexchange interactions.In the plane-wave impulse ap-

two-body Euler equations provide correlation functions variationally more effective than those obtained with the same technique in infinite nuclear matter.

We study the ground state properties of doubly closed shell nuclei 16 O and

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We study the ground state of a system of Bose hard spheres trapped in an isotropic harmonic potential to investigate the effect of the interatomic correlations and the accuracy of the Gross-Pitaevskii equation. We compare a local-density approximation, based on the energy functional derived from the low-density expansion of the energy of the uniform hard-sphere gas, and a correlated wave-function approach, which explicitly introduces the correlations induced by the potential. Both higher-order terms in the low-density expansion, beyond Gross-Pitaevskii, and explicit dynamical correlations have effects of the order of percent when the number of trapped particles becomes similar to that attained in recent experiments (Nϳ10 7 ). ͓S1050-2947͑99͒00109-2͔PACS number͑s͒: 03.75. Fi, 05.30.Jp, 32.80.Pj The recent discovery of Bose-Einstein condensation of magnetically trapped alkali atoms has generated a huge amount of theoretical investigations. A review of the present situation can be found in Refs. ͓1,2͔. Present experimental conditions are such that the atomic gas is very dilute, i.e., the average distance among the atoms is much larger than the range of the interaction. As a consequence, the physics should be dominated by two-body collisions, generally well described in terms of the s-wave scattering length. The case of a positive scattering length is equivalent to consider a very dilute system of hard spheres, whose diameter coincides with the scattering length itself. So, the Gross-Pitaevskii ͑GP͒ theory for weakly interacting bosons seems the logical tool to study these systems and most of the present days theoretical work is founded on ͑or has its starting point in͒ this theory ͓3͔. However, in very recent experiments the number of trapped atoms has spectacularly increased reaching N values of the order 10 6 and 10 7 atoms ͓4͔. Therefore, it seems logical to ask for a deeper study of the effect of the interatomic correlations and of the accuracy of the GrossPitaevskii scheme in this new scenario. First-order corrections to the mean field have been evaluated in Refs. ͓1,5͔. The dense condensate case was studied in a slave boson representation in Ref. ͓6͔. Exact quantum Monte Carlo methods ͓7,8͔ have been also employed, but only up to Nϭ10 5 . Here we study the ground state of a system of Bose hard spheres trapped by a harmonic potential. More precisely, we consider hard spheres with a diameter of 52.9 Å, corresponding to the s-wave triplet-spin scattering length of 87 Rb, in an isotropic harmonic trap characterized by an angular frequency /2ϭ77.78 Hz. We also examine the large N atomic sodium case of Ref. ͓4͔. We use and compare two methods: ͑i͒ a local-density approximation ͑LDA͒ based on an energy functional derived by the low-density expansion of the energy of an uniform hard-sphere gas and ͑ii͒ a correlated basis function ͑CBF͒ approach, which explicitly takes into account the dynamical correlations induced by the potential and which is not, in principle, limited to purely repulsive interactions.LDA theor...