The variational method complemented with the use of explicitly correlated Gaussian basis functions is one of the most powerful approaches currently used for calculating the properties of few-body systems. Despite its conceptual simplicity, the method offers great flexibility, high accuracy, and can be used to study diverse quantum systems, ranging from small atoms and molecules to light nuclei, hadrons, quantum dots, and Efimov systems. The basic theoretical foundations are discussed, recent advances in the applications of explicitly correlated Gaussians in physics and chemistry are reviewed, and the strengths and weaknesses of the explicitly correlated Gaussians approach are compared with other few-body techniques.
Abstract. The angular motion of a few-body system is described with global vectors which depend on the positions of the particles. The previous study using a single global vector is extended to make it possible to describe both natural and unnatural parity states. Numerical examples include three-and four-nucleon systems interacting via nucleon-nucleon potentials of AV8 type and a 3α system with a nonlocal αα potential. The results using the explicitly correlated Gaussian basis with the global vectors are shown to be in good agreement with those of other methods. A unique role of the unnatural parity component, caused by the tensor force, is clarified in the 0 − 1 state of 4 He. Twoparticle correlation function is calculated in the coordinate and momentum spaces to show different characteristics of the interactions employed.
Short-range correlations between nucleon pairs in different spin-isospin channels are investigated for light nuclei using the Argonne V8' interaction. At distances below 1 fm a universal behavior is found for the deuteron, 3H, 3He and for ground and first excited states in 4He. This behavior in coordinate space is reflected by a universal behavior for the high-momentum components in momentum space. The universality indicates that a pairwise renormalization is possible in order to obtain a universal effective two-body interaction that does not scatter to high momentum states. The exact two-body densities are compared with those obtained using the unitary correlation operator method with simple trial wave functions. The effect of three-body correlations due to the tensor force on the two-body densities is discussed.Comment: 13 pages, 17 figures, journal versio
We systematically analyze total reaction cross sections of carbon isotopes with N = 6-16 on a 12 C target for wide range of incident energy. The intrinsic structure of the carbon isotope is described by a Slater determinant generated from a phenomenological mean-field potential, which reasonably well reproduces the ground state properties for most of the even N isotopes. We need separate studies not only for odd nuclei but also for 16 C and 22 C. The density of the carbon isotope is constructed by eliminating the effect of the center of mass motion. For the calculations of the cross sections, we take two schemes: one is the Glauber approximation, and the other is the eikonal model using a global optical potential. We find that both of the schemes successfully reproduce low and high incident energy data on the cross sections of 12 C, 13 C and 16 C on 12 C. The calculated reaction cross sections of 15 C are found to be considerably smaller than the empirical values observed at low energy. We find a consistent parameterization of the nucleon-nucleon scattering amplitude, differently from previous ones. Finally, we predict the total reaction cross section of 22 C on 12 C.
We systematically study total reaction cross sections of carbon isotopes with N = 6-16 on a proton target for wide range of incident energies, putting an emphasis on the difference from the case of a carbon target. The analysis includes the reaction cross sections of 19,20,22 C at 40 AMeV, the data of which have recently been measured at RIKEN. The Glauber theory is used to calculate the reaction cross sections. To describe the intrinsic structure of the carbon isotopes, we use a Slater determinant generated from a phenomenological mean-field potential, and construct the density distributions. To go beyond the simple mean-field model, we adopt two types of dynamical models: One is a core+n model for odd-neutron nuclei, and the other is a core+n+n model for 16 C and 22 C. We propose empirical formulas which are useful in predicting unknown cross sections.
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