Continuum coupled-cluster expansion

One of the major endeavors in modern nuclear physics, is the ongoing quest for an effective nuclear many-body theory, a key element in the attempt to extrapolate existing experimental data to regimes which are not currently accessible in the laboratory. Ideally, one would like to begin with the experimental data available from nucleon-nucleon sNNd scattering experiments [1,2] and determine the underlying NN interaction [3–8]. Subsequent nuclear structure calculations are then necessary to determine a three-nucleon interaction [9], to account for the remaining differences between theory and experiment. Direct comparison of theory (calculations) to experimental data is ambiguous if the nuclear many-body problem is not solved accurately. Results of numerical calculations can be used to constrain fundamental aspects of the theory, provided that one has good approximations of the exact result in order to avoid introducing a bias due to the approximations involved. Much progress has been achieved recently by Green’s function Monte Carlo (GFMC) [10] collaboration in obtaining accurate description of nuclear structure properties of light nuclei sAø10d [11,12]. Such ab initio calculations, based on realistic interaction models, are a key to understand in a quantitative manner the experimental data provided by modern accelerator facilities at Jefferson Laboratory (JLAB) and the future Rare Isotope Accelerator (RIA). We believe that a crucial undertaking in modern physics involves the extension of this work to heavy nuclei. The limitations of the GFMC method to carry out calculations for arbitrary size nuclei originate both from the inherent Fermi sign problem associated with a nonrelativistic system of nucleons obeying Fermi statistics, and the fact that in the present implementation of the GFMC one carries out explicit summations over the spin-isospin degrees of freedom. As such, the relevant number of degrees of freedom increases as 2sZ d, and the size of the spin-isospin vector space quickly becomes prohibitive. A possible way around this technical problem is offered by the auxiliary field diffusion Monte Carlo method [13], where one attempts to sample the spin-isospin degrees of freedom in addition to the spatial coordinates of the nucleons. This method is currently under development, and encouraging results have been recently reported for neutron matter [14]. For nuclei with Aø4, the nonrelativistic Schrödinger equation with realistic nuclear interactions can be solved very precisely: In a recent benchmark [15] carried out for a 4He-like nucleus using the Argonne v88 interaction (central, spin-spin, tensor, spin-orbit, and the corresponding spinexchange counterparts), the binding energy calculated using seven “exact” many-body formalisms agreed within 0.5%. Unfortunately, few many-body formalisms are currently capable to offer accurate numerical solutions of the nuclear many-body problem with realistic interactions, when heavier systems are concerned. For finite nuclei with A.4, the no core shell model [16–18] and the coupled-cluster expansion (CCE) are the only methods which are able to directly compare results with the GFMC for the same type of Hamiltonian. Both methods, however, have serious limitations related to a slow convergence of the results with the size of the model space. As we are about to describe in this paper, the shortcomings of the CCE are not inherent in nature, and we like to believe that the approach to solving the CCE we propose here, will allow the CCE to provide accurate theoretical output for a medium to large domain of masses, in the framework of realistic nuclear interaction [5,19,9] and nuclear currents [20]. We call this new approach the continuum CCE, because continuum effects are accurately taken in account. The CCE, also called the expsSd method, was developed in the early 1960s by Coester and Kümmel [21,22]. While the method is viewed as exact, approximations are introduced stemming from truncations in the CCE equations, as well as truncations in the model space. Practical approaches for nuclear structure applications have been notoriously difficult to realize. It was not until the 1970s that Zabolitsky and co-workers [23] were able to carry out the first detailed calculations for finite nuclei, using a representation of the wave function in coordinate space together with common interactions of the time. The results for the binding energy of nuclei such as 4He, 16O, and 40Ca, were well above the Coester line and were taken as evidence for the presence of 3N and higher-order interactions. While the CCE was extensively used in other areas in physics and chemistry (see Refs. [24,25] for additional information), further applications to nuclear structure calculations based on realistic nuclear interactions proved difficult to *Electronic address: [email protected] PHYSICAL REVIEW C 68, 054327 (2003)