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Along the nuclear chart, there are a number of weakly bound states, as in the case of halo nuclei or isotopes close to the drip lines. These states are characterized by binding energies in the keV range rather than in the range of a few MeV, typical for nuclear binding. Such loosely (or weakly) bound states are thus located close to decay thresholds and the corresponding continuum of states. Under these circumstances, the coupling of such a bound state to the continuum can no longer be neglected; for reviews see, e.g., [1-3]. For conventional nuclear models, such as the shell model or the no-core-shell model, the coupling to the continuum based on, e.g., Berggren's representation [4,5], which treats bound, resonant continuum states on the same footing, is well established, see, e.g., [6-8]. In addition,ab initiocalculations for systems such as4He+n+nand
$ A = 7 $ isotopes, which include continuum effects, have been performed [9-11].Nuclear lattice effective field theory (NLEFT) is a novel method for performingab initiocalculations in nuclear structure and reaction physics [12,13]. The basic idea is to discretize space-time on a finite volume
$ L^3\times L_t $ , where$ L \, (L_t) $ is the spatial (temporal) size. Nucleons are placed on the lattice sites, and their interactions are given in terms of properly modified chiral potentials, consisting of pion exchanges and short-distance operators. Strong isospin-breaking effects and the long-ranged Coulomb potential are also included, leading to a number of intriguing results, such as theab initiocalculation of the Hoyle state in12C [14] or the first microscopic calculation of low-energy$ \alpha -\alpha $ scattering [15]. What is missing in this framework is the coupling to the continuum. Clearly, on the lattice, we have only real-valued energies, so a direct application of the Berggren approach is not possible. However, as shown by Lüscher in his seminal work, the complex-valued scattering phase shift can be mapped onto the volume-dependence of the lattice energy levels [16,17]. We seek a similar formalism to explicitly describe the continuum coupling.In this work, we use a simple model of a heavy core
$ A $ coupled to one or two nucleons$ N $ , as described in Sect. II. In Sect. III, we consider$ AN\to AN $ scattering and adjust the$ AN $
Towards the continuum coupling in nuclear lattice effective field theory I: A three-particle model
- Received Date:2020-07-21
- Available Online:2020-12-01
Abstract:Weakly bound states often occur in nuclear physics. To precisely understand their properties, the coupling to the continuum should be worked out explicitly. As the first step, we use a simple nuclear model in the continuum and on a lattice to investigate the influence of a third particle on a loosely bound state of a particle and a heavy core. Our approach is consistent with the Lüscher formalism.