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Register a new userEmbedding nuclear physics inside the unitary window
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The large values of the singlet and triplet scattering lengths locate the two-nucleon system close to the unitary limit, the limit in which these two values diverge. As a consequence, the system shows a continuous scale invariance which strongly constrains the values of the observables, a well-known fact already noticed a long time ago. The three-nucleon system shows a discrete scale invariance that can be observed by correlations of the triton binding energy with other observables as the doublet nucleon-deuteron scattering length or the alpha-particle binding energy. The low-energy dynamics of these systems is universal; it does not depend on the details of the particular way in which the nucleons interact. Instead, it depends on a few control parameters, the large values of the scattering lengths and the triton binding energy. Using a potential model with variable strength set to give values to the control parameters, we study the spectrum of $A=2,3,4,6$ nuclei in the region between the unitary limit and their physical values. In particular, we analyze how the binding energies emerge from the unitary limit forming the observed levels.
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In this contribution I will review some of the researches that are currently being pursued in Padova (mainly within the In:Theory and Strength projects), focusing on the interdisciplinary applications of nuclear theory to several other branches of physics, with the aim of contributing to show the centrality of nuclear theory in the Italian scientific scenario and the prominence of this fertile field in fostering new physics. In particular, I will talk about: i) the recent solution of the long-standing electron screening puzzle that settles a fundamental controversy in nuclear astrophysics between the outcome of lab experiments on earth and nuclear reactions happening in stars; the application of algebraic methods to very diverse systems such as: ii) the supramolecular complex H2@C60, i.e. a diatomic hydrogen molecule caged in a fullerene and iii) to the spectrum of hypernuclei, i.e. systems made of a Lambda particles trapped in (heavy) nuclei.
We prove that the amplitudes for the (d,p), (d,pn) and (e,ep) reactions determining the asymptotic behavior of the exact scattering wave functions in the corresponding channels are invariant under unitary correlation operators while the spectroscopic factors are not. Moreover, the exact reaction amplitudes are not parametrized in terms of the spectroscopic factors and cannot provide a tool to determine the spectroscopic factors.
We study the feasibility of applying the Generator Coordinate Method (GCM) of self-consistent mean-field theory to calculate decay widths of composite particles to composite-particle final states. The main question is how well the GCM can approximate continuum wave functions in the decay channels. The analysis is straightforward under the assumption that the GCM wave functions are separable into internal and Gaussian center-of-mass wave functions. Two methods are examined for calculating decays widths. In one method, the density of final states is computed entirely in the GCM framework. In the other method, it is determined by matching the GCM wave function to an asymptotic scattering wave function. Both methods are applied to a numerical example and are found to agree within their determined uncertainties.
The three-body system inside the unitary window is studied for three equal bosons and three equal fermions having $1/2$ spin-isospin symmetry. We perform a gaussian characterization of the window using a gaussian potential to define trajectories for low-energy quantities as binding energies and phase shifts. On top of this trajectories experimental values are placed or, when not available, quantities calculated using realistic potentials that are known to reproduce experimental values. The intention is to show that the gaussian characterization of the window, thought as a contact interaction plus range corrections, captures the main low-energy properties of real systems as for example three helium atoms or three nucleons. The mapping of real systems on the gaussian trajectories is taken as indication of universal behavior. The trajectories continuously link the physical points to the unitary limit allowing for the explanation of strong correlations between observables appearing in real systems and which are known to exist in that limit. In the present study we focus on low-energy bound, scattering and virtual states.
Physical systems characterized by a shallow two-body bound or virtual state are governed at large distances by a continuous-scale invariance, which is broken to a discrete one when three or more particles come into play. This symmetry induces a universal behavior for different systems, independent of the details of the underlying interaction, rooted in the smallness of the ratio $ell/a_B ll 1$, where the length $a_B$ is associated to the binding energy of the two-body system $E_2=hbar^2/m a_B^2$ and $ell$ is the natural length given by the interaction range. Efimov physics refers to this universal behavior, which is often hidden by the on-set of system-specific non-universal effects. In this work we identify universal properties by providing an explicit link of physical systems to their unitary limit, in which $a_Brightarrowinfty$, and show that nuclear systems belong to this class of universality.
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