218 research outputs found
Weakly bound states with spin-isospin symmetry
We discuss weakly bound states of a few-fermion system having spin-isospin
symmetry. This corresponds to the nuclear physics case in which the singlet,
, and triplet, , scattering lengths are large with respect to
the range of the nuclear interaction. The ratio of the two is about
. This value defines a plane in which and can
be varied up to the unitary limit, and , maintaining its
ratio fixed. Using a spin dependant potential model we estimate the
three-nucleon binding energy along that plane. This analysis can be considered
an extension of the Efimov plot for three bosons to the case of three
-spin-isospin fermions.Comment: Proceedings of the 21st International Conference on Few-Body Problems
in Physics. May 18-22, 2015. Chicago, Illinois, US
Recombination rates from potential models close to the unitary limit
We investigate universal behavior in the recombination rate of three bosons
close to threshold. Using the He-He system as a reference, we solve the
three-body Schr\"odinger equation above the dimer threshold for different
potentials having large values of the two-body scattering length . To this
aim we use the hyperspherical adiabatic expansion and we extract the -matrix
through the integral relations recently derived. The results are compared to
the universal form, , for
different values of and selected values of the three-body parameter
. A good agreement with the universal formula is obtained after
introducing a particular type of finite-range corrections, which have been
recently proposed by two of the authors in Ref.[1]. Furthermore, we analyze the
validity of the above formula in the description of a very different system:
neutron-neutron-proton recombination. Our analysis confirms the universal
character of the process in systems of very different scales having a large
two-body scattering length
Embedding nuclear physics inside the unitary window
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 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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