Three-body analysis of the occurrence of Efimov states in2nhalo nuclei such as19B,

Abstract

By employing separable potentials for the binary, i.e., n-n and n-core subsystems, we compute the threebody integral equations to solve for the 2n-separation energies in the ground and excited states of halo nuclei like 19 B, 22 C, and 20 C. We show through numerical analysis and also from analytical considerations that Borromean-type halo nuclei like 19 B and 22 C, where n-n and n-core are both unbound, are much less vulnerable to respond to the existence of the Efimov effect. On the contrary, those nuclei, like 20 C in which the halo neutron is supposed to be in the intruder low lying bound state with the core, appear to be the promising candidates to search for the occurrence of Efimov states at energies below the n-(nc) breakup threshold which can be within the experimental limits to measure.

Range corrections for two-neutron halo nuclei in effective theory

“…The result for 11 Li, r 2 nn exp = (6.6 ± 1.5) fm, is in close agreement with both the LO, r 2 nn = (6.8 ± 1.8) fm, and NLO, r 2 nn = (6.3 ± 0.5) fm, calculations found using the two-body virtual energy reported in [48], E nc = −800 keV. However, due to the large uncertainties in both the theoretical and experimental values for 11 Li, there exists a large range of E nc values which would produce a r 2 nn value in agreement with the experimental value of Marqués et al [50]. The LO result for 14 Be, r 2 nn = (4.1 ± 0.5) fm, is about a Fermi below the the experimental value from Ref.…”

“…For the Borromean halo nuclei 11 Li and 14 Be, in which all two-body subsystems are unbound, the general tendency is for a positive effective range to shift all mean square radii to smaller values. The only exception is the case of 11 Li using the central value of the n-c energy E nc = (−25 ± 15) keV [39].…”

Universal properties and structure of halo nuclei

“…From the earliest studies of halo nuclei, 20 C has been suggested as a good candidate for Efimov states [18], with future theoretical work supporting this prediction [19,20]. We critically examine these earlier studies and perform an improved analysis in the framework of an effective theory.…”

“…III C, there possibly exists one Efimov excited state in 20 C for E nc < 165 keV. The mean square radii for this excited state were calculated over a range of E nc values and plotted, with leading order error bands, in Fig.…”

How to Study Efimov States in Exotic Nuclei?

“…The properties of halo nuclei can be understood by treating the nucleus as an effective three body system consisting of a Core and two neutrons (Core-n-n) [4,[8][9][10] with the assumption that excitation energies of the core, E * core , are much larger than the other energy scales, E nn and E nc . It is found that the relative properties of the Efimov states can be expressed in terms of ratios (see for example Ref.…”