Efimov Effect in Nuclear Three-Body Resonance Decays

Abstract

We investigate the effects of the nearly fulfilled Efimov conditions on the properties of three-body resonances. Using the hyper-spheric adiabatic expansion method we compute energy distributions of fragments in a three-body decay of a nuclear resonance. As a realistic example we investigate the 1 − state in the halo nucleus 11 Li within a three-body 9 Li + n + n model. Characteristic features appear as sharp peaks in the energy distributions. Their origin, as in the Efimov effect, is in the large two-body s-wave scattering lengths between the pairs of fragments. Introduction. The Efimov effect was introduced more than thirty years ago as an anomaly in a three-body system arising when at least two of the three two-body swave scattering lengths approach infinity [1]. Then an increasing number of three-body bound states appear close to the two-body threshold even if there are no two-body bound states. The effect is prohibited by the Coulomb potential while only diminished by higher angular momentum [2]. Although entirely possible in molecules [3] the effect is unlikely to appear in nuclei due to unfavorable mass ratio [4,5].Still there exists a number of nuclear systems, called halos [3], which are natural three-body systems -a core plus two neutrons -where the Efimov condition of at least two large scattering lengths is nearly fulfilled. Although the unfortunate combination of the heavy core and light neutrons prohibits the appearance of bound Efimov states in the discrete spectrum, they still may appear as peculiar structures in the continuum. Very little, however, is known theoretically about the Efimov states in the continuum.

Spectroscopy of9Be and observation of neutron halo structure in the states of positive parity rotational band

“…2 together with the results of the DWBA calculations. Some disagreements may be connected with the influence of the 5 He transfer reaction reflecting the predicted [1,3] contribution of the 5 He + 4 He configuration in the 9 Be structure. The latter one possibly manifests itself in the strong oscillation structure at the backward angles (Fig.3), as observed at E (α) = 50 MeV [9].…”

“…The head of the second band is the first excited state 1/2 + , 1.68 MeV (σ-band, K = 1/2 + ) located only 15 keV above the 8 Be + n threshold. This particular level was the object of intensive theoretical study and is considered to be either a virtual state [2] or a combination of 5 He + 4 He and 8 Be + n configurations [3]. Accordingly, both bands are characterized by large moments of inertia, which are either equal to that of 8 Be (the π-band) or even larger (the σ-band).…”

NEUTRON HALO ROTATION IN 11Be AND 9Be AND MEASURING THE RADII OF NUCLEAR EXCITED STATES

“…The cluster configuration of 8 Be + n dominates in the internal structure of 9 Be (see [1] and refs. there), however, the 5 He + 4 He one also can play some role [2]. Possessing very large deformation parameter 9 Be has two well developed rotational bands (π-band, K = 3/2 -) and (σ-band, K = 1/2 + ) based on the ground and the first excited (1.68 MeV) states correspondingly.…”

Halo nuclei, stepping stones across the drip-lines

“…Recent studies with trapped ions [40,41] showed that these Efimov states really manifest themselves when being specifically set up in the freely tunable environment of a tailored quantum system. For nuclear systems these conditions have to be met by finding the necessary boundary conditions by selecting a three-body system with the appropriate interactions [42] in the binary subsystems.…”