Continuum resonances with shielded Coulomb-like potential and Efimov effect
- PDF / 640,699 Bytes
- 5 Pages / 612 x 792 pts (letter) Page_size
- 80 Downloads / 157 Views
NUCLEI Theory
Continuum Resonances with Shielded Coulomb-Like Potential and Efimov Effect∗ D. S. Tusnski1)** , M. T. Yamashita1)*** , T. Frederico2), and L. Tomio1), 3) Received January 29, 2013 12 Abstract—Motivated by the possibility of the second energy level (0+ C (in a three-alpha model) to 2 ) of turn into an Efimov state, we study a simple non-realistic toy model formed by three bosons interacting by the phenomenological s-wave Ali–Bodmer potential plus a Coulomb interaction. An artificial three-body 12 C, 0.38 MeV. The potential was used to create a resonance with energy close to the energy of the 0+ 2 of strength of the Coulomb potential is decreased until the energies of the two alpha pairs are zero. The system was placed inside a harmonic trap and a stabilization method has been used to calculate the energies of the resonances. We found that the shielded-Coulomb potential, which keeps the long tail, is not able to produce the Efimov effect. The energy of the three alphas decreases only to 0.19 MeV when the two-body energy crosses the threshold to become bound.
DOI: 10.1134/S1063778814040152
We cordially dedicate this work to Vladimir B. Belyaev on the occasion of his 80th birthday 1. INTRODUCTION The theoretical prediction of Efimov states in 1970 [1] was made in the context of nuclear physics. However, the experimental achievement of this counterintuitive phenomenon has been made in an ultracold gas of cesium atoms [2]. Since then, once realized that such effect is not a simple mathematical artifact emerging in the limit of zero two-body binding, lot of papers have been published in this topic, starting a new branch of quantum few-body physics, called “Efimov Physics” [3]. Originally, the Efimov effect was derived for a system of three spinless neutral particles of equal mass and their possible implications have been considered for the nuclei 12 C and 3 H [1]. This effect is manifested by the appearance of an infinite number of three-body bound states as the two-body energy tends to zero, or equivalently the two-body scattering length tends to infinity, which can be explained by the ∗
The text was submitted by the authors in English. ´ Instituto de F ´ısica Teorica, UNESP—Universidade Estad˜ Paulo, Brazil. ual Paulista, Sao 2) ´ ´ Instituto Tecnologico de Aeronautica—DCTA, S. J. dos Campos, Brazil. 3) Universidade Federal do ABC, Santo Andre,´ Brazil. ** E-mail: [email protected] *** E-mail: [email protected] 1)
appearance of an effective potential proportional to 2 + r 2 + r 2 , where r is the distance 1/R2 (R2 = r12 ij 13 23 between particles ij) [4]. The energy ratio between two consecutive states is given by e2π/s0 , where the constant s0 depends on the mass ratio of the particles (for equal masses s0 ≈ 1.006 24). Their rootmean-square radii, R2 , also present a constant ratio between two consecutive states given by eπ/s0 . Nowadays, we know that this effect is possible for several systems with different masses and also for more than three particles [5]. Efimov states are very weakly bound systems, the
Data Loading...
