Deformed relativistic Hartree-Bogoliubov theory in continuum

Abstract

A deformed relativistic Hartree Bogoliubov (RHB) theory in continuum is developed aiming at a proper description of exotic nuclei, particularly those with a large spatial extension. In order to give an adequate consideration of both the contribution of the continuum and the large spatial distribution in exotic nuclei, the deformed RHB equations are solved in a Woods-Saxon (WS) basis in which the radial wave functions have a proper asymptotic behavior at large distance from the nuclear center. This is crucial for the proper description of a possible halo. The formalism of deformed RHB theory in continuum is presented. A stable nucleus, 20 Mg and a weakly-bound nucleus, 42 Mg, are taken as examples to present numerical details and to carry out necessary numerical checks. In addition, the ground state properties of even-even magnesium isotopes are investigated. The generic conditions of the formation of a halo in weakly bound deformed systems and the shape of the halo in deformed nuclei are discussed. We show that the existence and the deformation of a possible neutron halo depend essentially on the quantum numbers of the main components of the single particle orbitals in the vicinity of the Fermi surface.

The limits of the nuclear landscape explored by the relativistic continuum Hartree–Bogoliubov theory

“…9, 60 Ca is the neutron drip-line nucleus in the calculations without pairing, while with 20 more neutrons, 80 Ca is the neutron drip-line nucleus in the RCHB calculations. In the calculations without pairing, the neutron Fermi surface of 60 Ca is 1f 5/2 , the last bound level. The occupation of the next level 1g 9/2 which has a positive single particle energy will lead to the unbound nucleus 62 Ca.…”

“…To illustrate the extension of the neutron drip line in RCHB theory, by taking 60,66,80 Ca, 118,124,136 Kr and 188,194,230 Sm as examples, we compare the neutron single particle levels in canonical basis from the RCHB calculations with those of 60 Ca, 118 Kr and 188 Sm from the calculations without pairing, respectively in Figs. 9-11.…”

“…The occupation of the next level 1g 9/2 which has a positive single particle energy will lead to the unbound nucleus 62 Ca. In RCHB theory, due to the pairing correlations, the neutron Fermi surface locates between 1f 5/2 and 1g 9/2 , and the continuum in the canonical basis also have small occupation probabilities in 60 Ca. Adding more neutrons, see 66 Ca in the figure, although the occupation probabilities of the continuum in the canonical basis become larger, the neutron Fermi surface remains negative.…”

“…The RCHB theory has been generalized to treat the odd nucleon system [57], and together with the Glauber model, the charge-changing cross sections from carbon (C) to fluorine (F) isotopes on a carbon target have been well reproduced [58]. For deformed nuclei, much effort has been made to develop a deformed RHB theory in continuum and an interesting shape decoupling between the core and the halo was predicted [59,60]. Later, the deformed RHB theory in continuum has been extended to incorporate the density-dependent meson-nucleon couplings [61], and the blocking effect which is required for the description of odd-nucleon systems [62].…”

Towards the drip lines of the nuclide landscape

“…The half-life for the β decay of 21 N is determined to be 82.9±7.5 ms which gave an accurate measured value so far [54]. Theoretical studies cover many different topics including cluster structures and decays [57][58][59][60][61][62], resonances in unstable nuclei [63][64][65], heavy and superheavy nuclei [66][67][68][69][70] (see [71] for the experimental synthesis of 271 Ds), rotational states [72][73][74][75][76][77][78][79][80], shape transitions [81][82][83], mean-field models [84][85][86][87], nuclear symmetry energy [88][89][90][91][92][93] and some other topics [94,95]. The theoretical works have motivated model developments, and also provided many useful theoretical predictions and explanations for the experiments.…”