Theoretical description of deformed proton emitters: Nonadiabatic coupled-channel method

Abstract

The newly developed nonadiabatic method based on the coupled-channel Schrödinger equation with Gamow states is used to study the phenomenon of proton radioactivity. The new method, adopting the weak coupling regime of the particle-plus-rotor model, allows for the inclusion of excitations in the daughter nucleus. This can lead to rather different predictions for lifetimes and branching ratios as compared to the standard adiabatic approximation corresponding to the strong coupling scheme. Calculations are performed for several experimentally seen, non-spherical nuclei beyond the proton dripline. By comparing theory and experiment, we are able to characterize the angular momentum content of the observed narrow resonance.

Asymptotic normalization coefficients and continuum coupling in mirror nuclei

“…[4], even though approximations and boundary conditions are different in the real-energy R-matrix approach and complex-energy Gamow-state formalism [53]. Expressing the total width Γ ℓ in terms of the sum of partial widths Γ ℓj gives total ANC constant C ℓ (3):…”

“…To get rid of the explicit r-dependence in Eq. (47), further approximations are necessary [53]. Neglecting ℑ(k) in the Coulomb wave functions of the numerator of Eq.…”

Bound states of dipolar molecules studied with the Berggren expansion method

“…Some recent applications of Gamow-Siegert states, also in the context of a CC formalism relevant to the problem of dipole anions, can be found in, e.g., Refs. [74][75][76][77][78]. This paper is organized as follows.…”

Decay rate of triaxially deformed proton emitters

“…In the rare-earth region, the proton emitters are predicted to have large static quadrupole deformations [2]. For these cases, analysis of the measurements has been carried out using a particle-rotor model, with the unbound proton interacting with an axially-symmetric deformed core [3,4,5,6,7,8,9,10,11]. The results of such analyses over the past several years has been to obtain a good description of the groundstate properties of deformed rare-earth proton emitters, including deformations, occupation factors, Nilsson orbitals for the decaying protons, and wave function decompositions.…”