Comment on “αdecay in the complex-energy shell model”

Abstract

A recent paper by Id Betan and Nazarewicz re-opened the problem of the absolute width of the α-decay leading to a doubly magic nucleus. I point out a problematic aspect of this work, and reaffirm the correctness of the classical results.The α-decay width (Γ = 1.5 × 10 −15 MeV) of 212 Po was reproduced in a clusterconfiguration shell model [1] as well as in a shell model with a stochastically optimized Gaussian [2] basis twenty years ago. It looked [3] as though the problem had been settled once and for all. In these models the widths are extracted from the tail of the wave function in the α-decay channel. The amount of clustering turned out to be comparable with unity (S ≈ 0.3), which shows that even the extreme cluster models are viable [4,5]. In the meantime, the applications of the extreme cluster model to heavy nuclei and radioactive decay have been spectacularly extended (see, e.g., Ref.[6]).In the paper I am commenting on [7], however, Γ is reproduced in a shell model that yields S = 0.011, and that is obviously inconsistent with the cluster model and even with the classical microscopic calculations [1,2,8]. This calculation of Γ relies on the amount of clustering S, thus the correctness of S is crucial. I will argue for the validity of the classical results.The conventional α-formation amplitude g(R) and the amplitude G(R) of the amount of clustering S are defined as the radial factors ofwhere Φ P , Φ α , and Φ D are the intrinsic wave functions of the parent nucleus, the α-particle and the daughter, respectively, and N is the α-D norm operator. That is expressed as N = ν |ϕ ν n ν ϕ ν |, where N ϕ ν = n ν ϕ ν is the eigenvalue equation of N . The daughter being a heavy closed-shell core, the parent state is expressible as Φ P = A{Φ D Φ val }, with Φ val describing the valence nucleons.

Recent developments in radioactive charged-particle emissions and related phenomena

“…But this paper was strongly criticized, as incorrect, in Ref. [156]. The authors of [155] answered in [157].…”

“…In a recent experiment, the fine structure has been observed in the α decay of the high spin isomeric states in nuclei 155 Lu(25/2 − ) and 156 Hf(8 + ) [249]. A significantly strong hindrance is seen for the decay to the seniority v = 3 and 2 states in the corresponding daughter nuclei.…”