Systematic study of two-proton radioactivity with a screened electrostatic barrier *

Abstract

In this study, a phenomenological model is proposed based on Wentzel-Kramers-Brillouin (WKB) theory and applied to investigate the two-proton ( ) radioactive half-lives of nuclei near or beyond the proton drip line. The total diproton-daughter nucleus interaction potential is composed of the Hulthen-type electrostatic term and the centrifugal term. The calculated radioactive half-lives can accurately reproduce the existing 10 experimental datasets of five true radioactive nuclei with σ = 0.736. In addition, we extend this model to predict the half-lives of possible radioactive nuclei whose radioactivity is energetically allowed or observed but not yet quantified in NUBASE2016. The predicted results are in agreement with those obtained using the Gamow-like model, generalized liquid drop model, Sreeja formula, and Liu formula.

Systematic study of two proton radioactivity within the effective liquid drop model

“…proton decay the separation energy varies lager compared to two proton ranges from −0.051 for 26 S to −15.945 for 34 Ca. From these table it clear that two proton separation energy is less than one proton separation energy in the nuclei of 6 Be, 6 B, 8 C, 12 O, 15,16 Ne, 17 Na, 19 Mg, 22 Si, 26 S, 28 Cl, 30 Ar, 38,39 Ti, 40 V, 42 Cr, 45 Fe, 48,49 Ni, 54 Zn, 58, 59, 60 Ge, and 64 Se. These results show a higher chance of two-proton decay than one-proton decay in these nuclei.…”

“…Here we selected theoretically predicted and experimentally observed decay cases to study the most probable decay case from these nuclei using the separation energy concept and they are listed in the table 5. The separation energy for one proton decay is positive for 6 Be, 19 Mg, 22 Si, 32 K, 39 Ti, 40 V, 42 Cr, 45 Fe, 48,49 Ni, 54 Zn, and 64 Se, so this reaction is not energetically possible but all other decay case are energetically possible. The separation energy of two proton ranges between from −0.044 MeV for 14 F to −7.422 MeV for 6 B. but for one Figure 3.…”

“…So those nuclei with the minimum driving potential are most probable to decay from this nucleus. In the second part of the work, we computed the driving potential for each nucleus for all possible fragments (1p, 2p, 3 He, 4 He, 4 Li, 5 Li, 6 Li, etc.) using the ELDM.…”

“…In the majority of cases, fragments other than one proton and two protons exhibit a high value of driving potential, resulting in a significantly low probability for these clusters to undergo decay. Figure 2 shows that the driving potential for 6 Be and 6 B nuclei is lowest for the 2p+daughter configuration. The combinations 4 He+2p (for 6 Be) and 4 Li+2p (for 6 B) display the minima in the driving potential, so these are the most probable decay configurations for these nuclei.…”

“…The findings obtained from the driving potential agree with the separation energy calculations. For the isotopes 6 Be, 8 C, and 12 O, the two-proton fragment has the lowest driving potential for all angular momentum. 6 B and 7 B have low driving potentials for 2p decay and 1p decay in the ground state, respectively.…”