Systematic study of proton radioactivity based on Gamow-like model with a screened electrostatic barrier

Abstract

In the present work we systematically study the half-lives of proton radioactivity for 51 ≤ Z ≤ 83 nuclei based on the Gamow-like model with a screened electrostatic barrier. In this model there are two parameters while considering the screened electrostatic effect of Coulomb potential with the Hulthen potential i.e. the effective nuclear radius parameter r 0 and the screening parameter a. The calculated results can well reproduce the experimental data. In addition, we extend this model to predict the proton radioactivity half-lives of 16 nuclei in the same region within a factor of 2.94, whose proton radioactivity are energetically allowed or observed but not yet quantified. Meanwhile, studying on the proton radioactivity half-life by a type of universal decay law has been done. The results indicate that the calculated half-lives are linearly dependent on Coulomb parameter with the same orbital angular momentum.Systematic study of proton radioactivity based on Gamow-like model with a screened electrostatic barrier2 been identified between Z = 51 and Z = 83 [5,6]. As an important decay mode of unstable nuclei, proton radioactivity is an useful tool to obtain spectroscopic information because the decaying proton is the unpaired proton not filling its orbit and to extract important information about nuclear structure lying beyond the proton drip line, such as the coupling between bound and unbound nuclear states, the shell structure [7] and so on. There are a lot of models and empirical formulas having been proposed to deal with the proton radioactivity such as the effective interactions of densitydependent M3Y (DDM3Y) [8,9], the single-folding model [9][10][11], the distorted-wave Born approximation [12], Jeukenne, Lejeune and Mahaux (JLM) [8], the generalized liquid-drop model [13-15], the finite-range effective interaction of Yukawa form [16], the R-matrix approach [18], the Skyrme interactions [19], the relativistic density functional theory [20], the phenomenological unified fission model [21, 22], the twopotential approach (TPA) [5] which is also successfully applied to the α decay and cluster radioactivity [23-28], the Coulomb and proximity potential model (CPPM) [29], a simple empirical formula proposed by Delion et al. [30] and so on. For more details about different theories of proton radioactivity, the readers are referenced to Ref. [17].Recently, Budaca et al. used a simple analytical model based on the WKB approximation considering the screened effect of emitted proton-daughter nucleus Coulomb interaction with the Hulthen potential to systematically study the half-lives of proton radioactivity for 41 nuclei with Z ≥ 51 [31]. The results indicate that the difference between the outer turning point radii corresponding to pure Coulomb and Hulthen barriers increases with the proton number Z increasing. Whereas the penetration probability is sensitive to the outer turning point radii. In 2016, Zdeb et al. [32] calculated the half-life of proton radioactivity with a Gamow-like model, which has much deeper ...

Systematic study on proton radioactivity of spherical proton emitters within two-potential approach

“…In the Fig. 5, the calculated half-lives are evaluated by the present method, UDLP [41] and Gamow-like model [13] without Fig. 5 Decimal logarithm deviations between the experimental data of proton radioactivity half-lives and calculations.…”

“…Klepper et al [4] a e-mail: lixiaohuaphysics@126.com (corresponding author) b e-mail: wuxijun1980@yahoo.cn c e-mail: kyois@126.com and Faestermann et al [5] observed proton emission from the ground state of 147 Tm and 109 I, 113 Cs in 1982 and 1984, respectively. With the development of advanced experimental facilities and radioactive beams, an increasing number of proton emissions from the ground state or low isomeric states have been discovered in the proton regions Z = 50 − 82 [6][7][8][9][10][11][12][13]. As an important decay mode of unstable nuclei, proton radioactivity is an useful tool to obtain spectroscopic information because the decaying proton is the unpaired proton not filling its orbit, and extract information on nuclear structure and the internuclear potential [14].…”

“…The proton radioactivity has the lowest Coulomb potential among all charged particles and mass being smallest it suffers the highest centrifugal barrier, enabling this process suitable to be dealt within WKB barrier penetration model [15]. Up to now, there are a lot of models having been put forward to deal with the proton radioactivity such as the effective interactions of density-dependent M3Y (DDM3Y) [16,17], the singlefolding model (SFM) [15,18], the generalized liquid-drop model (GLDM) [9,19,20], the phenomenological unified fission model (UFM) [21,22], the Coulomb and proximity potential model (CPPM) [10,23,24], the Gamow-like model (GLM) [13,25], the two-potential approach with Skyrme-Hartree-Fock (TPA-SHF) [26] and so on. As we all known, in the process of studying the charged particles radioactivity, selection of the emitted particle-nucleus interaction potential is key to improve the accuracy of half-life.…”

Systematic study on proton radioactivity of spherical proton emitters within two--potential approach

“…[5] observed proton emission from the ground state of 147 Tm and 109 I, 113 Cs in 1982 and 1984, respectively. With the development of advanced experimental facilities and radioactive beams, an increasing number of proton emissions from the ground state or low isomeric states have been discovered in the proton regions Z = 50 − 82 [6][7][8][9][10][11][12][13]. As an important decay mode of unstable nuclei, proton radioactivity is an useful tool to obtain spectroscopic information because the decaying proton is the unpaired proton not filling its orbit, and extract information on nuclear structure and the internuclear potential [14].…”

“…The proton radioactivity has the lowest Coulomb potential among all charged particles and mass being smallest it suffers the highest centrifugal barrier, enabling this process suitable to be dealt within WKB barrier penetration model [15]. Up to now, there are a lot of models having been put forward to deal with the proton radioactivity such as the effective interactions of density-dependent M3Y (DDM3Y) [16,17], the singlefolding model (SFM) [15,18], the generalized liquiddrop model (GLDM) [9,19,20], the phenomenological unified fission model (UFM) [21,22], the Coulomb and proximity potential model (CPPM) [10,23,24], the Gamow-like model (GLM) [13,25], the two-potential approach with Skyrme-Hartree-Fock (TPA-SHF) [26] and so on. As we all known, in the process of studying the charged particles radioactivity, selection of the emitted particle-nucleus interaction potential is key to improve the accuracy of half-life.…”