The generalized liquid drop model alpha-decay formula: Predictability analysis and superheavy element alpha half-lives

Abstract

The predictive accuracy of the generalized liquid drop model (GLDM) formula for alpha decay half-lives has been investigated in a detailed manner and a variant of the formula with improved coefficients is proposed. The method employs the experimental alpha half-lives of the well-known alpha standards (REFERENCE) to obtain the coefficients of the analytical formula using the experimental Q α values (the DSR-E formula), as well as the finite range droplet model (FRDM) derived Q α values (the FRDM-FRDM formula). The predictive accuracy of these formulae were checked against the experimental alpha half-lives of an independent set of nuclei (TEST) that span approximately the same Z,A region as the standards and possess reliable alpha spectroscopic data, and were found to yield good results for the DSR-E formula but not for the FRDM-FRDM formula. The two formulae were used to obtain the alpha half-lives of super-heavy (SHE) and heavy nuclides where the relative accuracy was found to markedly improve for the FRDM-FRDM, which corroborates the appropriateness of the FRDM masses and the GLDM prescription for high Z,A nuclides. Further improvement resulted, especially for the FRDM-FRDM formula, after a simple linear optimization over the calculated and experimental half-lives of TEST was used to re-calculate the half-lives of the SHE and heavy nuclides. The advantage of this optimization was that it required no recalculation of the coefficients of the basic DSR-E or FRDM-FRDM formulae. The halflives for 324 medium-mass to super-heavy alpha decaying nuclides, calculated using these formulae and the comparison with experimental half-lives, are presented. Often the main and sometimes the only decay mode of these nuclei is alpha decay.For the SHE, the product nuclides of hot-fusion heavy ion reactions closest to the shell model predicted Island of Stability, decay by the emission of alpha particles. Chains of successive alpha decays are terminated by spontaneous fission as the shell-stabilized region is left behind [5,2].Thus identifying and characterizing the alpha decay sequences form a crucial part of the identification of SHE. Theoretically the mechanism is described by quantum mechanical tunneling through the potential energy barrier leading from the mother nucleus to the daughter nucleus and alpha particle. Consequently the predicted half-lives remain very sensitive to the shape and energetics of the barrier which as such, serve to test the particular theoretical model of the potential energy surfaces of these exotic nuclei. Various theoretical prescriptions since 1930 [6] have been proposed. Some of these as well as some empirical observations have been reduced to analytical formulae [7][8][9][10][11][12] that connect Q α , and the Z,A of the parent nuclide and wherein coefficients are typically obtained from fits to known alpha half-lives. The underlying model's description of the potential barrier lies implicit in the formula's functional form and its coefficients and this in part determines the merit of the formula....

Analytic expressions for alpha-decay half-lives and potential barriers

“…[4] to describe the whole data set of total α decay half-lives and its predicted power on new data, particularly for the heaviest elements, has been verified recently [19,26,27].…”

“…Since, different expressions have been proposed [4,20,21,22,23,24,25,26,27] to calculate log 10 T α from A, Z and the Q α value. Formulas taking into account the proximity of the magic numbers have also been provided [17].…”

Structural and decay properties of Z = 132, 138 superheavy nuclei

“…There are also several phenomenological formulas available in the literature for calculating the (sec) = 9.54(Z − 2) 0.6 / Q α − 51.37 (15) where Z is the atomic number of parent nucleus and Q α is in MeV. Another formula proposed by Dasgupta-Schubert and Reyes [72] based on generalized liquid drop model and obtained by fitting the experimental half-lives for 373 alpha emitters for determining the half-lives of superheavy nuclei is given as …”

“…To analyze the dominant mode of decay(alpha), the alpha decay half-lives are estimated using various empirical formulas such as Viola-Seaborg (VSS) [71], generalized liquid drop model (GLDM) [72], Brown [73], Royer [74], NI et al [75]. Spontaneous fission half-lives are computed using the semi-empirical formula of Ren and Xu [76] and made a comparison with alpha decay half lives to predict a possible decay mode of considered nuclides.…”

Quantum design using a multiple internal reflections method in a study of fusion processes in the capture of alpha-particles by nuclei

“…α-nucleus interactions have been studied most intensively in the context of the α-decay of nuclei (see experimental information [4][5][6][7][8][9][10][11][12][13][14][15][16], various microscopic models [17][18][19][20][21][22][23][24][25][26][27][28][29][30], macroscopic cluster models [31][32][33][34][35][36][37][38][39][40][41][42][43][44], fission models [3,46]), and the scattering of the α-particles off nuclei [47][48][49][50][51]. The physics of the fusion processes during α-capture have been investigated less deeply …”