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

Abstract

From an adjustment on a recent selected data set of partial α-decay half-lives of 344 ground state to ground state transitions, analytical formulas are proposed for log 10 T 1/2 (s) depending or not on the angular momentum of the α particle. In particular, an expression allows to reproduce precisely the partial α-decay half-lives of even-even heavy nuclei and, then, to predict accurately the partial α-decay half-lives of other very heavy elements from the experimental or predicted Q α . Comparisons have been done with other empirical approaches. Moreover, the potential barrier against α-decay or α-capture has been determined within a liquid drop model including a proximity energy term. Simple expressions are provided to calculate the potential barrier radius and height.

Theoretical Studies on the α-decay Half-Lives of Even-Even Lv Isotopes

“…The α-decay half-lives have been studied by using Royer formula [12,[22][23], Royer developed formula by fitting procedure using 373 nuclei transition from ground state to ground state which is given as…”

Alpha clustering and nuclear molecules in8Be, 12C, 16O, 20Ne, 24Mg, and32S

“…The ground state may also be described using double closed shell wave functions but several excited states may also be viewed within the 12 C+ 4 He cluster picture. The potential energies of the 12 C+ 4 He, 8 Be+ 8 Be, and aligned 6 Li+ 4 He+ 6 Li systems have been determined assuming a spherical shape for all nuclei (see Fig. 1).…”

“…The generalized liquid drop model (GLDM) describing correctly the fusion [7], alpha emission [8] and fission [9] processes has been used to calculate the L-dependent potential energy of the following α clusters: aligned α chains, isosceles triangle, square, tetrahedron, pentagon, trigonal bipyramid, square pyramid, hexagon, octahedron, octagon and cube [10,11]. The proximity energy is included in this model to take into account the effects of the nuclear forces between the surfaces in regard in a gap or a neck between nuclei.…”

Alpha decay calculations with a new formula

“…We shall use three data sets, belongs to DNP's group, and the set C was taken from G. Royer [48]; few Q-values have been updated using the AME12 evaluation of experimental atomic masses [18]. Comparison with ASAF, UNIV, and semFIS will be made using both A, B and C data sets.…”

“…Comparison with ASAF, UNIV, and semFIS will be made using both A, B and C data sets. The Royer formula [48] is defined as We may compare the results obtained by using the set A, B and C in tables I and II. We can see a slight improvement by using the set B.…”