Theoretical description of the decay width of neutron emission in light nuclei

Abstract

<p indent="0mm">The study of nuclear decay is an important field for investigating nuclear structures and nucleosynthesis. The existence of Coulomb interaction makes the emission of charged particles have a relatively long half-life. Based on the WKB approximation and the R-matrix method, several empirical formulas describing the proton decay, alpha decay, and emission of charged clusters have been proposed, e.g., the new Geiger-Nutall formula and the Universal Decay Law. The investigation of beta delayed proton(s) decay enhances understanding of isospin symmetry breaking and mixing. Because of the absence of Coulomb interaction, the half-life of neutron emission is much shorter. For neutron-unbound states, the experimentalists concentrate more on discovering neutron-rich nuclei beyond the neutron-drip line. The theorists are more interested in establishing models for a specific nucleus to describe the one- and two-neutron emission phenomenon. The universal law describing the general characteristics of single neutron emission is rarely taken into account. This paper applies the WKB approximation and the R-matrix method to investigate the decay width of the single neutron emission. The square well potential and the harmonic oscillator potential are used as input of nuclear potential. As to the R-matrix method, the sine function basis and the Lagrange basis are applied, respectively. Both the WKB approximation and the R-matrix method calculate the decay width in two parts: The formation factor and the penetration factor. A three-variable formula is deduced from the penetration factor of these two theories. As to the ground states emitting a single neutron, the root-mean-square of log₁₀<italic>Γ</italic>_exp/<italic>Γ</italic>_cal for the three-variable formula is only 0.31, which shows a good description ability. The decay widths of the other 13 nuclides are thus predicted. For the excited states, the direct application of the two theories presents deviation within an order of about 3. The decay width is found to be sensible to the radius of nuclear force and less sensible to the depth of nuclear potential according to the comparison between the square well potential and the harmonic oscillator potential. The hard-core effect is intrinsically considered by the R-matrix method, compared with the WKB approximation, which shows an overall overestimation. After removing such an overestimation, the deviation of the WKB approximation is reduced to be in the order of about 0.8. The three-variable formula shows better description capability, and the deviation is reduced to be in the order of 0.56. The suggested formula is the first try to describe the decay width of a single neutron emission well, which is beneficial to further investigate the characteristics of nuclei near the neutron drip line. Moreover, the influence of spin-orbit interaction, the tensor force, and the shell effect can be taken into account for amelioration. Besides, the fission products of heavy nuclei are generally in highly excited states and will be deexcited through beta decay, emitting neutrons, etc. The neutron emission and beta-delayed neutron emission in these processes are important for the chain reaction and the control of the nuclear reactor. For further investigation, the results of this paper will be extended and applied to the region of nuclear fission products.