Quantum mechanics

Nuclear fission

Random phase approximation

Nuclear physics

Atomic physics

Neutron

Physics

Superconductivity

Neutron emission

Fission

Excited state

Quasiparticle

Delayed neutron

Physical review. C

Background: $\ensuremath{\beta}$-delayed neutron emission and fission are essential in $r$-process nucleosynthesis. Although the number of experimental studies covering $r$-process nuclei has recently increased, the uncertainties of $\ensuremath{\beta}$-delayed neutron emission and fission are still large for $r$-process simulations.Purpose: Our aim is to introduce a theoretical framework for the description of $\ensuremath{\beta}$-delayed neutron-emission and fission rates based on relativistic nuclear energy density-functional and statistical models and investigate their properties throughout the nuclide map.Methods: To obtain $\ensuremath{\beta}$ strength functions, the relativistic proton-neutron quasiparticle random-phase approximation is employed. Particle evaporations and fission from highly excited nuclear states are estimated by the Hauser-Feshbach statistical model. $\ensuremath{\beta}$-delayed neutron branching ratios ${P}_{n}$ are calculated and compared with experimental data, and the $\ensuremath{\beta}$-delayed fission branching ratio ${P}_{f}$ are also assessed by using different fission barrier data.Results: Calculated ${P}_{n}$ are in a good agreement with the experimental data and the root mean square deviation is comparable to results of preceding works. It is found that energy withdrawal by $\ensuremath{\beta}$-delayed neutron-emission sensitivity varies ${P}_{n}$, especially for nuclei near the neutron drip line. ${P}_{f}$ depend sensitively on fission barrier data. It is found that not only the barrier height but also the number of barrier humps is important to evaluate ${P}_{f}$.Conclusions: The framework introduced in this work provides an improved theoretical description of the $\ensuremath{\beta}$-delayed neutron emission and fission. Since ${P}_{f}$ as well as ${P}_{n}$ depend strongly on fission barrier information, four kinds of fission barrier data are used in this work to allow further sensitivity studies of the $r$-process nucleosynthesis on the nuclear fission. More studies on fission barrier are highly requested to assess the role of $\ensuremath{\beta}$-delayed fission in the $r$-process study. A complete set of calculated data for $\ensuremath{\beta}$-delayed neutron emission and fission are summarized as a table in supplemental material for its use in $r$-process studies as well as to complement a part of nuclear data in which no experimental data are available.

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math> -delayed neutron-emission and fission calculations within relativistic quasiparticle random-phase approximation and a statistical model

β -delayed neutron-emission and fission calculations within relativistic quasiparticle random-phase approximation and a statistical model