Time-dependent Dirac equation applied to one-proton radioactive emission

Abstract

Relativistic energy-density functional (REDF) theory has been developed and utilized for self-consistent meanfield calculations of atomic nuclei. The proton-emitting radioactivity can provide a suitable reference to improve the predicting ability of REDF especially on the proton-drip line. One needs to consider the quantum tunneling effect, which plays an essential role in nucleon-emitting radioactive processes. However, the relativistic quantum tunneling has been less investigated compared with the non-relativistic case. This work is devoted to a theoretical evaluation of one-proton ($1p$) radioactivity based on the relativistic Dirac formalism. For this purpose, I develop the time-dependent (TD) Dirac-spinor calculation to simulate the $1p$ emission. By utilizing the relativistic Hartree-Bogoliubov (RHB) calculation with the DD-PCX parameters, single-proton potentials for the time-dependent Dirac spinor are determined. The TD-Dirac calculation is applied to the $1p$ emissions from the ${}^{37}$Sc and ${}^{39}$Sc nuclei, which can be well approximated as the valence proton and the proton-close-shell cores. The sensitivity of $1p$-emission energy and decaying width to the mass number is demonstrated. Remarkable sensitivity exists due to the size of system, which affects the nuclear part of potentials and energy levels, whereas the Coulomb barrier is common with the same atomic number. The calculated $1p$ energy and decaying lifetime are roughly consistent to the experimental limitation. The present TD-Dirac calculation is expected as applicable widely to proton-rich nuclides in order to improve the REDF by utilizing the $1p$-emission data.

arXiv comment11 pages, 10 figures, 3 tables

References in corpus (39)

• Relativistic Continuum Hartree Bogoliubov Theory for Ground State Properties of Exotic Nuclei
• Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects
• Relativistic Nuclear Energy Density Functionals: Mean-Field and Beyond
• Pairing in nuclear systems: from neutron stars to finite nuclei
• Radioactive decays at limits of nuclear stability
• DIRHB -- a relativistic self-consistent mean-field framework for atomic nuclei
• Gamow Shell Model Description of Neutron-Rich Nuclei
• Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (II) HFBTHO v2.00d: a new version of the program
• Time-dependent Hartree-Fock calculations for multinucleon transfer processes in ${}^{40,48}$Ca+${}^{124}$Sn, ${}^{40}$Ca+${}^{208}$Pb, and ${}^{58}$Ni+${}^{208}$Pb reactions
• Recent development of complex scaling method for many-body resonances and continua in light nuclei
• Pairing and continuum effects in nuclei close to the drip line
• Recent developments in radioactive charged-particle emissions and related phenomena
• Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (VII) HFODD (v2.49t): a new version of the program
• Gamow shell model and realistic nucleon-nucleon interactions
• Modified two-potential approach to tunneling problems
• Optimizing the relativistic energy density functional with nuclear ground state and collective excitation properties
• The landscape of two-proton radioactivity
• Charge radii in covariant density functional theory: a global view
• Probing the resonance of Dirac particle by the application of complex momentum representation
• Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
• Green's function method for single-particle resonant states in relativistic mean field theory
• The Proton Electric Pygmy Dipole Resonance
• Fermion Pair Dynamics in Open Quantum Systems
• Complex scaling : physics of unbound light nuclei and perspective
• Quantum Shock Waves and Domain Walls in the Real-Time Dynamics of a Superfluid Unitary Fermi Gas
• Microscopic analysis of induced nuclear fission dynamics
• Continuum Random Phase Approximation for Relativistic Point Coupling Models
• Continuum Hartree-Fock-Bogoliubov theory for weakly bound deformed nuclei using coordinate-space Green's function method
• Comment on "Evolution of a Quasi-Stationary State"
• Green's function method for the single-particle resonances in a deformed Dirac equation
• Probing the resonance in the Dirac equation with quadruple-deformed potentials by complex momentum representation method
• Mapping the proton drip line from Z=31 to Z=49
• Time-dependent approach to many-particle tunneling in one-dimension
• Dependence of two-proton radioactivity on nuclear pairing models
• Proton drip-line nuclei in Relativistic Hartree-Bogoliubov theory
• Research on the halo in ${}^{31}$Ne with complex momentum representation method
• Time-dependent properties of proton decay from crossing single-particle metastable states in deformed nuclei
• Continuum Skyrme-Hartree-Fock-Bogoliubov theory with Green's function method for odd-$A$ nuclei
• Formal Aspects of Quantum Decay

Cited by in corpus (1)

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