Proton radioactivity described by covariant density functional theory with the similarity renormalization group method

Abstract

Half-life of proton radioactivity of spherical proton emitters is studied within the scheme of covariant density functional (CDF) theory, and for the first time the potential barrier that prevents the emitted proton is extracted with the similarity renormalization group (SRG) method, in which the spin-orbit potential along with the others that turn out to be non-negligible can be derived automatically. The spectroscopic factor that is significant is also extracted from the CDF calculations. The estimated half-lives are found in good agreement with the experimental values, which not only confirms the validity of the CDF theory in describing the proton-rich nuclei, but also indicates the prediction power of present approach to calculate the half-lives and in turn to extract the structural information of proton emitters. With continuous development of the radioactive ion beam facilities, the exotic nuclei far away from the β-stability line attract extensive interests for the new phenomena they present. One of the typical representatives is the proton radioactivity at the vicinity of proton drip line, firstly observed in an isomeric state of 53 Co in 1970 [1, 2]. Since then more and more proton emitters ranging from Z = 51 to 83 have been identified with nuclear ground states or isomeric states [3]. Essentially, it is significant to study the proton emission which corresponds to the fundamental existence limits of neutron-deficient nuclei, i.e., the proton drip line, and it also can be treated as the inverse reaction of the rapid proton capture process that plays an important role in understanding the origin of the elements in the universe [4]. Moreover specific aspects of nucleonic interactions could be isolated and amplified in the proton emitters due to their extreme proton excess [5]. In particular combined with theoretical analysis, nuclear structural information can be extracted from measurements of half-life, proton branching ratio (fine structure), the energy and angular momentum transfer l carried away by the emitted proton, etc. The fact that the half-life of proton emission is sensitive to the Q-value and angular momentum transfer l, not only helps to determine the orbit of the emitted proton in parent nucleus in experiments, but also provides an efficient way to test theoretical models in exploring the neutron-deficient nuclear systems.Theoretically various methods have been employed in describing the properties of proton emitters, such as the spectroscopic factor and the half-life (for review see Ref.[6]). For the half-life that can be measured experimentally, a semiclassical method is applied by treating the proton emission as quantum tunneling through a potential barrier, which is composed of the Coulomb repulsion, centrifugal barrier and effective nuclear potential. Several approaches have been employed in constructing the effective nuclear potential, e.g., in terms of the density-dependent M3Y effective interaction [7], the effective interaction of Jeukenne, Lejeume, and Mahaux [8], the renormalized...

Systematic study on proton radioactivity of spherical proton emitters within two-potential approach

“…The formation probability of proton radioactivity containing a lot of nuclear structure properties is also called by spectroscopy factor, which plays an important role in the calcula- d . The methods include BCS-Lim [40], RMF+BCS-Zhang [9], CDF+BCS [39], RCHB+PC-PL1 [40], RMF+BCS-NL1 [38] and RMF+BCS -NL3 [38] Table 1 Calculations of proton radioactivity half-lives for spherical proton emitters different methods and formation probability of proton radioactivity using Eq. 14 tion of half-life.…”

“…Both the semi-microscopic method and the phenomenological method are used to calculate the probability of formation of proton radioactivity [9,19,[37][38][39][40][41][42][43][44]. In 2012, Qi et al [41] proposed a universal decay law for proton emission (UDLP).…”

“…Moreover, since the formation probability (spectroscopic factor) of proton radioactivity being one of the most important considerations in the calculation of half-life, it has becoming a hot topic [35][36][37][38][39][40]. There are several semimicroscopic methods to computationally study the formation probability such as relativistic mean field theory (RMF) with BCS method [9,19,[35][36][37][38], covariant density functional (CDF) with BCS method [39] and relativistic continuum Hartree-Bogoliubov (RCHB) [40] and so on. While the phenomenological methods in relation to nuclear structure are also adopted to study the formation probability such as a phenomenological discussion about its linear relationship given by Qi et al [41][42][43].…”

Towards an ab initio covariant density functional theory for nuclear structure

“…It was found that the angular momentum of the pseudospin doubletsl is nothing but the orbital angular momentum of the lower component of the Dirac spinor (61), and the pseudospin symmetry is exact when the sum of vector and scalar potentials V +S vanishes [369], or a more general condition d(V +S )/dr = 0 which can be approximately fulfilled in exotic nuclei [370,371]. Since then, pseudospin symmetry as a relativistic symmetry has been realized and much work has been done for investigating its origin and its properties using phenomenological single-particle Hamiltonians, relativistic mean field theory, or relativistic Hartree-Fock (RHF) theory [212,213,[372][373][374][375][376][377][378][379][380][381][382][383][384].…”

Proton emission with a screened electrostatic barrier

“…These traditionally include phenomenological [9][10][11][12], microscopic [13][14][15] and semi-classical formalisms [16][17][18][19]. The involved phenomenological and microscopic approaches include many fitted parameters and gross approximations or rely on the spectroscopic information regarding the single-particle configuration of the decaying state, which is unfortunately lacking for the most of the proton emitting nuclei.…”