A high precision method to determine fusion in the capture of $α$-particles by nuclei is presented. For $α$-capture by $^{40}{\rm Ca}$ and $^{44}{\rm Ca}$, such an approach gives (1) the parameters of the $α$--nucleus potential and (2) fusion probabilities. This method found new parametrization and fusion probabilities and decreased the error by $41.72$ times for $α+ ^{40}{\rm Ca}$ and $34.06$ times for $α+ ^{44}{\rm Ca}$ in a description of experimental data in comparison with existing results. We show that the sharp angular momentum cutoff proposed by Glas and Mosel is a rough approximation, Wong's formula and the Hill-Wheeler approach determine the penetrability of the barrier without a correct consideration of the barrier shape, and the WKB approach gives reduced fusion probabilities. Based on our fusion probability formula, we explain the difference between experimental cross-sections for $α+ ^{40}{\rm Ca}$ and $α+ ^{44}{\rm Ca}$, which is connected with the theory of coexistence of the spherical and deformed shapes in the ground state for nuclei near the neutron magic shell $N=20$. To provide deeper insight into the physics of nuclei with the new magic number $N=26$, the cross-section for $α+ ^{46}{\rm Ca}$ is predicted for future experimental tests. The role of nuclear deformations in calculations of the fusion probabilities is analyzed.
We have constructed new proximity function particularly for interaction between two superheavy nuclei based on the experimental alpha decay half-lives. The new proximity function is used to produce the alpha decay half-lives of superheavy nuclei whose experimental values are known. The new proximity function produces the alpha decay half-lives close to the experiments. Hence we can conclude that the new proximity function can be used to study the interaction between two superheavy nuclei.
Alpha decay favoured isotopes of some superheavy nuclei: Spontaneous fission versus alpha decay
自发裂变和α衰变是超重核的主要衰变方式。与自发裂变半衰期相比，具有较小α衰变半衰期的超重核将在裂变中存活，并且可以通过α衰变在实验室中检测到。我们研究了Z = 100-130原子范围内的一些超重元素的α衰变半衰期和自发半衰期。超重核的自发裂变半衰期已经用唯象公式计算，α衰变半衰期用Viola-Seaborg-Sobiczewski公式（Sobiczewski et al. 1989）、Brown（1992）的半经验关系式和Dasgupta-Schubert and Reyes（2007）基于广义液滴模型的公式计算。结果报告于此。
The competition between alpha- and beta+/EC-decay modes is studied systematically in nuclei along the alpha-decay chains following the synthesis of superheavy nuclei with Z = 119 and Z = 120. A microscopic approach based on deformed self-consistent Hartree-Fock mean-field calculations with Skyrme forces and pairing correlations is used to describe the beta+ and electron capture weak decays, whereas the alpha-decay is estimated from existing phenomenological expressions. It is shown that alpha-decay is in most cases the dominant decay mode, but interesting instances are identified where the hal…
We propose a novel mechanism to explain nuclear decay by emission of an alpha particle. We show that the famous Geiger-Nuttall law can be explained by post-forming an alpha particle outside the range of the nuclear interaction with the daughter nucleus. This contrasts with the commonly accepted mechanism of first alpha particle pre-formation followed by emission through barrier penetration. We predict that the post-formation mechanism is more likely to occur for alpha-particles with higher energy.
The experimentally available data on the alpha decay half lives and Q? values for 96 superheavy nuclei are used to fix the parameters for a modified version of the Brown empirical formula through two fitting procedures which enables its comparison with similar fits using Viola-Seaborg and Royer formulas. The new expressions provide very good agreement with experimental data having fewer or the same number of parameters. All formulas with the obtained parameters are then extrapolated to generate half lives predictions for 125 unknown superheavy alpha emitters. The nuclei where the employed empi…
It is shown, that the Gamow-like model with only one adjustable parameter - radius constant is able to reproduce well the alpha-decay half-lives for all even-even nuclei with the proton number larger than 50. The systematics for odd-A and odd-odd isotopes can be also well described when ones introduces an additional hindrance factor. Similar model based on the W. J. Swiatecki idea from 1955 is developed to reproduce the spontaneous fission half-lives of transactinide nuclei. The achieved accuracy of reproduction of the data is better than that obtained in more advanced theories.
Alpha-decay energies for several chains of super-heavy nuclei are calculated within the self-consistent mean-field approach by using the Fayans functional FaNDF$^0$. They are compared to the experimental data and predictions of two Skyrme functionals, SLy4 and SkM*, and of the macro-micro method as well. The corresponding lifetimes are calculated with the use of the semi-phenomenological formulas by Parkhomenko and Sobiczewski and by Royer and Zhang.
The Woods-Saxon-Gaussian (WSG) potential is proposed as a new phenomenological potential to describe systematically the level scheme, electromagnetic transitions, and alpha-decay half-lives of the alpha-cluster structures in various alpha+closed shell nuclei. It modifies the original Woods-Saxon (WS) potential with a shifted Gaussian factor centered at the nuclear surface. We determine the free parameters in the WSG potential by reproducing the correct level scheme of $^{212}\text{Po}={}^{208}\text{Pb}+α$. It is found that the resulting WSG potential matches with the M3Y double-folding potenti…
We study the possibility to use the cluster-daughter overlap as a new probe of alpha-cluster formation in medium-mass and heavy even-even nuclei. We introduce a dimensionless parameter $\mathfrak{O}$, which is the ratio between the root-mean-square (rms) intercluster separation and the sum of rms point radii of the daughter nucleus and the alpha particle, to measure the degree of the cluster-daughter overlap quantitatively. By using this parameter, a large (small) cluster-daughter overlap between the alpha cluster and daughter nucleus corresponds to a small (large) $\mathfrak{O}$ value. The al…
The updated data for the ground-state-to-ground-state alpha-transition half-lives in 401 nuclei and the alpha capture cross sections of 40Ca, 44Ca, 59Co, 208Pb and 209Bi are well described in the framework of the unified model for alpha-decay and alpha-capture. The updated values of the alpha decay half-lives, the binding energies of nuclei, the spins of parent and daughter nuclei, and the surface deformation parameters are used for the reevaluation of the model parameters. The data for the ground-state-to-ground-state alpha-decay half-lives are also well described by the empirical relationshi…
Description of a nuclear system in its ground state and at low excitations based on the equation of state (EoS) around normal density is presented. In the expansion of the EoS around the saturation point additional spin polarization terms are taken into account. These terms, together with the standard symmetry term, are responsible for appearance of the $α$-like clusters in the ground state configurations of the N=Z even-even nuclei. At the nuclear surface these clusters can be identified as alpha particles. A correction for the surface effects is introduced for atomic nuclei. Taking into acco…
The nucleonic localization function has been used for a decade to study the formation of alpha-particles in nuclei, by providing a measure of having nucleons of a given spin in a single place. However, differences in interpretation remain, compared to the nucleonic density of the nucleus. In order to better understand the respective role of the nucleonic localization function and the densities in the alpha-particle formation in cluster states or in alpha-decay mechanism, both an analytic approximation and microscopic calculations, using energy density functionals, are undertaken. The nucleonic…
We considered the systematics of $α$-decay (AD) half-life (HL) of super-heavy nuclei versus the decay energy and the total $α$-kinetic energy. We calculated the HL using the experimental Q_{$α$} values. The computed half-lives are compared with the experimental data and also with the existing empirical estimates and are found in good agreement. Also, we obtained $α$-preformation factors from the ratio between theoretical and experimental results for some super heavy nuclei SHN and evaluated the standard deviation. The results indicate the acceptability of the approach.
A broad extension of periodic system into the sector of antimatter could be possible sometimes in a remote future. We expect that anti-alpha spontaneous emission from an antimatter nucleus will have the same Q-value and half-life as alpha emission from the corresponding mirror nucleus. This is the consequence of the invariance of binding energy as well as of the surface and Coulomb energy when passing from matter to antimatter nuclei with the the same mass number and the same atomic number. The Q-values and half-lives of all measured up to now 27 cluster radioactivities are given together with…
Bose-Einstein condensation of alpha clusters in light and medium-heavy nuclei is studied in the frame of the field theoretical superfluid cluster model. The order parameter of the phase transition from the Wigner phase to the Nambu-Goldstone phase is a superfluid amplitude, square of the moduli of which is the superfluid density distribution. The zero mode operators due to the spontaneous symmetry breaking of the global phase in the finite number of alpha clusters are rigorously treated. The theory is systematically applied to N alpha nuclei from12C-52Fe at various condensation rates. In 12C i…
The advent of radioactive ion beam facilities and new detector technologies have opened up new possibilities to investigate the radioactive decays of highly unstable nuclei, in particular the proton emission, $α$ decay and heavy cluster decays from neutron-deficient (or proton-rich) nuclei around the proton drip line. It turns out that these decay measurements can serve as a unique probe for studying the structure of the nuclei involved. On the theoretical side, the development in nuclear many-body theories and supercomputing facilities have also made it possible to simulate the nuclear cluste…
In this contribution, I discuss an algebraic treatment of alpha-cluster nuclei based on the introduction of a spectrum generating algebra for the relative motion of the alpha-clusters. Particular attention is paid to the discrete symmetry of the geometric arrangement of the alpha-particles, and the consequences for the structure of the rotational bands in the 12C and 16O nuclei.
An intense study of the alpha decay properties of the isotopes of superheavy element Z=113 have been performed within the Coulomb and proximity potential model for deformed nuclei (CPPMDN) within the wide range 255 l.e. A l.e. 314. The predicted alpha decay half lives of $^{278}$113 and $^{282}$113 and the alpha half lives of their decay products are in good agreement with the experimental data. 6{α) chains and 4α chains predicted respectively for $^{278}$113 and $^{282}$113 are in agreement with the experimental observation. Our study shows that the isotopes in the mass range 278 l.e. A l.e. …
The breaking of rotational symmetry on the lattice for bound eigenstates of the two lightest alpha conjugate nuclei is explored. Moreover, a macroscopic alpha-cluster model is used for investigating the general problems associated with the representation of a physical many-body problem on a cubic lattice. In view of the descent from the 3D rotation group to the cubic group symmetry, the role of the squared total angular momentum operator in the classification of the lattice eigenstates in terms of SO(3) irreps is discussed. In particular, the behaviour of the average values of the latter opera…
In this work study on alpha decay chains emerging from isotopes of Z = 122 superheavy nuclei is carried out with emphasize on nuclear deformations and Langer modification. The interest in this particular superheavy nuclei is due to the recent experimental efforts to synthesize the isotope ^{299}120 in a fusion reaction at the velocity filter SHIP (GSI Darmstadt), which makes synthesis of Z = 122 nuclei to occur in the near future, and in turn will give the experimentalist the chance observe the decays associated with the isotopes of this nuclei. We perform our calculations by choosing the Wood…
The present paper is a comment regarding the robustness of the chirality in presence of the space-reflection asymmetry, which leads to pairs of interleaved positive- and negative-parity bands. The recent results reported in Ref. \cite{2006.12062} which introduced the $chiture$ and $chiplex$ quantum numbers to describe an ideal nuclear system with simultaneous chiral and reflection symmetry breaking, are commented.
Scattering of Antiprotons by Nuclei (Atoms) in the Range of Low Energies $E\lesssim 10^5$ eV. Mirror Reflection, Diffraction, and Channeling of Antiprotons in Crystals
