Some proposals of new experiments on cluster radioactivity

Measurement of elastic scattering and fusion-fission cross sections of the cluster decay products is proposed for the study of the mechanism of cluster radioactivity. The obtained data on ¹²C+²⁰⁸Pb allow to select between different theoretical models. The experiment on search of the exotic nucleus ¹¹²Ba and its cluster decay is discussed.     

Stability of Cf isotopes against alpha and cluster radioactivity

Stability of ^248–254Cf nuclei against alpha and cluster emissions is studied within our Coulomb and proximity potential model (CPPM). It is found that these nuclei are stable against light clusters (except alpha particles) and unstable against heavy cluster (A₂≥40)$(A_2\ge 40)$ emissions. For heavy cluster emissions the daughter nuclei lead to doubly magic ²⁰⁸Pb or the neighbouring one. The effects of quadrupole and hexadecapole deformations of parent nuclei, daughter nuclei and emitted cluster on half lives are also studied. The computed alpha decay half life values (including quadrupole deformation β₂${\beta }_2$) are in close agreement with experimental data. Inclusion of quadrupole deformation reduces the height and width of the barrier (increases the barrier penetrability) and hence half life decreases.     

Constraints on neutron skin thickness and symmetry energy of 208Pb through Skyrme forces and cluster model

We used the cluster structure properties of the 212Po to estimate the neutron skin thickness of 208Pb.For this purpose,we considered two important components:(a)alpha decay is a low energy phenomenon;therefore,one can expect that the mean-field,which can explain the ground state properties of 212Po,does not change during the alpha decay process.(b)212Po has a high alpha cluster-like structure,two protons and two neutrons outside its core nucleus with a double magic closed-shell,and the cluster model is a powerful formalism for the estimation of alpha decay preformation factor of such nuclei.The slope of the symmetry energy of 208Pb is estimated to be 75±25 MeV within the selected same mean-fields and Skyrme forces,which can simultaneously satisfy the ground-state properties of parent and daughter nuclei,as their neutron skin thicknesses are consistent with experimental data.     

Behavior of the giant-dipole resonance in 120Sn and 208Pb at high excitation energy

The properties of the giant-dipole resonance (GDR) are calculated as a function of excitation energy, angular momentum, and the compound nucleus particle decay width in the nuclei ¹²⁰Sn and ²⁰⁸Pb, and are compared with recent experimental data. Differences observed in the behavior of the full-width-at-half-maximum of the GDR for ¹²⁰Sn and ²⁰⁸Pb are attributed to the fact that shell corrections in ²⁰⁸Pb are stronger than in ¹²⁰Sn, and favor the spherical shape at low temperatures. The effects shell corrections have on both the free energy and the moments of inertia are discussed in detail. At high temperature, the FWHM in ¹²⁰Sn exhibits effects due to the evaporation width of the compound nucleus, while these effects are predicted for ²⁰⁸Pb.     

Neutron and proton shell closure in the superheavy region via cluster radioactivity in <Superscript>280–314</Superscript>116 isotopes

Based on the concept of cold valley in fission and fusion, the radioactive decay of superheavy^280–314116 nuclei was studied taking Coulomb and proximity potentials as the interacting barrier. It is found that the inclusion of proximity potential does not change the position of minima but minima become deeper which agrees with the earlier findings of Gupta and co-workers. In addition to alpha particle minima, the other deepest minima occur for ⁸Be, ^12,14C clusters. In the fission region two deep regions are found each consisting of several comparable minima, the first region centred on ²⁰⁸Pb and the second is around ¹³²Sn. The cluster decay half-lives and other characteristics are computed for various clusters ranging from alpha particle to ⁷⁰Ni. The computed half-lives for alpha decay match with the experimental values and with the values calculated using Viola-Seaborg-Sobiczewski (VSS) systematic. The plots connecting computed Q values and half-lives against neutron number of daughter nuclei were studied for different clusters and it is found that the next neutron shell closures occur at N = 162, 172 and 184. Isotopic and isobaric mass parabolas are studied for various cluster emissions and minima of parabola indicate neutron shell closure at N = 162, 184 and proton shell closure at Z = 114. Our study shows that ₁₆₂²⁷⁶114 is the deformed doubly magic and ₁₈₄²⁹⁸114 is the spherical doubly magic nuclei.      

Generalization of α-Decay Cluster-Model to Nuclei Near Spherical and Deformed Shell Closures

The cluster model of a-decay is extended to the regions around doubly magic spherical nucleus ^208Pb and around deformed shell closure ^270Hs, respectively. The effects of spherical shell closures (N=126 and Z=82) on α-decay are investigated by introducing an N-dependent α-preformation factor and a Z-dependent one inspired by a microscopic model. Good agreement between the theoretical a-decay half-lives and the measured ones is obtained for the spherical nuclei near the doubly magic nucleus ^208Pb, where the nuclear shell effect is included in the expression of α-preformation factor. The cluster model is also generalized for the decay of deformed nuclei. The branching ratios of α-decays from the ground state of a parent nucleus to the ground state (0^ ) of its deformed daughter nucleus and to the first excited state (2^ ) are calculated in the framework of the cluster model. The results indicate that a measurement of α spectroscopy is a feasible method to extract the information of nuclear deformation of superheavy nuclei around the deformed nucleus ^270Hs.     

A windowless hydrogen gas target for the measurement of 7Be(p, $ \gamma$ )8B with the recoil separator ERNA

Using the Coulomb and proximity potential model (CPPM) we have investigated the cluster decays of the isotopes ^212-240Pa, ^219-245Np, ^228-246Pu, ^230-249Am and ^232-252Cm leading to doubly magic ²⁰⁸Pb and its neighboring nuclei, which are not experimentally detected but which may be detectable in the future. It is found that most of the decays are favourable for experimental measurements (i.e., $T_{1/2}<10^{30}$ s) and this observation will serve as a guide to future experiments. Our study reveals the role of doubly magic ²⁰⁸Pb daughter nuclei and near doubly magic nuclei in the cluster decay process. In order to make a comparison with CPPM we also calculated the logarithmic half-lives using the Universal formula for the cluster decay (UNIV) by Poenaru et al., the Universal Decay Law (UDL) and the Scaling Law of Horoi et al., and they are found to be in good agreement. The Geiger-Nuttall plots of $log_{10}(T_{1/2})$ versus $Q^{-1/2}$ for various clusters from different isotopes of heavy parent nuclei have been studied and are found to be linear.     

Fine structure in 14C cluster emission from 225Ac

A fine structure in the ¹⁴C decay of ²²⁵Ac is predicted quantitatively by accounting dynamical aspects during the disintegration process. Transitions to the excited states of the daughter nucleus are considered to be mainly directed by the Landau–Zener promotion mechanism in the region of avoided crossing levels. The level scheme is evaluated with the superasymmetric two–center shell model. The half–lives are computed considering the cluster decay as a superasymmetric fission process. Received: 31 July 1998 / Revised version: 27 November 1998     

238Pu cluster decay in the macroscopic-microscopic approach

The experimental half-life of ³²Si cluster decay from ²³⁸Pu was reproduced by using the microscopic-macroscopic approach. Several microscopic models for the inertia were tested. The best results were obtained with an effective mass given by the Gaussian overlap approximation formalism. The most probable cluster decay modes of the same parent were also predicted. A superasymmetric fission trajectory for the magic radioactivity was found by using the minimal action principle. A magic valley in the deformation energy was confirmed and its origin explained. It is due to strong shell effects of the daughter ²⁰⁶Hg . The nuclear shape parametrization takes into account five degrees of freedom associated to the elongation, necking, mass asymmetry and deformations of nascent fragments. The single particle energies and the nucleon wave functions are obtained within the superasymmetric Woods-Saxon two-center shell model.     

Internal bremsstrahlung of strongly interacting charged particles

A universal theoretical model intended for calculating internal-bremsstrahlung spectra is proposed. In this model, which can be applied to describing nuclear decays of various type (such as alpha decay, cluster decay, and proton emission), use is made of realistic nucleus–nucleus potentials. Theoretical internal-bremsstrahlung spectra were obtained for the alpha decay of the ²¹⁴Po nucleus, as well as for the decay of the ²²²Ra nucleus via the emission of a ¹⁴C cluster and for the decay of the ¹¹³Cs nucleus via proton emission, and the properties of these spectra were studied. The contributions of various regions (internal, subbarrier, and external) to the internal-bremsstrahlung amplitude were analyzed in detail. It is shown that the contribution of the internal region to the amplitude for internal bremsstrahlung generated in nuclear decay via proton emission is quite large, but that this is not so for alpha decay and decay via cluster emission. Thus, a process in which strong interaction of nuclear particles affects the internal-bremsstrahlung spectrum if found.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Cluster radioactivities of odd-mass nuclei

The partial half-lives of the hypothetical even-even equivalent of an odd-mass nucleus for cluster transitions toward various excited states of the daughter, used as a reference to find the hindrance factor, can be calculated within analytical superasymmetric fission model, by taking into account the angular momentum of the emitted cluster. Detailed tables are presented for ¹⁴C radioactivity of ²²¹Fr, ^221,223Ra, ²²⁵Ac; ²⁴Ne radioactivity of ²³³U, ²³¹Pa, and ²³F decay of ²³¹Pa, showing that, except for ²²⁵Ac, the existing experimental evidences, do not exclude (moderate) hindered transitions to the ground states of the daugther nuclei.     

超重核α衰变寿命的理论研究

建立了计算球形核α衰变寿命的新模型——密度依赖的结团模型(DDCM)。在此基础上,通过引入子核的形变自由度,发展了形变的密度依赖的结团模型, 编写了形变的DDCM程序。并系统计算了Z=106—110的超重核α衰变寿命。通过与已有的实验数据的对比分析, 发现理论结果和实验数据符合得很好,验证了DDCM在超重核区域的适用性。We proposed a deformed version of density dependent cluster model (DDCM) by including nuclear deformation of the daughter nucleus. A systematic calculation of α decay half lives of superheavy nuclei (Z=106—110) is carried out by the deformed DDCM. The good agreement between theory and data is obtained. It is shown that the deformed DDCM works well in the superheavy mass region.     

Stability of <Superscript>244–260</Superscript>Fm isotopes against alpha and cluster radioactivity

Taking Coulomb and proximity potentials as the interacting barrier we have studied the cold valley in the radioactive decay of ^244–260Fm isotopes. It is found that in addition to alpha particle minima, other minima occur at S, Ar and Ca clusters. We have computed the half-lives and other characteristics of different clusters emitted from these parents treating parent, daughter and emitted cluster as spheres. Our study reveals that most of these parents are unstable against alpha and heavy cluster (⁴⁶Ar, ^48,50Ca) emissions and stable against light cluster emission, except ⁸Be from ^244–248Fm isotopes. The most probable clusters from these parents are predicted to be ⁴⁶Ar, ^48,50Ca which indicate the role of doubly or near doubly magic clusters (Z = 20, N = 28) and also stress the role of doubly magic ²⁰⁸Pb daughter. The computed half-lives for alpha decay are in good agreement with the experimental data. It is found that the presence of neutron excess in the parent nuclei slows down the cluster decay process. The effect of quadrupole (β ₂) and hexadecapole (β ₄) deformations of parent and fragments on half-lives are also studied. It is found that inclusion of β ₂ and β ₄ reduces the height and shape of the barrier (increases barrier penetrability) and hence the half-life decreases.     

Cold reaction valleys in the radioactive decay of superheavy 286112, 292114, and 296116 nuclei

Cold reaction valleys in the radioactive decay of superheavy nuclei ²⁸⁶112, ²⁹²114, and ²⁹⁶116 are studied taking Coulomb and Proximity Potential as the interacting barrier. It is found that in addition to alpha particle, ⁸Be, ¹⁴C, ²⁸Mg, ³⁴Si, ⁵⁰Ca, etc. are optimal cases of cluster radioactivity since they lie in the cold valleys. Two other regions of deep minima centered on ²⁰⁸Pb and ¹³²Sn are also found. Within our Coulomb and Proximity Potential Model half-life times and other characteristics such as barrier penetrability, decay constant for clusters ranging from alpha particle to ⁶⁸Ni are calculated. The computed alpha half-lives match with the values calculated using Viola-Seaborg-Sobiczewski systematics. The clusters ⁸Be and ¹⁴C are found to be most probable for emission with T _1/2 < 10³⁰ s. The alpha-decay chains of the three superheavy nuclei are also studied. The computed alpha-decay half-lives are compared with the values predicted by Generalized Liquid Drop Model and they are found to match reasonably well.     

Absolute alpha-decay width of212Po in a mixed shell-and-cluster model

We have reproduced the absolute width of theα decay of the ground state of²¹²Po in a model in which the shell model is combined with a²⁰⁸Pb+α cluster model, and found that the amount of core+α clustering in the parent state is ～30%.     

Fine structure in the alpha-cluster radioactivity of the255Fm nucleus

Within the one level R-matrix approach several hindrance factors for the radioactive decay of the²⁵⁵Fm nucleus in which are emitted alpha-nuclei are calculated. The interior wave functions are supposed to be given by the shell model with effective residual interactions. The exterior wave functions are calculated from a cluster-nucleus double-folding model potential obtained with the Michigan 3-Yukawa (M3Y) interaction. As example of the cluster decay fine structure we analyzed the case of alpha-decay of²⁵⁵Fm nucleus. Good agreement with the experimental data is obtained.The author would like to thank Dr. O. Dumitrescu for fruitful discussions concerning different parts of this work and help in computing different quantities entering the expressions of the hindrance factors.     

Alpha-decay fine structures of U isotopes and systematics for isotopic chains of Po and Rn

A model of the cluster radioactivity of even-even nuclei is presented. In this model, the zero-point vibrations in the charge-asymmetry coordinate determine the cluster formation (spectroscopic factor), while the tunneling in the coordinate of the relative separation of the centers of mass of the cluster and the daughter nucleus determines the penetrability of the barrier of the nucleus-nucleus potential. The quality of the model is demonstrated for describing cluster decay half-lives and the fine structure in alpha decays of even-even U isotopes. The model is applied to describe the alpha decays in the isotopic chains of Po, Rn, and U. The correspondence of the calculated half-lives to the Geiger-Nuttall law is discussed.     

Production and decay of269110

In an experiment carried out to identify element 110, we have observed anα-decay chain, that can be unambiguously assigned to²⁶⁹110. In a scries of preexperiments the excitation functions of the fusion reactions⁵⁰Ti +²⁰⁸Pb→²⁵⁸104^* and⁵⁸Fe +²⁰⁸Pb→²⁶⁶108^* were measured with high precision in order to get the optimum projectile energies for the production of these heavy elements. The cross-section maxima of the 1n evaporation channels were observed at excitation energies of 15.6 MeV and 13.4 MeV, respectively. These data result in an optimum excitation energy of 12.3 MeV of the compound nucleus for the production of²⁶⁹110 in the reaction⁶²Ni +²⁰⁸Pb→²⁶⁹110 + 1n. In irradiations at the corresponding beam energy of 311 MeV we have observed a decay chain of 4 subsequent a decays. This can be assigned to the isotope with the mass number 269 of the element 110 on the basis of delayed α-α coincidences. The accurately measured decay data of the daughter isotopes of the elements 108 to 102, obtained in the previous experiments, were used. The isotope²⁶⁹110 decays with a hair-life of (270 _-120 ⁺¹³⁰⁰ ) μs by emission of (11.132±0.020) MeV alpha particles. The production cross-section is (3.3 _-2.7 ^+6.2 ) pb.