Alpha-decay Half-lives Research Articles

Systematic calculations of the ground state properties of superheavy nuclei

We investigate the ground state properties of the nuclei with proton number $Z=94--110$ within the framework of deformed relativistic mean-field (RMF) theory. A systematic comparison between calculated binding energies and experimental data is made. The calculated binding energies are in good agreement with experimental ones. The reliability of the RMF model for superheavy nuclei has been tested by this comparison. The experimental data of alpha-decay energies and half-lives are reasonably reproduced by calculations. Calculated results further show that a prolate deformation is important for the ground state of these nuclei. The properties of some unknown nuclei are predicted and these are useful for future experimental researches of superheavy nuclei.

Estimation of Alpha-decay Half-lives and Fission Barriers from the Viewpoint of a New Mass Formula

We estimate the alpha-decay half-lives from Qα-values with a phenomenological relation. The parameter values of the phenomenological formula are adjusted by using the experimental half-lives and Q-values of the Evaluated Nuclear Structure Data File (ENSDF) for a wide nuclidic region. The half-lives Tα for unknown nuclei are estimated by this phenomenological formula with the use of Qα-values taken from KUTY mass formula. In addition to the half-lives, we calculate the potential energy surface for spontaneous fission calculated by the same method as used for obtaining the shell energies of KUTY mass formula. In the superheavy region, the fission barrier heights of the nuclei near the nucleus 304 122 are about 8 MeV and their widths are fairly wide. Therefore the spontaneous-fission half-lives are expected to be very longer than the alpha-decay half-lives. On the contrary, there are some neutron-deficient nuclei whose spontaneous-fissi! on half-lives expected to be rather short because their fission barrier heights are small and the widths of them are narrow.

Alpha-decay Half-lives and Fission Barriers for Superheavy Nuclei Predicted by a Nuclear Mass Formula

We estimate α-decay half-lives from Qα values with phenomenological formulas. The parameter values of the formulas are adjusted by using experimental half-lives and Q values of the Evaluated Nuclear Structure Data File (ENSDF) for a wide nuclidic region. The half-lives Tα for unknown nuclei are estimated by this phenomenological formula with the use of Qα values taken from KUTY mass formula. In addition to the half-lives, we estimate spontaneous fission barriers calculated by the method to obtain the shell energies of KUTY formula. In the superheavy region, the barrier heights of the nuclei near the nucleus 304 122 are about 8 MeV and their widths are fairly wide. Therefore these spontaneous-fission half-lives are expected to be very long. On the other hand, there are some neutron-deficient nuclei whose spontaneous-fission half-lives expected to be rather short because their fission barrier heights are small and the widths of them are narrow.

EFFECT OF NUCLEAR DEFORMATION ON THE ALPHA-DECAY HALF-LIFE OF EVEN-EVEN ALPHA EMITTERS

Alpha-decay half-life of even-even emitters has been calculated in terms of tunnelling through a quantum mechanical potential barrier. A multipolar expansion of Coulomb potential has been developed taking into account the nuclear quadrupole, hexadecapole, and hexacontatetrapole deformations. We show that using a free-parameter model the calculated half-lives do not vary significantly with higher order multipolarities of the daughter nucleus deformation.

Alpha decay and nuclear deformation: the case forfavoured alpha transitions of even-even emitters*

Alpha decay half-life for ground-state to ground-statetransitions of 174 even-even alpha emitters has been calculatedfrom a simple, Gamow-like model in which the quadrupoledeformation of the product nucleus (assumed to have anellipsoidal shape) is taken into account. The assumption made isthat before tunnelling through a purely Coulomb potentialbarrier the two-body system oscillates isotropically, thusgiving rise to an equivalent, average polar direction θ0(referred to the symmetry axis of the ellipsoid) for alphaemission. It is shown that the experimental half-life data aremuch better reproduced by the present description than in thespherical shaped approximation for the daughter nucleus.

Role of pairing degrees of freedom and higher multipolarity deformations in spontaneous fission process

Spontaneous fission ( T sf) and alpha-decay half-lives ( T α ) of the heaviest nuclei with atomic number 100 ≤ Z ≤ 114 are calculated on the basis of the deformed Woods-Saxon potential. The calculations of ( T sf) are performed by the WKB approximation, in the multi-dimensional dynamical-programing method (MDP). We have examined three different effects: the effect of higher even-multipolarity shape parameters ( β 6 and β 8), the role of reflection-asymmetry ( β 3 and β 5) and the influence of pairing degrees of freedom ( Δ p and Δ n ). Alpha-decay half-lives ( T α ) have been calculated by the Viola-Seaborg (V-S) formula with the parameters modified to the latest experimental data.

-decay characteristics of neutron-deficient 190, 192Po nuclei and alpha branching ratios of 186, 188Pb isotopes

By using complete fusion reactions and , leading to and compound nuclei, improved -decay characteristics for neutron-deficient isotopes have been obtained. The experiments have been performed at the fragment mass analyzer (Argonne) and at the RITU gas-filled separator (Jyvaskyla). In the l = 0 decay to the excited state in is two times faster than the decay to the ground state. For more precise values of the alpha-decay energy keV and half-life ms were measured. By using correlated -decay chains -branching ratios of 38(9)% and 9.3(8)% were experimentally deduced for the first time for and , respectively. The reduced -width systematics is extended for even Po isotopes, confirming a persistence of the saturation towards the lighter isotopes. Absence of any anomalies in the reduced -widths for the neutron-deficient Pb isotopes is confirmed.

Effective liquid drop description for alpha decay of atomic nuclei

Alpha-decay half-lives are presented in the framework of an effective liquid drop model for different combinations of mass transfer descriptions and inertia coefficients. Calculated half-life values for ground-state-ground-state-favoured alpha transitions are compared with available, updated experimental data. Results have shown that the present model is very suitable to treat the alpha-decay process on an equal footing as cluster radioactivity and cold fission processes. Better agreement with the data is found when the subset of even-even alpha emitters is considered in the calculation.

PRESCOLD: Calculation of the half-life for alpha decay, cluster radioactivity and cold fission processes

A numerical code to evaluate the half-lives for alpha decay, cluster radioactivity and cold fission processes for a given parent nucleus is presented. The Gamow penetrability factor is obtained by considering the pre-scission phase of two intersecting spheres in the effective one-dimensional barrier potential. Two inertia coefficients and two different modes for the shape parametrization are implemented in order to discuss the effect of the inertia coefficient on the half-lives of the spontaneous processes under study.

Anisotropy of favoured alpha transitions producing even-even deformed nuclei

The anisotropy in favoured alpha transitions which produce even-even deformed nuclei is discussed. A simple, Gamow-like model which takes into account the quadrupole deformation of the product nucleus has been formulated to calculate the alpha decay half-life. It is assumed that before tunneling into a purely Coulomb potential barrier the two-body system oscillates isotropically, thus giving rise to an equivalent, average preferential polar direction θ0 (referrred to the symmetry axis of the ellipsoidal shape of the product nucleus) for alpha emission in favoured alpha transitions of even-even nuclei.

Determination of the half-life of the spontaneous fission of240PU

Two metallic240Pu sources were certified as reference standards of spontaneous-fission activity and neutron flux. The certification results were used to determine the ratio TαTs&f of the alpha-decay and spontaneousfission half-lives of240Pu. The ratio was found to be (5.68+-0.11)·10−8, which corresponds to Ts&f=(1.16+0.02)·1011 yr for an assumed value Tα=6563+7yr.

An illustration of Benford's first digit law using alpha decay half lives

Benford's law states that the first digits of a large body of naturally occurring numerical data in decimal form are not uniformly distributed but follow a logarithmic probability distribution. The values of radioactive decay half lives, which have been accumulated throughout the present century and vary over many orders of magnitude, afford an excellent opportunity to test the predictions of this law. To this end, we examine the frequency of occurrence of the first digits of both measured and calculated values of the half lives of 477 unhindered alpha decays and compare them with the predictions of Benford's law. Good agreement is found, and a similar distribution law for second digits is also considered.

Emission of 23F and 24Ne in cluster radioactivity of 231Pa.

Using a track-recording phosphate glass detector with a standard deviation ${\mathrm{\ensuremath{\sigma}}}_{\mathit{Z}}$=0.23 charge unit, we collected \ensuremath{\sim}2100 tracks of energetic clusters emitted from $^{231}\mathrm{Pa}$. Of these, 1348 survived cuts on energy, angle of incidence to the detectors, and ${\mathrm{\ensuremath{\chi}}}^{2}$. All but one of them are consistent with $^{24}\mathrm{Ne}$, and our measured branching ratio, B(Ne/\ensuremath{\alpha})=(13.4\ifmmode\pm\else\textpm\fi{}1.7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}12}$, for an alpha-decay half-life for $^{231}\mathrm{Pa}$ of 3.28\ifmmode\times\else\texttimes\fi{}${10}^{4}$ yr. This value of B is a factor of 2.2 greater than was determined by Tretyakova et al., who observed 252 Ne decays. We identify one event as $^{23}\mathrm{F}$, the nucleus predicted by cluster emission models to have the second highest branching ratio for emission from $^{231}\mathrm{Pa}$. This corresponds to a branching ratio B(Ne/F)=${1347}_{\mathrm{\ensuremath{-}}940}^{+6440}$, the 1\ensuremath{\sigma} limits being governed by inverse Poisson statistics. Published models predict lower values of B(Ne/F), ranging from 3 to 400. Our event, if its 4\ensuremath{\sigma} deviation from Ne is regarded as sufficient evidence for F, would be the first example of emission of an odd-Z cluster in spontaneous cluster radioactivity.

Potential energy and fission barriers of superheavy nuclei calculated in multidimensional deformation space

The ground-state collective potential energy of even-even superheavy nuclei with the proton numberZ=112–130 and the neutron numberN=152–210 is analyzed in a multidimensional deformation space. The energy is calculated by the macroscopic-microscopic method. The Yukawa-plus-exponential model is used for the macroscopic part of the energy and the Strutinski shell correction, based on the Woods-Saxon single-particle potential, is taken as the microscopic part. Three axial-symmetric deformations:β2,β4,β6, and quadrupole and hexadecapole non-axial deformations are taken into account. The spontaneous-fission and alpha-decay half-lives are also calculated. Rather low fission barriers (3–7 MeV lower than calculated previously) are obtained, especially when non-axial shapes of a nucleus are considered. Nevertheless, the calculated fission lifetimes are larger than the alpha-decay half-lives for most of considered nuclides. A large number of nuclides withZ=112–122 is predicted to have the total half-life long enough to be detected, when synthesized in the laboratory.

RECENT DEVELOPMENTS IN THE THEORY OF ALPHA DECAY

We examine the extensive experimental data on partial half-lives for alpha-decay, and discuss some interpretations, with emphasis on the use of a simple three parameter cluster model. In this model, the alpha-particle moves in a potential well of fixed depth, in an orbit with a large value of a global quantum number. With the model parameters fixed at values consistent with those suggested by the underlying nucleon orbits, we obtain excellent agreement with the data, and reproduce the discontinuities associated with shell closure in a natural way.

Ground state to ground state alpha decays of heavy even-even nuclei

The authors examine the experimental data on partial half lives for alpha decay of heavy even-even nuclei. When presented in the traditional form of Geiger-Nuttall plots (1911) for various isotopic sequences, these data clearly indicate the existence of different linear relations for neutron numbers N above and below the magic value of 126. They present a simple cluster model, employing three fixed parameters, which is able to give an excellent account of all these half lives. In particular, it can reproduce the values for all even-even nuclei having 76<or=Z<or=100 to within a factor of approximately two. An important feature of the model is that it envisages preformed alpha particles in the parent nuclei to be moving in orbits with a large value of a global quantum number. The discontinuity in the Geiger-Nuttall plots at N=126 is then naturally explained by an increase of this global quantum number as the alpha particle is forced into a higher orbit by the shell closure.

Deformed superheavy nuclei

Abstract The study of superheavy nuclei is extended to include deformed nuclei. Even-even nuclei with proton number Z=112−130 and neutron number N=152−210 are considered. The ground-state potential energy, equilibrium deformation, fission barrier, alpha-decay and spontaneous-fission half-lives of the nuclei are studied. It is found that in addition to the “traditional” spherical nuclei, also deformed superheavy nuclei, with half-lives long enough for their detection, are expected to exist.

Reduced alpha widths for nuclei with N >= 84,Z

The reduced alpha widths of even-even nuclei with N\ensuremath{\ge}84,Z\ensuremath{\le}84 display a systematic behavior with only few anomalies. The widths were deduced from the known alpha-decay half-lives and branching ratios, with penetration factors calculated from realistic cluster wave functions. Predictions are reported for the half-lives of naturally occurring long-lived nuclei as well as the half-lives and branching ratios of short-lived proton-rich nuclei away from the line of beta stability.

Do the superheavy nuclei really form an island?

The spontaneous-fission and alpha-decay half-lives are calculated for even-even nuclei with Z = 104−110. Rather large values of the lifetimes are obtained, indicating that the usual peninsula of relatively long-lived nuclides may extend further than has been believed. Due to this, the region of hypothetical superheavy nuclei (around the nucleus 298114) may constitute a part of the peninsula, rather than form an island separated from it by a region of deep instability.

Theoretical half-lives for the heaviest nuclei

Spontaneous-fission and alpha-decay half-lives are calculated for even-even nuclei with the atomic numberZ=104–110. The results reproduce rather well the existing experimental data for these nuclei and predict rather large total lifetimes for nuclei even heavier than observed up to now. The latter is mainly due to a deformed shell at the neutron numberN=162–164, obtained in calculations.