Α-nucleus Potential Research Articles

Construction of density-dependent α-nucleon interaction to describe α-nucleus scattering

We provide a global density-dependent α-nucleon (DD-αN) interaction to construct the α-nucleus optical potential in a wide range of incident energies. The α-nucleus potential based on the folding model with the present DD-αN interaction reproduces the experimental data up to backward angles using the point-nucleon density obtained by the mean-field model. The present DD-αN interaction is based on the phenomenological optical potential to reproduce the p + 4He elastic scattering at the incident energies at 12.04–1000 MeV. Namely, the α-nucleon system is considered an elementary process. The density dependence (medium effect) of the DD-αN interaction is phenomenologically added to reproduce the α elastic scatterings by the 16O, 40Ca, 58Ni, 90Zr and 208Pb targets at E/A = 10–342.5 MeV. The total reaction cross sections are also compared with the experimental data.

Alpha decay around shell closures and correlation of half-life times with the neutron energy levels of the emitting nuclei

The α-decay half-lives (T1/2) for 16 isotopic chains of even-even and even-odd nuclei, from 52Te to 82Pb were investigated by employing the density dependent cluster model. The α-nucleus potential was calculated by the double-folding model (DFM) using the M3Y-Reid NN interaction with the zero-range exchange part assuming spherical and deformed density distributions of the daughter nuclei. In the framework of the WKB approximation, the half-lives of the α-emitters were calculated and compared using six analytic formulas (UDL, Horoi, BKAG, UNIV, NRDX and TM formulas). We found a clear similarity in the behavior of log10⁡T1/2 versus the neutron daughter number (Nd) when the calculations performed using both DFM and these mentioned analytical formulas for each isotopic chain. In addition, the theoretical results of log10⁡T1/2 obtained with the UDL and UNIV formulas slightly better agree with the DFM calculations than those calculated from the other analytical methods. Moreover, the present work pointed out some magic or semi-magic neutron numbers of the daughter nuclei corresponding to dips in the behavior of log10⁡T1/2 with variation in Nd. The interplay of these magic (semi-magic) numbers is inspected as the total number of neutrons filling the upper neutron level in the parent nucleus. We test the predicted results of the above mentioned models by comparing them with the available experimental α-decay half-lives. Starting from the number of neutrons needed for level closure and the small available values of the confirmed spin of parent and daughter nuclei, we predicted the level schemes around the known magicities N=50, 82 and 126. We found changes in the neutron levels for isotopes of the same element which become too large for heavy nuclei. Example for these changes is the repetition of the spin value 1/2− for the three isotopes 195−199Hg and their daughters, we need five different neutron level arrangements with 3p1/2 level at the top.

Constraining the α-nucleus potential for α-decay calculation with nuclear rainbow scattering

Introduction: The emission of a particles is a powerful probe for the α-cluster structure of heavy nuclei. The α-nucleus potential is a crucial ingredient in the a-decay calculation within the preformed cluster model. One of the most reliable ways to construct this potential is the double folding model, where an effective nucleon-nucleon interaction is folded with the nuclear densities. In the folding model calculation, there are many ambiguities in the choice of the nuclear densities of the daughter nucleus for α-decay. We propose to directly constrain the α-nucleus potential for α- decay and choose the daughter nuclear density using the nuclear rainbow scattering phenomenon. Methods: The refractive rainbow pattern in the elastic scattering cross section within the optical model can probe deep into the interior region of the α-nucleus potential. We apply this method to investigate the reliability of the nuclear potential used in the α-decay of the 212Po nucleus leading to the 208Pb daughter nucleus by examining the elastic a scattering on 208Pb. In such an approach, we perform the double-folding calculation to construct the α-nucleus potential using several common parametrizations of the daughter nuclear densities. These parametrizations include the mean-field Hartree-Fock-Bogoliubov calculations with the BSk14 and D1S interactions, the independent particle model, and the 2-parameter Fermi distributions. The obtained nuclear potentials are applied to the optical model to calculate the elastic α-208Pb scattering cross sections that are compared with the experimental data. These nuclear potentials are further used in the preformed cluster model to study thea-decay half-life of 212Po. Results: The nuclear densities from the Hartree-Fock-Bogoliubov calculations are shown to provide the best description for both the nuclear rainbow scattering anda-decay half-life. The results indicate a strong correspondence between the capabilities of the nuclear potential to reproduce the cross section ofa scattering and the α-decay half-life. The extracteda preformation factors from the semiclassical preformed cluster model with folding potentials are in good agreement with those from other studies. Conclusion: The nuclear rainbow scattering phenomenon can be used to provide reliable a-nucleus potential for α-decay studies within the preformed cluster model. The nuclear densities from the mean-field Hartree-Fock-Bogoliubov method with the BSk14 and D1S interactions are the appropriate choices for the DFM calculation used in the α-decay study.

Exploring the uncertainties of (α, xn) reactions for the weak r-process

“Light” heavy elements (Z = 38 − 47) can be synthesized in the neutrino–driven ejecta of core–collapse supernovae via the weak r–process. This nucleosynthesis scenario exhibits uncertainties from the absence of experimental data from (α, n) reactions on neutron–rich nuclei, and are mostly based on statistical model calculations. We present preliminary results from a recent sensitivity study, using the Atomki–V2 α-nucleus potential to identify the most important (α, n) reactions that can affect the production of “light” heavy elements between strontium and silver under different astrophysical conditions. We also discuss the planning of studies to experimentally determine (α, xn) reaction rates using the MUSIC detector at Argonne National Laboratory and the SECAR recoil separator at FRIB.

Astrophysical reaction rates of [formula omitted]-induced reactions for nuclei with [formula omitted] from the new Atomki-V2 [formula omitted]-nucleus potential

The new Atomki-V2 α-nucleus potential is applied to calculate astrophysical reaction rates NA〈σv〉 of intermediate mass and heavy target nuclei from iron (Z=26) up to bismuth (Z=83). Overall, reaction rates of α-induced reactions are provided for 4359 target nuclei, covering as well neutron-deficient as extremely neutron-rich target nuclei from the proton to the neutron dripline. Contrary to previous rate compilations, these new calculations include all relevant exit channels with the dominating (α, xn) reactions for neutron-rich target nuclei.

Activation measurement of a-induced cross sections for 197Au: analysis in the statistical model and beyond

Cross sections of ( α,γ), (α,n), and (α,2n) reactions for 197Au were measured below the Coulomb barrier using the activation technique. The new data are analyzed in the statistical model and in a simple barrier transmission model. Sensitivities of the resulting cross sections on the underlying parameters are discussed. It is found that the cross sections in the statistical model depend sensitively on the tail of the imaginary α-nucleus potential at large radii outside the colliding nuclei. Contrary, the cross sections in the barrier transmission model depend only on the real part of the α-nucleus potential. The calculated cross sections in the barrier transmission model agree nicely with the new experimental data. Furthermore, the available experimental data for heavy targets above A ≈150 are also well reproduced within the barrier transmission model.

Analysis of α+11B elastic and inelastic scattering using microscopic and semi-microscopic representations

In the present study angular distributions of the differential cross section for elastic and inelastic scattering of alpha (α)-particles of 11В nuclei at different bombarding energies have been analyzed in the framework of the optical model (OM) potential. Two OM folding approaches were adopted in order to construct the real part of the α-nucleus potential. First, we generated the semi-microscopic single folding (SF) potential by folding an effective α-nucleon (α-N) interaction over the nuclear matter density of the target (11B) nucleus. In addition, the double folding (DF) approach was employed in order to deduce a microscopic representation of the optical potential by folding an effective density-dependent (DDM3Y) nucleon–nucleon interaction over the matter densities of the colliding nuclei. Successful theoretical predictions of six sets of experimental elastic scattering data have been obtained over the whole measured angular range. However, it was found that introducing real renormalization coefficients (∼0.9–1.6) is essential in order to obtain best fits with data. On the other side, sixteen sets of the inelastic scattering data at several excited states of 11B nucleus were analyzed using the constructed SF and DF deformed potentials. In general, reasonable description of the data is obtained. However underestimated predictions of data were obtained at backward measured angles. The deduced reaction (absorption) cross sections and nuclear deformation lengths were also investigated.

Systematic analysis of elastic α scattering on [formula omitted] nuclei around the Coulomb barrier

Alpha elastic scattering angular distributions on target nuclei 118, 124Sn and 120-130Te at energies near the Coulomb barrier are analyzed. We used three versions of the nuclear optical model potentials (OMP) to analyze twenty-nine data sets. JLM and the density and energy-dependent DDM3Y1 with finite range exchange term effective interactions were used to generate these potentials. Two real folded potentials based on JLM and DDM3Y1 effective interactions supplied with the conventional Wood–Saxon (WS) imaginary potential are used in the cross sections calculations. These potentials are denoted as JLM-R and DDM3Y1-FR, respectively. In addition, we used the full complex folded OMP, denoted as JLM-RI, to analyze the same data. These potentials successfully predict the cross section of the systems under study. We found that the JLM-R and DDM3Y1-FR could reproduce the measured cross sections over the full angular range very well compared to microscopic JLM-RI potential. Our calculated potentials have a clear energy dependence and in addition a weak target mass dependence. The total reaction cross section and volume integral are investigated in comparison to previous studies. The derived potentials are very promising for the construction of a new global α-nucleus potential and provide new parameters of α–induced reactions and scattering at the energy range 17–27 MeV.

Significant improvement of half-life calculation of α decays by considering the nuclear medium effect

We incorporate the nuclear medium effect into α-decay calculation through a reformulation of the conventional double-folding model. The improved model enables the α cluster to simultaneously change its size at different nuclear density during the Coulomb penetration process, thus reflecting the effect from the variation of nuclear mean field and Pauli blocking at the nuclear surface. To evaluate the result of such a dynamic effect, we perform a systematic calculation of α-decay half-lives for even-even α-emitters within a deformed cluster model. We found that the medium effect optimises the shape of α-nucleus potential at the surface region, leading to a remarkable reduction in the deviations between the theoretical and experimental decay rates. The result implies the importance of the dynamic aspect of α clustering in describing a realistic α-nucleus interaction.

Unified approach to alpha decay calculations

With the discovery of a large number of superheavy nuclei undergoing decay through α emissions, there has been a revival of interest in α decay in recent years. In the theoretical study of α decay the α-nucleus potential, which is the basic input in the study of α-nucleus systems, is also being studied using advanced theoretical methods. In the light of these, the Wentzel–Kramers–Brillouin (WKB) approximation method often used for the study of α decay is critically examined and its limitations are pointed out. At a given energy, the WKB expression uses barrier penetration formula for the determination of the transmission coefficient. This approach utilizes the α-nucleus potential only at the barrier region and ignores it elsewhere. In the present era, when one has more precise experimental information on decay parameters and better understanding of α-nucleus potential, it is desirable to use a more precise method for the calculation of decay parameters. We describe the analytic S-matrix (SM) method which gives a procedure for the calculation of decay energy and mean life in an integrated way by evaluating the resonance pole of the S-matrix in the complex momentum or energy plane. We make an illustrative comparative study of WKB and S-matrix methods for the determination of decay parameters in a number of superheavy nuclei.

Elastic alpha scattering experiments and the alpha-nucleus optical potential at low energies

High precision angular distribution data of (α,α) elastic scattering are presented for the nuclei 89Y, 92Mo, 106,110,116Cd, 112,124Sn, and 144Sm at energies around the Coulomb barrier. Such data with small experimental uncertainties over the full angular range (20–170°) are the indispensable prerequisite for the extraction of local optical potentials and for the determination of the total reaction cross section σreac. A systematic fitting procedure was applied to the experimental scattering data presented to obtain comprehensive local potential parameter sets that are composed of a real folding potential and an imaginary potential of Woods–Saxon surface type. The potential parameters obtained were used in turn to construct a new systematic α-nucleus potential with very few parameters. Although this new potential cannot reproduce the angular distributions with the same small deviations as the local potential, the new potential is able to predict the total reaction cross sections for all cases under study.

α-decay half-lives in medium mass nuclei

Systematical calculations on the α-decay half-lives of even–even medium mass nuclei with 82 < N ⩽ 126 are carried out within the density-dependent cluster model using a two-potential approach. The decay width is achieved in terms of the bound state wavefunction, the scattering wavefunction and the outer potential, where the effective α-nucleus potential is obtained from the double-folded integral of the realistic nucleon–nucleon interaction with the mass distributions of α particle and daughter nucleus. Instead of the Wentzel–Kramers–Brillouin (WKB) barrier penetration probability, the numerical solution of the Schrödinger equation for the bound state is presented. In addition, the shell effect on the α-preformation factor has been taken into account for even–even N = 126 isotones. The calculated α-decay half-lives are found to agree with experimental data with a mean factor of less than 2.

The superheavy elements: overview

Superheavy Elements (SHE) up to Z = 118 have been produced and studied. The Relativistic Mean Field (RMF) theory provides a reasonably good description of the ground state properties (binding energies, Q-values, deformation, radii, densities etc.) of these elements. Shell closures revealed by the vanishing/ minimum pairing energy, are predicted for specific combination of neutron number N and proton number Z, specifically at N = 38, 164, 172, 184 and 198. Some of these have been confirmed experimentally. Future experiments are expected to validate the remaining predictions. Microscopic α-nucleus potential generated in the frame work of double folding model, employing the RMF densities for the daughter nucleus and the experimental densities for the α, along with the density dependent M3Y nucleon — nucleon interaction, qualitatively reproduce the experimental half lives for α — decay, calculated in the WKB approximation.

RESONANCES AND ANGULAR DISTRIBUTION IN α DECAY

Tunneling of a particles through the Coulomb barrier is consecutively treated. The effect of sharp peaks arising in the case of coincidence of the α energy with that of a quasistationary state within the barrier is elucidated. Peaks' energy depend on the α-nucleus potential. They can give rise to “anomalous” properties of some neutron resonances. The peaks can also be observed in the incoming α-nucleus channel. The method is also applied for calculation of the angular distribution of the emitted α particles from the α decay of a compound nucleus of135Pr . Next fundamental test of the theory is proposed to be the α decay of superheavies.

NON-MONOTONIC ALPHA- AND6Li-POTENTIALS FROM ENERGY DENSITY FUNCTIONAL FORMALISM

The present status of the α-nucleus potential, generated from the energy density functional (EDF) formalism using a realistic two-nucleon potential, which incorporates the Pauli principle, is discussed. The EDF potentials, calculated using a density distribution of α-particle that yields a binding energy of 20 MeV with a reasonable root-mean-squared radius and observed density distributions of6Li and various target nuclei, are found to be shallow and non-monotonic in character. This non-monotonic EDF potential reproduces satisfactorily the experimental elastic scattering data, particularly at energies above the Coulomb barrier. Since the elastic scattering data and the binding energies of all nuclei considered herein are well reproduced using the mean field generated from a realistic two-nucleon potential for nuclear and nucleonic matter, one may conclude to have reasonable information on the equation of states of nuclear and nucleonic matter from a very low to the saturation density from the present investigation.

The α-nucleus potential for fusion and decay

The α-nucleus fusion cross sections at energies around and below the barrier and the α-decay half lives are calculated in the semi-classical WKB approach using the same microscopic as well as empirical α-nucleus potentials. The microscopic potential is generated within the double-folding framework using M3Y nucleon–nucleon interaction along with the required neutron and proton density distributions calculated in the relativistic mean field theory. It is found that in spite of the excellent results for the half lives the fusion cross sections are underestimated by almost a factor of 3. However, the experimental fusion cross sections can be reproduced by introducing a norm factor (overall multiplicative factor to the potential) 1.3 but this then worsens the agreement for half lives. To verify this observation and for comparison the calculations are repeated using some of the representative empirical potentials available in the literature. The same conclusion emerged. The present study thus indicates that the same α-nucleus potential may yield accurate description for both the α-nucleus fusion cross sections and α-decay half lives only with the introduction of additional parameter(s).

Resonances in alpha-nuclei interaction

Tunnelling of α particles through the Coulomb barrier is considered. The main attention is given to the effect of sharp peaks arising in the case of coincidence of the α energy with that of a quasistaionary state within the barrier. The question of the α-nucleus potential is discussed in this light. The method is applied to the α decay of a compound nucleus of 135Pr. The appearance of the peaks in the spectrum of emitted particles is predicted. They can give rise to ‘anomalous’ properties of some neutron resonances. The peaks can also be observed in the incoming α-nucleus channel. Observation of the peaks would give unique information about the α-nucleus potential.

α-nucleus potential for α-decay and sub-barrier fusion

The set of parameters for \ensuremath{\alpha}-nucleus potential is derived by using the data for both the \ensuremath{\alpha}-decay half-lives and the fusion cross sections around the barrier for reactions $\ensuremath{\alpha}+$$^{40}\mathrm{Ca}$, $\ensuremath{\alpha}+$$^{59}\mathrm{Co}$, and $\ensuremath{\alpha}+$$^{208}\mathrm{Pb}$. The \ensuremath{\alpha}-decay half-lives are obtained in the framework of a cluster model using the WKB approximation. The evaluated \ensuremath{\alpha}-decay half-lives and the fusion cross sections agreed well with the data. Fusion reactions between \ensuremath{\alpha} particles and heavy nuclei can be used for both the formation of very heavy nuclei and spectroscopic studies of the formed compound nuclei.

Molecular versus squared Woods–Saxon α-nucleus potentials in the 27Al(α, t)28Si reaction

The differential cross-section of the 27Al(α, t)28Si reaction for 64.5 MeV incident energy has been reanalysed in DWBA with full finite range using a squared Woods–Saxon (Michel) α-nucleus potential with the modified value of the depth parameter α = 2.0 as reported in a comment article by Michel and Reidemeister. This new value produces significant improvement in fitting the data of the reaction with its overall performance, in some cases, close to that previously observed for the molecular potential. Although the non-monotonic shallow molecular potential with a soft repulsive core and the Michel potentials produce the same quality fits to the elastic scattering and non-elastic processes, they are not phase equivalent. The two types of potential produce altogether different cross-sections, particularly at large reaction angles. The importance of the experimental cross-sections at large angles for both elastic scattering and non-elastic processes is elucidated.

α-nucleus potentials and photon-induced nucleosynthesis

New data for the 112,124Sn(α,α) 112,124Sn reaction have been measured and are presently analyzed. Results of the 112 Sn ⊗ α potential at the energy E c.m. ≈ 14 MeV are presented. The determination of this α-nucleus potential may allow a prediction of the 112Sn(α,γ) 116Te cross section.