Α-decay Half-lives Research Articles

Calculation of α-decay half-lives of 186−218Po isotopes and actinide nuclei using a new phenomenological potential

This paper is devoted to the calculations of alpha decay half-lives of [Formula: see text]Po [Formula: see text] isotopes and actinide nuclei between the atomic numbers Z = 90 and Z = 102, using an energy-dependent potential model. The [Formula: see text]-nucleus effective potential employed in this study includes a Coulomb potential, a centrifugal barrier potential, and a nuclear potential. The nuclear potential is chosen to be the energy-dependent singularized harmonic potential, typical of nuclear interactions. The role of the energy-dependent potential is very significant in this study. Indeed, when compared to the experimental data, our results are found to be improved when energy-dependent interaction potential is employed compared to when energy-independent interactions are used, especially for small values of the parameter [Formula: see text] as evidenced by the values of the root mean square deviation.

Empirical relations for α -decay half-lives: The effect of deformation of daughter nuclei

The influence of the daughter nuclei deformations on the α decay's half-life is modeled by adding the term depending on the quadrupole deformation parameter value to the empirical relations for the α-decay half-lives. It is shown that the addition of the deformation-dependent term led to a better description of the experimental data by the empirical expressions for the half-lives of the α decay than the ones without it. A new empirical expression for a description of the α-decay half-lives is proposed. The empirical relation for the α decay half-lives for the transitions from the ground state to the ground state and the lowest 2+ state of the even-even nuclei is discussed. Published by the American Physical Society 2024

Alpha radioactivity deep-underground as a probe of axion dark matter

We propose to investigate the time modulation of radioisotope decays deep underground as a method to explore axion dark matter. In this work, we focus on the α-decay of heavy isotopes and develop a theoretical description for the θ-dependence of α-decay half-lives, which enables us to predict the time variation of α-radioactivity in response to an oscillating axion dark matter background. To probe this scenario, we have recently constructed and installed a setup deep underground at the Gran Sasso Laboratory, based on the α-decay of Americium-241. This prototype experiment, named RadioAxion-α, will allow us to explore a broad range of oscillation's periods, from a micro-second up to one year, thus providing competitive limits on the axion decay constant across 13 orders of magnitude in the axion mass, ranging from 10−9 eV to 10−20 eV after one month of data collection, and down to 10−22 eV after three years.

Effects of deformation on the cluster and the [formula omitted]-decay half-lives for isotopes of the Trans-lead and the undetected superheavy nuclei

In the present investigation, based on the Wentzel–Kramers–Brillouin (WKB) approximation, and by considering deformation of the cluster and the daughter nuclei, the cluster radioactivity half-lives of 22 Trans-lead isotopes ranging from 221Fr to 242Cm are calculated. Also, the α-decay half-lives of even–even isotopes for the superheavy nuclei with Z in the range 104≤Z≤118 are computed. For the cluster radioactivity, a preformation factor, Pc depending on the atomic numbers of the cluster and the daughter nuclei is used according to the Santhosh and Jose (2021). The α preformation factor, Pα is evaluated based on the cluster-formation model (CFM). A universal decay law (UDL) proposed by Qi et al. (2009), was used to obtain the decay half-lives of the cluster and the α-decay for checking the credibility of our approach. The effects of the deformation of decay products on the half-lives of the cluster and the α-decay have also been investigated by comparing the obtained half-lives considering deformation with ones of the spherical nuclei and the results of the UDL as well as the available experimental data. Comparison indicates that our calculated cluster and α-decay half-lives considering deformation reproduce the experimental data more accurately than the UDL and the spherical nuclei. Furthermore, the cluster radioactivity half-lives of some isotopes that whose cluster radioactivity is energetically allowed but not observed preciously yet, are predicted. Also, the cluster and the α-decay half-lives and the branching ratios between them for some not yet discovered superheavy isotopes with Z=122 and Z=124 are obtained.

Exploring the competition between α-decay and proton radioactivity: A comparative study of proximity potential formalisms

We have conducted a comprehensive and systematic study of the proton radioactivity and α-decay half-lives of neutron-deficient nuclei. This investigation involved the utilization of various Proximity potentials and also considered the incorporation of thermal effects. For the half-life calculations, we employed both temperature-independent and temperature-dependent interaction potentials. We observed that proton radioactivity serves as the dominant mode of decay for nuclides situated very close to the proton drip-line. We explored a universal curve that examines the correlation between the decimal logarithm of experimental half-lives and the negative decimal logarithm of the penetrability for both proton radioactivity and α-decay.

Theoretical investigation of heavy cluster decay from Z=118 and 120 isotopes: A search for an empirical formula in superheavy region

Various decay modes in superheavy nuclei have been of significant interest among which cluster radioactivity has recently gained sizable attention. The α-decay being a predominant decay mode in the superheavy region, the accurate determination of cluster decay half-lives is also crucial in this region as it has tremendous potential to be explored as one of the major decay channels. The usability of the Royer analytical formula [Nuclear Physics A 683 (2001) 182], which is based on the asymmetric fission model, has been investigated for the cluster and α-decay in superheavy region, by comparing it with several other (semi)empirical/analytical formulas. After fitting the formula on around 100 cluster-decay data and around 423 α-decay data, the refitted Royer formula (RRF) is found to be very robust which is able to estimate the cluster decay and α-decay half-lives with good accuracy. In fact, a comparison of the half-lives of both the decay modes using the same formula points towards a substantial chance of heavy cluster (Kr and Sr) decay from various isotopes of Z=118 and 120. Hence, the formula proposed in this study works fairly well for the estimation of cluster decay half-lives in superheavy regions where most empirical formulas fail to match with the half-lives from the various established theories.

α-decay properties of superheavy nuclei with 117 ≤ Z ≤ 120 from the systematics of decay chains and isotopic chains* *Supported by the National Natural Science Foundation of China (12075121), the Natural Science Foundation of Jiangsu Province (BK20190067), and the Fundamental Research Funds for the Central Universities (30922010312)

Recently, the synthesis of new elements above Z = 118 has been a hot topic in nuclear physics. Meanwhile, the α-decay chain is expected to be the unique tool to identify these heaviest nuclei. We have systematically calculated the α-decay energies and half-lives on the same footing for superheavy nuclei (SHN) within the cluster model along with a slightly modified Woods-Saxon (W.S.) potential as the nuclear potential. Based on the available experimental data, the key radius parameter (R) in the α-core potential is determined via the systematic trend from the α-decay and isotopic chains. The α-decay energy ( ) values and half-lives are then obtained simultaneously for those unknown SHN in the range of 117 ≤ Z ≤ 120, during which the decay width is obtained using a new treatment for the asymptotic behavior of the α-core wave function. The theoretical values and experimental data are found to be in excellent agreement for the nuclei 117 and 118 regardless of the method used to determine the R parameter. Predicting the α-decay chains for new elements Z = 119 and Z = 120 can be useful in ongoing or forthcoming experiments.

α decay half-lives of nuclei W, Re, Os, Ir and Pt in the range 157≤A≤193 using the modified generalised liquid drop model (MGLDM)

The α-decay half-lives for the isotopes of nuclei W, Re, Os, Ir and Pt in the range have been studied by using the Modified Generalised Liquid Drop Model (MGLDM). The half-lives predicted for some even–even nuclei by using the deformed Two Potential Approach (TPA) [Comm. Theo. Phys. 74, 055301 (2022)] are considered and included for the comparison. Additionally, we have analysed the α-decay half-lives using eight ℓ-dependent empirical formulae, and compared the results with the experimental data. The standard deviation and the average deviation for by using MGLDM is obtained as 0.6025 and 0.5403, respectively. Also, the results of MGLDM match well with predictions of TPA, with standard deviation of 0.47 and 0.44 respectively. A dip in the half-life curve or a peak in the decay energy curve at 82, a magic neutron number of the daughter nuclei of increases the viability of the calculations. Also, the linear nature of Geiger-Nuttall law, Universal law, the relation connecting and and the New Geiger-Nuttall law helps to calculate the half-lives of newly synthesized and unknown isotopes, making MGLDM more reliable.

A systematic study of α-decay half-lives for Ac, Th, Pa, U and Np isotopes with A = 205–245 using the modified generalized liquid drop model

The Modified Generalized Liquid Drop Model (MGLDM) has been used for calculating the ground-to-ground states of [Formula: see text]-decay half-lives for various Ac, Th, Pa, U and Np isotopes in the mass number range of [Formula: see text]. To account for the nuclear proximity energy, the potential of Blocki et al. 74 [J. Blocki, J. Randrup, W. J. Swiatecki and C. F. Tsang, Ann. Phys. NY 105 (1977) 427] is used. The experimental [Formula: see text] values are used to evaluate the [Formula: see text]-decay half-lives. It can be observed that the logarithm of [Formula: see text]-decay half-life increases with increasing neutron number ([Formula: see text]), with evident minimum at the magic number 126, where the neutron shell is closed. The calculated results are compared with available experimental data and with the predictions of different empirical formulae such as, ARF, MARF, Royer, AKRE, Akrawy, NRB, VS, MVS, YQZR and MYQZR. It is found that the MGLDM is able to predict the experimental half-lives with a standard deviation of 0.6892 (the lowest one among all the other applied empirical formulae), and is therefore suitable for predicting the [Formula: see text]-decay half-lives for unknown and new heavy nuclei.

Study of α-decay half-life for axially symmetric deformed even–even isotopes of nuclei with atomic numbers 88≤Z≤104

In this paper, [Formula: see text]-decay half-life of axially symmetric deformed even–even isotopes with atomic numbers [Formula: see text] had been studied for the transition between the ground states of the parent and daughter nuclei. Quadrupole deformation of daughter nuclei (if any) is considered in calculations. The interaction between the [Formula: see text]-particle and daughter nucleus includes the nuclear double-folding, the Coulomb and rotational terms. Wang’s formula is used for coulomb interaction between spherical [Formula: see text]-particle and deformed daughter nucleus. The Q-value of [Formula: see text]-decay is calculated and used to obtain its half-life, based on the WKB approximation for the penetration probability of [Formula: see text]-particle through the potential barrier. A Q-value-related formula is used to estimate the [Formula: see text]-particle preformation factor. The calculated [Formula: see text]-decay half-lives are compared with the available experimental data. The standard deviation between computed results and experimental data is obtained equal to 0.288. Comparison of our obtained standard deviation indicates well the validity of our chosen theoretical model. Furthermore, the characteristic of [Formula: see text]-decay energy and half-lives confirms the shell effects at [Formula: see text] magic number. Also, the obtained results predict similar closed shells behavior at [Formula: see text] and [Formula: see text] neutron numbers.

Determining the probable isotopic existence of superheavy nuclei

Superheavy nuclei, due to a higher neutron to proton ratio, its formation is highly complicated and predicting the feasible isotope which can be synthesised is an important task in the research on superheavy nuclei. Here we propose a method for predicting the isotopic feasibility by determining the coexistence of odd-even effect in the context of calculating Eα, T1/2(α) using the binding energy by FRDM model. The prominent decay mode of Superheavy nuclei, α-decay, is been evaluated for Z=101-130 with A= 220-360 by considering both preformed α-cluster and 2n+2p instant decay. The intersection points in the graphs corresponding to the minimum difference between odd and even neutron contribution yield the most probable isotope to be formed and is compared with α-decay half-life calculations by Brown formula. Comparison of the results with known synthesised nuclei yield a close agreement with each other.

Examining the impact of α -decay energies on the odd-even staggering in half-lives: α -decay spectroscopy of Ac207–209

The α decays of Ac207–209, located near the proton drip-line, were reinvestigated by means of α-decay spectroscopy. They were produced in the fusion reaction Ar36+Hf176 and separated in flight using the gas-filled recoil separator SHANS. A new α-decay line at 7483(15) keV was observed and assigned as the decay from the ground state of Ac208 to the excited (2+) or (4+) state in Fr204. In addition, the previously known α-decay properties of Ac207–209 were measured with improved precision. The half-lives obtained, together with the existing decay data of other N≤126 actinium isotopes, were compared with the values calculated with the Wentzel-Kramers-Brillouin approximation and without considering the α-preformation factors. It is shown that the calculated half-lives exhibit a distinct odd-even staggering (OES) following the same trend as the experimental data, whereas the amplitudes of the exhibited OES are 30–60 % of the real ones. This implies that apart from the α-preformation factors, the α-decay energies also contribute significantly to the OES of α-decay half-lives.Received 20 September 2022Accepted 10 November 2022DOI:https://doi.org/10.1103/PhysRevC.106.064311©2022 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasNuclear structure & decaysProperties190 ≤ A ≤ 219Nuclear Physics

Estimation of the double alpha-decay half-life

The model for the description of the simultaneous emission of two α-particles from the opposite sides of the nucleus (the double α-decay) is discussed in detail. The 32 smallest values of the half-lives of the double α-decay of nuclei are calculated. The daughter nuclei formed after the double α-decay are even-even and spherical in the ground state in the model. It is shown that the half-lives of the double α-decay are much smaller than the emission of 8Be cluster with sequential decay of 8Be into two α-particles. The calculated values of the double α-decay half-lives show that measuring this decay is possible in the accelerator experiments by forming the proton-rich nuclei. A detailed comparison of the characteristics of the single and double α-decays as well as the emission of 8Be cluster is presented.

Theoretical calculation of alpha decay half-lives of Neptunium nuclei using modified generalized liquid drop model

We considered the α-decay half-lives of neptunium (ZNp = 93) nuclei in the case of deformed nuclei in the range 219 ≤ A ≤ 239 using the generalized liquid-drop model (GLDM) with 1977 nuclear proximity potential suggested by Blocki et al. (1977) [29]. Also, we analyzed the α-decay half-lives of Np isotopes within the WKB method and the Deformed Proximity Potential Model (DPPM). We consider the quadrupole and hexadecapole deformations at θ=0, θ=30, θ=45, and θ=90 degrees. The calculated half-lives and the alpha decay branching ratios are compared with experimental data and are in good agreement. We compared the results obtained with the corresponding experimental data and with the models UNIV, UDL, SemFIS, the Coulomb and Proximity Potential Model (CPPM), SLB and Royer and it is found that they match well over a wide range. The calculated results are in reasonable agreement with the experimental data. Therefore, DPPM gives reliable and accurate results for favored α-decays in the neptunium mass region.

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.

Theoretical calculations of the alpha decay half-lives of 166−190Pt

Calculations of the α-decay half-lives of Pt isotopes have been carried out using the modified Gamow-like model (MGLM) and deformed Woods-Saxon potential model. In order to see the effect of using deformed nuclear potential on the α-decay half-lives of the Platinum isotopes, the spherical Woods-Saxon potential has also been employed in the computation. When compared with experimental data, all the modelsgive very good descriptions of the experimental half-lives. The comparison also suggests that the calculated half-lives considering deformation give better agreement with the experimental data than the results using spherical configuration. New parameter values were obtained for the MGLM model (termed MGLM2). The MGLM2 model gives better descriptions of the half-lives than the MGLM1 model.

An improved Gamow-like formula for α-decay half-lives

An improved Gamow-like (IMGL) formula for α-decay half-lives is proposed by introducing an accurate charge radius formula, an analytic expression of assault frequency, the angular momentum taken by α-particle and the isospin effect. The parameters of the IMGL formula are obtained by fitting the experimental α-emitter data with Zp=52–118 (515 α emitters. Zp is the charge number of a parent nucleus) and those with Zp=92–118 (178 α emitters). Correspondingly, the IMGL formula with the parameters fitted the experimental data with Zp=52–118 is named as the IMGL1 formula and the other one is called as the IMGL2 formula. By using the two formulas, a large number of α-decay half-lives are calculated. It is shown that the accuracy of the IMGL1 and IMGL2 formulas is improved significantly compared to their predecessors. Moreover, the accuracy of the IMGL1 and IMGL2 formulas is higher than that of other types of empirical formulas, including the Royer formula, modified Royer (MR) formula, Viola-Seaborg-Sobiczewski (VSS) formula, modified Viola-Seaborg-Sobiczewski (MVSS) formula, formula proposed by Y. Qian and Z. Ren (YQZR) and modified YQZR (MYQZR) formula. In addition, the experimental α-decay half-lives of the synthesized newly neutron-deficient Actinide nuclei and the superheavy nuclei are reproduced well by the two formulas. Then, the α-decay half-lives of the neutron-deficient nuclei with Zp=94-119 are predicted within the IMGL2 formula because its accuracy is higher slightly than that of the IMGL1 formula. Finally, the competition between α-decay and spontaneous fission (SF) with Zp=120 α-decay chains is investigated in detail within the IMGL2 formula and the modified Swiatecki's formula. The predictions of the neutron-deficient nuclei with Zp=94-119 and the superheavy nuclei with Zp=120 are useful for identifying the new nuclides in future experiments.

Systematic study on α-decay half-lives of uranium isotopes with a screened electrostatic barrier* *Supported in part by the National Natural Science Foundation of China (12175100, 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province, China (21B0402, 18A237), the Natural Science Foundation of Hunan Province, China (2018JJ2321), the Innovation Group

In the present work, we systematically study the α-decay half-lives of uranium (Z=92) isotopes based on the Gamow model with a screened electrostatic barrier. There are only two adjustable parameters in our model i.e. the parameter g and the screening parameter t in the Hulthen potential for considering the screened electrostatic effect of the Coulomb potential. The calculated results are in good agreement with experimental data, and the corresponding root-mean-square (rms) deviations of uranium isotopes with α transition orbital angular momentum l=0 and l=2 are 0.141 and 0.340, respectively. Moreover, we extend this model to predict α-decay half-lives of uranium isotopes whose α decay is energetically allowed or observed but not yet quantified in NUBASE2020. For comparison, the modified Hatsukawa formula (XLZ), the unified Royer formula (DZR), the universal decay law (UDL) and the Viola–Seaborg–Sobiczewski formula (VSS) are also used. The predictions are basically consistent with each other. Meanwhile, the results also indicate that N=126 shell closure is still robust at Z=92 and the spectroscopic factor is almost the same for uranium isotopes with the same l.

Structure and Decay Properties of Th Isotopes Using E-RMFT Formalism

In the present scenario, the search for the thermally fissile nuclei is crucial and also important not only for the research background of nuclear physics but also for the great social and economic impact on the country. Many theoretical works have been performed to analyze a series of Th and U-isotopes and found that some of these isotopes are stable against α-decays and spontaneous fission. Here, we have chosen the isotopic chain of Th-nuclei for the present analysis using relativistic mean-field formalism. The work also explores a few stable isotopes in this region of the nuclear landscape, which is crucial for understanding the exotic region of the nuclear landscape. The objective of this work is to study the bulk properties such as binding energies, root mean square charge radii, neutron-proton radii, neutron skin-thickness as well as intrinsic properties such as excitation energy and specific heat for the 216-238 Th-isotopic chain. Furthermore, the stability of these isotopes is investigated through their possible decay chain analysis. The relativistic mean-field theory was used to obtain the nuclear bulk properties, namely, binding energies, root-mean-square charge radii, neutron skin-thickness, and excitation energy. The steady solution of the temperature-dependent effective relativistic mean-field equations was obtained self-consistently by taking different inputs of the initial deformations. All the calculations were done for NL3, FSUGarnet and IOPB-I parameter sets for 216-238 Th-isotopes. The decay energy of α (Q α ) and β-decay (Q β ) were calculated from the binding energies and were further used to obtain the corresponding half-lives. We have analyzed the structural and decay properties of 216-238 Th isotopes. The excitation energy and specific heat are also estimated for these considered nuclei by using the temperature-dependent effective relativistic mean-field (E-RMFT) formalism for NL3, FSUGarnet and IOPB-I parameters sets. The calculated results are compared with the available experimental data and found similar observations for all the parameter sets at a given temperature. The excitation energy study signifies the shell melting point where maybe the shape transition occurs. Three phenomenological formulae such as Viola-Seaborg, Royer and modified universal decay law are adopted for the calculation of α-decay half-lives. We found lower values of α-decay half-lives indicating a higher rate of β-decay for the isotopic chain.

Empirical formula for pre-formation probability in actinide region within unified fission model

Abstract An improved semi-empirical formulae for pre-formation probability is proposed within unified fission model. The role of pairing effect and shell correction term were taken in to account. Around 39 even–even (E–E) nuclei, 24 even–odd (E–O), 29 odd–even (O–E) and 14 odd–odd (O–O) nuclei were considered in the atomic and mass number range 89 ≤ Z ≤ 103 and 206 ≤ A ≤ 257 respectively. The standard deviation are evaluated for Zhang et al. [Phys. Rev. C 95, 014311 (2017)], Ismail and Adel [Phys. Rev. C 88.054604 (2013)], Seif et al. [Phys. Rev. C 92, 044302 (2015)] are evaluated. We have also compared the standard deviation of present work with that of available semi-empirical formulae. The standard deviation using Royer [J. Phys. G: Nucl. Part. Phys. 26 1149 (2000)] in case of E–E is smaller when compared to present work. In all other cases the standard deviation obtained from the present work is smaller when compared to other studied semi-empirical relations. Hence, involvement of pairing effect and shell correction term of parent nuclei in the pre-formation probability reproduces experimental α-decay half-lives in the actinide nuclei. As a result, the current work’s detailed examination of the unified fission model and application of pre-formation probability may be utilised to anticipate unexplored isotopes in actinide nuclei.