Decay Half-lives Of Nuclei Research Articles

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.

Roles of tensor and isoscalar pairing interactions in β-decay calculations for possible r-process waiting point nuclei with N ~ 82 and 126* *Supported by the National Natural Science Foundation of China (11575120, 11822504), and Science Specialty Program of Sichuan University (2020SCUNL210)

In this study, we adopt the self-consistent Hartree-Fock-Bogoliubov (HFB) theory with the proton-neutron quasi-particle random phase approximation (pnQRPA) based on the Skyrme force for calculation of the β − decay half-lives for nuclei with N ~ 82 and 126 on possible r-process paths. In the calculations, the Skyrme interaction (e.g., SKO') is adopted, and the tensor interaction is added self-consistently in both HFB and QRPA calculations. We systematically study how the half-life is changed by varying the strength of the triplet-even (TE) and triplet-odd (TO) components as well as the IS pairing. We find that a variation in strength of the IS pairing of approximately 20% does not produce a substantial effect on β-decay rates with or without the tensor force, while a strength variation of the TO tensor force considerably affects the change in the β-decay half-lives for the very neutron rich N ~ 82 and 126 isotonic chains. In addition, with the inclusion of the tensor force, the GT decay becomes dominant for very neutron-rich nuclei.

Studying the $$\alpha$$-Decay Half-Lives of Nuclei in the Range $${68\leqslant Z\leqslant 118}$$ by Double-Folding and Cluster Formation Formalisms

Studying the $$\alpha$$-Decay Half-Lives of Nuclei in the Range $${68\leqslant Z\leqslant 118}$$ by Double-Folding and Cluster Formation Formalisms

-Decay Half-Lives for Waiting Point Nuclei Around N = 126**Supported by the National Natural Science Foundation of China under Grant Nos. 11565010, U1731238, 11365006, 11761161001; Guizhou Province Science and Technology Innovation Talent Team under Grant No. 2015(4015); The Innovation Team Foundation of the Education Department of Guizhou Province under Grant No. 2014-35; the Training Program for Excellent Young Talents in

We have systematically analyzed the experimental -decay half-lives of waiting point heavy nuclei around neutron number N = 126. A new set of parameters for the exponential formula of -decay half-lives is proposed. The forbidden transition effects are included in the new set of parameters self-consistently. Theoretical -decay half-lives of nuclei around N = 126 are compared with recent theoretical results and experimental data. It is found that the new theoretical results are in better agreement with experimental data. The unknown -decay half-lives of some nuclei in this region are predicted for studies on nuclear structure far from stability and the nucleosynthesis in stars.

Empirical formula for β −-decay half-lives of r-process nuclei

Experimental data of $\beta^{-}$-decay half-lives of nuclei with atomic number between 20 and 190 are investigated. A systematic formula has been proposed to calculate $\beta^{-}$-decay half-lives of neutron-rich nuclei, with a particular consideration on shell and pair effects, the decay energy $Q$ as well as the nucleon numbers ($Z$, $N$). Although the formula has relatively few parameters, it reproduces the experimental $\beta^{-}$-decay half-lives of neutron-rich nuclei very well. The predicted half-lives for the r-process relevant nuclei obtained with the current formula serve as reliable input in the r-process model calculations.

Self-consistent relativistic quasiparticle random-phase approximation and its applications to charge-exchange excitations

The self-consistent quasiparticle random-phase approximation (QRPA) approach is formulated in the canonical single-nucleon basis of the relativistic Hatree-Fock-Bogoliubov (RHFB) theory. This approach is applied to study the isobaric analog states (IAS) and Gamov-Teller resonances (GTR) by taking Sn isotopes as examples. It is found that self-consistent treatment of the particle-particle residual interaction is essential to concentrate the IAS in a single peak for open-shell nuclei and the Coulomb exchange term is very important to predict the IAS energies. For the GTR, the isovector pairing can increase the calculated GTR energy, while the isoscalar pairing has an important influence on the low-lying tail of the GT transition. Furthermore, the QRPA approach is employed to predict nuclear $\beta$-decay half-lives. With an isospin-dependent pairing interaction in the isoscalar channel, the RHFB+QRPA approach almost completely reproduces the experimental $\beta$-decay half-lives for nuclei up to the Sn isotopes with half-lives smaller than one second. Large discrepancies are found for the Ni, Zn, and Ge isotopes with neutron number smaller than $50$, as well as the Sn isotopes with neutron number smaller than $82$. The potential reasons for these discrepancies are discussed in detail.

Nuclear β−-decay half-lives for and shell nuclei

In the present work we calculate the allowed -decay half-lives of nuclei with and N 50 systematically under the framework of the nuclear shell model. A recent study shows that some nuclei in this region belong to the island of inversion. We perform calculation for fp shell nuclei using the KB3G effective interaction. In the case of Ni, Cu, and Zn, we used the JUN45 effective interaction. Theoretical results of Q values, half-lives, excitation energies, logft values, and branching fractions are discussed and compared with the experimental data. In the Ni region, we also compared our calculated results with recent experimental data (Xu et al 2014 Phys. Rev. Lett. 113 032505). The present results agree with the experimental data of half-lives in comparison to QRPA.

Decay law of allowed and forbidden transitions in -decay half-lives

-beta-decay half-lives are not only important parameters for studying the structures and decay properties of the exotic nucleus far from stability, but also basic parameters for understanding the astrophysical phenomenon. Astrophysicists need exact data of -decay half-lives as input to build nucleosynthesis models for understanding the elements abundances of our universe and solar system. For nuclei far from stability, experimental synthesis and further measurements on their half-lives are rather difficult due to the rarity and radioactivity of target material for synthesizing these nuclei. In theoretical respect, although there are many models such as finite-range droplet model plus quasi-particle random-phase approximation (QRPA), microscopic density functional theory plus QRPA, Hatree-Fock-Bogoliubov theory plus QRPA, and shell model etc., it is still a challenge to calculate -decay half-lives in a reliable way for nuclei far from the -stable line, partly because of the intrinsic complexity of nuclear multi-body problem. In empirical respect, Sargent made an empirical study of -decay half-lives in 1933 and discovered a law which is consistent with the Fermi -decay theory proposed one year later. From then on, there have been a few parametric models based on some of real physical behaviors, which describe complex quantum many-body systems, such as the Kratz-Herrmann formula and the gross theory. Recently, Zhang et al. discovered an exponential law describing -decay half-lives and the nucleon number (Z,N) of parent nuclei far from the stable line. A formula is proposed to calculate the -decay half-lives of nuclei far from stability, which can describe experimental data reasonably well. However, the differences between allowed transitions and forbidden transitions are not fully considered in this formula. Zhang et al. used a set of parameters to describe both allowed transitions and forbidden transitions. In this paper, we consider the different -decay half-lives of allowed transitions and forbidden transitions, and propose an updated parameterization of this formula. A set of parameters is obtained through fitting experimental data of different kinds of transitions with a least-square method. With these new parameters, the theoretical calculation results are in good agreement with the experimental values. The calculation accuracy is improved compared with previous version. By comparison with the complicated and time-consuming microscopic calculation, the improved exponential formula can give the results of -decay half-lives for the allowed transitions and the forbidden transitions in an effective and reliable way. According to the updated formula, we predict half-lives of --decay half-lives of some unknown nuclei far from the -stable line. These predictions are very useful references for the experimental study of --decay of nuclei far from stability and for astrophysical applications.

β--decay half-lives for waiting point nucleiaround N=82

Based on the exponential formula of β--decay half-lives for nuclei far from stable line, the half-lives of nuclei around N=82 (R-process waiting point nuclei) are calculated. The results are compared with recent theoretical and experimental data. It is shown that compared with the complicated and time-consuming microscopic calculation, the exponential formula including the shell effect can give the results of β--decay half-lives for R-process waiting point nuclei quicker and better. The results can be used as reliable inputs for the network calculation for nuclei synthesis in cosmos.

Shell model calculations for the β−-decays of Z = 9–13 nuclei

We calculate the allowed β−-decay half-lives of nuclei with charge number Z = 9–13 and neutron number N ⩾ 18 under the framework of the nuclear shell model. Some nuclei in this region have been found to have intruder configurations in their ground and low excitation states. This property has great influence on the nuclear β-decay half-lives which has been confirmed by experiments. We used the WBMB interaction (Warburton et al 1990 Phys. Rev. C 41 1147), which is applicable to nuclei with active valence nucleons in both the (1s, 0d) and (0f, 1p) major shells, to describe or predict the β-decay properties of concerned nuclei. Theoretical results of Q values, half-lives, excitation energies, log ft values, branching fractions, and β-delayed one neutron emission probabilities are discussed and compared with experimental data.

Multiple CP non-conserving mechanisms of (ββ)0ν -decay and nuclei with largely different nuclear matrix elements

We investigate the possibility to discriminate between different pairs of CP non-conserving mechanisms inducing the neutrinoless double beta $\betabeta$-decay by using data on $\betabeta$-decay half-lives of nuclei with largely different nuclear matrix elements (NMEs). The mechanisms studied are: light Majorana neutrino exchange, heavy left-handed (LH) and heavy right-handed (RH) Majorana neutrino exchanges, lepton charge non-conserving couplings in SUSY theories with R-parity breaking giving rise to the "dominant gluino exchange" and the "squark-neutrino" mechanisms. The nuclei considered are $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te and $^{136}$Xe. Four sets of nuclear matrix elements (NMEs) of the decays of these five nuclei, derived within the Self-consistent Renormalized Quasiparticle Random Phase Approximation (SRQRPA), were employed in our analysis. While for each of the five single mechanisms discussed, the NMEs for $^{76}$Ge, $^{82}$Se, $^{100}$Mo and $^{130}$Te differ relatively little, the relative difference between the NMEs of any two nuclei not exceeding 10%, the NMEs for $^{136}Xe$ differ significantly from those of $^{76}$Ge, $^{82}Se$, $^{100}$Mo and $^{130}$Te, being by a factor $\sim (1.3 - 2.5)$ smaller. This allows, in principle, to draw conclusions about the pair of non-interfering (interfering) mechanisms possibly inducing the $\betabeta$-decay from data on the half-lives of $^{136}Xe$ and of at least one (two) more isotope(s) which can be, e.g., any of the four, $^{76}Ge$, $^{82}Se$, $^{100}Mo$ and $^{130}Te$. Depending on the sets of mechanisms considered, the conclusion can be independent of, or can depend on, the NMEs used in the analysis. The implications of the EXO lower bound on the half-life of $^{136}Xe$ for the problem studied are also exploited.

Alpha decay chains from superheavy nuclei

Magic islands for extra-stable nuclei in the midst of the sea of fission-instability were predicted to be around Z = 114 , 124 or, 126 with N = 184 , and Z = 120 , with N = 172 . Whether these fission-survived superheavy nuclei with high Z and N would live long enough for detection or, undergo α -decay in a very short time, remains an open question. α -decay half lives of nuclei with 130 ≥ Z ≥ 100 have been calculated in a WKB framework using density-dependent M3Y interaction with Q-values from different mass formulae. The results are in excellent agreement with the experimental data. Fission survived Sg nuclei with Z = 106 , N = 162 is predicted to have the highest α -decay half life (∼3.2 h) in the Z = 106 – 108 , N = 160 – 164 region called small island/peninsula. Superheavy nuclei with Z > 118 are found to have α -decay half lives of the order of microseconds or less.

Search for long lived heaviest nuclei beyond the valley of stability

The existence of long lived superheavy nuclei (SHN) is controlled mainly by spontaneous fission and \ensuremath{\alpha}-decay processes. According to microscopic nuclear theory, spherical shell effects at $Z=114$, 120, 126 and $N=184$ provide the extra stability to such SHN to have long enough lifetime to be observed. To investigate whether the so-called ``stability island'' could really exist around the above $Z$, $N$ values, the \ensuremath{\alpha}-decay half-lives along with the spontaneous fission and \ensuremath{\beta}-decay half-lives of such nuclei are studied. The \ensuremath{\alpha}-decay half-lives of SHN with $Z=102$--120 are calculated in a quantum tunneling model with DDM3Y effective nuclear interaction using ${Q}_{\ensuremath{\alpha}}$ values from three different mass formulas prescribed by Koura-Uno-Tachibana-Yamada (KUTY), Myers-Swiatecki (MS), and Muntian-Hofmann-Patyk-Sobiczewski (MMM). Calculation of spontaneous fission (SF) half-lives for the same SHN are carried out using a phenomenological formula and compared with SF half-lives predicted by Smolanczuk et al. A possible source of discrepancy between the calculated \ensuremath{\alpha}-decay half-lives of some nuclei and the experimental data of GSI, JINR-FLNR, RIKEN, is discussed. In the region of $Z=106$--108 with $N~$ 160--164, the \ensuremath{\beta}-stable SHN ${}_{106}^{268}{\text{Sg}}_{162}$ is predicted to have highest \ensuremath{\alpha}-decay half-life (${T}_{\ensuremath{\alpha}}~3.2$ h) using ${Q}_{\ensuremath{\alpha}}$ value from MMM. Interestingly, it is much greater than the recently measured ${T}_{\ensuremath{\alpha}}$ ($~22$ s) of deformed doubly magic ${}_{108}^{270}{\text{Hs}}_{162}$ nucleus. A few fission-survived long-lived SHN which are either \ensuremath{\beta}-stable or having large \ensuremath{\beta}-decay half-lives are predicted to exist near ${}^{294}{110}_{184}$, ${}^{293}{110}_{183}$, ${}^{296}{112}_{184}$, and ${}^{298}{114}_{184}$. These nuclei might decay predominantly through \ensuremath{\alpha}-particle emission.

Systematics of β−-decay half-lives of nuclei far from the β-stable line

Experimental data of nuclear β−-decay half-lives are systematically analyzed and investigated. We have discovered an exponential law between β−-decay half-life and the nucleon number (Z, N) of parent nuclei far from the β-stable line. Based on the exponential law, we have proposed new formulae in which the shell effects are included to describe the β−-decay half-lives of nuclei far from the β-stable line. Experimental data are well reproduced by the formula. In addition, we have systematically studied the shell effects on β−-decay half-lives for nuclei far from stability. The correlation between the major shell or subshell closures and β−-decay half-lives is discussed. This correlation provides the feasibility of obtaining information about the major shell or subshell closures of nuclei far from the β-stable line according to the exponential law.

New exponential law ofβ+-decay half-lives of nuclei far from β-stable line

Experimental data of the nuclear \ensuremath{\beta}-decay half-lives are systematically analyzed and investigated. We have discovered a new formula for the ${\ensuremath{\beta}}^{+}$-decay half-lives of nuclei far from the \ensuremath{\beta}-stable line. It is stated that the logarithm of the half-life of ${\ensuremath{\beta}}^{+}$ decay with a same order depends linearly on the neutron number of parent nuclei along any isotopic chain. This shows that there is a new exponential law between the half-life of the ${\ensuremath{\beta}}^{+}$ decay and the nucleon number ($Z,N$). The possible physics behind this new law is discussed. Experimental data are well reproduced by this simple and accurate formula with four parameters. This new formula can be used to predict the ${\ensuremath{\beta}}^{+}$-decay half-lives of nuclei far from stability. It is useful for experimental physicists to analyze the data of ${\ensuremath{\beta}}^{+}$ decay.

Systematical calculation of α decay half-lives by density-dependent cluster model

Systematical calculations on the α decay half-lives of nuclei are carried out in a new cluster model (density-dependent cluster model) where the effective potential between α cluster and daughter nucleus is obtained from the double folded integral of the renormalized M3Y nucleon–nucleon interaction with the density distributions of the α particle and the daughter nucleus. The model reproduces the experimental half-lives within a factor of 3 for many nuclei. The model also works well for new superheavy elements which are the current interests of nuclear physics and chemistry. This successful description of α decay data is due to the correct incorporation of the low-density behavior of the effective nucleon–nucleon interaction in the popular M3Y potential. The effective α-core potential of the density-dependent cluster model is analyzed and discussed.

Systematic study of nuclear beta decay.

\ensuremath{\beta}-decay properties of nuclei are studied in the framework of proton-neutron quasiparticle random-phase approximation with a schematic Gamow-Teller residual interaction. Particle-hole and particle-particle terms of the separable Gamow-Teller force are consistently included for both ${\mathrm{\ensuremath{\beta}}}^{+}$ and ${\mathrm{\ensuremath{\beta}}}^{\mathrm{\ensuremath{-}}}$ directions, and their strengths are fixed as smooth functions of mass number A of nuclei in such a way that the calculation reproduces observed \ensuremath{\beta}-decay properties of nuclei. Using the fixed interaction strengths, \ensuremath{\beta}-decay half-lives of nuclei up to A=150 are calculated, and generally good agreement with experiment is obtained. A schematic force which is relevant to the unique first-forbidden decay is also included in a similar way to the Gamow-Teller force, and its effects are studied. \textcopyright{} 1996 The American Physical Society.

Operation of the r-process and cosmochronology

The rapid neutron capture process produced about half of the heavy elements in nature beyond the Fe-peak. In the past quite a number of astrophysical sites have been suggested, but none of them has yet been uniquely identified. Without assuming a particular site or model, we deduce the conditions responsible for the production of r-process nuclei by making use of the following information: (1) the solar r-process abundances and (2) nuclear masses and beta decay half lives for nuclei far from stability - in particular experimental information near magic neutron numbers, which determines the shape of the r-process peaks. In addition, we review briefly galactic age determinations based on the long-lived r-process chronometer nuclei 232Th, 235U and 238U.

Beta decay half lives of nuclei far from stability

Beta decay half lives have been calculated microscopically for ∼6000 nuclei with Z=6–114 between the line of beta stability and the neutron drip line, with an accuracy considerably improved over earlier predictions. The calculated half lives are of particular importance for astrophysical applications.