Two-proton Separation Energies Research Articles

Structural and decay properties of even–even trans-lead nuclei

A systematic study of the ground-state properties of even–even Po, Rn, Ra and Th isotopes is conducted using the self-consistent Skyrme-Hartree–Fock–Bogoliubov (HFB) theory. Different Skyrme interactions are employed in the study. The bulk properties such as binding energy, two-neutron separation energies, two-proton separation energies and neutron skin thickness are investigated. The obtained results from the Skyrme-HFB formalism are compared with the calculated results from the Finite Range Droplet Model (FRDM) and the available experimental data. Our theoretical values were found to be consistent with their counterparts. In addition, the density-dependent cluster model is utilized to estimate [Formula: see text]-decay half-lives. A good agreement is achieved between the calculated results and the recent experimental data.

Properties and synthesis of the superheavy nucleus Fl114298

The one-nucleon separation energy ${S}_{n}$, two-nucleon separation energy ${S}_{2n}$, one-proton separation energy ${S}_{p}$, two-proton separation energy ${S}_{2p}, \ensuremath{\alpha}$-decay energy ${Q}_{\ensuremath{\alpha}}, \ensuremath{\alpha}$-decay half-life and spontaneous fission half-life of $Z=114$ isotopes and $N=184$ isotones are calculated by the finite-range droplet model (FRDM2012). It is found that $N=184$ is a neutron magic number, and $Z=114$ is a proton magic number. The properties of $Z=114$ isotopes and $N=184$ isotones provide a vital signal that $_{114}^{298}\mathrm{Fl}$ may be a spherical double-magic nucleus and also the center of the stability island of superheavy nuclei. Based on this, we began to investigate the optimal conditions for the synthesis of superheavy nucleus $_{114}^{298}\mathrm{Fl}$ within the dinuclear system model. To produce such neutron-rich compound nucleus, we consider using the extremely neutron-rich radioactive beams to bombard actinide targets. The evaporation residue cross section of superheavy nuclei synthesized by radioactive beam is analyzed in detail. Finally, we suggest that for the synthesis of $_{114}^{298}\mathrm{Fl}$, the radioactive beam-induced fusion reaction $^{64}\mathrm{Ti}+^{238}\mathrm{U}$ in the $4n$ evaporation channel with an excitation energy of 43 MeV is optimal.

Shell-model study on properties of proton dripline nuclides with Z, N = 30–50 including uncertainty analysis * *Supported by the National Natural Science Foundation of China (11775316, 11825504, 11961141004), the Tip-top Scientific and Technical Innovative Youth Talents of Guangdong special support program (2016TQ03N575), the Guangdong Major Project of Basic and Applied Basic Research (2021B0301030006)

The binding and proton separation energies of nuclides with are investigated based on the shell model, with an uncertainty analysis via statistical methods. Several formulas are used to obtain the binding and proton separation energies according to shell-model calculations. The non-parametric bootstrap method is applied to establish an uncertainty decomposition and recomposition framework. Moreover, this is used to estimate the stability of proton(s) emission for each nuclide. Two formulas for calculating the binding energies with a systematic uncertainty of MeV are proposed, and a reliable extrapolation ability is examined. These binding energy formulas deduce similar forms for their respective and energies, which predict the extension of the nuclear boundary of this region. A good description of the binding and proton separation energies is provided. The one- and two-proton separation energies and partial half-lives of proton emission are predicted, thus revealing a new dripline. Furthermore, there are 30 unstable nuclides predicted to be bound against proton(s)-emission. These nuclear properties will be useful in nuclear astrophysics.

Mass relations of mirror nuclei in terms of Coulomb energies based on relativistic continuum Hartree-Bogoliubov calculations

In this paper we study mass relations of mirror nuclei in terms of Coulomb energies calculated by the microscopic relativistic continuum Hartree-Bogoliubov theory. An additional term corresponding to the Nolen-Schiffer anomaly is assumed to take the same form as the well-known empirical formula. The resultant root-mean-square deviations of these mass relations are typically less than 100 keV. Based on these relations, 61 unknown proton-rich nuclear masses are predicted for $18\ensuremath{\leqslant}A\ensuremath{\leqslant}87$ with positive two-proton separation energies and are tabulated in the Supplemental Material of this paper.

Isobaric-multiplet mass equation in a macroscopic-microscopic approach

We study the a, b and c coefficients of the isobaric-multiplet mass equation using a macroscopic-microscopic approach developed by P. Moeller and his collaborators in ADNDT 59, 185 (1995) and ADNDT 109-110, 1 (2016). We show that already the macroscopic part of the finite-range liquid-drop model (FRLDM) describes the general trend of the a and b coefficients relatively well, while the staggering behavior of b coefficients for doublets and quartets can be understood in terms of the difference of average proton and neutron pairing energies. The sets of isobaric masses, predicted by the full macroscopic-microscopic approaches, are used to explore the general trends of IMME coefficients up to A=100. We conclude that while the agreement for a coefficients is quite satisfactory, the global approaches have less sensitivity to predict the staggering pattern observed for b coefficients of doublets and quartets. The best set of theoretical b coefficients for multiplets up to about A=100 is used to predict masses of proton-rich nuclei based on the known experimental masses of neutron-rich mirror partners, and subsequently to investigate their one- and two-proton separation energies. The estimated position of the proton-drip line is in fair agreement with known experimental data. These masses are important for simulations of the astrophysical rp-process.

Beyond the proton drip line: Bayesian analysis of proton-emitting nuclei

The limits of the nuclear landscape are determined by nuclear binding energies. Beyond the proton drip lines, where the separation energy becomes negative, there is not enough binding energy to prevent protons from escaping the nucleus. Predicting properties of unstable nuclear states in the vast territory of proton emitters poses an appreciable challenge for nuclear theory as it often involves far extrapolations. In addition, significant discrepancies between nuclear models in the proton-rich territory call for quantified predictions. With the help of Bayesian methodology, we mix a family of nuclear mass models corrected with statistical emulators trained on the experimental mass measurements, in the proton-rich region of the nuclear chart. Separation energies were computed within nuclear density functional theory using several Skyrme and Gogny energy density functionals. We also considered mass predictions based on two models used in astrophysical studies. Quantified predictions were obtained for each model using Bayesian Gaussian processes trained on separation-energy residuals and combined via Bayesian model averaging. We obtained a good agreement between averaged predictions of statistically corrected models and experiment. In particular, we quantified model results for one- and two-proton separation energies and derived probabilities of proton emission. This information enabled us to produce a quantified landscape of proton-rich nuclei. The most promising candidates for two-proton decay studies have been identified. The methodology used in this work has broad applications to model-based extrapolations of various nuclear observables. It also provides a reliable uncertainty quantification of theoretical predictions.

Proton drip line evaluation by complementing the Finite Range Droplet Model with neural networks

We evaluate the location of the proton drip line in the regions 31≤Z≤49 and 73≤Z≤91 based on the one- and two-proton separation energies predicted by our latest Hybrid Mass Model. The latter is constructed by complementing the mass-excess values ΔM predicted by the Finite Range Droplet Model (FRDM) of Moeller et al. with a neural network model trained to predict the differences ΔMexp − ΔMFRDM between these values and the experimental mass-excess values published in the 2003 Atomic Mass Evaluation AME03.

PROTON DRIPLINE FOR ISOTONE N = 18, 20, AND 22 USING MODIFIED RELATIVISTIC MEAN FIELD (MRMF) MODEL

Determining the position of one- and two-proton dripline for isotone of N = 18, 20, and 22 has been studied through Modified Relativistic Mean Field (MRMF). The model exemplifies three impacts, namely isovector-isoscalar coupling, tensors, and electromagnetic exchange through five parameter set variations. The position of one- and two-proton dripline for the isotones is predicted by applying two methods, which are two-proton separation energy, and Fermi energy. The research shows that the prediction of one- and two-proton dripline for isotone of N = 18, and N = 20 is positioned at Z = 22 and Z = 26 consecutively. Then, the prediction of one- and two-proton dripline for isotone of N = 22 has two positions, Z = 26 and Z = 28. The calculation result indicates that the position prediction for isotone of N = 18, N = 20, and N = 22 is following the research result conducted by Nazarewicz with RMF+NLSH model [1]. Meanwhile, isovector-isoscalar coupling, tensors, and electromagnetic exchange do not affect massively for the position prediction of two-proton dripline. However, the three methods affect one-proton dripline.

Nuclear properties for astrophysical and radioactive-ion-beam applications (II)

We tabulate the ground-state odd-proton and odd-neutron spins and parities, proton and neutron pairing gaps, one- and two-neutron separation energies, quantities related to β-delayed one- and two-neutron emission probabilities, average energy and average number of emitted neutrons, β-decay energy release and half-life with respect to Gamow–Teller decay with a phenomenological treatment of first-forbidden decays, one- and two-proton separation energies, and α-decay energy release and half-life for 9318 nuclei ranging from 16O to 339136 and extending from the proton drip line to the neutron drip line. This paper is a new and improved version of Atomic Data And Nuclear Data Tables [66 131 (1997)]. The starting point of our present work is the new study (FRDM(2012)) of nuclear ground-state masses and deformations based on the finite-range droplet model and folded-Yukawa single-particle potential published in a previous issue of Atomic Data And Nuclear Data Tables [109–110, 1 (2016)]. The β-delayed neutron-emission probabilities and Gamow–Teller β-decay rates are obtained from a quasi-particle random-phase approximation with single-particle levels and wave functions at the calculated nuclear ground-state shapes as input quantities. A development since 1997 is we now use a Hauser–Feshbach approach to account for (n, γ) competition and treat first-forbidden decay in a phenomenological approach.

Minimal nuclear energy density functional

We present a minimal nuclear energy density functional (NEDF) called "SeaLL1" that has the smallest number of possible phenomenological parameters to date. SeaLL1 is defined by 7 significant phenomenological parameters, each related to a specific nuclear property. It describes the nuclear masses of even-even nuclei with a mean energy error of 0.97 MeV and a standard deviation 1.46 MeV, two-neutron and two-proton separation energies with r.m.s. errors of 0.69 MeV and 0.59 MeV respectively, and the charge radii of 345 even-even nuclei with a mean error $\epsilon_r=$0.022 fm and a standard deviation $\sigma_r=$0.025 fm. SeaLL1 incorporates constraints on the EoS of pure neutron matter from quantum Monte Carlo calculations with chiral effective field theory two-body (NN) interactions at N3LO level and three-body (NNN) interactions at the N2LO level. Two of the seven parameters are related to the saturation density and the energy per particle of the homogeneous symmetric nuclear matter, one is related to the nuclear surface tension, two are related to the symmetry energy and its density dependence, one is related to the strength of the spin-orbit interaction, and one is the coupling constant of the pairing interaction. We identify additional phenomenological parameters that have little effect on ground-state properties, but can be used to fine-tune features such as the Thomas-Reiche-Kuhn sum rule, the excitation energy of the giant dipole and Gamow-Teller resonances, the static dipole electric polarizability, and the neutron skin thickness.

Stability of super heavy nuclei associated with the updated nuclear data**Supported by National Natural Science Foundation of China (11675066, 11647306), Fundamental Research Funds for the Central Universities (lzujbky-2017-ot04) and Feitian Scholar Project of Gansu province

The stability of super heavy nuclei (SHN) from Z=104 to Z=126 is analyzed systematically, associated with the following theoretical mass tables: FRDM2012 [At. Data Nucl. Data Tables 109-110(2016)], WS2010 [Phys. Rev. C 82, 044304(2010)], WS-LZ-RBF [J. Phys. G: Nucl. Part. Phys. 42, 095107(2015)] and the updated experimental data AME2016 [Chinese Physics C 41, 040002(2017)]. The nucleus with the biggest mean binding energy in each isotopic chain shows systematic regular behavior, indicating that the mean binding energy is a good criterion to classify SHN by their stability. Based on binding energy, the α-decay energy Qα, two-proton separation energy S2p, and two-neutron separation energy S2n are extracted and analyzed. It is found that N=152 and N=162 are sub-magic numbers, N = 184 is a neutron magic number, and Z = 114 is a proton magic number, which may provide useful information for the synthesis and identification of SHN.

Improved mass extrapolations by the Garvey–Kelson relations

In this paper we extrapolate binding energies by using the Garvey–Kelson (GK) mass relations, in each of which four binding energies are replaced by two-neutron separation energies, two-proton separation energies, α decay energies and (or) double-β decay energies. Prior to the extrapolation, these separation energies are obtained by using the ‘–’ relations suggested in a previous work (Phys. Rev. C 90 064304). To reduce large uncertainties of experimental data used in the extrapolation, we perform uncertainty analysis and replace a few experimental data with theoretical values having smaller uncertainties. In comparison with the root mean squared deviation (RMSD) of the extrapolation from the AME1995 (or AME2003) to the AME2012 by using the original GK relations, the RMSD of the extrapolation from the above modified database by using our approach is reduced by 339 (or 57) keV. At last we tabulate our predicted values of unknown binding energies based on the AME2012 in the Supplemental Material of this paper.

Isospin-symmetry breaking in superallowed Fermi β-decay due to isospin-nonconserving forces

We investigate isospin-symmetry breaking effects in the sd-shell region with large-scale shell-model calculations, aiming to understand the recent anomalies observed in superallowed Fermi β-decay. We begin with calculations of Coulomb displacement energies (CDE's) and triplet displacement energies (TDE's) by adding the T=1,J=0 isospin nonconserving (INC) interaction into the usual isospin-invariant Hamiltonian. It is found that CDE's and TDE's can be systematically described with high accuracy. A total number of 122 one- and two-proton separation energies are predicted accordingly, and locations of the proton drip-line and candidates for proton-emitters are thereby suggested. However, attempt to explain the anomalies in the superallowed Fermi β-decay fails because these well-fitted T=1,J=0 INC interactions are found no effects on the nuclear matrix elements. It is demonstrated that the observed large isospin-breaking correction in the 32Cl β-decay, the large isospin-mixing in the 31Cl β-decay, and the small isospin-mixing in the 23Al β-decay can be consistently understood by introducing additional T=1,J=2 INC interactions related to the s1/2 orbit.

Mass excesses of Si21–24 and S24

I have used a recent parametrization of mirror energy differences to predict two-proton separation energies for $^{21\ensuremath{-}24}\mathrm{Si}$ and $^{24}\mathrm{S}$. Results are in good agreement with experimental values for $^{22,24}\mathrm{Si}$.

α -decay chains of the superheavy nuclei Rg255–350

The decay modes and half-lives of 96 isotopes of the superheavy element roentgenium (Rg) within the range of $255\ensuremath{\le}A\ensuremath{\le}350$ come under investigation in the present paper. The isotopes which lie beyond the proton drip line are identified by calculating the one-proton and two-proton separation energies. The $\ensuremath{\alpha}$-decay half-lives are calculated using the Coulomb and proximity potential model for deformed nuclei (CPPMDN). For a theoretical comparison the $\ensuremath{\alpha}$ half-lives are also evaluated using the Viola-Seaborg semiempirical relation, the universal curve of Poenaru et al., the analytical formula of Royer, and the universal decay law of Qi et al. Spontaneous fission half-lives are computed with the shell-effect-dependent formula of Santhosh and Nithya and the semiempirical formula of Xu et al. The decay modes are predicted by comparing the $\ensuremath{\alpha}$-decay half-lives within the CPPMDN with the corresponding spontaneous fission half-lives computed by the shell-effect-dependent formula of Santhosh and Nithya. In our paper it is seen that the isotopes $^{255\text{--}271,273}\mathrm{Rg}$ lie beyond the proton drip line and hence decay through proton emission. The isotopes $^{272,274\text{--}277}\mathrm{Rg}$ exhibit long $\ensuremath{\alpha}$ chains. Three $\ensuremath{\alpha}$ chains are predicted from the isotopes $^{278\text{--}282}\mathrm{Rg}$. The isotopes $^{283\text{--}345}\mathrm{Rg}$ decay through spontaneous fission. The isotopes $^{346\text{--}350}\mathrm{Rg}$ are found to be stable against $\ensuremath{\alpha}$ decay. The theoretical results are compared with the available experimental results and are seen to be matching well. We hope that our predictions will be useful in future experimental investigations.

Predictions on the modes of decay of even [formula omitted] superheavy isotopes within the range [formula omitted

The decay modes and half lives of all the even Z isotopes of superheavy elements within the range 104≤Z≤136 have been predicted by comparing the alpha decay half-lives with the spontaneous fission half-lives. The Coulomb and proximity potential model for deformed nuclei (CPPMDN) and the shell-effect-dependent formula of Santhosh et al. are used to calculate the alpha half-lives and spontaneous fission half-lives respectively. For theoretical comparison the alpha decay half-lives are also calculated using Coulomb and proximity potential model (CPPM), the Viola–Seaborg–Sobiczewski semi-empirical (VSS) relation, the universal (UNIV) curve of Poenaru et al., the analytical formula of Royer and the universal decay law (UDL) of Qi et al. Another tool used for the evaluation of spontaneous fission half-lives is the semi-empirical formula of Xu et al. The nuclei with alpha decay half-lives less than spontaneous fission half-lives will survive fission and hence decay through alpha emission. The predicted half lives and decay modes are compared with the available experimental results. The one-proton and two-proton separation energies of all the isotopes are calculated to find nuclei which lie beyond the proton drip line. Among 1119 even Z nuclei within the range 104≤Z≤136, 164 nuclei show sequential alpha emission followed by subsequent spontaneous fission. Since the isotopes decay through alpha decay chain and the half-lives are in measurable range, these isotopes are predicted to be synthesized and detected in laboratory via alpha decay. 2 nuclei will decay by alpha decay followed by proton emission, 54 nuclei show full alpha chains, 642 nuclei will decay through spontaneous fission, 166 nuclei exhibit proton decay and 91 isotopes are found to be stable against alpha decay. All the isotopes are tabulated according to their decay modes. The study is intended to enhance further experimental investigations in superheavy region.

Observation of β-delayed two-proton emission in the decay of 22Si

The decay of the lightest nucleus with Tz=−3 , 22 Si, was studied by a silicon array. A charged-particle group at 5600 (70) keV in the decay-energy spectrum was identified experimentally as β -delayed two-proton emission from the isobaric analog state (IAS) of 22 Al. Experimental results of the IAS fed by a superallowed Fermi transition were compared with our large-scale shell-model calculations. The ground-state mass of 22 Si was obtained indirectly in the experiment for the first time. Two-proton separation energy for 22 Si is deduced to be −108 (125) keV, which indicates that it is a very marginal candidate for two-proton ground-state emission.

Search of islands of stability for hypothetical superheavy nuclei using covariant density functional theory

A systematic search for the location of islands of stability has been performed for the proton number $100\le Z\le 220$ and the neutron number $Z+30\le N\le 2Z+30$ using covariant density functional theory (CDFT), a relativistic Hartree-Bogoliubov (RHB) formalism with separable pairing, for two different force parameters, DD-ME2 and NL3*. Locations of the islands of stability are identified by analysis of the two-neutron and two-proton separation energy, two-nucleon shell gaps, vanishing neutron and proton pairing gap, energy surface, and the single particle states. The results show that beyond $^{292}120$ only Z = 154 and N $>$ 220 can be a center of a new island of stability.

Exploringsd-shell nuclei from two- and three-nucleon interactions with realistic saturation properties

We study ground- and excited-state properties of all sd-shell nuclei with neutron and proton numbers 8 <= N,Z <= 20, based on a set of low-resolution two- and three-nucleon interactions that predict realistic saturation properties of nuclear matter. We focus on estimating the theoretical uncertainties due to variation of the resolution scale, the low-energy couplings, as well as from the many-body method. The experimental two-neutron and two-proton separation energies are reasonably well reproduced, with an uncertainty range of about 5 MeV. The first excited 2+ energies also show overall agreement, with a more narrow uncertainty range of about 500 keV. In most cases, this range is dominated by the uncertainties in the Hamiltonian.

Predictions for the α-decay chains ofZ=120superheavy nuclei in the range272≤A≤319

The predictions on the $\ensuremath{\alpha}$-decay chains of the isotopes of the superheavy nuclei with $Z=120$ in the range $272\ensuremath{\le}A\ensuremath{\le}319$ have been done within the Coulomb and proximity potential model for deformed nuclei. A comparison of our calculated $\ensuremath{\alpha}$ half-lives with the values computed using the Viola-Seaborg [J. Inorg. Nucl. Chem. 28, 741 (1966)] systematic, the universal curve of Poenaru et al. [Phys. Rev. C 74, 014312 (2006)], and the analytical formulas of Royer [J. Phys. G: Nucl. Part. Phys. 26, 1149 (2000)] show good agreement with each other. An extensive study on the spontaneous fission half-lives of all the isotopes under study has been performed to identify the mode of decay of these isotopes. The study reveals that the $\ensuremath{\alpha}$-decay half-lives and the mode of decay of the isotopes of $^{298,299}120$, which are evaluated by using our formalisms, agree well with the experimental observations of Oganessian et al. [Phys. Rev. C 79, 024603 (2009)]. Our study on the isotopes of $Z=120$ predicts that the $\ensuremath{\alpha}$ decay restricts within the range $277\ensuremath{\le}A\ensuremath{\le}308$ as those isotopes with $A\ensuremath{\le}276$ and those nuclei with $A \ensuremath{\ge}$ 309 do not survive fission. We have also forecasted the mode of decay of $^{288\ensuremath{-}302}120$ superheavy nuclei as six consistent $\ensuremath{\alpha}$ chains from the nuclei of $^{288,289,291\ensuremath{-}295}120$, seven consistent $\ensuremath{\alpha}$ chains from the nuclei of $^{290}120$, five consistent $\ensuremath{\alpha}$ chains from the nuclei of $^{296,297}120$, and three consistent $\ensuremath{\alpha}$ chains from the nuclei of $^{300\ensuremath{-}302}120$, which could be of great interest to the experimentalists. The one-proton and two-proton separation energy calculations on $^{272\ensuremath{-}319}120$ superheavy nuclei have revealed that the isotopes spanning the range $273\ensuremath{\le}A\ensuremath{\le}291$ may be considered to be the probable proton emitters.