Two-proton radioactivity of the excited state within the Gamow-like and modified Gamow-like models

In this study,we systematically investigated the two-proton(2p)radioactivity half-lives from the excited state of nuclei near the proton drip line within the Gamowlike model(GLM)and modified Gamow-like model(MGLM).The calculated results were highly consistent with the theoretical values obtained using the unified fission model[Chin.Phys.C 45,124105(2021)],effective liquid drop model,and generalized liquid drop model[Acta Phys.Sin 71,062301(2022)].Furthermore,utilizing the GLM and MGLM,we predicted the 2p radioactivity halflives from the excited state for some nuclei that are not yet available experimentally.Simultaneously,by analyzing the calculated results from these theoretical models,it was found that the half-lives are strongly dependent on Qand l.

Two-proton radioactivity from excited states of proton-rich nuclei within Coulomb and Proximity Potential Model

In the present work,we extend the Coulomb and Proximity Potential Model(CPPM)to study two-proton(2p)radioactivity from excited states while the proximity potential is chosen as AW95 proposed by Aage Withner in 1995.Demonstration reveals that the theoretical results acquired by CPPM exhibit a high level of consistency with prior theoretical models such as the unified fission model(UFM),generalized liquid-drop model(GLDM)and effective liquid-drop model(ELDM).Furthermore,within the CPPM,we predicted the half-lives of potential 2p radioactive nuclei for which experimental data are currently unavailable.The predicted results were then assessed,compared with UFM,ELDM and GLDM models,and examined in detail.

Systematic study of proton radioactivity half‑lives

In the present study,on the basis of the screened electrostatic effect of the Coulomb potential,we propose an improved Gamow model within the centrifugal potential in which there are only two adjustable parameters,i.e.,the screened parameters t and g,which represent the combined effect of the interaction potential and reduced mass of the emitted proton-daughter nucleus on the half-life of proton radioactivity in the overlapping region.Using this model,we systematically calculated the proton radioactivity half-lives of 31 spherical nuclei and 13 deformed nuclei and obtained corresponding root-mean-square deviations of 0.274 and 0.367,respectively.The relationship between the proton radioactivity half-life of 177Tlm and the corresponding angular momentum l removed by the emitted proton is also discussed.In addition,we used the proposed model to predict the proton radioactivity half-lives of 18 nuclei whose proton radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.For comparison,we used the universal decay law of proton radioactivity proposed by Qi et al.(Phys Rev C 85:011303,2012.https://doi.org/10.1103/PhysR evC.85.011303),and the new Geiger–Nuttall law of proton radioactivity proposed by Chen et al.(Eur Phys J 55:214,2019.https://doi.org/10.1140/epja/i2019-12927-7).

Structure the radiation dose curve of continuous slope

The traditional interpolation and fitting can not restore the radiation dose curve with the radiation source characteristic. Therefore, during the reduction the field of one dimensional radiation dose, the mathematical structure method was used to restore the curve with the dose value of the radioactive source is inversely proportional to the square of the distance from the radioactive source.

Research on the Distribution of Major Metal Elements in the Typical Landslide Soil of the Three Gorges Reservoir Area

In this article, a laboratory-built experimental system-laser-induced breakdown spec-troscopy （LIBS）, is used to measure soil samples. It explores landslides band soil of five typical land-slides in Xiangxi （香溪） River Section of the Three Gorges Reservoir area, which include Bazimen （八字门） landslide, Baijiabao （白家堡） landslide, Jiajiadian （贾家店） landslide, Sixiangxi （泗乡溪）landslide and an unnamed landslide that has already slipped. Soil samples of the five landslides are taken in dif-ferent latitudes, and in relatively consistent altitude. Through experimental measurement, the authors get spectrum of those soil samples, and then do qualitative and quantitative analyses of elements （Mg, Si, K, Al, etc.） in them. The authors conclude that main metal elements in the soil change according to different longitudes and latitudes, which opens up a new way of thinking for the quantitative analysis of the function of soil and water, and for the establishment of relations between chemical environment factors and soil engineering mechanics effects.

Systematic study of α preformation probability of nuclear isomeric and ground states

In this paper, based on the two-potential approach combining with the isospin dependent nuclear potential, we systematically compare the α preformation probabilities of odd-A nuclei between nuclear isomeric states and ground states. The results indicate that during the process of α particle preforming, the low lying nuclear isomeric states are similar to ground states. Meanwhile, in the framework of single nucleon energy level structure, we find that for nuclei with nucleon number below the magic numbers, the α preformation probabilities of high-spin states seem to be larger than low ones. For nuclei with nucleon number above the magic numbers, the α preformation probabilities of isomeric states are larger than those of ground states.

Systematic study of proton radioactivity half-lives based on the relationship between Skyrme-Hartree-Fock and the macroscopic quantities of nuclear matter

In this study,we systematically investigate the proton radioactivity half-lives of 33 spherical nuclei based on the relationship between Skyrme parameters and the macroscopic quantities of nuclear matter.Using the two-potential approach with the spherical Skyrme-Hartree-Fock model,the correlation between proton radioactivity half-life and the macroscopic quantities is analyzed.Moreover,we obtain a new Skyrme parameter set by fitting the two most weighted macroscopic quantities.Compared with the Skyrme parameters MSLO and the theoretical model of proton radioactivity UDLP,the theoretical proton radioactivity half-life calculated using the new Skyrme parameter set can better reproduce the experimental data.

Systematic study of two-proton radioactivity half-lives using the two-potential and Skyrme-Hartree-Fock approaches

In this work,we systematically study the two-proton(2_(p))radioactivity half-lives using the two-potential approach,and the nuclear potential is obtained using the Skyrme-Hartree-Fock approach and the Skyrme effective interaction of SLy8.For true 2_(p) radioactivity(Q2_(p)>0 and Q_(p)<0,where Q_(p) and Q2_(p) are the released energies of the one-proton and two-proton radioactivity,respectively),the standard deviation between the experimental half-lives and our theoretical calculations is 0.701.In addition,we extend this model to predict the half-lives of 15 possible 2_(p) radioactivity candidates with Q2_(p)>0 obtained from the evaluated atomic mass table AME2016.The calcu-lated results indicate a clear linear relationship between the logarithmic 2_(p) radioactivity half-lives(logio10T_(1/2))and coulomb parameters[(Z_(d)^(0.8)+l^(0.25))Q_(2_(p))^(-1/2)]considering the effect of orbital angular momentum proposed by Liu et al.[Chin.Phys.C 45,024108(2021)].For comparison,the generalized liquid drop model(GLDM),effective liquid drop model(ELDM),and Gamow-like model are also used.Our predicted results are consistent with those obtained using other relevant models.

CONVERGENT AND DIVERGENT SOLUTIONS OF TWO-DIMENSIONAL NONLINEAR DIFFERENCE SYSTEM

In this paper, we are concerned with the existence of convergent or divergent solutions of two-dimensional nonlinear difference system of the form{xn＋1=αnxn＋bnf（yn）,yn=cnyn-1＋dng（xn）.We＇ classify their solutions according to asymptotic behavior and give some sufficient and necessary conditions for the existence of solutions of such classes by using the method of the fixed point theorem. We also give an example and show how the results can be applied to certain difference systems.

NECESSARY AND SUFFICIENT CONDITION FOR OSCILLATION OF IMPULSIVE DELAY HYPERBOLIC DIFFERENTIAL SYSTEM

This paper deals with the oscillation problems of impulsive delay hyperbolic system. A necessary and sufficient condition is obtained.

Design anchoring system

The establishment of transmission node for offshore observation network related information on China＇ s marine transport is of great significance and use, to ensure the safe operation of the transmission node in harsh natural conditions, the key problem is the design of the mooring system. In this paper, according to the stress analysis of the mooring system, the equilibrium equation is established to calculate the inclined angle, the shape of the anchor cable, the depth of the draft and the area of the floating.

Inferring the spin distribution of binary black holes using deep learning

The spin characteristics of black holes offer valuable insights into the evolutionary pathways of their progenitor stars.This is crucial for understanding the broader population properties of black holes.Traditional hierarchical Bayesian inference techniques employed to discern these properties often demand substantial time,and consensus regarding the spin distribution of binary black hole(BBH)systems remains elusive.In this study,leveraging observations from GWTC-3,we adopted a machine learning approach to infer the spin distribution of black holes within BBH systems.Specifically,we developed a deep neural network(DNN)and trained it using data generated from a Beta distribution.Our training strategy,involving the segregation of data into 10 bins,not only expedites model training but also enhances the versatility and adaptability of the DNN to accommodate the growing volume of gravitational wave observations.Utilizing Monte Carlo-bootstrap(MC-bootstrap)to generate observation-simulated samples,we derived spin distribution parameters:α=1.3_(-0.18)^(+0.25),β=1.70_(-0.29)^(+0.24)for the larger BH sample and α=1.37_(-0.20)^(+0.31),β=1.63_(-0.20)^(+0.30) for the smaller BH sample.Within our constraints,the distributions of component spin magnitudes suggest the likelihood of both black holes in the BBH merger possessing non-zero spin.

Systematic study of cluster radioactivity in trans-lead nuclei with various versions of proximity potential formalisms

In this study,based on the framework of the Coulomb and proximity potential model(CPPM),we systematically investigate the cluster radioactivity half-lives of 26 trans-lead nuclei by considering the cluster preformation probability,which possesses a simple mass dependence on the emitted cluster according to R.Blendowske and H.Walliser[Phys.Rev.Lett.61,1930(1988)].Moreover,we investigate 28 different versions of the proximity potential formalisms,which are the most complete known proximity potential formalisms proposed to describe proton radioactivity,two-proton radioactivity,αdecay,heavy-ion radioactivity,quasi-elastic scattering,fusion reactions,and other applications.The calculated results show that the modified forms of proximity potential 1977,denoted as Prox.77-12,and proximity potential 1981,denoted as Prox.81,are the most appropriate proximity potential formalisms for the study of cluster radioactivity,as the root-mean-square deviation between experimental data and relevant theoretical results obtained is the least;both values are 0.681.For comparison,the universal decay law(UDL)proposed by Qi et al.[Phys.Rev.C 80,044326(2009)],unified formula of half-lives forαdecay and cluster radioactivity proposed by Ni et al.[Phys.Rev.C 78,044310(2008)],and scaling law(SL)in cluster radioactivity proposed by Horoi et al.[J.Phys.G 30,945(2004)]are also used.In addition,utilizing CPPM with Prox.77-12,Prox.77-1,Prox.77-2,and Prox.81,we predict the half-lives of 51 potential cluster radioactive candidates whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.The predicted results are in the same order of magnitude as those obtained using the compared semi-empirical and/or empirical formulae.At the same time,the competition betweenαdecay and cluster radioactivity of these predicted nuclei is discussed.By comparing the half-lives,this study reveals thatαdecay predominates.

EXISTENCE FOR PERIODIC BOUNDARY VALUE PROBLEM OF FIRST-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, by means of iterative analysis, the existence for periodic boundary value problem of first-order integro-differential differential equations are considered. Some new results are obtained.

TRIPLE POSITIVE SOLUTIONS TO A CLASS OF NONLINEAR BEAM EQUATIONS

In this paper, an existence criterion of triple positive solutions to a class of nonlinear beam equations is established using the Leggett-Williams fixed point theorem.An example is also included to demonstrate the result. The interesting point is that the nonlinear term is involved with all low-level derivatives.

MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF INTEGRAL BOUNDARY VALUE PROBLEM

In this paper,the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem{u(4)(t)+βu″(t)-au(t)=f(t,u(t),u″(t)),t∈(0,1),u″(0)=u″(1)=0,u(0)=0,u(1)=(1/λ2-1/λ1)∫01q(s)f(s,u(s),u″(s))ds with two parameters are established by using the Guo-Krasnoselskii's fixedpoint theorem,where f∈C([0,1]×[0,+∞)×(-∞,0],[0,+∞)),q(t)∈L1[0,1]is nonnegative,α,β∈R and satisfyβ<2π2,α>0,α/π4+β/π2<1,λ1,2=(-β+√β^2+4a)/2.The corresponding examples are raised to demonstrate the results we obtained.

α decay properties of ^(296)Og within the two-potential approach

The present work is a continuation of our previous paper[J.-G. Deng, et al., Chin. Phys. C, 41：124109 （2017）]. In the present work, the α decay half-life of the unknown nucleus 296Og is predicted within the two-potential approach and the hindrance factors of all 20 even-even nuclei in the same region as 296Og, i.e. proton number 82 〈 Z 〈 126 and neutron number 152 〈 N 〈 184, from 250Cm to 294Og, are extracted. The prediction is 1.09 ms within a factor of 5.12. In addition, based on the latest experimental data, a new set of parameters of α decay hindrance factors for the even-even nuclei in this region, considering the shell effect and proton-neutron interaction, are obtained.

Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei

In the present work,based on the Wentzel-Kramers-Brillouin(WKB)theory,considering the cluster preformation probability(Pc),we systematically investigate the cluster radioactivity half-lives of 22 trans-lead nuclei ranging from221Fr to242Cm.When the mass number of the emitted cluster Ac<28,Pcis obtained by the exponential relationship of Pcto theαdecay preformation probability(Pα)proposed by R.Blendowskeis et al.[Phys.Rev.Lett.61,1930(1988)],while Pαis calculated through the cluster-formation model(CFM).When Ac≥28,Pcis calculated through the charge-number dependence of Pcon the decay products proposed by Ren et al.[Phys.Rev.C70,034304(2004)].The half-lives of cluster radioactivity have been calculated by the density-dependent cluster model[Phys.Rev.C 70,034304(2004)]and by the unified formula of half-lives for alpha decay and cluster radioactivity[Phys.Rev.C 78,044310(2008)].For comparison,a universal decay law(UDL)proposed by Qi et al.[Phys.Rev.C 80,044326(2009)],a semi-empirical model for bothαdecay and cluster radioactivity proposed by Santhosh[J.Phys.G:Nucl.Part.Phys.35,085102(2008)],and a unified formula of half-lives for alpha decay and cluster radioactivity[Phys.Rev.C 78,044310(2008)]are also used.The calculated results of our work,Ni’s formula,and the UDL can well reproduce the experimental data and are better than those of Santhosh’s model.In addition,we extend this model to predict the half-lives for 51 nuclei,whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.

Systematic study of two-proton radioactivity with a screened electrostatic barrier

In this study,a phenomenological model is proposed based on Wentzel-Kramers-Brillouin(WKB)theory and applied to investigate the two-proton(2p)radioactive half-lives of nuclei near or beyond the proton drip line.The total diproton-daughter nucleus interaction potential is composed of the Hulthen-type electrostatic term and the centrifugal term.The calculated 2p radioactive half-lives can accurately reproduce the existing 10 experimental datasets of five true 2p radioactive nuclei withσ=0.736.In addition,we extend this model to predict the half-lives of possible 2p radioactive nuclei whose 2p radioactivity is energetically allowed or observed but not yet quantified in NUBASE2016.The predicted results are in agreement with those obtained using the Gamow-like model,generalized liquid drop model,Sreeja formula,and Liu formula.

Systematic study on α-decay half-lives of uranium isotopes with a screened electrostatic barrier

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 a 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 S_(α) is almost the same for uranium isotopes with the same l.