Alpha decay half-lives of heavy nuclei within a generalized liquid drop model

Theoretical α-decay half-lives of the heaviest nuclei are calculated using the experimental Qα value. The barriers in the quasi-molecular shape path is determined within a Generalized Liquid Drop Model (GLDM) and the WKB approximation is used. The results are compared with calculations using the DensityDependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulae. The calculations provide consistent estimates for the half-lives of the α decay chains of these superheavy elements. The experimental data stand between the GLDM calculations and VSS ones in the most time.     

理论预测超重核274-291Cn和266-287Ds的衰变模式

自发裂变和α衰变是影响超重核稳定性的两个主要因素。为了探索270Ds附近的长寿命的超重核,系统地计算了电荷数在104 ≤ Z ≤ 112范围内的α衰变与自发裂变之间的竞争。采用推广的液滴模型和唯象的解析公式计算了α衰变半衰期。基于包括壳效应和同位旋效应的WKB近似方法估算了相同超重核的自发裂变半衰期,进而预测了未知超重核274-276,279Cn与267-269Ds的衰变模式。The stability of superheavy nuclei (SHN) is controlled mainly by spontaneous fission and α decay processes. To investigate whether long lived SHN could really exist around 270Ds, the competition between α decay and spontaneous fission in the region 104 ≤ Z ≤ 112 are studied systematically. The α decay half-lives are investigated by employing a generalized liquid drop model (GLDM) and phenomenological analytical formula. Calculations of spontaneous fission half-lives for the same SHN are carried out based on the Wenzel-Kramers-Brillouin(WKB) approximation with both the shell effect and the isospin effect included. Decay modes are predicted for the unknown nuclei 274-276,279Cn and 267-269Ds.     

α-decay half-lives of superheavy nuclei and general predictions

The generalized liquid drop model (GLDM) and the cluster model have been employed to calculate the α-decay half-lives of superheavy nuclei (SHN) using the experimental α-decay Q values. The results of the cluster model are slightly poorer than those from the GLDM if experimental Q values are used. The prediction powers of these two models with theoretical Q values from Audi et al. (Qaudi) and Muntian et al. (QM) have been tested to find that the cluster model with Qaudi and QM could provide reliable results for Z>112 but the GLDM with Qaudi for Z≤112. The half-lives of some still unknown nuclei are predicted by these two models and these results may be useful for future experimental assignment and identification.     

超重核294118和291116及其α衰变链上各核素半衰期的研究

运用推广的液滴模型（GLDM）确定了超重核294118和291116及其α衰变链上各核素的衰变势垒, 采用量子力学中的WKB方法计算α衰变中的势垒穿透几率, 对该链上各原子核的α衰变半衰期进行了研究。 此外, 还利用Royer公式对该链上各原子核的α衰变半衰期进行了计算。 结果表明, GLDM 考虑亲和能与Royer公式给出的α衰变半衰期与超重核区的实验值符合很好, 验证了GLDM和Royer公式在超重核区的适用性,可以用来预测超重核的半衰期。 最后, 预言了Z=118 和116 同位素链上各核素的半衰期, 结果表明, 在Z=118和116中存在α衰变长寿命同位素, 这需要实验上的检验。The α decay potential barrier of the newly synthesized superheavy nuclei starting from 294118 and 291116 have been determined and their half lives have been studied with the Generalized Liquid Drop Model(GLDM) connected with WKB approximation and Royer’s formulae．The α decay half lives of the nuclei belonging to the superheavy nuclei starting from 294118 and 291116 have been calculated．The calculated results are in agreement with the experimental data, which show that the α decay half lives of superheavy nuclei with the GLDM and Royer’s formulae can be applied in the studying on superheavy nuclei successfully．Finally, the half lives of Z=118 and 116 isotopes have been predicted, and the results suggest there may be some long lived superheavy nuclei for α decay in those isotopes.     

锕系原子核自发裂变性质的理论研究

运用推广的液滴模型（GLDM）来确定锕系原子核的自发裂变势垒, 采用量子力学中的WKB近似方法对相应自发裂变的半衰期进行了研究。 在GLDM中, 首次考虑了微观Strutinsky壳修正对裂变势垒的影响。 理论计算的锕系区重核自发裂变半衰期与实验值符合得很好, 表明包括微观壳修正的GLDM可以成功研究重核的自发裂变性质。 The spontaneous fission half lives of the actinides are calculated by the WKB approximation and the potential barriers are constructed by a General Liquid Drop Model (GLDM) including the proximity energy, the mass and charge asymmetry, and an accurate nucleus radius. The microscopic shell correction which plays a key role for the spontaneous fission barrier is considered for the first time. The two parameter quasi molecular shape and the proximity are described in details within the GLDM. The effects of the microscopic shell correction and proximity energy for fission barrier are discussed separately. The calcula ted spontaneous fission half lives for the actinides reasonably accord with the experimental data, implying the present GLDM combined with the microscopic shell correction can be used to study the spontaneous fission properties of heavy nuclei successfully.     

Proton radioactivity within the generalized liquid drop model with various versions of proximity potentials

In the present work, we systematically investigate the proton radioactivity half-lives of spherical proton emitters adopting a generalized liquid drop model(GLDM) with 16 different proximity potentials, of which the proximity potential Prox.77-13 gives the closest results to the experimental data. Combined with the previous conclusion that the GLDM with proximity potential Prox.77-13 can also best describe α decay half-lives, which makes the model more uniform and consistent.Further, we use the proximity potential Prox.77-13 in GLDM to predict the proton radioactivity half-lives of 14 spherical proton emitters that are allowed energetically but not yet observed experimentally or specifically quantified. Finally, we research the Geiger-Nuttall law for proton radioactivity. The results reveal that the Geiger-Nuttall law can also be well used to study the proton radioactivity half-lives of isotopes with the same orbital angular momentum l.     

超重核292-310122同位素链的α衰变和自发裂变的竞争

基于推广的液滴模型(GLDM) 理论框架,计算了292-310122 同位素链的 衰变和自发裂变的半衰期。计算时的基本输入量为两子核的质量数和电荷数以及反应Q 值。GLDM能很好地描述重核和超重核的 衰变和自发裂变过程。计算结果表明,A < 308 时在同位素链上N = 176~184 的区域α衰变为主要衰变模式。A > 308 时在同位素链上自发裂变为主要衰变模式。308122 是α衰变和自发裂变的分界点,暗示着N = 184 为中子幻数。Based on the framework of the Generalized Liquid Droplet Model (GLDM), alpha decay and spontaneous fission half-lives for 292-310122 isotopes are studied. The calculation of the basic inputs which only need the two fragmentmass numbers, charge numbers and the Q value. GLDM can describe alpha decay and spontaneous fission the nuclei. It is found that the alpha decay is the dominant mode of decay for isotopes with mass number A < 308, and for those with A > 308 spontaneous fission is dominant. The demarcation between alpha decay and spontaneous fission is at 308122, which shows the presence of a spherical neutron shell closure at N = 184.     

超重原子核与新元素研究

当前,原子核物理研究的一个重要前沿是探索原子核的电荷与质量极限,研究超重原子核与超重元素的性质,以及合成超重原子核。20世纪60年代,基于量子壳效应,理论预言质子数为114、中子数为184的原子核及其相邻核具有较长的寿命,甚至可能是稳定的,形成一个超重稳定岛。这个理论预言促进了重离子加速器及相关探测设备的建造,推动了重离子物理的发展。到目前,已经合成到了118号元素,填满了元素周期表的第7行。然而,合成更重的超重元素或包含更多中子的超重原子核面临着很多挑战,需要理论与实验密切结合,探索超重原子核的性质与合成机制,以登上超重稳定岛。文章概要评述超重原子核与新元素研究。首先介绍超重原子核与超重元素研究的背景及理论预言,包括超重核存在的根源、理论预言的概况等。之后简要给出实验合成超重核取得的主要进展和新元素命名情况。关于合成更重的超重元素面临的挑战,文章将针对利用重离子熔合蒸发反应合成超重核的截面低、所合成的超重核缺中子等情况展开讨论。最后评述近年来超重原子核结构性质、衰变、裂变与合成机制等方面的理论研究进展,包括超重核区的幻数和超重岛的位置,超重核的稳定性,利用重离子熔合蒸发反应合成超重核的三步过程及其复杂性,利用多核子转移合成超重核的探索,等等。The exploration of charge and mass limits of atomic nuclei and the synthesis of long-lived or stable superheavy nuclei (SHN) are at the frontier of modern nuclear physics. In the 1960s, based on the stability originating from quantum shell effects, the possible existence of an island of stability around 298114 was predicted. This prediction advanced the construction of heavy ion accelerators and detectors and the development of heavy ion physics. So far, superheavy elements (SHE) with Z up to 118 have been synthesized via heavy ion fusion reactions in laboratories. Recently the IUPAC/IUPAP Joint Working Party (JWP) concluded that criteria for the discovery of new elements have been met for those with Z=113, 115, 117 and 118. Therefore the seventh period of the periodic table of elements is completed. To synthesize even heavier elements or more neutron-rich SHN by using heavy ion fusion reactions, one confronts many challenges. More efforts should be made to study the properties of SHN both experimentally and theoretically. In this short review on the study on SHN and SHE, we will first introduce the background and theoretical predictions of SHN, including the origin of the possible existence of SHN and the predicted island of stability of SHN, etc. Then we will present progresses made up to now concerning the synthesis of SHN and the naming of the four new elements. As for the challenges nuclear physicists confront in synthesizing even heavier SHEs, we will detail those connected with heavy ion fusion-evaporation reactions, namely, the tiny cross sections to produce SHN and the fact that only neutron-deficient SHNs can be synthesized. Finally we will discuss some theoretical progresses on the study of SHN, including the structure of SHN and proton and neutron magic numbers after 208Pb, the stability and the synthesis mechanism of SHN as well as what we should focus on in the future.     

超重核性质与合成机制的理论研究

探索原子核的电荷与质量极限,合成长寿命超重核是当前原子核物理研究的重要前沿问题之一。本文综述了我们近几年在超重原子核结构性质与合成机制方面取得的理论研究进展。在结构性质方面,利用处理对关联的粒子数守恒方法,基于推转壳模型,系统研究了锕系核与超镄核低激发谱,发展了多维形状约束的协变密度泛函理论并用于研究锕系核势能面和裂变位垒以及N=150同中子素中的非轴对称八极关联等。在超重核合成机制方面,系统研究了利用重离子熔合反应合成超重核的三步过程,包括俘获过程——提出了一个位垒穿透概率新公式、熔合过程——提出了一个基于动力学形变势能面的双核模型、存活过程——系统研究了激发态超重复合核存活概率等。系统研究了合成超重核的热熔合反应,得到的熔合蒸发截面与实验符合,并预言了合成119和120号超重元素的生成截面。     

Dipole Polarizabilities of the Ground States for Berylliumlike Ions

Dipole polarizabilities of the ground states for berylliumlike ions with nuclear charge Z = 4 to 10 are calculated by using the Rayleigh-Ritz variational method with multiconfiguration interaction wave functions. The representative models of convergence are listed and compared with other theoretical data for nuclear charge Z = 4 to 6. The present dipole polarizabilities are in good agreement with previous accurate theoretical values available in the literature. For results with greater nuclear charge number, the present calculations may provide benchmarked data for future theoretical and experimental studies. Dynamic dipole polarizabilities of the ground state for the beryllium atom at selected frequencies are also calculated and compared with other theoretical values in the literature.     

Search for decay modes of heavy and superheavy nuclei

Spontaneous fission(SF) with a new formula based on a liquid drop model is proposed and used in the calculation of the SF half-lives of heavy and superheavy nuclei(Z = 90–120). The predicted half-lives are in agreement with the experimental SF half-lives. The half-lives of decay(AD) for the same nuclei are obtained by using the Wentzel-Kramers-Brillouin(WKB) method together with Bohr-Sommerfeld(BS) quantization condition considering the isospin-dependent effects for the cosh potential. The decay modes and branching ratios of superheavy nuclei(Z =104-118) with experimental decay modes are obtained, and the modes are compared with the experimental ones and with the predictions found in the literature. Although some nuclei have predicted decay modes that are different from their experimental decay modes, decay modes same as the experimental ones are predicted for many nuclei. The SF and AD half-lives, branching ratios, and decay modes are obtained for superheavy nuclei(Z = 119–120) with unknown decay modes and compared with the predictions obtained in a previous study. The present results provide useful information for future experimental studies performed on both the AD and SF of superheavy nuclei.     

r-过程路径核β——衰变半衰期的估算

分析了20 < A < 190范围内丰中子核β衰变的实验数据,根据半衰期随质子数、中子数以及衰变能变化所呈现的壳效应和对效应等特点,提出了一种有效估算丰中子核β衰变寿命的公式。新的计算公式形式简单包含了较少的参数、计算量小。用该公式能较为准确地再现丰中子核的β衰变半衰期。用RIKEN最新测量丰中子核半衰期检验了该公式的外推能力,本工作可以为r-过程研究提供可靠的输入数据。Experimental data of the β--decay half-lives for the nuclei with atomic number between 20 and 190 are investigated. We have systematically studied the shell effects and pairing effects on β--decay half-lives versus the decay energy Q and nucleon numbers (Z, N). An empirical formula has been proposed to calculate the β--decay half-lives of neutron-rich nuclei. The empirical formula is simple and has relatively few parameters. Experimental β--decay half-lives of the neutron-rich nuclei are well reproduced by the new formula. In addition, the extrapolating capacity of this formula has been checked with the very recent experimental data from RIKEN. The predicted half-lives for r-process relevant nuclei with the current formula can be served as the reliable input of r-process model calculations.     

Empirical formula for <Emphasis Type="Italic">β</Emphasis><Superscript>−</Superscript>-decay half-lives of r-process nuclei

Experimental data of β ^?-decay half-lives of nuclei with atomic number between 20 and 190 are investigated. A systematic formula has been proposed to calculate β ^?-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 —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.     

Calculation of decay half-lives for superheavy elements using the double folding model

α decay half-lives of some new synthesized superheavy elements, possibly synthesized superheavy elements and decay products are calculated theoretically within the WKB approximation by using microscopic m-nucleus interaction potentials. These nuclear potentials between the α particle and daughter nuclei are obtained by using the double folding integral of the matter density distribution of the α particle and daughter nuclei with a density-dependent effective nucleon-nucleon interaction, in which the zero-range exchange term is supplemented. The calculated α decay half-lives are compared with those of the different models and experimental data. It is shown that the present calculation successfully provides the half-lives of the observed αdecays for some new superheavy elements and therefore gives reliable predictions for α decay of possibly synthesized superheavy elements in future experiments.     

Cluster decay half-lives using asymmetry dependent densities

By adopting different neutron and proton density distributions, cluster decay half-lives were investigated using double-folding potentials with constant and nuclear asymmetry dependent sets of nuclear density parameters. Two adopted asymmetry dependent sets of parameters were fitted based on microscopic calculations, and they were calculated based on the neutron skin/halo-type nuclei assumption and by employing experimental rms charge radii. A bulk agreement between theory and experiment was obtained for all sets of parameters using a calculated cluster preformation probability. Few differences were observed between the skin and halo-type assumptions. However, the notable role of the asymmetry parameter was observed in the relatively large differences between the skin and skin-type with zero thickness.     

Double beta decay

Double beta decay is a rare nuclear process changing the nuclear charge by two units leaving atomic number unchanged. The detection of the neutrino accompanied mode (A,Z)→(A,Z + 2) + 2e^? + &;2v^? ₂ with half-lives around 10²⁰ years is among the rarest decays ever observed. Of outmost importance for particle physics and especially neutrino physics, is the neutrinoless mode (A,Z)→(A,Z + 2) + 2e^?. This process is violating lepton number by two units and requires massive Majorana neutrinos, i.e. neutrino and antineutrino are identical. The current experimental status is reviewed and an outlook towards future activities is given.     

The analysis of predictability of \alpha -decay half-life formulae and the \alpha partial half-lives of some exotic nuclei

The predictabilities of the three $ \alpha$ -decay half-life formulae, the Royer GLDM, the Viola-Seaborg and the Sobiczewski-Parkhomenko formulae, have been evaluated by developing a method based on the ansatz of standard experimental benchmarking. The coefficients of each formula were re-derived using the reliable data of the $ \alpha$ -standards nuclei. The modified formulae that resulted were used to evaluate the accuracies of the formulae towards the prediction of half-lives of a set of nuclides with well-studied $ \alpha$ spectroscopic data as well as a set of exotic $ \alpha$ emitters. Further, a simple linear optimisation of the modified formulae allowed adjustments for the insufficient statistics of the primary data set without changing the modified formulae. While the three modified formulae showed equivalent results for all the medium heavy nuclei except the odd-odd, the modified GLDM showed relatively the best figures of merit for the odd-odd and superheavy nuclides.     

Systematic study of survival probability of excited superheavy nuclei

The stability of excited superheavy nuclei (SHN) with 100 Z 134 against neutron emission and fission is investigated by using a statistical model. In particular, a systematic study of the survival probability against fission in the 1n-channel of these SHN is made. The present calculations consistently take the neutron separation energies and shell correction energies from the calculated results of the finite range droplet model which predicts an island of stability of SHN around Z = 115 and N = 179. It turn...     

Proton Radioactivity Within a Hybrid Method

The proton radioactivity half-lives are investigated theoretically within a hybrid method.The potential barriers preventing the emission of protons are determined in the quasimolecular shape path within a generalized liquid drop model (GLDM). The penetrability is calculated with the Wentzel-Kramers-Brillouin (WKB) approximation. The spectroscopic factor has been taken into account in halflife calculation, which is obtained by employing the relativistic mean field (RMF) theory combined with the Bardeen-Cooper-Schrieffer (BCS) method. The half-lives within the present hybrid method reproduced the experimental data very well. Some predictions for proton radioactivity are made for future experiments.     

Role of the cluster deformations in explaining the exotic decay half-lives

We investigate the influence of nuclear deformations of the cluster and daughter nuclei on the exotic cluster decay half-lives of $\ensuremath 221\leq A \leq 242$ for the favored cluster decay of the radioactive nuclei by using the semiclassical WKB method and the Bohr-Sommerfeld quantization condition. The results have also been presented for the spherical nuclei case in order to show clearly the effects of the deformations on the exotic decay half-lives. The half-lives become close to the experimental data when both the deformation of daughter and cluster nuclei are taken into account in the calculations. Furthermore, considering cluster deformations together with the orientation angles of daughter and cluster also provides positive contributions to the results.