Fusion theory for synthesis of the superheavy elements

Recent developments on reaction mechanisms in fusion of massive systems are briefly reviewed, especially on a two-step model. The fusion hindrance observed experimentally is simply explained in connection with the fluctuation-dissipation dynamics of shape evolutions and of two-body collisions. Examples are given for fusion excitation functions and compared with the available data on ⁴⁸Ca+actinide target systems.     

Fusion hindrance and roles of shell effects in superheavy mass region

We present the first attempt of systematically investigating the effects of shell correction energy for a dynamical process, which includes fusion, fusion–fission and quasi-fission processes. In the superheavy mass region, for the fusion process, shell correction energy plays a very important role and enhances the fusion probability when the colliding partner has a strong shell structure. By analyzing the trajectory in three-dimensional coordinate space with the Langevin equation, we reveal the mechanism of the enhancement of the fusion probability caused by ‘cold fusion valleys’. The temperature dependence of shell correction energy is considered.     

Reaction dynamics of synthesis of superheavy elements

Based on the theory of the compound nucleus reaction, a brief review is given on the special aspects of the reaction dynamics in the synthesis of the superheavy elements (SHE), where the fusion probability is the most unknown factor. A new viewpoint of the fusion reaction is proposed that it consists of two processes; the first process up to the contact of two nuclei of the incident channel and the second one of a dynamical evolution to the spherical compound nucleus from the contact configuration. The fusion probability is, thus, given as a product of a contact probability and a formation probability. Analytic studies of the latter probability are discussed in the one-dimensional model, where a simple expression is given to the so-called extra-push energy in terms of the reduced friction, the curvature parameter of the conditional saddle point and the nuclear temperature. Preliminary results of numerical analyses of the contact probability are given, using the surface friction model (SFM). Remarks are given on the present status of our knowledge and for future developments. Received: 1 May 2001 / Accepted: 4 December 2001     

Fusion near the Coulomb barrier for the synthesis of heavy and superheavy elements: A theoretical approach

The compound nucleus formation is considered as a two-step process of touching and subsequent tunneling of the projectile into the target. The deep minima in the potential energy curve are due to shell effects in the experimental binding energies and give possible target-projectile combinations for the synthesis of heavy and superheavy elements. The asymmetric channels thus obtained are in remarkable agreement with the known experimental channels. In our model, the colliding partners are first shown to be captured in the pocket behind the outer (touching) barrier and the composite system so formed finally tunnels through the inner (fusion) barrier to form the resulting compound nucleus. These calculations reveal the importance of the fusion barrier, which occur only for the asymmetric target-projectile combinations. The calculated fusion cross-sections show a reasonable comparison with the observed one-neutron evaporation residue cross-sections. An estimate of the excitation energy carried by the compound nucleus is also obtained from our model calculations.     

超重原子核与超重元素

研究超重原子核和超重元素,探索原子核的电荷和质量极限,是重要的科学前沿领域。超重原子核的存在源于量子效应。上个世纪60年代,理论预言存在一个以质子数114和中子数184为中心的超重稳定岛,这极大地促进了重离子加速器及相关探测设备的建造和重离子物理的发展。到目前为止, 实验室合成了118号及之前的超重元素。其中116号、114号和113号以下的新元素已被命名。利用重离子熔合反应合成更重的超重元素还面临着很多挑战,需要理论与实验密切结合,探索超重原子核性质与合成机制,以登上超重稳定岛。文章概要介绍了超重原子核和超重元素的研究背景、实验进展以及面临的挑战,并展望了未来的发展。     

Effect of the entrance channel on the synthesis of superheavy elements

Cross-sections for the synthesis of superheavy elements were analyzed using the concept of a dinuclear system. Experimental values for the production of elements Z = 104, 108, 110, 111 and 112 by cold fusion reactions with targets of ²⁰⁸Pb and ²⁰⁹Bi were reproduced. The model reveals the importance of entrance channel dynamics and competition between quasi-fission and complete fusion processes. Energy windows were observed which allow capture of the reacting nuclei and formation of the compound nucleus. The quantities were studied which are significant for the interaction dynamics of massive nuclei in the entrance channel.     

Basic distinctions between cold- and hot-fusion reactions in the synthesis of superheavy elements

Superheavy elements (SHE) of charge number in the range of Z = 106–112 were synthesized in so-called cold-fusion reactions. The smallness of the excitation energy of compound nuclei is the main advantage of cold-fusion reactions. However, the synthesis of SHEs of charge number in the region of Z ≥ 112 is strongly complicated in cold-fusion reactions by a sharp decrease in the cross section of a compound nucleus formation in the entrance channel because of superiority of quasifission in the competition with complete fusion. Two favorable circumstances contributed to the success of the experiments aimed at the synthesis of the Z = 113–118 elements and performed at the Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research: large cross sections for the production of a compound nucleus, which are characteristic of hot-fusion reactions, and an increase in the fission barrier for nuclei toward the stability island. The factor that complicates the formation of a compound nucleus in cold-fusion reactions is discussed.     

Magic numbers in superheavy elements

The energy density method is used to study the magic character of neutron and proton numbers corresponding to N > 126 and Z > 82. It is found that N = 184 and N = 228 are the next neutron magic numbers. For the protons, however, no sign of a shell closure appears for 82 < Z ? 130. Some simple criteria for the β^? - and α-stability of N = 184 and N = 228 isotones are also discussed.     

Status and prospects of synthesizing superheavy elements

The nuclear shell model predicts that the next doubly magic shell-closure beyond ²⁰⁸Pb is at a proton number between Z = 114 and 126 and at a neutron number N = 184. The outstanding aim of experimental investigations is the exploration of this region of spherical “Superheavy Elements”. This article describes the experiments that were performed at the GSI SHIP. They resulted in an unambiguous identification of elements 107 to 112. They were negative so far in searching for elements 113, 116 and 118 at SHIP; however, positive results were reported from experiments in Dubna on elements 114 and 116 and from experiments in Berkeley on element 118. The measured decay data are compared with theoretical predictions. Some aspects concerning the reaction mechanism and the use of radioactive beams are also presented. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: S.Hofmann@gsi.de     

The way to superheavy elements

This review is devoted to the studies of heavy and superheavy elements and the methods of their synthesis and identification. Special attention is paid to the latest discoveries in the area of superheavy elements with Z = 107–112 in cold fusion reactions and Z = 113–118 in reactions between ⁴⁸Ca and actinides.     

New analog electronics for the new challenges in the synthesis of superheavy elements

A new series of experiments aimed at the synthesis and study of decay properties of the most neutron-deficient isotopes of element Fl (Z = 114) and of the heaviest isotopes of 118 element is planned at the DGFRS (FLNR JINR). An appropriate registering system is to be implemented to transfer spectrometric data from double-sided silicon strip detector (DSSD). New analog modules were designed that allow to simplify existing multi-channel measurement system and to improve the real-time method of “active correlations” in search for the rare events of SHE formation and decay. The main features of the new modules the 16-channel charge-sensitive preamplifier, the 16-channel analog multiplexer and the 1.25 MSPS 12-bit Parallel ADC are presented.     

Theory of fusion for superheavy elements

A new model is proposed for fusion mechanisms of massive nuclear systems, where so-called fusion hindrance exists. The model describes the whole process in two steps: two-body collision processes in an approaching phase and shape evolutions of an amalgamated system into the compound nucleus formation. It is applied to ⁴⁸Ca-induced reactions and is found to reproduce the experimental fusion cross sections extremely well, without any free parameter. A schematic case is solved in an analytic way, the results of which shed light on fusion mechanisms. Combined with statistical decay theory, residue cross sections for superheavy elements can be readily calculated. Examples are given.     

The relative stability of superheavy elements

The relative stability of superheavy elements against beta-decay and spontaneous fission has been investigated. A simple criterion of beta-stability using the Fermi gas model has been developed, tested in the range of stable nuclei and extended to the superheavy region. Spontaneous fission half-lives have been calculated using the statistical model in the expected region of relative beta-stability for superheavy nuclei. Our results have been compared with previous calculations.     

On the production of superheavy elements

Since the discovery of Deformed Superheavy Nuclei (1983–85) a bridge connects the island of SHE to known isotopes of lighter elements. What we know experimentally and theoretically on the nuclear structure of SHE is reported in a first section. The making of the elements, with an analysis of production cross sections, and the macroscopic limitation to Z=112+ε is presented in a second section. The break-down of fusion cross sections in the ‘Coulomb Falls’ within a range of about 10 elements is introduced as the universal limiting phenomenon. How the nuclear structure of the collision partners modifies the on-set of this limitation is presented in Section 3. Reactions induced by deformed nuclei are pushed by side collisions to higher excitation energies (4n- and 5n-channels), whereas reactions driven by the cluster-like, closed-shell nuclei, ²⁰⁸₁₂₆Pb and ¹³⁸₈₂Ba, are kept at low excitation energies (1n- and 2n-channels). The on-set of production limitation for deformed collision partners is moved to smaller effective fissilities x=0.68⩽0.72, whereas for spherical clusters the on-set is delayed x=0.76⩾0.72 and x=0.79⩾0.72 for ¹³⁸Ba and ²⁰⁸Pb, respectively. An outlook, what remains to be studied in the future, ends the article. To cite this article: P. Armbruster, C. R. Physique 4 (2003).     

QED and relativistic corrections in superheavy elements

In this paper we review the different relativistic and QED contributions to energies, ionic radii, transition probabilities and Landé g-factors in super-heavy elements, with the help of the MultiConfiguration Dirac-Fock method (MCDF). The effects of taking into account the Breit interaction to all orders by including it in the self-consistent field process are demonstrated. State of the art radiative corrections are included in the calculation and discussed. We also study the non-relativistic limit of MCDF calculation and find that the non-relativistic offset can be unexpectedly large.     

Transition rates of electrons in superheavy elements

Transition rates for electrons in the superheavy elementsZ=114, 126, 134, 145, 164 and 173 are calculated.K, L andM-shells are considered as final states. The 2s-1s transition of multipolarityM 1 is dominant for Z = 173 with a transition time of 10^?18 s. The radical expectation values 〈r〉 and 〈r²〉^1/2 are given.     

合成和发现超铀化学元素、探索超重核稳定岛

合成新元素拓展元素周期表、探索原子核存在极限是核物理前沿研究领域。相关研究工作涉及的重大物理问题有：存在多少种化学元素？超重元素具有什么样的化学性质？超重元素化学性质是否符合元素周期律的外推预期？最大的核幻数是什么？是否存在稳定的或长寿命的超重核素？在极强库仑场中原子核具有哪些奇特的结构和性质？等等。经过逾半个世纪的不懈努力,元素合成取得了巨大成就,已将周期表从92号扩展至118号元素,完成了周期表上第七周期元素填充。文章回顾了在自然界寻找超重元素的历程,评述了利用人工核反应合成超铀元素和探索理论预言的超重核稳定岛的进展、成果、现状以及目前面临的困难,展望了未来的研究工作,简介了基于国家重大科技基础设施——强流重离子加速器装置开展超重研究的计划。     

Route to islands of stability of superheavy elements

Problems concerning the existence of hypothetical superheavy elements for which theoretical nuclear models predict high stability with respect to various modes of radioactive decay are discussed. The synthesis of superheavy nuclei and the possibilities for performing experiments aimed at detecting rare events of their production and decay in heavy-ion beams are considered. Experimental results suggesting a considerable increase in the lifetime of nuclei as they approach the closed proton and neutron shells determining the islands of stability of superheavy elements are presented.