About
There occur in nature about 300 nuclei, representing isotopes of elements containing from one to at most 94 protons. Some 2200 nuclei have been made artificially during the past 70 years. The artificial, heavy and superheavy elements, synthesized in scientific laboratories, have at present a mass numbers starting up to Z=116. Ds (experimentally were observed nuclei with proton number up to 116, but there no an official name for these elements).
An importance of shell effects.
Nuclear fission prompted Niels Bohr and John Wheeler to propose the liquid-drop model, which treats the nucleus as a drop of charged liquid without any structure. As long as the surface tension in the drop is larger than the repulsive Coulomb force due to the protons, a potential barrier prevents it from splitting. However, this fission barrier can be overcome if we supply enough energy to the nucleus or if the nucleus "tunnels" through the barrier.
According to Bohr and Wheeler, the potential barrier disappears completely when the atomic number reaches about 106. The lifetimes of the first "transuranium" elements - such as plutonium, curium and californium - were very close to the values predicted by the liquid-drop model. In 1962, however, it was found that many isotopes of transuranium elements which have a very low excitation energy undergo spontaneous fission in just 10^{-10}-10^{-2} s. This is inconsistent with the liquid-drop model predictions. Furthermore, the model could not account for considerable variations in the spontaneous-fission half-lives of these "isomers".
Researchers soon realized that the probability of spontaneous fission depends on the internal structure of the nucleus. It was well known, for example, that the total nuclear binding energies measured in experiments deviated from the predictions of the liquid-drop model in a regular way. The binding energies were highest for specific numbers of protons, Z=2, 8, 20, 28, 50, 82, and neutrons, N=2, 8, 20, 50, 82, 126. These "magic" numbers of protons and neutrons are called closed shells, and are similar to the electron shells of atomic physics.
By the end of the 1960s these observations led to a new microscopic theory of the nucleus, which showed that closed shells of protons and neutrons allow nuclei to be stable beyond the limits defined by the liquid-drop model (i.e. for atomic numbers greater than 106). Initially, there were the studies of spherical nuclei surrounding the expected doubly magic nucleus with Z=114 protons and N=184 neutrons. Indeed, the lifetimes of superheavy nuclei in the N=184 region are predicted to be up to 30 orders of magnitude longer than they would be in the absence of shells. Later, the analysis of half-lives has shown that also deformed superheavy nuclei, situated around the nucleus with Z=108 and N=162, may have long enough lifetimes to be observed.
The shell effect was predicted to be particularly strong for nuclei with magic numbers Z=108 and N=162, and even stronger for nuclei with Z=114 and N=184 - which is why these regions came to be known as "islands of stability".
Stability of these SHE is closely connected with their shell structure. Significance of the shell effects is fundamental, since many of them would not exist without these effects.
This is because the potential energy calculated within the macroscopic model without any shell effects, forms a very small barrier or even no barrier at all for heaviest nuclei, but the fact of taking into account the shell structure of these nuclei, increases with not too large increase of elongation of a nucleus leading to the enlargement or even creation of the potential energy barrier.
This theoretical model includes shell effects and gives a shell correction to the macroscopic energy of a nucleus calculated within liquid-drop model. Our calculations are done within such a model, called macroscopic-microscopic approach, used by many people for a long time.
Directions of the studies of SHE
The focus of superheavy element research can be divided into synthesis of new elements and new isotopes of elements in transuranium and transfermium regions, spectroscopy of known isotopes in these regions plus improving the data for the known ones and investigation of reaction mechanism around the closed proton and neutron shells.
Intensive experimental studies of SHE cause a fast increase of spectroscopic data for nuclei from these region. The data comes almost exclusively from measurements of alpha-particle energies appearing in alpha-decay chains, mainly of odd-A nuclei. Gamma-spectroscopic studies, which are also intensive in recent years, are done for lighter nuclei (up to rutherfordium, Z=104) and only approach presently the region of superheavy nuclei. So, the theoretical predictions would be very helpful for an experimental identification of the excited states and their quantum characteristics.
For the identification of new nuclides undergoing alpha-decay, a method for the investigation of consistent alpha-decays, the so-called alpha-alpha correlation analysis, has been employed since mid-60ties. This method is based on the fact that a decay chain starting from unknown isotopes should be ended in the known region of isotopes with the known decay properties. One observes alpha-particles, their kinetic energies, half-lives of all nuclei in alpha-decay chain of synthesized nucleus and spontaneous fission residues of known nucleus.
There is a close connection of alpha-spectroscopy with gamma-spectroscopy: using the information about excited states (their energies and quantum characteristics) of a superheavy nucleus, one can estimate the probabilities of alpha-transition to the excited states of daughter nuclei and compare them to the probability of gamma-transitions to the states in the parent nuclei. In such a way it is possible to interpret an experimental data from alpha-decay chains.
In present paper theoretical calculations of one-quasiparticle excitations of odd-A nuclei were done. Also were done the systematics for neutron-odd and proton-odd nuclei. Alpha-decay chain of Darmstatium 271 was plotted with taking into account single-particle structure of decaying odd-A nuclei. In this analysis, we mainly concentrate on deformed superheavy nuclei. Many results are given, however, for a wider region of nuclei to see the boundaries of this region and also to see the behaviour of nuclear properties, when one moves across these boundaries and outside of them.
Besides the theoretical interpretation and prediction of spectroscopic data, there has been proposed an empirical five-parameter formula for alpha-decay half-live. For even-even nuclei were used three parameters and two parameters, which include averaged effects of transitions from excited states to excited states, were added for odd-A group of superheavy nuclei. An important thing is that there are no adjustable parameters for odd-odd nuclei in the formula.