Magic nuclei

In atomic nuclei, SRPA was derived [9,10,19] for the demanding Skyrme functional involving a variety of densities and currents (see [20] for the recent review on Skyrme forces). SRPA calculations for isoscalar and isovector giant resonances (nuclear counterparts of electronic plasmons) in doubly magic nuclei demonstrated high accuracy of the method [10]. 

The extended model has been subjected to a number of tests. Without any parameter adjustments, the model reproduces the energie and B(E2) values of the lowest 2 states of doubly magic nuclei. 

A substantial improvement can he obtained, if the parameters in Eq. (2.3) are fitted to experimental values for magic nuclei, and a sixth term (—kP) is added to the right-hand side. Here P= ZN/(Z+ N) is the promiscuity factor. Angeli proposed the following new formula (Angeli 1991b) ... 

Seniority is defined as the number of unpaired nucleons in a state. In the low-seniority scheme, it is supposed that the ground states of even-even semi-magic nuclei consist of pairs of identical nucleons that are coupled to spin zero. In the excited states, one or more pairs are broken. In the ground state of odd-A nuclei, there is one valence nucleon and in the excited states, 1, 3, 5, etc., valence nucleons. The low-seniority scheme calculations (Lawson 1980 Allaart et al. 1988 Talmi 1993) give a reasonable description of numerous semi-magic nuclei that have not too many valence particles (or holes). 

In Sect. 2.3.1 the shell model of spherical and deformed nuclei was discussed. The model gives a good description of various phenomena observed in the light (A < 80), near double-magic (e.g., around Pb) and well-deformed nuclei (e.g., in the regions 150 < A < 190, A > 220). The shell model is a microscopic nuclear model, i.e., it is formulated at the nucleonic level. At the same time, the application of the model far from magic nuclei leads sometimes to very complicated calculations. Furthermore, many observations clearly show the existence of collective behavior in nuclei (surface vibration, collective rotation), which can be treated in macroscopic framework much more simply. 

The only successful method to synthesize transactinide elements is through the complete fusion of heavy ions (Schmidt and Morawek 1991 Vandenbosch 1992 Reisdorf 1994). Two types of reactions have been employed to create new chemical elements cold fusion with Pb or Bi targets and hot fusion with Ca projectiles (O IHg. 19.19). The success of reactions involving doubly magic nuclei has been explained in the framework of the fragmentation model (Sandulescu et al. 1976). 

These elements near the predicted islands of nuclear stability around the spherical closed shells at proton numbers 110-114 (or even 126) and 184 neutrons are typically referred to as SHEs. Although arguments have been made (Armbruster and Miinzenberg 1989) that the heavy elements that would not exist except for stabilization by nuclear shells, whether or not they are spherical, should be designated as SHEs, the term has usually been reserved for those elements in the region of the predicted spherical doubly magic nuclei. 

In addition four of these elements have doubly magic nuclei since they have magic numbers with respect to both protons and neutrons. The doubly magic nuclei are He, O, °Ca, Pb. 

An example where nonlinear phenomena in connection with laser-rf spectroscopy have been used in atomic beams, is the recent work on calcium isotopes carried out in our laboratory. The goal of these experiments was to determine nuclear electric quadrupole moments from precise hyperfine structure data of the atomic spectrum. This is of some importance in the case of calcium, since Ca as well as Ca are so-called double-magic nuclei, i.e., with closed proton and neutron shells. Radioactive Ca (t = 1.03 X 10 yr) and the stable isotope Ca have been investigated by laser-rf spectroscopy. The measurements allow to study the influence of a single neutron and three neutrons, respectively, on the double-magic °Ca core. 

Hence, one can see a remarkably large contribution through a valence nucleon mechanism when, first, the neutron energy is sufficiently large (about 1 keV), and, second, the level density of the compound nuclei is small (light or close to magic nuclei). Then, in the vicinity of the resolved compound resonance, we obtain... 

The second problem, that of low excitation of the compound nucleus, stems from what Swiatecki calls the brittleness of superheavy nuclei. They can withstand only a small amount of distortion from the spherical shape, and any appreciable deformation invariably involves a lowering of the fission barrier. Heavy-ion reactions are particularly bad in this respect as a large amount of vibrational and rotational energy can be involved. Moretto has considered the question quantitatively. It is also treated extensively by Lefort who concludes that projectiles with Z between 35 and 40 (Br to Zr) on to targets of Th, U, or Pu show most promise. Greiner argues that excitation will be minimized if the nuclei involved are hard , that is relatively incompressible, as would occur with closed-shell magic nuclei, when the amount of coulombic interaction in the fusion reaction would be small. Kr, with 50 neutrons, is an attractive candidate. 

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