Y. K. Gambhir

The α-nucleus potential for fusion and decay

The α-nucleus fusion cross sections at energies around and below the barrier and the α-decay half lives are calculated in the semi-classical WKB approach using the same microscopic as well as empirical α-nucleus potentials. The microscopic potential is generated within the double-folding framework using M3Y nucleon–nucleon interaction along with the required neutron and proton density distributions calculated in the relativistic mean field theory. It is found that in spite of the excellent results for the half lives the fusion cross sections are underestimated by almost a factor of 3. However, the experimental fusion cross sections can be reproduced by introducing a norm factor (overall multiplicative factor to the potential) 1.3 but this then worsens the agreement for half lives. To verify this observation and for comparison the calculations are repeated using some of the representative empirical potentials available in the literature. The same conclusion emerged. The present study thus indicates that the same α-nucleus potential may yield accurate description for both the α-nucleus fusion cross sections and α-decay half lives only with the introduction of additional parameter(s).

STUDY OF ALPHA DECAY OF SUPER HEAVY ELEMENTS USING S-MATRIX AND WKB METHODS

A comparative study of the S-matrix and the WKB methods for the calculation of the half widths of alpha decay of super heavy elements is presented. The extent of the reliability of the WKB methods is demonstrated through simple illustrative examples. Detailed calculations have been carried out using the microscopic alpha-daughter potentials generated in the framework of the double-folding model using densities obtained in the relativistic mean field theories. We consider alpha-nucleus systems appearing in the decay chains of super heavy parent elements having A = 277, Z = 112 and A = 269, Z = 110. For negative and small positive log T-1/2 values the results from both methods are similar even though the S-matrix results should be considered to be more accurate. However, when log inverted perpendicular(1/2) values are large and positive, the width associated with such state is infinitesimally small and hence calculation of such width by the S-matrix pole search method becomes a numerically difficult problem. We find that overall, the WKB method is reliable for the calculation of half lives of alpha decay from heavy nuclei.

S-MATRIX-BASED UNIFIED CALCULATION OF Q-VALUES AND HALF-LIVES OF α-DECAY OF SUPER HEAVY ELEMENTS

The Q-values and half-lives of several heavy α decaying systems are calculated using the relativistic mean field (RMF) theory-based microscopic α-daughter nucleus potential. A unified procedure is adopted, using analytic S-matrix method and treating α-decay as the decay of the resonance state of the α-daughter nucleus system. The resonance parameters are obtained from the pole positions of the S-matrix in the complex k-plane and using these Q-values and half widths are evaluated. The calculation reproduces the experimental results well. We find that the present unified approach gives a good description of the data and compare well with those obtained by empirical formulae.

The highest limiting Z in the extended periodic table

The problem of finding the highest limiting Z in the extended periodic table is discussed. The upper limit suggested by the atomic many body theory at Zuf0a0=uf0a0172 may be reached much earlier due to nuclear instabilities. Therefore,an extensive set of calculations based on the relativistic mean field formulation are carried out for the ground state properties of nuclei with Zuf0a0=uf0a0100 to 180 nand N/Z ratio ranging from 1.19 to 2.70. This choice of Z and N extends far beyond the corresponding values of all the known heavy to superheavy elements.To facilitate the analysis of the huge quantity of calculated results, nvarious filters depending upon the pairing energies, one and two nucleon separation energies, binding energy per particle (BE/A) and α-decay plus fission half lives, are introduced. The limiting value of Z is found to be 146. nFor the specific filter with BE A = 5.5MeV a few nuclei with Zuf0a0=uf0a0180 also appear. No evidence for the limiting Z value 172 is found. We stress the need to bridge the atomic and nuclear findings and to arrive at an acceptable limiting value of highest Z (or rather combination of Z and N) of the extended periodic table.

EVOLUTION OF SHELL STRUCTURE IN NUCLEI

Systematic investigations of the pairing and two-neutron separation energies which play a crucial role in the evolution of shell structure in nuclei, are carried out within the framework of relativistic mean-field model. The shell closures are found to be robust, as expected, up to the lead region. New shell closures appear in low mass region. In the superheavy region, on the other hand, it is found that the shell closures are not as robust, and they depend on the particular combinations of neutron and proton numbers. Effect of deformation on the shell structure is found to be marginal.

A systematic analysis of microscopic nucleon–nucleus optical potential for p–Ni scattering

A microscopic proton–nucleus optical potential is calculated for all even isotopes 52–112Ni within the Brueckner–Hartee–Fock framework. The reaction matrices calculated using three (Argonne v18, Reid93 and NijmII) realistic inter-nucleon potentials with and without three-body forces (Urbana IX (UVIX) and the density dependent three-nucleon interaction (TNI) model of Lagaris, Friedman and Pandharipande), have been folded over the neutron and proton density distributions of the relevant targets obtained by using the relativistic mean field approach. It is observed that the inclusion of both models of the three-body forces somewhat reduces the strength of the central part of the optical potential in the nuclear interior and affects only marginally the spin–orbit part of the potential. Further, the calculated volume integral of the real part of the spin–orbit optical potential as well as its peak value are found to decrease systematically with the addition of neutrons. The calculated optical potentials reproduce remarkably well the existing experimental differential cross section (dσ/dθ) and the polarization (Ay) data for p–58–64Ni scattering at 39.6 and 65 MeV projectile energies. The inclusion of three-body forces (UVIX and TNI) does not lead to any change in the calculated observables (dσ/dθ and Ay) indicating that the p–Ni scattering data analyzed here are not sensitive to the nuclear interior. Identical observations are also found in the Zr, Sn and Pb isotopic chains. Therefore, these observed features of the microscopic optical potential seem general and may hold globally.

Systematics of strong absorption radii and its relevance to the calculation of reaction cross sections

Based on the detailed analysis of the reaction cross sections obtained using the finite range Glauber model, a systematic study of strong absorption radii is carried out. A simple phenomenological expression is proposed to calculate reaction cross sections directly using the average nucleon–nucleon cross section for a given target–projectile combination at given energy. Reliability of the nmodel expression is demonstrated through a variety of illustrative examples.