A. Bhagwat

Microscopic-macroscopic approach for binding energies with the Wigner-Kirkwood method

The semiclassical Wigner-Kirkwood (Planck constant/2pi) expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in (Planck constant/2pi). A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme, are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a root mean square (rms) deviation of 630 keV. It is shown that the proposed approach is indeed promising for the prediction of nuclear masses.

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.

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 Z=172 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 Z=100 to 180 and 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, various 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. For the specific filter with BE A = 5.5MeV a few nuclei with Z=180 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.

Applications to nuclear properties of the microscopic–macroscopic model based on the semiclassical Wigner–Kirkwood method

Some time ago we proposed a new microscopic–macroscopic model where the semiclassical Wigner–Kirkwood expansion of the energy up to fourth-order in hbar is used to compute the shell corrections in a deformed Woods–Saxon potential instead of the usual Strutinsky averaging scheme. For a set of 558 even–even nuclei computed with this new model, we found a rms deviation of 610 keV from the experimental masses, similar to the value obtained using the well-known finite range droplet model and the Lublin–Strasbourg drop model for the same set of nuclei. In this paper we analyze the α radioactivity in nuclei with mass number

Recent developments in the Wigner - Kirkwood mass formula

A\sim 100

Microscopic–Macroscopic Mass Calculations with Wigner–Kirkwood expansion

, finding good agreement with the available experimental results. We have also estimated spontaneous fission half-lives for superheavy nuclei in the region between Z = 102 and Z = 110. We find that our model predicts reasonably well the experimental half-lives in the considered nuclei, in spite of the fact that the fission barriers turn out to be somewhat too high.

WIGNER-KIRKWOOD METHOD FOR MICROSCOPIC-MACROSCOPIC CALCULATION OF BINDING ENERGIES

The recently proposed microscopic - macroscopic model for nuclear masses, based on the shell corrections obtained by using the semi - classical Wigner - Kirkwood (WK) ℏ expansion of one body quantal partition function, has been extended to the even - even deformed nuclei. The nuclear potential is assumed to be deformed Woods - Saxon with spin - orbit contribution. The Coulomb potential is obtained by folding charge densities. The resulting partition function is expanded upto the fourth order in ℏ to obtain averaged energies. The shell corrections thus obtained along with pairing energies determined within the framework of the Lipkin - Nogami scheme constitute microscopic part of the model. The macroscopic part is obtained from a liquid drop formula, with nine adjustable parameters. These parameters are fitted by considering a large set of 561 even - even nuclei with Z ≥ 8 and N ≥ 8. The fit yields rms deviation of merely 610 keV from the corresponding experimental masses. A few applications of the mass formula are presented and discussed in this paper.

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

The systematic study and calculation of ground state nuclear masses continues to be one of the active and important areas of research in nuclear physics. The present work is an attempt to determine the ground state masses of nuclei spanning the entire periodic table, using the Microscopic–Macroscopic approach. The semi-classical Wigner–Kirkwood (WK) expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is achieved upto the fourth order in . The shell corrections, along with the pairing energies obtained by using the Lipkin–Nogami scheme, constitute the microscopic part of the nuclear masses. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. It is shown that the Microscopic–Macroscopic mass calculation thus achieved, yields reliable description of ground state masses of nuclei across the periodic table. The present status of the WK mass calculations and the possible future perspectives are discussed.