C S Shastry
Articles written in Pramana – Journal of Physics
Volume 61 Issue 1 July 2003 pp 51-66
The variation of fusion cross-section (σJfus) with energy in the12C+12C collision is linked to the underlying resonance phenomenon through the behavior of reaction cross-section (σ) of which σfus is taken as a part. The calculation of σfus is done through an energy-dependent imaginary potential in the optical model potential (OMP). Through dispersion relation, such an imaginary potential gives rise to energy-dependent real potential which is incorporated in the OMP. In our calculation, a form of potential for the nuclear part which has a soft repulsive in-built core is introduced based on similar works done earlier. The calculated results of σfus are used to explain the oscillatory structure, astrophysical S-factor and the decreasing trend at higher energies of the experimental σfus data in the case of12C+12C system with remarkable success. The potential used for fusion calculation is tested for fitting elastic scattering data at some energies and is found good in forward angles. Further improvement of the fitting of these data is obtained by incorporating a coupling potential in the surface region. About twenty resonances are observed in our calculation in the specific partial waves and some of them are found close to the experimentally identified resonances in12C+12C reaction. Thus, we provide an integrated and comprehensive analysis of fusion, resonance and scattering data in the best studied case of12C+12C reaction within the framework of optical potential model.
Volume 73 Issue 6 December 2009 pp 969-988
In analogy with the definition of resonant or quasi-bound states used in three-dimensional quantal scattering, we define the quasi-bound states that occur in one-dimensional transmission generated by twin symmetric potential barriers and evaluate their energies and widths using two typical examples: (i) twin rectangular barrier and (ii) twin Gaussian-type barrier. The energies at which reflectionless transmission occurs correspond to these states and the widths of the transmission peaks are also the same as those of quasi-bound states. We compare the behaviour of the magnitude of wave functions of quasi-bound states with those for bound states and with the above-barrier state wave function. We deduce a Breit–Wigner-type resonance formula which neatly describes the variation of transmission coefficient as a function of energy at below-barrier energies. Similar formula with additional empirical term explains approximately the peaks of transmission coefficients at above-barrier energies as well. Further, we study the variation of tunnelling time as a function of energy and compare the same with transmission, reflection time and Breit–Wigner delay time around a quasi-bound state energy. We also find that tunnelling time is of the same order of magnitude as lifetime of the quasi-bound state, but somewhat larger.
Volume 82 Issue 5 May 2014 pp 867-878
With the discovery of a large number of superheavy nuclei undergoing decay through 𝛼 emissions, there has been a revival of interest in 𝛼 decay in recent years. In the theoretical study of 𝛼 decay the 𝛼-nucleus potential, which is the basic input in the study of 𝛼-nucleus systems, is also being studied using advanced theoretical methods. In the light of these, theWentzel–Kramers–Brillouin (WKB) approximation method often used for the study of 𝛼 decay is critically examined and its limitations are pointed out. At a given energy, the WKB expression uses barrier penetration formula for the determination of the transmission coefficient. This approach utilizes the 𝛼-nucleus potential only at the barrier region and ignores it elsewhere. In the present era, when one has more precise experimental information on decay parameters and better understanding of 𝛼-nucleus potential, it is desirable to use a more precise method for the calculation of decay parameters. We describe the analytic 𝑆-matrix (SM) method which gives a procedure for the calculation of decay energy and mean life in an integrated way by evaluating the resonance pole of the 𝑆-matrix in the complex momentum or energy plane. We make an illustrative comparative study of WKB and 𝑆-matrix methods for the determination of decay parameters in a number of superheavy nuclei.
Volume 93 | Issue 6
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