N. G. Kelkar

Critical view of WKB decay widths

A detailed comparison of the expressions for the decay widths obtained within the semiclassical WKB approximation using different approaches to the tunneling problem is performed. The differences between the available improved formulas for tunneling near the top and the bottom of the barrier are investigated. Though the simple WKB method gives the right order of magnitude of the decay widths, a small number of parameters are often fitted. The need to perform the fitting procedure remaining consistently within the WKB framework is emphasized in the context of the fission model based calculations. Calculations for the decay widths of some recently found superheavy nuclei using microscopic alpha-nucleus potentials are presented to demonstrate the importance of a consistent WKB calculation. The half-lives are found to be sensitive to the density dependence of the nucleon-nucleon interaction and the implementation of the Bohr-Sommerfeld quantization condition inherent in the WKB approach.

Quantum reflection and dwell times of metastable states.

The concept of phase and dwell times used in tunneling is extended to quantum collisions to derive a relation between the phase and dwell time delays in scattering. This relation can be used to remove the near threshold s-wave singularities in the Wigner-Eisenbud delay times and amounts to an extension of the concept of quantum reflection to strong interactions. Dwell time delay emerges as the quantity which gives the correct behavior of the density of states of a metastable state at all energies. This fact is demonstrated by investigating some recently found metastable states of mesic nuclei.

Time delayed K+N reactions and exotic baryon resonances

Evidence and hints, from both the theoretical and experimental sides, of exotic baryon resonances with B = S, have been with us for the last 30 years. The poor status of the general acceptance of these Z* resonances is partly due to the prejudice against penta-quark baryons and partly due to the opinion that a proof of the existence of exotic states must be rigorous. This can refer to the quality and amount of data gathered, and also to the analytical methods applied in the study of these resonances. It then seems mandatory that all possibilities and aspects be exploited. We do that by analysing the time delay in K+N scattering, encountering clear signals of the exotic Z* resonances close to the pole values found in partial wave analyses.

Collision times in ππ and πK scattering and spectroscopy of meson resonances

Abstract Using the concept of collision time (time delay) introduced by Eisenbud and Wigner and its connection to on-shell intermediate unstable states, we study mesonic resonances in ππ and πK scattering. The time-delay method proves its usefulness by revealing the spectrum of the well known ρ - and K ∗ -mesons and by supporting some speculations on ρ -mesons in the 1200 MeV region. We use this method further to shed some light on more speculative meson resonances, among others the enigmatic scalars. We confirm the existence of chiralons below 1 GeV in the unflavoured and strange meson sector.

Possible η-mesic 3He states within the finite rank approximation

We extend the method of time delay proposed by Eisenbud and Wigner, to search for unstable states formed by η mesons and the 3He nucleus. Using few-body equations to describe η3He elastic scattering, we predict resonances and unstable bound states within different models of the η–N interaction. The η3He states predicted within this novel approach are in agreement with the recent claim of the evidence of η-mesic 3He made by the TAPS Collaboration.

Hidden evidence of nonexponential nuclear decay

The framework to describe natural phenomena at their basics being quantum mechanics, there exist a large number of common global phenomena occurring in different branches of natural sciences. One such global phenomenon is spontaneous quantum decay. However, its long time behavior is experimentally poorly known. Here we show, that by combining two genuine quantum mechanical results, it is possible to infer on this large time behavior, directly from data. Specifically, we find evidence for nonexponential behavior of alpha decay of

Determining the size of the proton

^{8}\mathrm{Be}

Quantum time scales in alpha tunneling

at large times from experiments.

Three body mechanism of eta production

Abstract A measurement of the Lamb shift of 49,881.88(76) GHz in muonic hydrogen in conjunction with theoretical estimates of the proton structure effects was recently used to deduce an accurate but rather small radius of the proton. Such an important shift in the understanding of fundamental values needs reconfirmation. Using a different approach with electromagnetic form factors of the proton, we obtain a new expression for the transition energy, Δ = E 2 P 3 / 2 f = 2 − E 2 S 1 / 2 f = 1 , in muonic hydrogen and deduce a proton radius, r p = 0.831 fm .

ηN scattering lengths favour ηd and ηα states

The theoretical treatment of alpha-decay by Gamow is revisited by investigating the quantum time scales in tunneling. The time spent by an alpha-particle in front of the barrier and traversing it before escape is evaluated using microscopic alpha-nucleus potentials. The half-life of a nucleus is shown to correspond to the time spent by the alpha knocking in front of the barrier. Calculations for medium and super heavy nuclei show that from a multitude of available tunneling time definitions, the transmission dwell time gives the bulk of the lifetime of the decaying state, in most cases.