arXiv subjects

N. G. Kelkar

Publications and source records attributed to N. G. Kelkar.

At least 55 records · Page 3Linked to original sources

arXiv2011

Breit Equation with Form Factors in the Hydrogen Atom

The Breit equation with two electromagnetic form-factors is studied to obtain a potential with finite size corrections. This potential with proton structure effects includes apart from the standard Coulomb term, the Darwin term, retarded potentials, spin-spin and spin-orbit interactions corresponding to the fine and hyperfine structures in hydrogen atom. Analytical expressions for the hyperfine potential with form factors and the subsequent energy levels including the proton structure corrections are given using the dipole form of the form factors. Numerical results are presented for the finite size corrections in the 1S and 2S hyperfine splittings in the hydrogen atom, the Sternheim observable $D_{21}$ and the 2S and 2P hyperfine splittings in muonic hydrogen. Finally, a comparison with some other existing methods in literature is presented.

hep-ph↗

arXiv2011

Comment on "Quasinormal modes in Schwarzschild-de Sitter spacetime: A simple derivation of the level spacing of the frequencies"

It is shown here that the extraction of quasinormal modes (QNMs) within the first Born approximation of the scattering amplitude is mathematically not well founded. Indeed, the constraints on the existence of the scattering amplitude integral lead to inequalities for the imaginary parts of the QNM frequencies. For instance, in the Schwarzschild case, $0 \leq ω_I < κ$ (where $κ$ is the surface gravity at the horizon) invalidates the poles deduced from the first Born approximation method, namely, $ω_n = i n κ$.

gr-qc↗

arXiv2010

No classical limit of quantum decay for broad states

Though the classical treatment of spontaneous decay leads to an exponential decay law, it is well known that this is an approximation of the quantum mechanical result which is a non-exponential at very small and large times for narrow states. The non exponential nature at large times is however hard to establish from experiments. A method to recover the time evolution of unstable states from a parametrization of the amplitude fitted to data is presented. We apply the method to a realistic example of a very broad state, the sigma meson and reveal that an exponential decay is not a valid approximation at any time for this state. This example derived from experiment, shows the unique nature of broad resonances.

quant-ph↗

arXiv2010

Three body dwell time

The lifetime of an unstable state or resonance formed as an intermediate state in two body scattering is known to be related to the dwell time or the time spent within a given region of space by the two interacting particles. This concept is extended to the case of three body systems and a relation connecting the three body dwell time with the two body dwell times of the substructures of the three body system is derived for the case of separable wave functions. The Kapur Peierls formalism is revisited to discover one of the first definitions of dwell time in literature. An extension of the Kapur Peierls formalism to the three body case shows that the lifetime of a three body resonance can indeed be given by the three body dwell time.

quant-ph↗

arXiv2009

Pairwise final state interactions in the p d --> p d eta reaction near threshold

A model for the p d --> p d eta reaction published earlier, including the final state interaction (FSI) of all particles, is revisited to investigate the low energy data on this reaction. The three body problem of p-d-eta scattering in the final state is approximated in terms of pairwise interactions between the three particles in the final state. Apart from a comparison with some preliminary data, two new findings relevant to the near threshold data analysis are reported. The first one points toward the limitations of an FSI factor used conventionally to extract the eta-deuteron scattering length and infer subsequently on the existence of eta-mesic states. The second result emphasizes the role of the $p-d$ FSI and the strong Coulomb repulsion near threshold. Finally, a comparison of the above model calculation with low energy data, excludes very large eta-nucleon scattering lengths.

nucl-th↗

arXiv2009

Eta meson rescattering effects in the p + 6Li --> eta + 7Be reaction near threshold

The p + 6Li --> eta + 7Be reaction has been investigated with an emphasis on the eta meson and 7Be interaction in the final state. Considering the 6Li and 7Be nuclei to be alpha-d and alpha-3He clusters respectively, the reaction is modelled to proceed via the p + d [alpha] --> 3He [α] + eta reaction with the alpha remaining a spectator. The eta meson interacts with 7Be via multiple scatterings on the 3He and alpha clusters inside 7Be. The individual eta-3He and eta-alpha scatterings are evaluated using few body equations for the eta-3N and eta-4N systems with a coupled channel eta-N interaction as an input. Calculations including four low-lying states of 7Be lead to a double hump structure in the total cross section corresponding to the $L = 1 (J = (1/2)^-, (3/2)^-)$ and $L = 3 (J = (5/2)^-, (7/2)^-)$ angular momentum states. The humps arise due to the off-shell rescattering of the eta meson on the 7Be nucleus in the final state.

nucl-th↗

arXiv2009

Quantum time scales in alpha tunneling

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.

nucl-th↗

arXiv2008

Quantum Reflection of S-wave Unstable States

The phase time in quantum tunneling can be disentangled into a dwell time plus a term arising due to the interference of the reflected and incident waves in front of the barrier. The interference term dominates at low energies and as E --> 0, this term and hence the phase time becomes singular. With the s-wave motion in three dimensions being equivalent to that of a one-dimensional motion in the radial coordinate, a similar singularity shows up in the phase time delay of s-wave resonances. Relating the scattering matrix in three dimensional collisions to the reflection amplitude, the interference term in tunneling can be identified as a term given in terms of the transition matrix in scattering. Subtraction of this term from the phase time delay gives the dwell time delay which is finite at all energies and is useful in characterizing s-wave resonances such as the sigma meson and mesic nuclei near threshold.

hep-ph↗

arXiv2008

Long Tail of Quantum Decay from Scattering Data

Whereas the short time behaviour of an unstable quantum mechanical system is well understood from its theoretical as well as experimental side, the long time tail of the very same systems has neither been measured experimentally nor is there a theoretical agreement on how to handle it. We suggest a possible way out of this unsatisfactory state of art. Theoretically we suggest that the correct spectral function entering the Fock-Krylov method to calculate the survival amplitude is proportional to the density of states of a resonance. The latter is essentially the energy derivative of a phase shift. As a bonus, we can connect the survival probability to scattering data via the phase shift. The method then not only establishes the spectral function, but is per se a semi-empirical method to extract the large time behaviour from scattering data.

hep-ph↗

arXiv2008

Study of the $η-^7Be$ Interaction Near Threshold in $p-^6Li$ Fusion

We present a calculation for $η$ production in the $p-^6Li$ fusion near threshold including the $η-^7Be$ final state interaction (FSI). We consider the $^6Li$ and $^7Be$ nuclei as $α-d$ and $α-^3He$ clusters respectively. The calculations are done for the lowest states of $^7Be$ with $J = ({3\over2}^-, {1\over2}^-)$ resulting from the $L = $1 radial wave function. The $η-^7Be$ interaction is incorporated through the $η-^7Be$ $T-$matrix, constructed from the medium modified matrices for the $η-^3He$ and $η-α$ systems. These medium modified matrices are obtained by solving few body equations, where the scattering in nuclear medium is taken into account.

nucl-th↗

arXiv2008

Analysis of averaged multichannel delay times

The physical significances and the pros and cons involved in the usage of different time delay formalisms are discussed. The delay time matrix introduced by Eisenbud, where only s-waves participate in a reaction, is in general related to the definition of an angular time delay which is shown not to be equivalent to the so-called phase time delay of Eisenbud and Wigner even for single channel scattering. Whereas the expression due to Smith which is derived from a time delayed radial wave packet is consistent with a lifetime matrix which is Hermitian, this is not true for any Eisenbud-type lifetime matrix which violates time reversal invariance. Extending the angular time delay of Nussenzveig to multiple channels, we show that if one performs an average over the directions and subtracts the forward angle contribution containing an interference of the incident and scattered waves, the multichannel angle dependent average time delay reduces to the one given by Smith. The present work also rectifies a recently misinterpreted misnomer of the relation due to Smith.

nucl-th↗

arXiv2007

Comment on "Hadronic $^3$He$η$ production near threshold"

Measurements of the differential and total cross sections for the $p d \to ^3$He $η$ reaction at five energies were recently reported [Phys. Rev. C {\bf 75}, 014004 (2007)] and comparisons with theoretical models were made. We point out that these comparisons involved a model based on ad hoc assumptions and hence the conclusions regarding the reaction mechanism as well as the role of the higher partial waves drawn in the above work are misleading. Revised conclusions based on better model calculations are presented.

nucl-th↗

arXiv2007

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 formulae 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 super heavy 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.

nucl-th↗

arXiv2007

Breit type equation for mesonic atoms

The finite size effects and relativistic corrections in pionic and kaonic hydrogen are evaluated by generalizing the Breit equation for a spin-0 - spin-1/2 amplitude with the inclusion of the hadron electromagnetic form factors. The agreement of the relativistic corrections to the energies of the mesonic atoms with other methods used to evaluate them is not exact, but reasonably good. The precision values of the energy shifts due to the strong interaction, extracted from data, are however subject to the hadronic form factor uncertainties.

nucl-th↗

arXiv2007

A study of the $p d \to p d η$ reaction

A study of the $p d \to p d η$ reaction in the energy range where the recent data from Uppsala are available, is done in the two-step model of $η$ production including the final state interaction. The $η-d$ final state interaction is incorporated through the solution of the Lippmann Schwinger equation using an elastic scattering matrix element, $T_{ηd \to ηd}$, which is required to be half off-shell. It is written in a factorized form, with an off-shell form factor multiplying an on-shell part given by an effective range expansion up to the fourth power in momentum. The parameters of this expansion have been taken from an existing recent relativistic Faddeev equation solution for the $ηNN$ system corresponding to different $η-N$ scattering amplitudes. Calculations have also been done using few body equations within a finite rank approximation (FRA) to generate $T_{ηd \to ηd}$. The $p-d$ final state interaction is included in the spirit of the Watson-Migdal prescription by multiplying the matrix element by the inverse of the Jost function. The $η-d$ interaction is found to be dominant in the region of small invariant $η-d$ mass, $M_{ηd}$. The $p-d$ interaction enhances the cross section in the whole region of $M_{ηd}$, but is larger for large $M_{ηd}$. We find nearly isotropic angular distributions of the proton and the deuteron in the final state. All the above observations are in agreement with data. The production mechanism for the entire range of the existing data on the $p d \to p d η$ reaction seems to be dominated by the two-step model of $η$ production.

nucl-th↗

arXiv2006

Neutron structure effects in the deuteron and one neutron halos

Although the neutron (n) does not carry a total electric charge, its charge and magnetization distributions represented in momentum space by the electromagnetic form factors, $F_1^{(n)} (q^2)$ and $F_2^{(n)} (q^2)$, lead to an electromagnetic potential of the neutron. Using this fact, we calculate the electromagnetic corrections to the binding energy, $B_d$, of the deuteron and a one neutron halo nucleus (11Be), by evaluating the neutron-proton and the neutron-charged core (10Be) potential, respectively. The correction to $B_d$ (~9 keV) is comparable to that arising due to the inclusion of the $Δ$-isobar component in the deuteron wave function. In the case of the more loosely bound halo nucleus, 11Be, the correction is close to about 2 keV.

nucl-th↗

arXiv2006

Small eta-N scattering lengths favour eta-d and eta-alpha states

Unstable states of the eta meson and the 3He nucleus predicted using the time delay method were found to be in agreement with a recent claim of eta-mesic 3He states made by the TAPS collaboration. Here, we extend this method to a speculative study of the unstable states occurring in the eta-d and eta-4He elastic scattering. The T-matrix for eta-4He scattering is evaluated within the Finite Rank Approximation (FRA) of few body equations. For the evaluation of time delay in the eta-d case, we use a parameterization of an existing Faddeev calculation and compare the results with those obtained from FRA. With an eta-N scattering length, $a_{ηN} = (0.42, 0.34)$ fm, we find an eta-d unstable bound state around -16 MeV, within the Faddeev calculation. A similar state within the FRA is found for a low value of $a_{ηN}$, namely, $a_{ηN} = (0.28, 0.19)$ fm. The existence of an eta-4He unstable bound state close to threshold is hinted by $a_{ηN} = (0.28, 0.19)$ fm, but is ruled out by large scattering lengths.

nucl-th↗

arXiv2006

Possible eta-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 eta mesons and the 3He nucleus. Using few body equations to describe eta-3He elastic scattering, we predict resonances and unstable bound states within different models of the eta-N interaction. The eta-3He states predicted within this novel approach are in agreement with the recent claim of the evidence of eta-mesic 3He made by the TAPS collaboration.

nucl-th↗