arXiv subjects

N. G. Kelkar

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

At least 19 recordsLinked to original sources

arXiv2026

Clustering in hadrons and light nuclei from Lorentz boosted form factors

The determination of nuclear charge radii is crucial for understanding the internal structure of nuclei and their fundamental interactions. A persistent discrepancy, not only in the measured proton charge radius but also in the light nucleus charge radius, between electron scattering and muonic spectroscopy has fueled ongoing debates in nuclear and particle physics. Using this discrepancy, we revisit the role of one of the proposed solutions, namely the use of Lorentz-boosted nuclear form factors to find a subtle connection between the boost and the cluster structure of nuclei. By applying two distinct relativistic formalisms, namely the Licht-Pagnamenta and Mitra-Kumari approaches, we systematically analyze corrections to the moments of the density distributions in hadrons and nuclei. Our results demonstrate that boosting the form factors from the Breit to the rest frame of the nucleus not only assists in reconciling the spectroscopic and scattering measurements but also provides a method to infer on the quark and nucleon cluster configurations within nuclei.

nucl-th↗

arXiv2024

Dissipation in quantum tunnel junctions

Based on experimental data, we propose a model to evaluate the energy dissipated during quantum tunneling processes in solid-state junctions. This model incorporates a nonlinear friction force expressed in the general form f(x)=γ v(x)^α, where γ is the frictional coefficient, which is fitted to data. We study this by applying voltages just below the barrier height up to near break down voltages. Furthermore, by lowering the temperature and adjusting the applied voltage to the junction, the effect on dissipation caused by the variation in barrier height is examined. We underline that the crucial dependency of dissipation on the fraction of particle energy lost is modulated by two primary mechanisms: the application of voltage and the variation of temperature. The fraction of energy dissipated decreases in general for increasing energies of the tunneling particles at a given temperature. However, for a given energy of the tunneling particle, the present work demonstrates a turning point at a temperature of 137 K, after which the dissipated energy starts increasing for higher temperatures. The latter can possibly be due to the increase of electron-phonon interactions which become predominant over barrier height reduction at higher temperatures and hence we identify T = 137 K as a critical temperature for change in dissipative characteristics of the solid-state junction under consideration. Notably, also the study identifies significant changes in dissipation parameters, γ and α, above 137 K, exhibiting a linear decline and underscoring the importance of further research at higher temperatures.

cond-mat.mes-hall↗

arXiv2024

Alpha decay law of excited nuclei and its role in stellar decay rates

$α$ decay is one of the prominent decay modes in the nucleosynthesis of heavy and super-heavy elements synthesized at temperatures of the order of Giga Kelvin. To facilitate the investigation of the role played by the $α$ decay half-lives of thermally excited nuclei in nucleosynthesis calculations, an empirical formula based on a model for the $α$ decay of nuclei in their ground and excited states to daughter nuclei in their ground or excited states is presented. Constants appearing in the analytical expression for the $α$ decay half-life obtained within the model are treated as adjustable parameters and fitted to experimental data on 342 $α$ decays in the range of 82 $\le Z_p \le$ 94, to obtain an excitation energy-dependent decay law. Under the assumption that thermal equilibrium has been reached between nuclear states, temperature ($T$)-dependent half-lives, $t_{1/2}(T)$, for several of the experimentally studied $α$ emitters with 65 $\le Z_p \le$ 94 are presented using available data on the half-lives of excited nuclei. Though the general trend is a decrease in $t_{1/2}(T)$ at elevated temperatures, exceptional cases with increased half-lives are found in the case of some isomeric states. A list of such isomers provided in this work motivates future work involving considerations of their thermal equilibration and role in shaping kilonova light curves.

nucl-th↗

arXiv2024

Quantum Corrections to the Decay Law in Flight

The deviation of the decay law from the exponential is a well known effect of quantum mechanics. Here we analyze the relativistic survival probabilities, $S(t,p)$, where $p$ is the momentum of the decaying particle and provide analytical expressions for $S(t,p)$ in the exponential (E) as well as the nonexponential (NE) regions at small and large times. Under minimal assumptions on the spectral density function, analytical expressions for the critical times of transition from the NE to the E at small times and the E to NE at large times are derived. The dependence of the decay law on the relativistic Lorentz factor, $γ= 1/\sqrt{1 - v^2/c^2}$, reveals several interesting features. In the short time regime of the decay law, the critical time, $τ_{st}$, shows a steady increase with $γ$, thus implying a larger NE region for particles decaying in flight. Comparing $S(t,p)$ with the well known time dilation formula, $e^{-Γt/γ}$, in the exponential region, an expression for the critical $γ$ where $S(t,p)$ deviates most from $e^{-Γt/γ}$ is presented. This is a purely quantum correction. Under particular conditions on the resonance parameters, there also exists a critical $γ$ at large times which decides if the NE region shifts backward or forward in time as compared to that for a particle at rest. All the above analytical results are supported by calculations involving realistic decays of hadrons and leptons.

hep-ph↗

arXiv2022

Temperature dependence of cluster decay

A universal decay law (UDL) for light cluster decay of excited nuclei is formulated by fitting the UDL half-lives to those evaluated within an excitation energy-dependent double folding model (DFM). The half-lives are evaluated within a preformed cluster model. The excitation energy dependence is introduced both in the energy of the emitted cluster and in the interaction potential through the density distributions of the interacting nuclei. The half-lives are found to decrease when the difference between the excitation energies of the parent and daughter nuclei, $ΔE^{*} > $ 0, increases, with the reduction being a few orders of magnitude for higher values of $ΔE^{*}$. This can be of importance for nucleosynthesis calculations of heavy elements formed in extremely hot environments, as well as in highly energetic heavy-ion collisions. The UDL for excited nuclei is used to provide an estimate of the enhancement in the cluster decay rates of thermally excited nuclei such as those produced in r-process nucleosynthesis.

nucl-th↗

arXiv2022

Alpha decay of thermally excited nuclei

One of the prominent decay modes of heavy nuclei which are produced in astrophysical environments at temperatures of the order of $10^9$ K is the $α$ ($^4$He) decay. Thermally enhanced $α$ decay rates are evaluated within the standard scheme of a tunneling decay where the $α$ particle tunnels through the potential barrier formed by its interaction with the daughter nucleus. Following the observation that there exist several excited levels with the possibility of an $α$ decay when the daughter nucleus is at a shell closure, we focus in particular on decays producing daughter nuclei with the neutron number, N = 126. Within a statistical approach we find that the half-lives, $t_{1/2}(T)$, for temperatures ranging from $T$ = 0 to 2.4 GK can decrease by 1 - 2 orders of magnitude with the exception of the decay of $^{212}$Po which decays to the doubly magic daughter $^{208}$Pb, where $t_{1/2}(T)$ decreases by 5 orders of magnitude. The effect of these thermally enhanced $α$ decays on the $r$-process nucleosynthesis can be significant in view of the mass build up at the waiting point nuclei with closed neutron shells.

nucl-th↗

arXiv2022

Massive white dwarfs in $f(R,L_m)$ gravity

In this work, we investigate the equilibrium configurations of massive white dwarfs (MWD) in the context of modified gravity, namely $f(R,L_m)$ gravity, where $R$ stands for the Ricci scalar and $L_m$ is the Lagrangian matter density. We focused on the specific case $f(R,L_m) = R/2 + L_m + σRL_m$, i.e., we have considered a non-minimal coupling between the gravity field and the matter field, with $σ$ being the coupling constant. For the first time, the theory is applied to white dwarfs, in particular to study massive white dwarfs, which is a topic of great interest in the last years. The equilibrium configurations predict maximum masses which are above the Chandrasekhar mass limit. The most important effect of the theory is to increase significantly the mass for stars with radius < 2000 km. We found that the theory can accommodate the super-Chandrasekhar white dwarfs for different star compositions. Apart from this, the theory recovers the General Relativity results for stars with radii larger than 3000 km, independent of the value of $σ$.

gr-qc↗

arXiv2022

Manifestation of deformation and nonlocality in $α$ and cluster decay

It is common to study the strong decay of a heavy nucleus as a tunneling phenomenon where the $α$ ($^4$He) or a light nuclear cluster tunnels through the Coulomb barrier formed by its interaction with the heavier daughter nucleus. The position and width of the Coulomb barrier are determined by the total interaction potential between the two daughter nuclei. We examine the effects of including nonlocality and deformation in the interaction potential by calculating the half-lives, $t_{1/2}$, and thereby phenomenological preformation factors of several nuclei which have the possibility of decaying by emitting either an $α$ or a light nuclear cluster. The effect of deformation manifests itself by a decrease in $t_{1/2}$ for all the decays studied. The effect of nonlocality is studied within two different models of the nuclear potential: the energy-independent but angular momentum ($l$) dependent Mumbai (M) potential and the energy-dependent Perey-Buck (PB) potential. The nonlocal nuclear interaction leads to a decrease in all half-lives studied. Though the decrease is larger due to the Perey-Buck potential, half-lives evaluated using the Mumbai potential show a strong sensitivity to the $l$ value in the decay. This feature of the $α$ and cluster decay half-lives can provide a complementary tool in addition to scattering data which are more commonly used to fix the parameters of a nonlocal potential in literature.

nucl-th↗

arXiv2021

Formal Aspects of Quantum Decay

The Fock-Krylov formalism for the calculation of survival probabilities of unstable states is revisited paying particular attention to the mathematical constraints on the density of states, the Fourier transform of which gives the survival amplitude. We show that it is not possible to construct a density of states corresponding to a purely exponential survival amplitude. he survival probability $P(t)$ and the autocorrelation function of the density of states are shown to form a pair of cosine Fourier transforms. This result is a particular case of the Wiener Khinchin theorem and forces $P(t)$ to be an even function of time which in turn forces the density of states to contain a form factor which vanishes at large energies. Subtle features of the transition regions from the non-exponential to the exponential at small times and the exponential to the power law decay at large times are discussed by expressing $P(t)$ as a function of the number of oscillations, $n$, performed by it. The transition at short times is shown to occur when the survival probability has completed one oscillation. The number of oscillations depend on the properties of the resonant state and a complete description of the evolution of the unstable state is provided by determining the limits on the number of oscillations in each region.

quant-ph↗

arXiv2020

Search for the $η$ mesic $^3$He in the $pd\rightarrow d p π^{0}$ reaction with the WASA-at-COSY facility

The excitation function for the $pd\rightarrow$ $d p π^{0}$ reaction has been measured by WASA-at-COSY experiment with the aim of searching for $^{3}\hspace{-0.03cm}\mbox{He}$-$η$ mesic nuclei. The measurement in the vicinity of $η$ meson production was performed using a ramped proton beam. The data analysis and interpretation was carried out with the assumption that the $η$-mesic Helium decays via the formation of an intermediate N$^{*}$(1535) resonance. No direct signal of the $η$-mesic nucleus is observed in the excitation function. We determine a new improved upper limit for the total cross section for the bound state production and decay in the $pd\rightarrow$ $(^{3}\hspace{-0.03cm}\mbox{He}$-$η)_{bound} \rightarrow$ $d p π^{0}$ process. It varies between 13 nb to 24 nb for the bound state with width in the range $Γ\in (5,50)$ MeV.

nucl-ex↗

arXiv2020

Electron interaction with the environment in tunnel ionization

The average dwell time of an electron in a potential barrier formed by an external electric field and the potential of a helium atom is evaluated within a semi classical one-dimensional tunneling approach. The tunneling electron is considered to interact with a nuclear charge screened by the electron in the helium ion. It is found that screening leads to smaller average dwell times of the tunneling electron. The dissipative effect of the environment on the tunneling electron is taken into account within a semiclassical model involving a velocity dependent frictional force and is found to change the average dwell time significantly.

quant-ph↗

arXiv2020

Search for eta mesic 3He with the WASA-at-COSY facility in the pd-> 3He 2gamma and pd-> 3He 6gamma reactions

We report on the experimental search for the bound state of an $η$ meson and $^{3}\hspace{-0.03cm}\mbox{He}$ nucleus performed using the WASA-at-COSY detector setup. In order to search for the $η$-mesic nucleus decay, the $pd\rightarrow$ $^{3}\hspace{-0.03cm}\mbox{He} 2γ$ and $pd\rightarrow$ $^{3}\hspace{-0.03cm}\mbox{He} 6γ$ channels have been analysed. These reactions manifest the direct decay of $η$ meson bound in $^{3}\hspace{-0.03cm}\mbox{He}$ nucleus. This non-mesonic decay channel has been considered for the first time. When taking into account only statistical errors, the obtained excitation functions reveal a slight indication for a possible bound state signal corresponding to an $^3$He-$η$ nucleus width $Γ$ above 20 MeV and binding energy $B_s$ between 0 and 15 MeV. However, the determined cross sections are consistent with zero in the range of the systematic uncertainty. Therefore, as final result we estimate only the upper limit for the cross section of the $η$-mesic $^{3}\hspace{-0.03cm}\mbox{He}$ nucleus formation followed by the $η$ meson decay which varies between $2$ nb and $15$ nb depending on possible bound state parameters.

nucl-ex↗

arXiv2019

Perturbing microscopic black holes inspired by noncommutativity

We probe into the instabilities of microscopic quantum black holes. For this purpose, we study the quasinormal modes (QNMs) for a massless scalar perturbation of the noncommutative geometry inspired Schwarzschild black hole. By means of a sixth order Wentzel-Kramers-Brillouin (WKB) approximation we show that the widely used WKB method does not converge in the critical cases where instabilities show up at the third order. By employing the inverted potential method, we demonstrate that the instabilities are an artifact of the WKB method. Finally, we discuss the usefulness of the asymptotic iteration method to find the QNMs.

gr-qc↗

arXiv2019

Critical view of nonlocal nuclear potentials in alpha decay

Different models for the nonlocal description of the nuclear interaction are compared through a study of their effects on the half-lives of radioactive nuclei decaying by the emission of alpha particles. The half-lives are evaluated by considering a pre-formed alpha particle ($^4$He nucleus) which tunnels through the Coulomb barrier generated by its interaction with the daughter nucleus. An effective potential obtained from a density dependent double folding strong potential between the alpha and the daughter nucleus within the nonlocal framework is found to decrease the half-lives as compared to those in the absence of nonlocalities. Whereas the percentage decrease within the older Perey-Buck and São Paulo models ranges between 20 to 40\% for medium to heavy nuclei, a recently proposed effective potential leads to a decrease of only 2 - 4 \%. In view of these results, we provide a closer examination of the approximations used in deriving the local equivalent potentials and propose that apart from the scattering data, the alpha decay half-lives could be used as a complementary tool for constraining the nonlocality models.

nucl-th↗

arXiv2019

Quantum decay law: Critical times and the Equivalence of approaches

Methods based on the use of Green's functions or the Jost functions and the Fock-Krylov method are apparently very different approaches to understand the time evolution of unstable states. We show that the two former methods are equivalent up to some constants and as an outcome find an analytic expression for the energy density of states in the Fock-Krylov amplitude in terms of the coefficients introduced in the Green's functions and the Jost functions methods. This model-independent density is further used to obtain an analytical expression for the survival amplitude and study its behaviour at large times. Using these expressions, we investigate the origin of the oscillatory behaviour of the decay law in the region of the transition from the exponential to the non-exponential at large times. With the objective to understand the failure of nuclear and particle physics experiments in observing the non-exponential decay law predicted by quantum mechanics for large times, we derive analytical formulae for the critical transition time, $t_c$, from the exponential to the inverse power law behaviour at large times. Evaluating $τ_c = Γt_c$ for some particle resonances and narrow nuclear states which have been tested experimentally to verify the exponential decay law, we conclude that the large time power law in particle and nuclear decay is hard to find experimentally.

quant-ph↗

arXiv2018

Short Range Interactions in the Hydrogen Atom

In calculating the energy corrections to the hydrogen levels we can identify two different types of modifications of the Coulomb potential $V_{C}$, with one of them being the standard quantum electrodynamics corrections, $δV$, satisfying $\left|δV\right|\ll\left|V_{C}\right|$ over the whole range of the radial variable $r$. The other possible addition to $V_{C}$ is a potential arising due to the finite size of the atomic nucleus and as a matter of fact, can be larger than $V_{C}$ in a very short range. We focus here on the latter and show that the electric potential of the proton displays some undesirable features. Among others, the energy content of the electric field associated with this potential is very close to the threshold of $e^+e^-$ pair production. We contrast this large electric field of the Maxwell theory with one emerging from the non-linear Euler-Heisenberg theory and show how in this theory the short range electric field becomes smaller and is well below the pair production threshold.

physics.atom-ph↗

arXiv2018

Different manifestations of S-matrix poles

Making use of the analytical properties of the $S$-matrix and a theorem of Mittag-Leffler, model independent non-relativistic expressions for cross sections in single channel elastic scattering, scattering phase shifts and survival probabilities of resonances are derived. Provided certain conditions are satisfied by the poles, the residues can also be estimated analytically. Considerations of the low energy behaviour of the $S$-matrix and cross sections reveal additional conditions on the residues of the poles appearing in the Mittag-Leffler expansions. The exact expressions for the resonant cross section and phase shift are shown to reduce to the commonly used Breit-Wigner formula plus corrections. The latter is shown to approach the exact result with the example of a meson and a baryon resonance. Finally, a comparison of the exact expressions with some realistic examples is presented. The calculations of survival probabilities in particular reveal the reason behind the non-observability of non-exponential decay.

hep-ph↗

arXiv2018

Constraining the optical potential in the search for eta-mesic 4He

A consistent description of the $ d d \rightarrow$ $^{4}\hspace{-0.03cm}\mbox{He} η$ and $ d d \rightarrow$ ($^4$He$η$)$_{bound} \rightarrow X $ cross sections was recently proposed with a broad range of real ($V_{0}$) and imaginary (W0), $η$-$^4$He optical potential parameters leading to a good agreement with the d d -> 4He eta data. Here we compare the predictions of the model below the $η$ production threshold, with the WASA-at-COSY excitation functions for the dd -> 3He N pi reactions to put stronger constraints on (V0, W0). The allowed parameter space (with |V_0| < \sim 60 MeV and |W_0| < \sim 7 MeV estimated at 90% CL ) excludes most optical model predictions of eta-4He nuclei except for some loosely bound narrow states.

nucl-ex↗