arXiv subjects

Raj Kumar

Publications and source records attributed to Raj Kumar.

At least 55 records · Page 3Linked to original sources

arXiv2021

Fusion dynamics of $^{12}$C+$^{12}$C reaction: An astrophysical interest within the relativistic mean-field approach

The $^{12}$C+$^{12}$C fusion reaction plays a significant role in the later phases of stellar evolution. For a better understanding of the evolution involved, one must understand the corresponding fusion-fission dynamics and reaction characteristics. In the present analysis, we have studied the fusion cross-section along with the S-factor for this reaction using the well-known M3Y and recently developed R3Y nucleon-nucleon (NN) potential along with the relativistic mean-field densities in double folding approach. The density distributions and the microscopic R3Y NN potential are calculated using the NL3$^*$ parameter set. The $\ell$- summed Wong model is employed to investigate the fusion cross-section, with $\ell_{max}$-values from the sharp cut-off model. The calculated results are also then compared with the experimental data. It is found that the R3Y interaction gives a reasonable agreement with the data.

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arXiv2021

Fusion cross section of the superheavy $Z$ = 120 nuclei within the relativistic mean-field formalism

Present theoretical investigations aim to explore the fusion characteristics of various isotopes of Z=120 within the relativistic mean-field (RMF) formalism. We predict the most suitable projectile-target combination for the synthesis of element Z=120. The microscopic nucleon-nucleon R3Y interaction and the RMF density distributions for targets and projectiles are used to calculate the nuclear interaction potential using the double folding approach. 17 different projectile-target combinations that allow a high $N$/$Z$ ratio are considered in the present analysis to calculate the capture and/or fusion cross-section of various isotopes of Z=120 within the $\ell-$summed Wong formula. Further, the equivalent surface diffusion parameter is estimated to correlate the surface properties interacting nuclei with the fusion cross-section. The four Ti-based reactions with the heaviest available target $^{x}$Cf, namely, $^{46}$Ti+$^{248}$Cf, $^{46}$Ti+$^{249}$Cf, $^{50}$Ti+$^{249}$Cf, and $^{50}$Ti+$^{252}$Cf, and also $^{54}$Cr+$^{250}$Cm are found to have the most suitable target-projectile combinations for the synthesis of various isotopes Z=120. We also notice that $^{48}$Ca beams merely provide the required number of protons to synthesize the element with Z=120. We established a correlation among the surface properties of interacting nuclei with the fusion characteristics in terms of the equivalent surface diffusion parameter.

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arXiv2021

Structural and decay properties of nuclei appearing in the $α$-decay chains of $^{296,298,300,302,304}$120 within the relativistic mean-field formalism

An extensive study of $α$-decay half-lives for various decay chains of isotopes of $Z$ = 120 is performed within the axially deformed relativistic mean-field (RMF) formalism by employing the NL3, NL3$^*$, and DD-ME2 parameter set. The structural properties of the nuclei appearing in the decay chains are explored. The binding energy, quadrupole deformation parameter, root-mean-square charge radius, and pairing energy are calculated for the even-even isotopes of $Z$ = 100 $-$ 120, which are produced in five different $α$-decay chains, namely, $^{296}$120 $\rightarrow$ $^{260}$No, $^{298}$120 $\rightarrow$ $^{262}$No, $^{300}$120 $\rightarrow$ $^{264}$No, $^{302}$120 $\rightarrow$ $^{266}$No, and $^{304}$120 $\rightarrow$ $^{268}$No. A superdeformed prolate ground state is observed for the heavier nuclei, and gradually the deformation decreases towards the lighter nuclei in the considered decay chains. The RMF results are compared with various theoretical predictions and experimental data. The $α$-decay energies are calculated for each decay chain. To determine the relative numerical dependency of the half-life for a specific $α$-decay energy, the decay half-lives are calculated using four different formulas, namely, Viola-Seaborg, Alex-Brown, Parkhomenko-Sobiczewski, and Royer for the above said five $α$-decay chain. We notice a firm dependency of the half-life on the $α$-decay formula in terms of $Q_α$-values for all decay chains. Further, the present study also strengthens the prediction for the island of stability in terms of magic number at the superheavy valley in the laboratories.

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arXiv2021

Chandrayaan-2 Dual-Frequency SAR (DFSAR): Performance Characterization and Initial Results

The Dual-Frequency synthetic aperture radar (DFSAR) system manifested on the Chandrayaan-2 spacecraft represents a significant step forward in radar exploration of solid solar system objects. It combines SAR at two wavelengths (L- and S-bands) and multiple resolutions with several polarimetric modes in one lightweight ($\sim$ 20 kg) package. The resulting data from DFSAR support calculation of the 2$\times$2 complex scattering matrix for each resolution cell, which enables lunar near surface characterization in terms of radar polarization properties at different wavelengths and incidence angles. In this paper, we report on the calibration and preliminary performance characterization of DFSAR data based on the analysis of a sample set of crater regions on the Moon. Our calibration analysis provided a means to compare on-orbit performance with pre-launch measurements and the results matched with the pre-launch expected values. Our initial results show that craters in both permanently shadowed regions (PSRs) and non-PSRs that are classified as Circular Polarization Ratio (CPR)-anomalous in previous S-band radar analyses appear anomalous at L-band also. We also observe that material evolution and physical properties at their interior and proximal ejecta are decoupled. For Byrgius C crater region, we compare our analysis of dual-frequency radar data with the predicted behaviours of theoretical scattering models. If crater age estimates are available, comparison of their radar polarization properties at multiple wavelengths similar to that of the three unnamed south polar crater regions shown in this study may provide new insights into how the rockiness of craters evolves with time.

astro-ph.IM↗

arXiv2020

Characteristics of SEPs during Solar Cycle 21-24

The study of the solar energetic particle events (SEPs) and their association with solar flares and other activities are very crucial to understand the space weather. Keeping this in view, in this paper, we present the study of the SEPs (intensity equal to or greater than 10 pfu) during the solar cycle 21 to 24 (1976-2017) in > 10 MeV energy channels associated with solar flares. For our analysis, we have used the data from different instruments onboard SOHO satellite. We have examined the flare size, source location, CMEs characteristics of associated SEPs. About 31% and 69% of the SEPs were originated from the eastern and western solar hemisphere respectively. The average CME speed and width were 1238 km/s and 253 deg respectively. About 58 % SEPs were associated with halo CMEs and 42% of SEPs associated with CMEs width varying from 10 deg to 250 deg respectively.

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arXiv2018

Fusion cross-section for Ni-based reactions within the relativistic mean field formalism

In this theoretical study, we establish an interrelationship between the nucleon-nucleon interaction potential and the nuclear fusion reaction cross-sections at low energies. The axially deformed self-consistent relativistic mean field with non-linear NL3$^*$ force is used to calculate the density distribution of the projectile and target nuclei for fusion. The Wong formula is used to estimate the fusion cross-section and barrier distribution from the nucleus-nucleus optical potential for Ni-based systems, which are known for fusion hindrance phenomena. The results of the application of the so obtained nucleus-nucleus optical potential for the fusion cross-section from the recently developed relativistic $NN-$interaction (R3Y) are compared with the well-known, phenomenological M3Y effective $NN$ potential. We found a relatively good results from R3Y interactions below the barrier energies as compare to the M3Y potential concerning the experimental data. We also observe the density dependence on the nuclear interaction potential in terms of nucleon-nucleon optical potentials.

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arXiv2015

Nuclear fusion as a probe for octupole deformation in $^{224}$Ra

$\textit{Background}$: Nuclear fusion has been shown to be a perfect probe to study the different nuclear shapes. However, the possibility of testing octupole deformation of a nucleus with this tool has not been fully explored yet. The presence of a stactic octupole deformation in nuclei will enhanced a possible permanent electric dipole moment, leading to a possible demonstration of parity violation. $\textit{Purpose}$: To check whether static octupole deformation or octupole vibration in fusion give qualitatively different results so that both situations can be experimentally disentangled. $\textit{Method}$: Fusion cross sections are computed in the Coupled-Channels formalism making use of the Ingoing-Wave Boundary Conditions (IWBC) for the systems $^{16}$O+$^{144}$Ba and $^{16}$O+$^{224}$Ra. $\textit{Results}$: Barrier distributions of the two considered schemes show different patterns. For the $^{224}$Ra case, the octupole deformation parameter is large enough to create a sizeable difference. $\textit{Conclusions}$: The measurement of barrier distributions can be an excellent probe to clarify the presence of octupole deformation.

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arXiv2014

Enhanced subbarrier fusion for proton halo nuclei

In this short note we use a simple model to describe the dynamical effects of break-up processes in the subbarrier fusion involving weakly bound nuclei. We model two similar cases involving either a neutron or a proton halo nucleus, both schematically coupled to the break-up channels. We find that the decrease of the coulomb barrier in the proton break-up channel leads, ceteris paribus, to a larger enhancement of the subbarier fusion probabilities with respect to the neutron-halo case.

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arXiv2014

Convolution properties of univalent harmonic mappings convex in one direction

Let $\ast$ and $\widetilde {\ast}$ denote the convolution of two analytic maps and that of an analytic map and a harmonic map respectively. Pokhrel [1] proved that if $f = h+\overline{g}$ is a harmonic map convex in the direction of $e^{iγ}$ and $ϕ$ is an analytic map in the class DCP, then $f\widetilde{\ast} ϕ= h\widetilde{\ast}ϕ+ \overline{g\widetilde{\ast}ϕ}$ is also convex in the direction of $e^{iγ}$, provided $f\widetilde{\ast}ϕ$ is locally univalent and sense-preserving. In the present paper we obtain a general condition under which $f\widetilde{\ast} ϕ$ is locally univalent and sense-preserving. Some interesting applications of the general result are also presented.

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arXiv2013

On harmonic convolutions involving a vertical strip mapping

Let f_β= h_β+\bar{g}_βand F_a = H_a +\bar{G}_a be harmonic mappings obtained by shearing of analytic mappings h_β+g_β= 1/(2i\sinβ)log((1 + ze^{iβ})/(1 + ze^{-iβ})), 0<β<πand H_a+G_a = z/(1-z), respectively. Kumar et al. [5] conjectured that if ω(z)=e^{iθ}z^n (θ\in R, n\in N) and ω_a(z)=(a-z)/(1-az), a\in(-1,1) are dilatations of f_βand F_a, respectively, then F_a\ast f_β\in S_H^0 and is convex in the direction of the real axis provided a\in[(n-2)/(n + 2), 1).They claimed to have verified the result for n = 1, 2, 3 and 4 only. In the present paper, we settle the above conjecture in the affirmative for β=π/2 and for all n\in N.

math.CV↗

arXiv2013

An application of Cohn's rule to convolutions of univalent harmonic mappings

Dorff et al. [4], proved that the harmonic convolution of right half-plane mapping with dilatation -z and mapping f_β= h_β+ \bar{g}_β, where f_βis obtained by shearing of analytic vertical strip mapping, with dilatation e^{iθ}z^n; n = 1,2,θ\in R, is in S_H^0 and is convex in the direction of the real axis. In this paper, by using Cohn's rule, we generalize this result by considering dilatations (a-z)/(1-az), a\in (-1,1) and e^{iθ} z^n (n\in N;θ\in R) of right half-plane mapping and f_β, respectively.

math.CV↗

arXiv2013

Linear combinations of univalent harmonic mappings convex in the direction of the imaginary axis

In the present paper, we introduce a family of univalent harmonic functions, which map the unit disk onto domains convex in the direction of the imaginary axis. We find conditions for the linear combinations of mappings from this family to be univalent and convex in the direction of the imaginary axis. Linear combinations of functions from this family and harmonic mappings obtained by shearing of analytic vertical strip maps are also studied.

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arXiv2013

Convolution properties of some harmonic mappings in the right-half plane

Dorff, proved in [2] that the convolution of two harmonic right-half plane mappings is convex in the direction of real axis provided that the convolution is locally univalent and sense preserving. Later, it was shown in [3] that the condition of locally univalent and sense preserving can be dropped in some special cases. In this paper, we generalize the main result from [3].

math.CV↗

arXiv2011

Barrier modification in sub-barrier fusion reactions using Dynamical cluster-decay and extended-Wong models

Fusion-evaporation cross-sections σevr in reactions known for fusion hindrance phenomenon in coupled-channels calculations at below-barrier energies, are studied in terms of the dynamical cluster-decay model (DCM) of one of us (RKG) and Collaborators and the Wong formula extended by us, both based on proximity potential, by using the concept of "barrier modification" at sub-barrier energies, first advocated by Misicu and Esbensen for M3Y potential. The DCM is shown to contain the "barrier lowering" as its inbuilt characteristic, and the same is found essential, and introduced empirically, in the extended-Wong formula.

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arXiv2011

Temeprature-dependent Seeger's liquid drop energy for nuclei up to Z=118

Seeger's semi-empirical mass formula is revisited for two of its constants (bulk constant α(0) and neutron-proton asymmetry constant a_{a}) readjusted to obtain the ground-state (g.s.) binding energies of nuclei within a precision of <1.5 MeV and for nuclei up to Z=118. The aim is to include the temperature T-dependence on experimental binding energies, and not to obtain the new parameter set of Seeger's liquid drop energy VLDM . Our proceedure is to define the g.s. binding energy B = V_{LDM} + δU, as per Strutinsky renormalization procedure, and using the empirical shell corrections δU of Myers and Swiatecki, fit the constants of V_{LDM} to obtain the experimental binding energy Bexpt or theoretically calculated Btheo if data were not available. The T-dependence of the constants of V_{LDM}, is introduced as per the work of Davidson et al., where the pairing energy δ(T) is modified as per new calculations on compound nucleus decays. The newly fitted constants of V_{LDM} at T=0 are made available here for use of other workers interested in nuclear dynamics of hot and rotating nuclei.

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arXiv2010

Sudden- or Frozen-density approximation in Semi-classical extended Thomas Fermi model for Wong formula used in 64Ni+64Ni reaction

The {\ell}-summed Wong expression is applied in the semiclassical extended Thomas Fermi (ETF) method of Skyrme energy density formalism (SEDF), using both the sudden and frozen-density approximations, to the case of 64Ni+64Ni reaction data. We find that a very much improved fit (almost exact, point to point) to the data is obtained for the frozen-density approximation with {\ell}max (Ec.m.) varying smoothly. On the other hand, the same could not be achieved in the sudden case, still requiring a modification of the barrier at both the below- and above-barrier energies. This result means to say that the phenomenon of hindrance, observed in coupled channel calculations for 64Ni+64Ni reaction, could be explained simply on the basis of the {\ell}-summed Wong expression, at least for the frozen-density approximation in ETF method of SEDF.

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arXiv2010

Barrier modification in sub-barrier fusion reactions using Wong formula with Skyrme forces in semiclassical formalism

We obtain the nuclear proximity potential by using semiclassical extended Thomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), and use it in the extended $\ell$-summed Wong formula under frozen density approximation. This method has the advantage of allowing the use of different Skyrme forces, giving different barriers. Thus, for a given reaction, we could choose a Skyrme force with proper barrier characteristics, not-requiring extra ``barrier lowering" or ``barrier narrowing" for a best fit to data. For the $^{64}$Ni+$^{100}$Mo reaction, the $\ell$-summed Wong formula, with effects of deformations and orientations of nuclei included, fits the fusion-evaporation cross section data exactly for the force GSkI, requiring additional barrier modifications for forces SIII and SV. However, the same for other similar reactions, like $^{58,64}$Ni+$^{58,64}$Ni, fits the data best for SIII force. Hence, the barrier modification effects in $\ell$-summed Wong expression depends on the choice of Skyrme force in extended ETF method.

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arXiv2010

Skyrme-force dependence of fusion cross-sections using Wong formula in semiclassical formalism

we use the nuclear proximity potential obtained recently for the Skyrme nucleus-nucleus interaction in the semiclassical extended Thomas Fermi (ETF) approach using Skyrme energy density formalism (SEDF) under frozen-density (sudden-without-exchange) approximation, and $Φ$=0$^0$. This method allows the barrier modifications by using different Skyrme forces, since a different Skyrme force would mean different barrier characteristics, and possibly a different force for different reaction cross-section.

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