arXiv subjects
Publications and source records attributed to S. Kundu.
This paper studies various completeness properties of the open-point and bi-point-open topologies on the space C(X) of all real-valued continuous functions on a Tychonoff space X. The properties range from complete metrizability to the Baire space property.
For the set C(X) of real-valued continuous functions on a Tychonoff space X, the compact-open topology on C(X) is a "set-open topology". This paper studies the separation and countability properties of the space C(X) having the topology given by the join of the compact-open topology and an "open-set topology" called the open-point topology, that was introduced in [6].
The even-even nucleus $^{26}$Mg has been studied through the reaction $^{27}$Al(d,$^{3}$He) at 25 MeV beam energy. The spectroscopic factors have been extracted upto 7.50 MeV excitation energy using local, zero range distorted wave Born approximation. The comparison of the spectroscopic factors have been done with previously reported values using the same reaction probe. The extracted spectroscopic factors for different excited states were found to be in good agreement with the previously reported values for the same. The present results were also compared with the predictions from shell model as well as rotational model. The analog states of $^{26}$Al and $^{26}$Mg were found to be in good agreement.
Mass distributions of the fragments in the fission of $^{206}$Po and the N=126 neutron shell closed nucleus $^{210}$Po have been measured. No significant deviation of mass distributions has been found between $^{206}$Po and $^{210}$Po, indicating the absence of shell correction at the saddle point in both the nuclei, contrary to the reported angular anisotropy and pre-scission neutron multiplicity results. This new result provides benchmark data to test the new fission dynamical models to study the effect of shell correction on the potential energy surface at saddle point.
We report static and dynamic properties of the antiferromagnetic compound Zn$_{2}$(VO)(PO$_{4}$)$_{2}$, and the consequences of non-magnetic Ti$^{4+}$ doping at the V$^{4+}$ site. $^{31}$P nuclear magnetic resonance (NMR) spectra and spin-lattice relaxation rate ($1/T_1$) consistently show the formation of the long-range antiferromagnetic order below $T_N= 3.8-3.9$\,K. The critical exponent $β=0.33 \pm 0.02$ estimated from the temperature dependence of the sublattice magnetization measured by $^{31}$P NMR at 9.4\,MHz is consistent with universality classes of three-dimensional spin models. The isotropic and axial hyperfine couplings between the $^{31}$P nuclei and V$^{4+}$ spins are $A_{\rm hf}^{\rm iso} = (9221 \pm 100)$ Oe/$μ_{\rm B}$ and $A_{\rm hf}^{\rm ax} = (1010 \pm 50)$ Oe/$μ_{\rm B}$, respectively. Magnetic susceptibility data above 6.5\,K and heat capacity data above 4.5\,K are well described by quantum Monte-Carlo simulations for the Heisenberg model on the square lattice with $J\simeq 7.7$\,K. This value of $J$ is consistent with the values obtained from the NMR shift, $1/T_1$ and electron spin resonance (ESR) intensity analysis. Doping Zn$_2$VO(PO$_4)_2$ with non-magnetic Ti$^{4+}$ leads to a marginal increase in the $J$ value and the overall dilution of the spin lattice. In contrast to the recent \textit{ab initio} results, we find neither evidence for the monoclinic structural distortion nor signatures of the magnetic one-dimensionality for doped samples with up to 15\% of Ti$^{4+}$. The Néel temperature $T_{\rm N}$ decreases linearly with increasing the amount of the non-magnetic dopant.
Constraining excitation energy at which nuclear shell effect washes out has important implications on the production of super heavy elements and many other fields of nuclear physics research. We report the fission fragment mass distribution in alpha induced reaction on an actinide target for wide excitation range in close energy interval and show direct evidence that nuclear shell effect washes out at excitation energy ~40 MeV. Calculation shows that second peak of the fission barrier also vanishes around similar excitation energy.
We report experimental signals of Bose-Einstein condensation in the decay of hot Ca projectile-like sources produced in mid-peripheral collisions at sub-Fermi energies. The experimental setup, constituted by the coupling of the INDRA 4$π$ detector array to the forward angle VAMOS magnetic spectrometer, allowed us to reconstruct the mass, charge and excitation energy of the decaying hot projectile-like sources. Furthermore, by means of quantum fluctuation analysis techniques, temperatures and mean volumes per particle "as seen by" bosons and fermions separately are correlated to the excitation energy of the reconstructed system. The obtained results are consistent with the production of dilute mixed (bosons/fermions) systems, where bosons experience a smaller volume as compared to the surrounding fermionic gas. Our findings recall similar phenomena observed in the study of boson condensates in atomic traps.
High-spin states in the doubly-odd $^{198}$Bi nucleus have been studied by using the $^{185,187}$Re($^{16}$O, xn) reactions at the beam energy of 112.5 MeV. $γ-γ$ coincidence were measured by using the INGA array with 15 Compton suppressed clover HPGe detectors. The observed levels have been assigned definite spin-parity. The high spin structure is grouped into three bands (B1, B2 and B3), of which two (B1 and B2) exhibit the properties of magnetic rotation (MR). Tilted axis cranking calculations were carried out to explain the MR bands having large multi-quasiparticle configurations. The calculated results explain the bands B1 and B2 very nicely, confirming the shears mechanism and suggest a crossing of two MR bands in both the cases. The crossing is from 6-qp to 8-qp in band B1 and from 4-qp to 6-qp in band B2, a very rare finding. A semiclassical model has also been used to obtain the particle-hole interaction strengths for the bands B1 and B2, below the band crossing.
The excited states in the odd-$A$ $^{197}$Tl nucleus have been studied by populating them using the $^{197}$Au($α$, 4$n$)$^{197}$Tl reaction at the beam energy of 48 MeV. The $γ-γ$ coincidence data were taken using a combination of clover, LEPS and single crystal HPGe detectors. Precise spin and parity assignments of the excited states have been done through the polarization and the DCO measurements. A new band structure has been identified and the evidence for a possible intruder $πi_{13/2}$ state has been found for the first time. Possible configurations of the observed bands have been discussed. The total Routhian surface calculations have been performed to study the shape of $^{197}$Tl for different configurations.
Detailed dc and ac magnetic properties of chemically synthesized Nd0.4Sr0.6MnO3 with different particle size (down to 27 nm) have been studied in details. We have found ferromagnetic state in the nanoparticles, whereas, the bulk Nd0.4Sr0.6MnO3 is known to be an A-type antiferromagnet. A Griffiths-like phase has also been identified in the nanoparticles. Further, critical behavior of the nanoparticles has been studied around the second order ferromagnetic-paramagnetic transition region (|(T-TC)/TC|£ 0.04) in terms of modified Arrott plot, Kouvel-Fisher plot and critical isotherm analysis. The estimated critical exponents (b,g,d) are quite different from those predicted according to three-dimensional mean-field, Heisenberg and Ising models. This signifies a quite unusual nature of the size-induced ferromagnetic state in Nd0.4Sr0.6MnO3. The nanoparticles are found to be interacting and do not behave like ideal superparamagnet. Interestingly, we find spin glass like slow relaxation of magnetization, aging and memory effect in the nanometric samples. These phenomena have been attributed to very broad distribution of relaxation time as well as to inter-particle interaction. Experimentally, we have found out that the dynamics of the nanoparticle systems can be best described by hierarchical model of spin glasses.
Inclusive energy spectra of the complex fragments (3 $\leq$ Z $\leq$ 5) emitted in the reactions $^{12}$C (77 MeV)+ $^{28}$Si, $^{11}$B (64 MeV)+ $^{28}$Si and $^{12}$C (73 MeV)+ $^{27}$Al (all having the same excitation energy of $ \sim$ 67 MeV), have been measured in the angular range of 10$^\circ$ $\lesssim θ_{lab} \lesssim$ 60$^\circ$. The fully energy damped (fusion-fission) and the partially energy damped (deep inelastic) components of the fragment energy spectra have been extracted. It has been found that the yields of the fully energy damped fragments for all the above reactions are in conformity with the respective statistical model predictions. The time scales of various deep inelastic fragment emissions have been extracted from the angular distribution data. The angular momentum dissipation in deep inelastic collisions has been estimated from the data and it has been found to be close to the corresponding sticking limit value.
The energy spectra of the $α$ particles emitted in the reactions $^{16}$O (7-10 MeV/nucleon) + $^{12}$C have been measured in the center of mass angular range of 25$^\circ$ $\lesssim θ_{c.m.} \lesssim$ 70$^\circ$. The experimental energy spectra have been compared with those obtained from the statistical model calculation with "deformability" parameters predicted by rotating liquid drop model (RLDM) and also fitted the same with optimized "deformability" parameters, which are quite different from the respective RLDM values. The data have also been found to be explained quite well using "frozen" deformation approximation, where the "deformability" parameters have been kept fixed at RLDM values of the parent nucleus throughout the decay process. The effective radius in the latter case is smaller compared to that obtained using the optimized parameters; however, in both cases, the deformations (effective radii) are larger than the corresponding RLDM values. So, considering the uncertainties in the estimation of actual compound nucleus deformations, it can, only qualitatively, be said that equilibrium orbiting, which is similar to particle evaporation in time scale, could also be one of the contributing factors for the observed deformation.
A detailed investigation of electronic-transport properties of Nd0.5Sr0.5CoO3 has been carried out as a function of grain size ranging from micrometer order down to an average size of 28 nm. Interestingly, we observe a size induced metal-insulator transition in the lowest grain size sample while the bulk-like sample is metallic in the whole measured temperature regime. An analysis of the temperature dependent resistivity in the metallic regime reveals that the electron-electron interaction is the dominating mechanism while other processes like electron-magnon and electron-phonon scatterings are also likely to be present. The fascinating observation of enhanced low temperature upturn and minimum in resistivity on reduction of grain size is found due to electron-electron interaction (quantum interference effect). This effect is attributed to enhanced disorder on reduction of grain size. Interestingly, we observed a cross over from positive to negative magnetoresistance in the low temperature regime as the grain size is reduced. This observed sign reversal is attributed to enhanced phase separation on decreasing the grain size of the cobaltite.
The high spin states in $^{195}$Bi has been studied by $γ$-ray spectroscopic method using the $^{181}$Ta($^{20}$Ne, 6n) fusion evaporation reaction at 130 MeV. The $γγ$ coincidence data were taken using an array of 8 clover HPGe detectors. The spin and parity assignments of the excited states have been made from the measured directional correlation from oriented states (DCO) ratios and integrated polarization asymmetry (IPDCO) ratios. The results show, for the first time, the evidence of a rotational like band based on a 13/2$^+$ band head in this nucleus, indicating the onset of deformation at neutron number $N = 112$ for the Bismuth isotopes. The results obtained were found to be consistent with the prediction of the total Routhian surface calculations using Woods Saxon potential. The same calculations also predict a change in shape from oblate to triaxial in $^{195}$Bi at high rotational frequency.
An excited state of $^{12}$C having excitation energy E$_x \sim$ 9.65 $\pm$ 0.02 MeV and width (FWHM) $\sim607\pm$ 55 keV, which decays to three $ α$-particles via Hoyle state ($E_x \sim$ 7.65 MeV), has been directly identified for the first time in the exclusive inelastic scattering of 60 MeV $^{4}$He on $^{12}$C, measured in coincidence with the recoiling $^{12}$C$ ^* $ Hoyle state (decaying mostly as $^{12}$C$ ^* $ $\rightarrow \ ^{8} $Be + $ α$ $\rightarrow \ α+ α+ α$) by event-by-event kinematic reconstruction of the completely detected (4$ α$) events. This state is likely to be a candidate for 2$_2^+$ first excited Hoyle state, the existence of which has recently been indirectly evidenced from the recent inclusive inelastic scattering studies.
The systematic evolution of the giant dipole resonance (GDR) width in the temperature region of 0.9 ~ 1.4 MeV has been measured experimentally for 119Sb using alpha induced fusion reaction and employing the LAMBDA high energy photon spectrometer. The temperatures have been precisely determined by simultaneously extracting the vital level density parameter from the neutron evaporation spectrum and the angular momentum from gamma multiplicity filter using a realistic approach. The systematic trend of the data seems to disagree with the thermal shape fluctuation model (TSFM). The model predicts the gradual increase of GDR width from its ground state value for T > 0 MeV whereas the measured GDR widths appear to remain constant at the ground state value till T ~ 1 MeV and increase thereafter indicating towards a failure of the adiabatic assumption of the model at low temperature.
We have described here the design and operation of an automated ac susceptibility set up using a closed cycle helium refrigerator. This set up is useful for measuring linear and nonlinear magnetic susceptibilities of various magnetic materials. The working temperature range is 2 K to 300 K. The overall sensitivity of the set up is found to be 10-3 emu.
The effect of doping of rare earth Gd 3+ ion replacing Nd 3+ in Nd0.7Sr0.3MnO3 is investigated in details. Measurements of resistivity, magnetoresistance, magnetization, linear and non linear ac magnetic susceptibility on chemically synthesized (Nd0.7-xGdx)Sr0.3MnO3 shows various interesting features with doping level x=0.3. Comparative study has been carried out between a bulk and a nanometric sample (grain size ~ 60 nm) synthesized from the same as prepared powder to maintain identical stoichiometry. Resistivity of the samples shows strong dependence on the magnetic field - temperature history. The magnetoresistance of the samples also show strong irreversibility with respect to sweeping of the field between highest positive and negative values. Moreover, resistivity is found to increase with time after field cooling and then switching off the field. All these phenomena have been attributed to phase separation effect and arrest of phases in the samples. Furthermore, the bulk sample displays a spin glass like behaviour as evident from frequency dependence of linear ac magnetic susceptibility and critical divergence of the nonlinear ac magnetic susceptibility. The experimentally obtained characteristic time t after dynamical scaling analysis of the frequency dependence of the ac susceptibility is found to be t=10-17 s which implies that the system is different from a canonical spin glass. An unusual frequency dependence of the second harmonic of ac susceptibility around the magnetic transition temperature led us to designate the magnetic state of the sample to be glassy ferromagnetic. On reduction of grain size low field magnetoresistance and phase arrest phenomena are found to enhance but the glassy state is observed to be destabilized in the nanometric sample.