Browsing by Author "S.N. Mukherjee"

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A simple coordinate space approach to three-body problems - Examples: Halo nucleus and double-λ hypernucleus
(Indian Academy of Sciences, 2001) S. Mahapatra; J. Nag; D.P. Sural; S.N. Mukherjee
We show how to treat the dynamics of an asymmetric three-body system consisting of one heavy and two identical light particles in a simple coordinate space variational approach. The method is constructive and gives an efficient way of resolving a three-body system to an effective two-body system. It is illustrated by explaining the structural properties of some nuclei of current interest, namely halo nuclei and double-λ hypernuclei. The ansatz used here may be of value in a number of three particle problems of similar nature.
Analytically soluble model for fusion time
(1990) V.J. Menon; S.N. Mukherjee; C.S. Shastry; B. Sahu
We derive an analytical expression for the essential parameters (viz., positions, heights, and curvatures) characterizing the extrema of the effective potential between two heavy ions. These parameters together with the energy are used to calculate, in closed form, the times for complete fusion above the Coulomb barrier. The method is found to work well for nuclear (and/or Coulomb) trajectories of zero or small orbital angular momentum when friction is absent. The inclusion of dissipation is shown to reduce the fusion time substantially for typical heavy-ion systems provided the energy satisfies certain kinematic constraints. © 1990 The American Physical Society.
Criterion for a unique non-relativistic quark model
(1989) R. Nag; S.N. Mukherjee; S. Sanyal
We have calculated the mean square charge radii of the neutron and proton, and compared them with the experimental values, to construct a unique non-relativistic quark potential model. It is shown for the first time that, contrary to general belief, it is possible to reproduce simultaneously the baryon mass spectrum and the electromagnetic sizes of neutron and proton using a single potential model. It was found necessary to add admixtures of excited states of the nucleon in the unperturbed ground state wavefunctions. © 1989, Indian Academy of Sciences. All rights reserved.
Deuteron breakup in the field of a heavy target
(1984) S.N. Mukherjee; L.N. Pandey; D.K. Srivastava; N.K. Ganguly
The effect of the deuteron breakup channel on the elastic scattering of deuteron lead targets around 80 MeV incident deuteron energy has been examined. It is found that the large difference between experimental values and folding model predictions could mostly be explained in terms of deuteron breakup effects. [NUCLEAR REACTIONS d-Pb208 elastic scattering, Ed=79.4 MeV breakup channel effects.] © 1984 The American Physical Society.
Distorted wave analysis of (d,p) reactions to decaying states
(1977) S.N. Mukherjee; R. Shyam; S. Pal; N.K. Ganguly
The distorted-wave Born approximation is used in the case of the stripping reaction S32(d,p)S*33 leading to decaying states in order to explain the strong dependence of the ratio of the energy differential (d,p) stripping cross section to the total neutron elastic scattering cross section on the same target, on transferred angular momentum (l) The necessity of using a distorted-waves approximation instead of a plane-waves approximation, which is much simpler to calculate and which also shows " l dependence," is discussed in the context of identification of levels. The slowly converging overlap integral appearing in the distorted-wave Born approximation is treated by employing a Gaussian convergence factor. It is also found that in the plane-wave calculation, the inclusion of the unscattered part in the neutron form factor affects only the l=0 resonances. The desirability of including the effect of the nuclear interior is discussed. The angular distribution for the reaction O6(d,p)O*17 has been obtained employing the distorted-wave Born approximation method. The spectroscopic factor for this reaction is obtained and compared with that reported previously. NUCLEAR REACTIONS S32(d,p), O16(d,p) reactions, unbound states, calculated [d2σ(d,p)]dΩdE, [dσ(d,p)]dΩ, ED=12-13.3 MeV, DWBA analysis. © 1977 The American Physical Society.
Effect of deuteron breakup on the 24Mg(p, d)23Mg( 1 2+, 2.36 MeV) cross section
(1982) G.H. Rawitscher; S.N. Mukherjee
The "spectacular" failure of the conventional DWBA to fit this Δl = 0 pick up reaction, first pointed out by Shepard et al. is not removed by inclusion of breakup. The calculation is approximate in that it includes only one breakup bin, and neglects spins as well as Pauli antisymmetrization effects. © 1982.
Effect of hard core on the photodisintegration cross sections of H3
(1962) V.S. Mathur; S.N. Mukherjee; M.L. Rustgi
The electric-dipole bremsstrahlung weighted cross section (b) and the integrated cross section (int) for the photodisintegration of H3 are calculated using the hard-core wave functions of Kikuta, Morita, and Yamada. A comparison with already published calculations indicates that the introduction of the hard core increases both b and int for the H3 nucleus by about 100 and 8%, respectively. © 1962 The American Physical Society.
Ehrenfest theorem and the classical trajectory of quantum motion
(1987) J. Nag; V.J. Menon; S.N. Mukherjee
Ehrenfest theorem asserts that the quantum mechanical motion of a particle when considered in the expectation value sense should agree with classical mechanics in the correspondence limit. An explicit verification of this result is presented in the orie-dimensional case for motion in an infinite potential well (large quantum number limit) and a brief mention is made of the case of a smooth potential (0 limit). © 1987, American Association of Physics Teachers. All rights reserved.
Electromagnetic structure of the proton and baryon spectrum in the nonrelativistic quark model
(1987) R. Nag; S. Sanyal; S.N. Mukherjee
The properties of the positive-parity ground-state baryons are analyzed in the nonrelativistic quark model using the hyperspherical harmonic expansion method to handle the dynamics of the three-quark system bound by a confinement potential. The usual contact term is made more flexible with an adjustable parameter to account for terms missing from the standard Fermi-Breit potential. The root-mean-square radius and charge form factor of the free proton are obtained and compared with experimental values. The reliability of the model is ascertained for the rms radius and charge form factor of the proton and the masses of the ground-state baryons. We also calculate the masses of the N*(1470), N*(1710), and *(1690) resonances. © 1987 The American Physical Society.
Energy levels of a muonic hydrogen atom with the use of a quark model
(1991) R. Nag; S.N. Mukherjee; S. Sanyal
The energy levels of the muonic hydrogen atom are calculated using proton charge distribution due to the nonrelativistic quark model. The charge form factor of the proton calculated in the model is in reasonable agreement with electron-scattering measurements. The effect of two orders of vacuum polarization and the finite size of the proton is included. We find good agreement with the results of earlier works, especially where the experimental charge distribution of the proton was employed. This calculation provides a useful test of nonrelativistic quark models. © 1991 The American Physical Society.
Hyperspherical formalism for the photoeffect of the alpha particle
(1985) S. Sanyal; S.N. Mukherjee
In this work we employ the hyperspherical harmonics formalism to calculate the moments of the photoeffect of the alpha particle. The grand orbital quantum number is increased until well-converged results are obtained. The adiabatic approximation is used to solve the coupled differential equations. The calculations are performed for a central N-N potential with Serber exchange. Lastly, the moments are inverted to obtain the photodisintegration cross section. Comparisons with experimental observations are presented. © 1985 The American Physical Society.
Inelastic electron scattering charge form factor of He4
(1987) S. Sanyal; S.N. Mukherjee
In this work we calculate the inelastic electron scattering charge form factor of He4 using several N-N interactions. We employ the hyperspherical harmonics expansion method and include the contribution of harmonics above the minimal subset (Lmin). We find that the inelastic electron scattering form factor obtained by us is in excellent agreement with the experimental observations of Walcher. However, the inelastic form factor is insensitive to the N-N interaction. Further, we find that the minimal subset approximation is inadequate for form factor calculations when the momentum transfer is large. We also calculate the elastic electron scattering form factor and find the usual disagreement between theory and experiment. A possible explanation for this discrepancy is given. © 1987 The American Physical Society.
New ansatz for bound states of four identical particles. Example: Four inert gas atoms
(1982) W. Zickendraht; S.N. Mukherjee
A new Ritz variational ansatz for bound states of four identical particles is proposed which may be used as the starting point for more detailed calculations. The ansatz is tested for the case of four inert gas atoms bound by Lennard-Jones potentials. © 1982 The American Physical Society.
Octupole deformation in even-even medium mass nuclei
(1963) M.L. Rustgi; S.N. Mukherjee
The stability of octupole deformation for even-even medium mass nuclei with small spheroidal deformation has been studied in order to explain the existence of odd-parity excited states in some of them. The total single-particle energy is calculated by an exact diagonalization of the Nilsson Hamiltonian with octupole deformation, neglecting the residual two-particle interaction. Within this framework, it is found that these nuclei are stable against octupole deformation. © 1963 The American Physical Society.
On the size and binding energy of the helium nucleus
(Società Italiana di Fisica, 1962) S.N. Mukherjee
Irving wave function has been modified to fit the size and the binding energy of the4He nucleus. The wave function naturally reproduces the electric dipole bremsstrahlung weighted cross-section. © 1962 Società Italiana di Fisica.
Photodisintegration of helium
(1963) M.L. Rustgi; S.N. Mukherjee
The electric dipole bremsstrahlung-weighted cross section σb and integrated cross section σint for the photodisintegration of helium have been calculated using the modified Irving wave function. Good agreement has been obtained with the current experimental values: σb=2.4±0.15 mb and σint=95±7 MeV mb. The results have also been compared with the recent calculations of Goldhammer and Valk. © 1963 The American Physical Society.
Quantal dynamics of dissipation in heavy ion nuclear fission
(1983) S.N. Mukherjee; L.N. Pandey
Energy dissipation during heavy ion nuclear fission has been calculated by employing the one-dimensional time dependent frictional Schrödinger equation. The variation of loss of energy with respect to the shape of the fissioning system follows the same trend as the classical frictional matrix. The dissipative loss of kinetic energy with respect to time is also shown. NUCLEAR REACTIONS, FISSION Ar + Th, Elab=250 MeV, onedimensional quantized frictional motion, loss of energy. © 1983 The American Physical Society.
Quark potential approach to baryons and mesons
(1993) S.N. Mukherjee; R. Nag; S. Sanyal; T. Morii; J. Morishita; M. Tsuge
Applicability of quark potential models for nucleons, qqq, and heavy mesons like quarkonia QQ̄ and atomlike mesons Qq̄ is reviewed. Information regarding interquark potentials contained therein is used in predicting mass levels of these hadrons, and charge from factors and charge radii of nucleons. Related subjects such as quark cluster effects, heavy flavored baryons and heavy hybrid mesons, non-local potentials in baryons and possible superheavy toponium are reviewed for future development. Theoretical problems connected to the quark potential approach are spelled out. © 1993.
R-matrix plus potential analysis of unbound states of33S
(Springer India, 1985) Rama Das; S.N. Mukherjee
Single channel single level R-matrix plus potential analysis of the resonances observed in the32S(n, n) reaction for the neutron energy lying from 20-1100 keV has been carried out to determine the properties of these resonances. This analysis is further supported by a single channel multilevel R-matrix analysis of the data. Spectroscopic factors for the resonances have also been calculated by our R-matrix method. Its comparison with those obtained by dwba analysis of the (d, p) data is discussed. © 1985 Indian Academy of Sciences.
Radius anomaly in the diffraction model for heavy-ion elastic scattering
(1984) L.N. Pandey; S.N. Mukherjee
The elastic scattering of heavy ions, Ne20 on Pb208, Ne20 on U235, Kr84 on Pb208, and Kr84 on Th232, is examined within the framework of Frahn's diffraction model. An analysis of the experiment using the "quarter point recipe" of the expected Fresnel cross sections yields a larger radius for Pb208 than the radii for U235 and Th232. It is shown that inclusion of the nuclear deformation in the model removes the above anomaly in the radii, and the assumption of smooth cutoff of the angular momentum simultaneously leads to a better fit to elastic scattering data, compared to those obtained by the earlier workers on the assumption of sharp cutoff. [NUCLEAR REACTIONS Elastic scattering, Ne20+Pb208 (161.2 MeV), Ne20+U235 (175 MeV), Kr84+Pb208 (500 MeV), Kr84+Th232 (500 MeV), diffraction model, nuclear deformation.] © 1984 The American Physical Society.