Schrödinger picture formalism of Φ6 theory

The static effective potential for a scalar field with Φ⁶ interaction is calculated using the effective action in Schrödinger picture formalism. It is found that the effective potential obtained is same as the Gaussian effective potential as far as static case is concerned. Equivalence with the CJT formalism can also be established. As in CJT formalism after renormalization an unrenormalized mass term persists. Nonzero turning points are obtained both for positive and negativeλ. Results are analysed numerically. Graphical analysis indicates a behaviour similar to that obtained for CJT formalism at zero temperature.     

Exchange effects in nuclear rainbow scattering

A simple microscopic approach to the calculation of the exchange part of the real nucleus-nucleus optical potential based on a generalization of the double-folding model and the local density matrix formalism has been proposed. The model successfully reproduces the nuclear rainbow scattering data for α-particles, ⁶Li and ⁹Be. The role of knock-on exchange effects in these processes is considered in detail.     

Quantum-statistical mechanics of a system of charged particles at high temperatures

If a quantum-mechanical potential is introduced the calculation of the quantummechanical binary distribution function for a system with Coulomb interaction is reduced to the well-known mathematical formalism of classical statistical mechanics in the case ofnλ³?1 (λ being the thermal wavelength). The two-particle quantummechanical potential is determined by the two-particle Slater sum. In this paper we calculated the two-particle Slater sum using an expansion according toe ² and the resolvent formalism. From the binary distribution function the correlation energy and the free energy as well were determined up to ordere ⁶. Symmetry effects were taken into account.     

Die Spinstruktur von Kernreaktionen des Typs 1+1 → 0+0

The nondynamicalM-matrix formalism is applied to reactions of spin type 1 +1 → 0+0. For this purpose rectangular spin matrices are introduced. It is shown that there are only 7 linearly independent analyzing powers. Thus, to get complete information for reactions with all particles having parity +1, experiments with both beam and target being polarized have to be carried out. In the present, this is possible for the Li⁶(d, α)α reaction, where a polarized Li⁶ beam and a polarized deuteron beam or target are available.     

Evidence of a Proton Halo in <Superscript>23</Superscript>Al: A Mean Field Analysis

The structural properties of Al isotopes are analysed using the relativistic mean field formalism with NL3 parameter set. The Glauber model technique is implemented to study the reaction dynamics for ^23?28Al taking ¹²C as the target. The enhanced reaction cross section, high value of radius, narrow longitudinal momentum distribution and small proton separation energy of ²³Al favours a proton halo structure for this nucleus.     

Coulomb Forces in Three Charged Particles Interacting via Stripping Nuclear Reactions

Coulomb forces are examined for three charged interacting particles following the Faddeev formalism. Application of stripping nuclear reactions is studied for ⁶Li projectile incident on ¹²C target with alpha particle transfer. Differential corss-sections are calculated. The results are found to be improved by about 12.41% due to the inclusion of the Coulomb forces.     

Hamiltonian description and 6D calculations on the ammonia vibrational levels

In this work, a Hamiltonian formalism and a 6D vibrational calculation procedure is described and implemented, designed for the exploration of vibrational motion in ammonia (and any XH₃ molecule). The 6D potential energy surface of ammonia was modelled in simple analytical form (including the inversion potential) at the planar, totally symmetric (D_3h) reference configuration. Using the described method (which is an adaptation of the formalism, previously developed and applied to benzene), 6D calculations were carried out on the vibrational level system of ammonia ¹⁴NH₃, at the lower levels of vibrational excitation. On the basis of the satisfactory agreement between the calculated and the experimentally measured vibrational frequencies, the values of some important harmonic and anharmonic force constants, characterizing the ammonia PES were determined.     

Reduction of the Lane-Robson “calculable” reaction theory to standard R-matrix form

General dynamical equations derived from the Lane-Robson calculable reaction formalism are cast into a form amenable to standard R-matrix treatment, permitting the resonance content of the equations to be made explicit. Formulae are given which enable the collision matrix and the amplitudes of physical eigenfunctions to be calculated directly from the R-matrix with or without the isolation of resonance contributions. The present methodology permits a significant reduction of effort in numerical investigations of the energy dependence inherent in dynamical models of the nucleus. The formalism is illustrated by calculational results obtained from a potential model fitted to ¹⁶O + n scattering data.     

Capture cross-section and rate of the 1 4 C(n, γ) 1 5 C reaction from the Coulomb dissociation of 1 5 C

We calculate the Coulomb dissociation of ¹⁵C on a Pb target at 68 MeV/u incident beam energy within the fully quantum mechanical distorted wave Born approximation formalism of breakup reactions. The capture cross-section and the subsequently rate of the ¹⁴C(n, γ) ¹⁵C reaction are calculated from the photodisintegration of ¹⁵C, using the principle of detailed balance. Our theoretical model is free from the uncertainties associated with the multipole strength distributions of the projectile.     

Model dependence of the (π−, nn) reaction

The recoil momentum distribution for the (π^?, nn) reaction on ⁶Li is calculated using the one- and two-nucleon absorption interactions and the α-d cluster model for ⁶Li. It is found that the shapes of the distribution calculated with the two interactions do not differ much. Its magnitude, however, can differ substantially, depending upon the parameter of the correlation function in the one-nucleon model. From this and the comparison with the available experimental data it is argued that the two-nucleon model can be used to make a relative study of the correlations in nuclei, in addition to its utility for studying two-hole states in nuclei and the advantage of an easier formalism.     

Microscopic description of low-energy neutron scattering by nuclei

The Bloch and Gillet shell-model formalism extended to continuum states is applied to lowenergy neutron scattering by nuclei. It is shown that complete antisymmetrization leads in the r-representation to corrective terms which yield important corrections to the scattering lengths. Calculations are performed within a model restricted configuration space for the target nuclei ¹²C, ¹³C, ¹⁶O, ¹⁷O and ⁴⁰Ca. We predict values for the spin-dependent scattering amplitude for ¹³C and ¹⁷O. The antisymmetrization problem in the case of a large configuration mixing is studied for the ¹⁹F target nucleus. The resonant effects of the compound nucleus are then very important and the results become very sensitive to the configuration space and the interaction parameters.     

Coupling of one and two quasiparticles to a Bohr-Mottelson core in195,196,197,198Hg

A new model for coupling the motion of particles to that of a quadrupole collective core with rotations andβ andγ vibrations is proposed. The Hamiltonian describing the core is obtained by quantising the classical Hamiltonian associated with the quadrupole degrees of freedom. The inertial parameters and the deformation energy surface are determined microscopically. The spherical shell model particles interacting among themselves by pairing are coupled to the core by aλ ²-pole (λ=0, 2, 4) potential. The theory is applied to^195–198Hg. The predicted results agree very well the experimental data. A comparison of the present model to the other formalism is also given.     

Microscopic potentials for polarized triton elastic scattering

The double folding model is used to calculate real central and spin-orbit potentials for triton elastic scattering. These potentials are used to fit cross sections and analysing powers at 17 MeV for targets ranging from ²⁶Mg to ²⁰⁸Pb. For most targets the data are described as well as with phenomenological potentials. The real central potential can be used without any substantial renormalisation, but the spin-orbit potential needs to be increased in strength by a factor between 2 and 6. Comparisons are made with phenomenological studies of triton and ³He elastic scattering and with similar microscopic studies of ³He scattering.     

Finite temperature Cornwall-Jackiw-Tomboulis formalism of Φ6 theory

The finite temperature effective potential for a scalar field with Φ⁶ interaction is calculated by extending the CJT formalism for composite operators. It is found that unrenormalized terms appear in the effective potential due to the presence of an unrenormalized mass term. Nonzero turning points are obtained both for positive and negativeλ. High temperature expansion is performed and the results are analysed numerically. Graphical analysis indicates symmetry restoration whenT→0.     

Optical model analysis of the elastic scattering of 45 MeV 3He particles on 1p shell nuclei

Angular distributions of elastically scattered ³He particles from the 1p shell nuclei ⁶Li, ⁷Li, ⁹Be, ¹⁰B, ¹¹B, ¹²C and ¹⁶O were measured by using a 45 MeV ³He beam. The absolute differential cross section data obtained were analysed in terms of the standard optical model. Using the fact that the rms radius of the 1p shell nuclei is nearly constant a simple folding model allows finding an optical potential family whose real potential depth varies linearly with the target mass. The best fits exhibit a normalized volume integral of about 400 MeV · fm³ for the real potential. From the best-fit parameters a mean parameter set is deduced which varies smoothly with the target mass A_T. The average parameter set compares well with the systematics found for heavier nuclei.     

Evolution of ground state nuclear shapes in tungsten nuclei in terms of interacting boson model

The tungsten nuclei ^180–190W are investigated within the framework of the interacting boson model using an intrinsic coherent state formalism. The Hamiltonian operator contains only multipole operators of the subalgebra associated with the dynamical symmetries SU(3) and O(6). The study includes the behavior of potential energy surfaces (BES’s) and critical points in the space of the model parameters to declare the geometric character of the tungsten isotopic chain. Some selected energy levels and reduced E2 transition probabilities B(E2) for each nucleus are calculated to adjust the model parameters by using a computer code PH INT and simulated computer fitting programme to fit the experimental data with the IBM calculation by minimizing the root mean square deviations. The ^180–190W isotopes lies in shape transition SU(3)-O(6) region of the IBM such that the lighter isotopes comes very clare to the SU(3) limit, while the behavior ones tend to be near the γ-unstable O(6) limit.     

Recoil studies in the reaction of 12C ions with the enriched isotope 118Sn

The recoil properties of the product nuclei from the interaction of 2.2 GeV/nucleon ¹²C ions from Nuclotron of the Laboratory of High Energies, Joint Institute for Nuclear Research at Dubna with a ¹¹⁸Sn target have been studied via catcher foils method. The experimental data were analyzed using the mathematical formalism of the standard two-step vector model. The results for ¹²C ions are compared with those for deuterons and protons. Three different Los Alamos versions of the Quark-Gluon String Model were used for comparison with our experimental data.