International Journal of Modern Physics E

The eigenvalues and eigenfunctions of the Schrödinger equation with a non-relativistic electron in a uniform magnetic field are presented. A realization of the creation and annihilation operators for the radial wave-functions is carried out. It is shown that these operators satisfy the commutation relations of an SU(1,1) group. Closed analytical expressions are evaluated for the matrix elements of different functions ρ² and .

We present a simple physical explanation that measurements of the collision cross-sections with pure energy resolution can provide information on the reaction dynamics equivalent to that obtained using real-time methods of femtochemistry. For nuclear collisions, the method provides a time resolution of ~ 10^-21 sec. The method is sensitive enough to distinguish between the different scenarios of rotational dephasing for the highly-excited nuclear molecules, with strongly overlapping resonances, formed in ¹²C + ²⁴Mg scattering. We find that the dephasing is much slower than the intra-molecular energy redistribution. This reveals unusual states — nonergodic molecules in continuum. Anomalously long dephasing times observed in highly-excited polyatomic molecules may reflect this new type of nonergodicity.

The differential cross-sections for elastic ¹²C–¹²C scattering at 2400 and 1449 MeV are calculated on the basis of the multiple diffraction scattering theory and α-cluster model with dispersion. At the energy 2400 MeV the calculations were performed by means of "effective" and "free" α–α amplitudes. It is shown that the results obtained differ significantly.

We deal with some of the main characteristics of proton and deuteron production in Au + Au reactions at 11.6A GeV/c with the help of a new approach. From the viewpoint of the combination of two models and an important phenomenological parametrization, we analyze both laboratory data and the model-constructs from which we finally summarize two crucial features: (i) nucleon–nucleon and nucleus–nucleus collisions could be treated on a unified footing; (ii) production of hadrons like pions, protons etc. and deuterons as well, could be studied in a somewhat similar way. Besides, it is also shown that the totality of the approach outlined and utilized here is quite capable of obtaining the physical projections based on the popular relativistic quantum molecular dynamic (RQMD) model, and can also accommodate some actual measurements already made in the past.

Following the semiclassical formalism of Strutinsky et al.,¹¹ we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a spherical billiard in the limit η → 1.0. Inclusion of repetition of each family of the orbits with reference to the largest one significantly improves the eigenvalues of the sphere and an exact comparison with the quantum mechanical results is observed up to the second decimal place for kR₀ ≥ 7. The contributions of the equatorial, planar (in the axis of symmetry plane) and non-planar (three-dimensional) orbits are obtained from the same trace formula by using the appropriate conditions. The resulting eigenvalues compare very well with the quantum mechanical eigenvalues at normal deformation. It is interesting that the partial sum of equatorial orbits leads to eigenvalues with maximum angular momentum projection, while the summing of planar orbits leads to eigenvalues with L_z = 0 except for L = 1. The remaining quantum mechanical eigenvalues are observed to arise from the three-dimensional (3D) orbits. Very few spurious eigenvalues arise in these partial sums. This result establishes the important role of 3D orbits even at normal deformations.

We develop the Nuclear Schwinger–Dyson (NSD) formalism to include the effects of ladder diagrams by modifying the vertex. In this extension, the NSD equation sums up both ring diagrams and ladder diagrams self-consistently. The results are compared with mean field theory, Hartree Fock and bare-vertex NSD calculations. It is shown that the vertex correction is important from the following viewpoints. First, the vertex correction greatly modifies the meson propagators, and we can avoid the ghost-pole from meson propagators in a self-consistent way. Secondly, it gives a large negative correlation-energy compared with the other calculations; as a result, it gives a softer equation of state which is preferable according to the experimental data.

The Dirac equation is generalized to D + 1 space-time. The conserved angular momentum operators and their quantum numbers are discussed. The eigenfunctions of the total angular momenta are calculated for both odd D and even D cases. The radial equations for a spherically symmetric system are derived. The exact solutions for the system with a Coulomb potential are obtained analytically. The energy levels and the corresponding fine structure are also presented.

The low-lying states of ⁷¹Ge have been studied the via the ⁷¹Ga (p,n γ)⁷¹Ge reaction using proton beam energies of 2.5–4.3 MeV. The angular distributions have been used to assign the spins and the multipole mixing ratios using statistical theory for compound nuclear reactions. The ambiguity in the spin values for the various levels has been removed. The multipole mixing ratios for a few γ-transitions have been newly measured. The lifetimes of the levels at 747.0, 808.0, 831.1, 1377.8, 1406.6, 1414.4, 1422.1, 1558.8 and 1566.1 keV excitation energies have been measured for the first time using the Doppler shift attenuation method.