Abstract:
Mass calculations carried out by Strutinsky's shell correction method are based on the notion of smooth single particle level density. The smoothing procedure is always performed using curvature correction. In the presence of curvature correction a smooth function remains unchanged if smoothing is applied. Two new curvature correction methods are introduced. The performance of the standard and new methods are investigated using harmonic oscillator and realistic potentials.

Abstract:
Proton emission from deformed nuclei is described within the non-adiabatic weak coupling model which takes into account the coupling to $\gamma$-vibrations around the axially-symmetric shape. The coupled equations are derived within the Gamow state formalism. A new method, based on the combination of the R-matrix theory and the oscillator expansion technique, is introduced that allows for a substantial increase of the number of coupled channels. As an example, we study the deformed proton emitter $^{141}$Ho.

Abstract:
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified plane wave is considered. This decomposition leads a three-dimensional Schr\"odinger equation with source term. Partial wave expansion is carried out and the asymptotic form of the solution is determined. This splitting does not lead to simplification of the scattering boundary condition if complex scaling is invoked. A new splitting carried out only on partial wave level is introduced and this method is proved to be very useful. The scattered part of the wave function tends to zero at large inter-particle distance. This property permits of easy numerical solution: the scattered part of the wave function can be expanded on bound-state type basis. The new method can be applied not only for pure Coulomb potential butin the presence of short range interaction too.

Abstract:
Partial wave expansion of the Coulomb-distorted plane wave is determined and studied. Dominant and sub-dominant asymptotic expansion terms are given and leading order three-dimensional asymptotic form is derived. The generalized hypergeometric function $_2F_2(a,a;a+l+1,a-l;z)$ is expressed with the help of confluent hypergeometric functions and the asymptotic expansion of $_2F_2(a,a;a+l+1,a-l;z)$ is simplified.

Abstract:
A new method is presented for calculation of the shell correction with the inclusion of the continuum part of the spectrum. The smoothing function used has a finite energy range in contrast to the Gaussian shape of the Strutinski method. The new method is specially useful for light nuclei where the generalized Strutinski procedure can not be applied.

Abstract:
Shell corrections of the finite deformed Woods-Saxon potential are calculated using the Green's function method and the generalized Strutinsky smoothing procedure. They are compared with the results of the standard prescription which are affected by the spurious contribution from the unphysical particle gas. In the new method, the shell correction approaches the exact limit provided that the dimension of the single-particle (harmonic oscillator) basis is sufficiently large. For spherical potentials, the present method is faster than the exact one in which the contribution from the particle continuum states is explicitly calculated. For deformed potentials, the Green's function method offers a practical and reliable way of calculating shell corrections for weakly bound nuclei.

Abstract:
Mathematically rigorous theory of the two-body contact interaction in three dimension is reviewed. Local potential realizations of this proper contact interaction are given in terms of Poschl-Teller, exponential and square-well potentials. Three body calculation is carried out for the halo nucleus 11Li using adequately represented contact interaction.

Abstract:
A FORTRAN77 program is presented that calculates fusion cross sections and mean angular momenta of the compound nucleus under the influence of couplings between the relative motion and several nuclear collective motions. The no-Coriolis approximation is employed to reduce the dimension of coupled-channels equations. The program takes into account the effects of non-linear couplings to all orders, which have been shown to play an important role in heavy-ion fusion reactions at subbarrier energies.

Abstract:
Two methods the complex energy shell model (CXSM) and the complex scaling (CS) approach were used for calculating isobaric analog resonances (IAR) in the Lane model. The IAR parameters calculated by the CXSM and the CS methods were checked against the parameters extracted from the direct numerical solution of the coupled channel Lane equations (CC). The agreement with the CC results was generally better than 1 keV for both methods and for each partial waves concerned. Similarities and differences of the CXSM and the CS methods are discussed. CXSM offers a direct way to study the configurations of the IAR wave function in contrast to the CS method.

Abstract:
The coupled-channel Schrodinger equation with outgoing wave boundary conditions is employed to study the fine structure seen in the proton decay of deformed even-N, odd-Z rare earth nuclei 131-Eu and 141-Ho. Experimental lifetimes and proton-decay branching ratios are reproduced. The comparison with the standard adiabatic theory is made.