The unbound nucleus 12Li is evaluated by studying three-neutron one-proton excitations within the multistepshell model in the complex energy plane. It is found that the ground state of this system consists of anantibound 2− state. A number of narrow states at low energy are found which ensue from the coupling ofresonances in 11Li to continuum states close to threshold.

The recently proposed spin-aligned neutron-proton pair coupling scheme is studied within a non-orthogonal basis in term of the multistep shell model. This allows us to identify simultaneously the roles played by other configurations such as the normal pairing term. The model is applied to four-, six- and eight-hole N = Z nuclei below the core Sn-100.

A Monte Carlo method is presented to evaluate quantum states with many particles moving inthe continuum. The scattering state is generated at each time by a Monte Carlo random samplingalgorithm. The same calculation are repeated until the average energies of all calculations converge.For systems with one and two particles, our calculations show that the exact solution can beapproached with around only one hundred iterations.

The available experimental data on shell evolution indicate that the strength of the spin-orbit single-particle potential may be enhanced in neutron-rich nuclei. We observe that such a simple scheme destroys the harmonic oscillator magic numbers N = 8 and 20 and generates new magic numbers like N = 6, 14, 16, 32 and 34. The traditional magic numbers like N = 28 and 50 and N = 14 seen in O-22 are eroded in neutron-rich nuclei due to the sensitivity of larger-l orbitals to the depth of the central potential but they are more robust than the harmonic oscillator magic numbers. The N = 82 shell closure persists in neutron-rich nuclei while the previously proposed shell closures like N = 40 and 70 do not emerge. Both mechanisms contribute to enhancing the N = 56 and 90 gaps by splitting the 1d(5/2) and 0g(7/2) and the 0h(9/2) and 1f(7/2) orbitals.

For a system with three identical nucleons in a single-j shell, the states can be written as the angular-momentum coupling of a nucleon pair and the odd nucleon. The overlaps between these nonorthonormal states form a matrix that coincides with the one derived by Rowe and Rosensteel [Phys. Rev. Lett. 87, 172501 ( 2001)]. The propositions they state are related to the eigenvalue problems of the matrix and dimensions of the associated subspaces. In this work, the propositions are proven from the symmetric properties of the 6j symbols. Algebraic expressions for the dimension of the states, eigenenergies, as well as conditions for conservation of seniority can be derived from the matrix.

We have adopted the multistep shell model in the complex energy plane to study nuclear excitations occurring in the continuum part of the spectrum. In this method one proceeds by solving the shell model equations in a successive manner. That is, in each step one constructs the building blocks to be used in future steps. We applied this formalism to analyze the unbound nuclei Li-12,Li-13 starting from the one - particle states in Li-10 and two - particle states in Li-11. In the former case the excitations correspond to the motion of three particles partitioned as the product of a one - particle and two - particle systems. The ground state of Li-12 is thus calculated to be an antibound (virtual) state. In the four - particle system Li-13 the states can be constructed as the coupling of two correlated pairs. We found that there is no bound or antibound state in Li-13.

A partial conservation of the seniority quantum number in j = 9/2 shells has been found recently in a numerical application. In this paper an analytic proof for this problem is derived as an extension of the work [L. Zamick, P. Van Isacker, Phys. Rev. C 78 (2008) 044327]. We analyze the properties of the non-diagonal interaction matrix elements with the help of the one-particle and two-particle coefficients of fractional parentage (cfp's). It is found that all non-diagonal (and the relevant diagonal) matrix elements can be re-expressed in simple ways and are proportional to certain one-particle cfp's. This remarkable occurrence of partial dynamic symmetry is the consequence of the peculiar property of the j = 9/2 shell, where all it = 3 and 5 states are uniquely defined.

We present a systematic configuration-interaction shell-model calculation on the structure of light tin isotopeswith a global optimized effective interaction. The starting point of the calculation is the realistic CD-Bonnnucleon-nucleon potential. The unknown single-particle energies of the 1d3/2, 2s1/2, and 0h11/2 orbitals and theT = 1 monopole interactions are determined by fitting to the binding energies of 157 low-lying yrast states in102−132Sn. We apply the Hamiltonian to analyze the origin of the spin inversion between 101Sn and 103Sn that wasobserved recently and to explore the possible contribution from interaction terms beyond the normal pairing.