The ground state multiplet structure for nuclei over the wide range of mass number $A$ was calculated in $delta$-approximation and different mass relations for pairing energy was analysed in this work. Correlation between the calculated multiplet structure and experimental data offer a guideline in deciding between mass relations for nucleon pairing.
We explore two-particle transfer reactions as a unique probe of the occurence of shape coexistence in shape phase transitions. The (t,p) reactions to the ground state and to excited $0^+$ states are calculated for the isotope chain of even-even Zirconium isotopes starting from stable nuclei up to beyond current experimental limits. Two-particle spectroscopic factors derived from Monte Carlo Shell Model calculations are used, together with the sequential description of the two-particle transfer reaction mechanism. The calculation shows a clear signature for a shape phase transition between $^{98}$Zr and $^{100}$Zr, which displays coexistence of a deformed ground state with an excited spherical $0^+$ state. Furthermore, we show that there is a qualitative difference with respect to the case of a normal shape phase transition that can be discriminated with two-neutron transfer reactions.
We present microscopic valence-shell calculations of pairing gaps in the calcium isotopes, focusing on the role of three-nucleon (3N) forces and many-body processes. In most cases, we find a reduction in pairing strength when the leading chiral 3N forces are included, compared to results with low-momentum two-nucleon (NN) interactions only. This is in agreement with a recent energy density functional study. At the NN level, calculations that include particle-particle and hole-hole ladder contributions lead to smaller pairing gaps compared with experiment. When particle-hole contributions as well as the normal-ordered one- and two-body parts of 3N forces are consistently included to third order, we find reasonable agreement with experimental three-point mass differences. This highlights the important role of 3N forces and many-body processes for pairing in nuclei. Finally, we relate pairing gaps to the evolution of nuclear structure in neutron-rich calcium isotopes and study the predictions for the 2+ excitation energies, in particular for 54Ca.
The multi-particle states and rotational properties of two-particle bands in $^{254}$No are investigated by the cranked shell model (CSM) with pairing correlations treated by a particle-number conserving (PNC) method. For the first time, the rotational bands on top of two-particle $K^{pi}=3^+,8^-$ and $10^+$ states and the pairing reduction are studied theoretically in $^{254}$No. The experimental excitation energies and moments of inertia for the multi-particle state are reproduced well by the calculation. Better agreement with the data are achieved by including the high-order deformation $varepsilon_{6}$ which leads to enlarged $Z=100$ and $N=152$ deformed shell gaps. The rise of the $J^{(1)}$ in these two-particle bands compared with the ground-state band is attributed to the pairing reduction due to the Pauli blocking effects.
A new version of the improved quantum molecular dynamics model has been developed to include standard Skyrme interactions. Four commonly used Skyrme parameter sets, SLy4, SkI2, SkM* and Gs are adopted in the transport model code to calculate the isospin diffusion observables as well as single and double ratios of transverse emitted nucleons. While isospin diffusion observables are sensitive to the symmetry energy term, they are not very sensitive to the nucleon effective mass splitting parameters in the interactions. Our calculations show that the high energy neutrons and protons and their ratios from reactions at different incident energies provide a robust observable to study the momentum dependence of the nucleon effective mass splitting. However the sensitivity of effective mass splitting effect on the n/p yield ratios decreases with increasing beam energy, even though high energy proton and neutron are produced more abundantly at high beam energy. Our calculations show that the optimum incident energy to study nucleon effective masses is between 100-200 MeV per nucleon.
We review some applications of self-consistent Greens function theory to studies of one- and two-nucleon structure in finite nuclei. Large-scale microscopic calculations that employ realistic nuclear forces are now possible. Effects of long-range correlations are seen to play a dominant role in determining the quenching of absolute spectroscopic factors. They also enhance considerably (e,epn) cross sections in superparallel kinematics, in agreement with observations.