The nucleon pair shell model (NPSM) is cast into the so-called $M$ scheme for the cases with isospin symmetry and without isospin symmetry. The odd system and even system are treated on the same footing. The uncoupled commutators for nucleon pairs, which are suitable for the $M$ scheme, are given. Explicit formula of matrix elements in $M$ scheme for overlap, one-body operators, and two-body operators are obtained. It is found that the CPU time used in calculating the matrix elements in $M$ scheme is much shorter than that in the $J$ scheme of NPSM.

In this work, we derive the nuclear form factor for the spin-independent collision between the WIMPs and nucleus in terms of the relativistic mean field (RMF) theory. Comparison with the traditional form factors which are commonly used in literature is given and it is found that our results are slightly above that of the 2PF model by 4% to 8%, but deviate from the Helm form factor by 15% to 25% for the whole recoil energy spectrum of 0 ~ 100 keV. Moreover, taking Xe and Ge as examples, we show the dependence of the form factor on the recoil energy.

The properties of possible ${\Theta }^{+}$ bound states in nuclei are described in relativistic mean-field formalism (RMF), in which the ${\Theta }^{+}$-meson coupling constants are deduced from the underlying quark structure of ${\Theta }^{+}$ baryon. Our RMF results show that there is an attractive ${\Theta }^{+}$-nucleus interaction and the ${\Theta }^{+}$ particle can be bound in nuclei to form ${\Theta }^{+}$ hypernuclei, which are predicted to be bound much more strongly than λ hypernuclei. The potential depth of ${\Theta }^{+}$ in nuclear matter is estimated. The general range found for the depth is from 50 to 90 MeV at normal nuclear matter density, depending on the values we used for the coupling constants. Our RMF results are compatible with an evaluation of ${\Theta }^{+}$ self-energy in the nucleus.

The effects of possible noncollective pairs in even-even${}^{124\text{–}128}\mathrm{Sn}$ are studied in the nucleon-pair shell model, in which a few noncollective neutron pairs originating from the alignment of two neutrons in the $\nu h_{11/2}$ orbit are considered. From the low-lying-level energies, $B\left(E2\right)$ ratios, and excited states obtained from the model, it is shown that the yrast band structure can be explained as the evolution from vibrational to rotational type as a function of spin. The mechanism of the yrast band can be explained as band crossing between the ground-state band and the $S$ band constructed from the neutron alignment in the $\nu h_{11/2}$ orbit. The noncollective configurations may be crucial for describing the yrast states in even-even${}^{124,126,128}\mathrm{Sn}$ in the $SD$-pair shell model.

The bulk viscosity is studied in a thermodynamically enhanced perturbative QCD (EPQ) model that includes the running of both the strong coupling and the strange quark mass. Similar to the results in other effective models, the bulk viscosity in the EPQ model is larger by 1–2 orders of magnitude compared with that in the MIT bag model. Comparison among the different models indicates that the similarity in orders is mainly due to the inclusion of interactions between quarks. When the temperature is relatively low and enters the equation of state of quark matter, the bulk viscosity can be enormously enlarged. For the analytical expression of bulk viscosity, a reasonable range of model parameters is found. Moreover, due to the enlarged bulk viscosity, the damping time of a strange star with about 2 times the solar mass can be as short as ${10}^{-3}$ second, showing that massive quark stars could reach stability quickly after some radial unstable activities.

The properties of Σ-hyperons in pure Σ matter are studied with the finite-density quantum chromodynamics sum rule (QCDSR) approach. The $\Sigma \Sigma$ nuclear potential $U_{\Sigma }$ is most likely strongly attractive, it could be about $-50$ MeV or even more attractive at normal nuclear density. If this prediction is the case, the interactions between Σ-hyperons should play crucial roles in the strange nuclear matter, when there are multi-Σ hyperons. The bound state of the double-Σ may exist.