International Journal of Modern Physics E

In this paper, we summarize the theoretical development on the electric dipole moment (CEDM) of light nuclei. We first describe the nucleon level CP violation and its parametrization. We then present the results of calculations of the EDM of light nuclei in the ab initio approach and in the cluster model. The analysis of the effect of several models beyond standard model (CBSM) is presented together with the prospects for its discovery. The advantage of the EDM of light nuclei is focused in the point of view of the many-body physics. The evaluations of the nuclear EDM generated by the $\theta$-term and by the CP phase of the Cabibbo–Kobayashi–Maskawa (CKM) matrix are also reviewed.

Two-way cross-talk transitions between pairs of signature partners superdeformed (SD) bands in ${}^{191}$Hg (SD2,SD3), ${}^{193}$Hg (SD3,SD4) and ${}^{193}$T1(SD1,SD2) built on the configurations $\nu 3/2+[642],\nu 7/2+[624],\pi 5/2+[642]$, respectively, are proposed. The $\mathrm{\Delta }I=1$ energy staggering presented in these odd SD nuclei are investigated and parametrized by proposing two staggering functions depending on the dipole transitions linking the signature partners. These staggering functions differ from the conventional staggering functions employed in previous works which depend on the quadruple transitions within each band. For parametrization, we used the two-term formula of Bohr–Mottelson collective rotational model. The model parameters and the bandhead spins of the considered signature partners are determined by using a simulated fitting search program and the values of the adopted parameters are used to calculate transition energies $E_{\gamma }$, rotational frequencies $\hslash \omega$, kinematic $J^{(1)}$ and dynamic $J^{(2)}$ moments of inertia. The calculated results agree very well with the experimental ones. The bands exhibit the usual increasing trend. Large amplitude staggering has been found in the considered three signature partner pairs in ${}^{191,193}$Hg and ${}^{193}$T1 nuclei.

The SO(4) symmetry of a sector of the quantum chromodynamics (QCD) Hamiltonian was analyzed in a previous work. The numerical calculations were then restricted to a particle–hole (ph) space and the comparison with experimental data was reasonable in spite of the complexity of the QCD spectrum at low energy. Here on, we continue along this line of research and show our new results of the treatment of the QCD Hamiltonian in the SO(4) representation, including ground state correlations by means of the Random Phase Approximation (RPA). We are able to identify, within this model, states which may be associated to physical pseudo-scalar and vector mesons, like $\eta ,{\eta }^{\prime },K,\rho ,\omega ,\varphi$, as well as the pion ($\pi$).

In this paper, we applied the Langevin dynamical model to investigate the different aspects of the ${}^{16}$O+${}^{194}$Pt reaction. Elongation and orientation degree of freedom ($K$ coordinate) which are the first and second dimensions of dynamical calculations, are presented here. Fission time, fission cross-section, pre-scission neutron multiplicity, and fission probability were calculated using one- and two-dimensional Langevin equations. Also, anisotropy of fission-fragments angular distribution has been investigated based on the transition state model, one- and two-dimensional Langevin dynamical models. It was found that by adding the orientation degree of freedom to calculations, the fission time and pre-scission neutrons multiplicity increases whereas fission cross-section, and fission probability decreases. The two-dimensional dynamical calculations are a better match to the experimental data than the one-dimensional dynamical calculations, when using nominal values for the reduced dissipation coefficient and shape-dependent level density parameter. However, if model parameters are adjusted to reproduce the fission cross-section data, then both the one- and two-dimensional models give a satisfactory match to the fission fragment anisotropy data. Nonequilibrium $K$ distributions in the dynamical model can better explain the experimental anisotropy of the angular distribution of fission-fragments with respect to the equilibrium $K$ distribution in saddle and scission point transition state models.

For a wide range of the core-nuclei ($6\le A\le 207$), the scattering lengths, effective radii, and the other effective-range parameters (up to the order $\sim k^8$) for the angular momentum $\ell =0,1,2$ are calculated within a two-body $\mathrm{\Lambda }A$-model. For the same hypernuclear systems, the $S$-matrix residues as well as the corresponding Nuclear-Vertex and Asymptotic-Normalization constants (NVC’s and ANC’s) for the bound states are also found.

In this paper, we investigate the cooling of neutron stars with relativistic and nonrelativistic models of dense nuclear matter. We focus on the effects of uncertainties originated from the nuclear models, the composition of elements in the envelope region, and the formation of superfluidity in the core and the crust of neutron stars. Discovery of $2M_{\odot }$ neutron stars PSR J1614−2230 and PSR J0343$+$0432 has triggered the revival of stiff nuclear equation of state at high densities. In the meantime, observation of a neutron star in Cassiopeia A for more than 10 years has provided us with very accurate data for the thermal evolution of neutron stars. Both mass and temperature of neutron stars depend critically on the equation of state of nuclear matter, so we first search for nuclear models that satisfy the constraints from mass and temperature simultaneously within a reasonable range. With selected models, we explore the effects of element composition in the envelope region, and the existence of superfluidity in the core and the crust of neutron stars. Due to uncertainty in the composition of particles in the envelope region, we obtain a range of cooling curves that can cover substantial region of observation data.

Different aspects like multiplicity moments, $D_q$ moments and multiplicity fluctuations in terms of scaled variance of the shower particles has been carried out for central events of ${}^{16}\mathrm{\text{O}}-\mathrm{\text{AgBr}}$, ${}^{22}\mathrm{\text{Ne}}-\mathrm{\text{AgBr}}$ and ${}^{32}\mathrm{\text{S}}-\mathrm{\text{AgBr}}$ interactions at (4.1–4.5) AGeV/c. Comparison of our results with different experimental analysis of central collisions of emulsion data has been performed whenever available.

We analyze once again the $\gamma$ singles spectra and $\gamma$-$\gamma$-$t$ coincidence spectra following the ${\beta }^{+}+$EC decay of ⁸³Sr. Multipeaks are carefully separated and many $\gamma$ transition cascades are clearly obtained in the work. As a complement to our previous work, the uncertainties on $\gamma$-rays energies, $\gamma$-rays intensities and deduced level energies in the ${\beta }^{+}+$EC decay of ⁸³Sr are given now.

Elastic and inelastic scattering of $\alpha$-particles at 48.1MeV and ³He at 60MeV on ${}^{16}$O nuclei has been measured with excitation of states at 6.05 (0${}^{+}$)–6.13 (3${}^{-}$)MeV, 6.92 (2${}^{+}$)–7.12 (1${}^{-}$)MeV and 8.87 (2${}^{-}$)MeV. The center-of-mass beam momenta are the same for these two strongly absorbed particles. Analysis of angular distributions was performed in the frameworks of the optical model, the coupled channels method and the Distorted Wave Born Approximation (DWBA). A good description of experimental data was obtained over the full angular range without taking into account the spin-orbit interaction and the cluster transfer mechanism with real potentials that have volume integrals of about 400MeV fm³. Collective and microscopic models were used in the analysis of the inelastic scattering. The values of the octupole deformation lengths were extracted. It is shown that nuclear rainbow effects appear not only in the elastic, but also in the inelastic scattering with excitation of the 3${}^{-}$ state of ${}^{16}$O.

Interacting Boson Model (IBM -1) has been used to study the energy levels and $B(E2)$ transition rates in Ba–Dy ($N=92$) isotones. A simplified Hamiltonian is used which is written in the creation and annihilation form and for each nucleus, by fitting the selected experimental energy levels and $B(E2)$ transition rates with the calculated ones to get the best model parameters. Using the (IBM) Hamiltonian with an intrinsic state formalism, the potential energy surfaces (PES) for even–even Ba–Dy nuclei have been obtained and the contour plot of PES show that the shape phase transitions from spherical $U(5)$ to deformed shape $SU(3)$ has been determined for the ${}^{148}\mathrm{\text{Ba}}$, while ${}^{150}$Ce, ${}^{152}$Nd, ${}^{154}$Sm, ${}^{156}$Gd and ${}^{158}$Dy nuclei are deformed and have rotational-like characters. The behavior of energy and $B(E2)$ ratios in the ground state band are examined.

The essential point of Bohr–Mottelson theory is to assume an irrotational flow. As was already suggested by Marumori and Watanabe, the internal rotational motion, i.e., the vortex motion, however, may exist also in nuclei. So, we must take the vortex motion into consideration. In classical fluid dynamics, there are various ways to treat the internal rotational velocity. The Clebsch representation, $v(x)=-\nabla \varphi (x)+\lambda (x)\nabla \psi (x)(\varphi ;\text{velocity potential},\lambda \text{and}\psi :\text{Clebsch parameters})$ is very powerful and allows for the derivation of the equations of fluid motion from a Lagrangian. Making the best use of this advantage, Kronig–Thellung, Ziman and Ito obtained a Hamiltonian including the internal rotational motion, the vortex motion, through the term $\lambda (x)\nabla \psi (x)$. Going to quantum fluid dynamics, Ziman and Thellung finally derived the roton spectrum of liquid Helium II postulated by Landau. Is it possible to follow a similar procedure in the description of the collective vortex motion in nuclei? The description of such a collective motion has not been considered in the context of the Bohr–Mottelson model (BMM) for a long time. In this paper, we will investigate the possibility of describing the vortex motion in nuclei on the basis of the theories of Ziman and Ito together with Marumori’s work.

Transverse momentum distributions of primary charged particles have been studied using simulated data from the HIJING 1.0 event generator in the minimum bias p–Pb collisions at $\sqrt{s_{NN}}$ = 0.9, 1.8, 2.76 and 5.02$\mathrm{\text{TeV}}$, in the two forward pseudorapidity ($\eta$) regions: $1.3<\eta <1.8$ and $1.8<\eta <2.3$ and in the transverse momentum range of $0.5<p_T<20\mathrm{\text{GeV/c}}$. The simulated data in the pseudorapidity region of $1.3<\eta <1.8$ at 5.02$\mathrm{\text{TeV}}$ depicts some differences in the region of $p_T$ $>$ 2$\mathrm{\text{GeV/c}}$ when compared with CMS data. Model shows systematically higher values than the experimental measurements pointing out absorption effect for the experimental data. It is also observed that with increasing rapidity interval from $1.3<\eta <1.8$ to $1.8<\eta <2.3$ observed differences for the behavior of the transverse momentum distributions are shifted to high transverse momentum region. The nuclear modification factor as a function of transverse momentum is constructed using the HIJING 1.0 code. With incident energy, the values of nuclear modification factor increase, for 0.9 and 1.8 $\mathrm{\text{TeV}}$, the distributions seem to increase, but for 2.76 and 5.02 $\mathrm{\text{TeV}}$, the distributions look flat. Numerically, the value of nuclear modification factor increases with the increase in the number of jets. This result shows that for the considered more forward pseudorapidiry area, the influence of the incident energy dominates and this is the reason that main results in the areas are connected with the leading particles.