International Journal of Modern Physics E

The observation of neutrinoless double beta decay (DBD) will have important consequences. First it will signal that lepton number is not conserved and the neutrinos are Majorana particles. Second, it represents our best hope for determining the absolute neutrino mass scale at the level of a few tens of meV. To achieve the last goal, however, certain hurdles have to be overcome involving particle, nuclear and experimental physics. Particle physics is important since it provides the mechanisms for neutrinoless DBD. In this review, we emphasize the light neutrino mass mechanism. Nuclear physics is important for extracting the useful information from the data. One must accurately evaluate the relevant nuclear matrix elements (NMEs), a formidable task. To this end, we review the recently developed sophisticated nuclear structure approaches, employing different methods and techniques of calculation. We also examine the question of quenching of the axial vector coupling constant, which may have important consequences on the size of the NMEs. From an experimental point of view it is challenging, since the life times are extremely long and one has to fight against formidable backgrounds. One needs large isotopically enriched sources and detectors with good energy resolution and very low background.

A known phase-functions method (PFM) has been considered for calculation of a single-channel nucleon–nucleon scattering. The following partial waves of a nucleon–nucleon scattering have been considered using the phase shifts by PFM: ¹S₀-, ³P₀-, ³P₁-, ¹D₂-, ³F₃-states for nn-scattering, ¹S₀-, ³P₀-, ³P₁-, ¹D₂-states for pp-scattering and ¹S₀-, ¹P₁-, ³P₀-, ³P₁-, ¹D₂-, ³D₂-states for np-scattering. The calculations have been carried out using phenomenological nucleon–nucleon Nijmegen group potentials (NijmI, NijmII, Nijm93 and Reid93) and Argonne v18 potential. The scalar scattering amplitude has been calculated using the obtained phase shifts. Our results are not much different from those obtained by using the known phase shifts published in other papers. The difference between calculations depending on a computational method of phase shifts makes: for real (imaginary) parts 0.14–4.36% (0.16–4.05%) for NijmI. 0.02–4.79% (0.08–3.88%) for NijmII. 0.01–5.49% (0.01–4.14%) for Reid93 and 0.01–5.11% (0.01–2.40%) for Argonne v18 potentials.

In order to investigate negative parity states, it is necessary to consider negative parity-bosons additionally to the usual $s$- and $d$-bosons. The dipole and octupole degrees of freedom are essential to describe the observed low-lying collective states with negative parity. An extended interacting boson model (IBM) that describes pairing interactions among s, p, d and f-boson based on affine $\mathrm{\text{SU}}(1,1)$ Lie algebra in the quantum phase transition (QPT) field, such as spd-IBM, sdf-IBM and spdf-IBM, is composed based on algebraic structure. In this paper, a solvable extended transitional Hamiltonian based on affine $\mathrm{\text{SU}}(1,1)$ Lie algebra is proposed to describe low-lying positive and negative parity states between the spherical and deformed gamma-unstable shape. Three model of new algebraic solution for even–even nuclei are introduced. Numerical extraction to low-lying energy levels and transition rates within the control parameters of this evaluated Hamiltonian are presented for various $N$ values. We reproduced the positive and negative parity states and our calculations suggest that the results of spdf-IBM are better than spd-IBM and sdf-IBM in this literature. By reproducing the experimental results, the method based on signature of the phase transition such as level crossing in the lowest excited states is used to provide a better description of Ru isotopes in this transitional region.

We study the effects of isovector-scalar ($\delta$)-meson on neutron and hyperon stars. Influence of $\delta$-meson on both static and rotating stars is discussed. The $\delta$-meson in a neutron star consisting of protons, neutrons and electrons, makes the equations of states (EOS) stiffer at higher density, and consequently increases the maximum mass of the star. But induction of $\delta$-meson in the hyperon star decreases the maximum mass. This is due to the early evolution of hyperons in presence of $\delta$-meson.

Dynamical cluster decay model (DCM) based on the collective clusterization approach is employed to explore the dynamics of various even-mass Zr isotopes formed in ${}^{16}$O-induced reactions. In reference to the measured fusion cross-section data, various decay modes contributing towards ${}^{86,88,90,92}$Zr${}^{\ast }$ nuclei are investigated. Also, the role of deformations and orientation degree of freedom is analyzed by comparing results with spherical choice of fragmentation. In addition to this, the effect of entrance channel is explored for ${}^{92}$Zr${}^{\ast }$ and ${}^{76}$Kr${}^{\ast }$ nuclei formed in ${}^{16}$O and ${}^{18}$O-induced reactions. Besides this, the dynamics of relatively heavier mass Sn isotopes is exercised using ${}^{16}$O and ${}^{18}$O projectiles. The DCM calculated decay cross-sections find good agreement with available experimental data.

We present theoretical model comparison with published ALICE results for $D$-mesons ($D^0$, $D^{+}$ and $D^{\ast +}$) in $p+p$ collisions at $\sqrt{s}$ = 7 TeV and $p+\mathrm{\text{Pb}}$ collisions at $\sqrt{s_{NN}}=5.02$TeV. Event generator Heavy-Ion Jet Interaction Generator (HIJING), transport calculation of AMPT and calculations from Next-to-Leading Order (NLO)(MNR) and Fixed-Order Next-to-Leading-Logarithmic (FONLL) have been used for this study. We found that HIJING and AMPT model predictions are matching with published $D$-meson cross-sections in $p+p$ collisions, while both under predict the same in $p+\mathrm{\text{Pb}}$ collisions. Attempts were made to explain the $R_{p\mathrm{\text{Pb}}}$ data using NLO-pQCD(MNR), FONLL and other above mentioned models.

The nuclear level densities and single particle entropies are predicted for nuclei in the mass region $50<A<74$ within a framework of statistical theory of hot nuclei method. In this method, particle-number and energy conservation as well as nuclear pairing correlations are included in the partition function of grand canonical ensemble. The suppression of pairing correlations is distinctly noticed in temperature dependence of entropies between the critical temperatures $T_C\approx 0.7$ MeV and $T_C\approx 1.0$ MeV for ${}^{50,51}V$, ${}^{61,62}Ni$ and ${}^{73,74}\mathrm{\text{Ge}}$ isotopes of the elements. These structural thermodynamic entropies are interpreted as a remarkable signature of the superfluid to normal phase transition connected to the vanishing of pairing gap. The calculated level densities are compared with recent experimental values. In addition, the single particle entropy of intermediate-mass nuclei is depicted as half of the entropy of mid-shell nuclei in the rare-earth region. As a consequence, the $N=28$ shell closure of ${}^{51}$V carries low entropy at low excitation energy presents an interesting analogy to the $Z=28$ shell closure of ${}^{61}$Ni. Merely, in the case of odd–even ${}^{73}\mathrm{\text{Ge}}$ has higher entropy than the even–even ${}^{74}\mathrm{\text{Ge}}$ nucleus.

This paper describes the inversion of a scattering problem with coupled channels at fixed energy. The coupling potential matrix is obtained from the $S$-matrix with the modified Newton–Sabatier method with a special expansion of the integral kernel and a determination of the potential matrix by using the coupled radial equations. The method is applied to problems restricted to two channels and with a monopole, dipole and quadrupole coupling ($\lambda =0,1,2$) between the channels. The inversion is shown to work quite satisfactorily and is useful for heavy ion scattering in nuclear physics.

A general analytical expressions for the cross-section and the polarization of nucleons arising in the inclusive deuteron stripping reaction have been derived in the diffraction approximation. The nucleon–nucleus phases were calculated in the framework of Glauber formalism and making use of the double-folding potential. The tabulated distributions of the target nucleus density and the realistic deuteron wave function with correct asymptotic at large nucleon–nucleon distances were used. The calculated angular dependences for the cross-sections and the analyzing powers of the $(\overrightarrow{d},p)$ reaction are compared with corresponding experimental data.

The effects of the projectile deformation and orientation on the total potential characteristic have been studied for the reactions between weakly bound nucleus, ⁹Be, as the projectile and different targets. In this paper, the double-folding model is used to calculate the nuclear potentials and deformation of projectile included. It is shown that applying the deformation effects can modify the potential barrier height and depth in the interior regions of the potential. It is also shown that the gradient variation of the potential barrier height is linearly increased when the angle between the projectile and the target nuclei increases. The rate of the variation is constant in different reactions with ⁹Be. In order to study the possible effect of these deformation dependent potentials, application is made in the calculation of cross-sections of the different reactions. It is observed that the deformation and orientation are of important role in the dynamics of such reactions and improve the agreement with the experimental results.

In the Skyrme model of nucleons and nuclei, the spin excitation energy of the nucleon is traditionally calculated by a fit of the rigid rotor quantization of spin/isospin of the fundamental Skyrmion (the hedgehog) to the masses of the nucleon and the Delta resonance. The resulting, quite large spin excitation energy of the nucleon of about $73\mathrm{\text{MeV}}$ is, however, rather difficult to reconcile with the small binding energies of physical nuclei, among other problems. Here, we argue that a more reliable interval of values for the spin excitation energy of the nucleon, compatible with many physical constraints is between $15\mathrm{\text{MeV}}$ and $30\mathrm{\text{MeV}}$. The fit of the rigid rotor to the Delta, on the other hand, is problematic in any case, because it implies the use of a nonrelativistic method for a highly relativistic system.

Nuclear level densities of ${}^{207}$Pb and ${}^{89}$Y are calculated using the Lipkin–Nogami (LN) method and Bradeen–Cooper–Schrieffer (BCS) model. It is revealed that the calculated nuclear level densities are highly matched with the experimental data of Oslo group. The excitation energy and entropy are calculated for mentioned nuclei. In the case of two studied nuclei the characteristic of being magic for the number of neutrons or protons causes the decrease of the excitation energy and entropy contribution of magic system at low temperatures.

Shell model calculation has been performed for even–even ${}^{60,62,64,66}$Zn using NuShellX code in $f_{5/2}p{g}_{9/2}$ model space with two different effective Hamiltonians, viz. JUN45 and jj44b. The low-lying structure is studied up to angular momentum, $I$ = 10$\hslash$ by calculating level energies, reduced transition probabilities, occupation numbers, lifetimes, and quadrupole moments. The results of the calculations are compared with the available experimental data. It is observed that the inclusion of 1$g_{9/2}$ orbital in the model space is essential to understand nuclear structure in these isotopes. Shell model calculation with an improved set of effective Hamiltonian parameters and inclusion of $1f_{7/2}$ orbital in the model space are necessary in order to produce finer agreement with the experimental observations.

We have studied the $\alpha$-decay half-life and spontaneous fission half-lives of isotopes of superheavy element $Z=122$ in the range $275\le A\ge 326$. A comparison of calculated alpha half-lives with the literature [D. N. Poenaru, R. A. Gherghescu and W. Greiner, Phys. Rev. C 83 (2011) 014601, D. N. Poenaru, R. A. Gherghescu and W. Greiner, Phys. Rev. C 85 (2012) 034615] and the analytical formulas of Royer [G. Royer, J. Phys. G; Nucl. Part. Phys. 26 (2000) 1149] shows good agreement with each other. To identify the mode of decay of these isotopes, the spontaneous-fission half-lives were also evaluated using the semiempirical relation given by [C. Xu, Z. Ren and Y. Guo, Phys. Rev. C 78 (2008) 044329]. A comparative study on the competition of alpha decay versus spontaneous fission of superheavy nuclei (SHN) reveals that around eight isotopes (${}^{307-314}$122) survive fission and have alpha decay channel as the prominent mode of decay and hold the possibility to be synthesized in the laboratory. The alpha decay half-lives and spontaneous fission half-lives of SHN with $Z=122$, $A=299$–306, with $Z=120$, $A=294$–300, and with $Z=119$, $A=292$–297 are also studied. The present study will be useful in the synthesis of superheavy elements $Z>118$ by using the actinide based reactions with stable projectiles heavier than ${}^{48}$Ca.