International Journal of Modern Physics E

The Modified Generalized Liquid Drop Model (MGLDM) has been used for calculating the ground-to-ground states of $\alpha$-decay half-lives for various Ac, Th, Pa, U and Np isotopes in the mass number range of $205\le A\le 245$. To account for the nuclear proximity energy, the potential of Blocki et al. [J. Blocki, J. Randrup, W. J. Swiatecki and C. F. Tsang, Ann. Phys. NY 105 (1977) 427] is used. The experimental $Q_{\alpha }$ values are used to evaluate the $\alpha$-decay half-lives. It can be observed that the logarithm of $\alpha$-decay half-life increases with increasing neutron number ($N$), with evident minimum at the magic number 126, where the neutron shell is closed. The calculated results are compared with available experimental data and with the predictions of different empirical formulae such as, ARF, MARF, Royer, AKRE, Akrawy, NRB, VS, MVS, YQZR and MYQZR. It is found that the MGLDM is able to predict the experimental half-lives with a standard deviation of 0.6892 (the lowest one among all the other applied empirical formulae), and is therefore suitable for predicting the $\alpha$-decay half-lives for unknown and new heavy nuclei.

Using the double folding model (DFM), we reanalyzed 20 sets of experimental angular distributions for the elastic scattering $\alpha$+${}^{28}$Si system in a wide energy range of $\alpha$-particles from 12.7MeV to 240MeV. We used three effective nucleon–nucleon (NN) interactions that are CDM3Y6, São Paulo Potential (SPP2), and Brazilian Nuclear Potential (BNP) to generate the DF potentials. The data analysis was performed using semi-microscopic (SM) and fully microscopic (FM) methods. In the SM approach, the real part of the optical potential (OP) is created with the DFM, and the Woods–Saxon (WS) potential is considered for the imaginary part of the OP. In the FM approach, the DF potential renormalization factors $N_R$ and $N_I$ for the real and imaginary parts of the OP were extracted. We investigated the energy dependencies of the $N_R$ and $N_I$ factors, as well as of nuclear potential volume integrals and reaction cross-sections. We reasonably reproduced the data using $N_R$ and $N_I$ factors obtained from their energy-dependent functions.

The hot nucleus ${}^{162}\mathrm{\text{Dy}}$ is investigated using covariant density functional theory, where the shell-model-like approach treats the pairing correlation. Lee–Yang’s theorem is applied to classify the pairing phase transition by analyzing the distribution of zeros of the partition function in the complex temperature plane. The distribution of zeros of the partition function converges with increasing particle numbers and illustrates the characteristics of the phase transition. In our calculations, we determine the first-order of the phase transition near the critical temperature. Different seniority states show the pairing phase transition from a superfluid to a normal phase, ranging from fully paired states to completely unpaired states.

The new experimental results on the search and study of formation of a possible three-proton resonance state in a target fragmentation region in the total ensemble of collisions of deuterons (²H), $\alpha$-particles (⁴He), and carbon-12 nuclei with target carbon-12 nuclei at incident kinetic energy 3.37GeV per nucleon are presented. The narrow peak structure of a possible three-proton resonance state was observed with a four-sigma statistical significance in the spectrum of invariant masses of three protons in the analyzed ensemble of collisions in the collision events with four protons in the final state. The peak structure was not visible in the other channels with the number of protons equal 3, 5, and $\ge 5$. The mass and width of this possible three-proton resonance state were estimated to be $M(ppp)=2920\pm 2$MeV/$c^2$ and $\mathrm{\Gamma }=2.1\pm 0.8$MeV/$c^2$. The inclusive cross-section of formation of this possible resonance state was estimated to be $1.8\pm 0.2$mb. It was deduced that the three-proton resonances could possibly be formed as a result of capture by a two-proton resonance (with mass $\approx 1926$MeV/$c^2$) of one more proton with a close velocity. The observed three-proton as well as two-proton resonances are likely to be the hadronic molecules. Taking into account an alpha cluster structure of carbon-12 nuclei, one of the possible mechanisms of formation of three-proton resonances could be the effective fusing of pair of protons with opposite spins, from one fragmenting alpha cluster, with a proton, originating from the second fragmenting alpha cluster.

In this work, we construct the analytical solution of the Schrödinger equation for a combined nuclear plus atomic Hulthén potential with different range parameters, using the Frobenius method. The atomic Hulthén potential acts as the screened Coulomb potential to represent the very short-range electromagnetic interaction. It is intended to emphasize how the impact of the combined potential in these situations is routinely examined within the context of nuclear physics. The Jost function is calculated from its integral representation in terms of the regular solution. From the phase of the Jost function, the scattering phase shifts for different partial waves, and further differential scattering cross-section and total cross-sections are calculated for alpha-proton and proton–proton systems. On comparing with the existing experimental data, we conclude that the results obtained are in close conformity with the previous works that exist in the literature.

By using the Quantum Molecular Dynamics (QMD) model, a study on the nuclear vaporization in ${}^{40}\mathrm{\text{Ca}}+{}^{40}\mathrm{\text{Ca}}$ collision is presented for different nuclear equations of state along with a systematic comparison of different clusterization methods based on simple spatial correlations, spatial-momentum correlations, mass dependent binding energy cuts and Simulated Annealing Clusterization Algorithm (SACA). The effect of different nuclear equations of state i.e., Soft, Hard and Soft with Momentum Dependent (SMD) interactions on the energy of onset of vaporization for ${}^{40}\mathrm{\text{Ca}}+{}^{40}\mathrm{\text{Ca}}$ collisions is predicted by investigating gas/liquid content and probability of vaporization versus incident energy behavior. These two observables probe the critical point of nuclear vaporization very well. Further outcome of different clusterization algorithms on the energy of onset of nuclear vaporization is also probed and a comparison of calculations with the experimental data for ${}^{16}\mathrm{\text{O}}+{}^{80}\mathrm{\text{Br}}$ and ${}^{16}\mathrm{\text{O}}+{}^{107}\mathrm{\text{Ag}}$ collisions is carried out for different clusterization algorithms.