International Journal of Modern Physics E

To resolve the nonconvex optimization problem in partial wave analysis, this paper introduces a novel approach that incorporates fraction constraints into the likelihood function. This method offers significant improvements in the efficiency of pole searching within partial wave analysis.

The ⁷He nucleus was studied using the ⁶He${(d,p)}^7$He reaction in inverse kinematics at 29 $\text{A}\cdot$MeV ⁶He beam delivered by the ACCULINNA-2 fragment separator (FLNR, JINR). The registration of neutrons from ${}^7\mathrm{\text{He}}\to n{+}^6\mathrm{\text{He}}$ decay made it possible to derive the ⁷He ground state parameters, the decay energy of 0.38(2)MeV and width of 0.11(3)MeV.

The available experimental data for the elastic scattering of the isobar nuclei ⁶Li and ⁶He on ${}^{64}$Zn have been reanalyzed in the available energy range using the optical model, double folding (DF) (Sao Paulo), and crystal model (CM). Double-folding (DF) and crystal model (CM) have been used to investigate the experimental data as a real part of the optical potential, while the imaginary part was taken in Woods–Saxon (WS) shape. One value of the real part of the optical potential has been applied to the two systems under consideration. The distance of the closest approach of the ⁶Li (⁶He) + ${}^{64}$Zn systems has been extracted from the available experimental data using different methods. The extracted potential from the ⁶Li and ⁶He elastically scattered by ${}^{64}$Zn data could be used as the basis for the creation of a simple global optical potential for ⁶Li and ⁶He. The extracted normalization factor ($N_r$) was equal to the unity during the fitting process avoiding its unfortunate value (in the range 0.5–0.7) exists in the literature. It was observed that interaction distances vary slowly with the energy of the projectile and strongly depend on the projectile properties. The halo properties of ⁶He have a significant effect on the calculated reaction cross-sections. Different methods have been applied to ⁶He and ⁶Li elastically scattered by ${}^{64}$Zn, where fair agreement between them has been observed.

Physical quantities, such as entropy, dimensions and multifractal characteristics of multiplicity distributions of charged particles produced in ${}^{197}$Au–AgBr collisions, are examined and the findings are compared with the predictions of Monte Carlo model Ultra-Relativistic Quantum Molecular Dynamics (URQMD) and Heavy Ion Jet INteraction Generator (HIJING) and also with the results reported earlier in hadron–hadron and nucleus–nucleus collisions at different energies. Based on their azimuth distribution, the charged particles produced within narrow-bins exhibit two kinds of substructures, namely, ring-like and jet-like substructures. Thus, on applying the suitable criteria, the two different types of events are identified and analyzed separately. It is observed that the maximum entropy production occurs around a narrow mid-rapidity region. The analyses of ring-like and jet-like events suggest that the entropy production is much larger in ring-like events as compared to that in jet-like events. Furthermore, Rényi’s order-q information entropy is used to estimate the multifractal specific heat and to construct the spectrum of scaling indices. The findings reveal that the value of multifractal specific heat is higher in ring-like events as compared to that in jet-like events. The studies of generalized dimension and multifractal spectrum indicate that the multifractality is rather, more pronounced in ring-like events as compared to jet-like events. Various features of the experimental data are noticed to be nicely reproduced by the URQMD model.

It is known that pseudospin symmetry plays a crucial role in formation of many physical phenomena. By combining the relativistic mean field theory with the complex momentum representation method, the pseudospin symmetry in the single particle resonant states in the deformed nucleus ${}^{154}$Dy is investigated through the energy and width splittings, the quadrupole deformation parameter, the radial density distributions and occupation probabilities of the pseudospin doublets. Near the continuum threshold, the pseudospin symmetry is well reserved in both bound and resonant states. The energy and width splittings of pseudospin doublets in resonant states exhibit correlations with the deformation and quantum numbers. The good pseudospin symmetry is expected with lower pseudo-orbital angular momentum projection $\tilde{\mathrm{\Lambda }}$ and the main quantum number N. In general, an increase in deformation tends to weaken the quality of the pseudospin symmetry. The understanding of the evolution of the pseudospin doublets in the resonant states has been deepened by studying the pseudospin symmetry in the deformed nuclei.

For a sustainable nuclear energy program using fission reactors, the reduction or elimination of long-lived radioactive waste is essential. The hazardous Long-Lived Fission Products (LLFP), which are by-products of the operation of nuclear reactors, need to be converted to short-lived or stable nuclei. For nuclear transmutation, the knowledge of reaction cross-sections is important. The cross-section and half-life for the proton-induced transmutation of the LLFP, ${}^{126}$Sn, produced as nuclear waste from the reactor have been calculated. The cross-section for the (p,n) reaction on unstable ${}^{126}$Sn has been calculated using phenomenological as well as microscopic models of optical potentials and level densities in the framework of the statistical nuclear model using the latest version of the code TALYS-1.96. The Koning–Delaroche (KD) and Jeukenne–Lejeune–Mahaux–Bruyeres (JLMB) optical models, as well as back-shifted Fermi gas model (BFM) and Hartree–Fock (HF) level density, based on the Skyrme force from Gorielys tables, have been used. The renormalized optical model parameters and level density models obtained by comparing cross-sections with data for protons incident on stable ${}^{112,114,115,116,117,118,119,120,122,124}$Sn isotopes were extended to make a prediction of (p,n) cross-section on unstable ${}^{126}$Sn isotope. The excitation function obtained using JLMB-HF calculation for ${}^{126}$Sn reveals a peak at an incident proton energy of 8.5MeV with a corresponding cross-section of 269mb. It would be of interest to perform experiments for measurements of cross-section where data are unavailable, especially in the peak regions and beyond, to validate the predictions of this work. It is found that for a proton flux of $6.25\times 10^{14}$s${}^{-1}$cm${}^{-2}$, and a peak cross-section calculated using JLMB-HF calculation, the effective half-life of transmutation of ${}^{126}$Sn is about 65 years, thus justifying its feasibility.

We have proposed an empirical formula for one- and two-proton decays, including the angular momentum term. While investigating the first term in the Viola–Seaborg formula, we found a linear relationship between the logarithmic half-life and the expression $(aZ+b)Q^{-1/2}$ for each angular momentum state. Furthermore, we obtained a linear relationship between the slope and intercept as functions of the angular momentum (l). Using these relations, we proposed a generalized empirical formula for the half-lives of one- and two-proton radioactivity for all angular momentum states. We analyzed the accuracy of the formula predictions by computing the standard deviation between the predicted and experimental decay half-lives. For the decay of one proton, the standard deviation of the proposed formula is 0.389, while that of the generalized formula is 0.400. These values represent the lowest standard deviations compared to previous models and the empirical formula. In the case of two-proton decay, the standard deviation for the current formula is 1.31, and the generalized formula also exhibits a lower standard deviation of 1.32. This lowest standard deviation value indicates that the proposed formula is suitable for reproducing the experimental half-life. We extended the half-life predictions to another 207 nuclei for one-proton decay and 42 nuclei for two-proton decay cases, which are energetically possible. The estimated half-lives for both one- and two-proton decays agree well with other theoretical predictions.

The cluster radioactivity of ${}^{222,224,226}$Ra, ${}^{223,225}$Ac, ${}^{232,234,235,236}$U, ${}^{236,238}$Pu, ${}^{234,236}$U, ${}^{232,233,234,235,236}$U and ${}^{230,232}$Th isotopes which emitted ${}^{14}$C, ${}^{24}$Ne, ${}^{28}$Mg, ${}^{26}$Ne, ${}^{28}$Mg, ${}^{24}$Ne, respectively, has been analyzed with the help of fractional calculus for investigating the connection between order of the fractional derivative and nuclear structure. When the neutron number of daughter nuclei is equal to magic number, order of the fractional derivative shows a maximum. It is shown that there is a relationship between the order of fractional derivative and shell effect. This order has a similar role to the preformation factor in cluster radioactivity.