International Journal of Modern Physics E

Theoretical possibilities for the spontaneous emission of fission fragments from ${}^{237-256}$Cf parents are investigated within the framework of preformed cluster decay model (PCM). The fragmentation potential exhibits a modification from dominated asymmetric fission profile to symmetric splitting with the rise in the N/Z ratio of parent nuclei. The calculated spontaneous fission (SF) half-life times of Cf isotopes find nice agreement with the experimental data, except for ${}^{256}$Cf nucleus. Within the PCM, the hydrodynamical mass transfer among the outgoing binary fragments occurs through a cylindrical vessel connecting them. For the overlapping configuration $(R<R_T$), the two classical models namely Model A and Model B (differ in the way the radius of the connecting cylinder is controlled) are used to estimate mass transfer flow of binary fragmentation. It is observed that with change in the overlapping distance, the radius of the cylindrical vessel changes in Model A, whereas the same remains fixed in Model B. In case of Model B, the effect of cylindrical radii parameter (${\alpha }_c$) is also analyzed for ${}^{237-256}$Cf parents at optimum neck-length ($\mathrm{\Delta }$R) in view of different observable such as most probable SF fragments, preformation probability, mass transfer, the SF half-lives and the results are compared with Model A calculations. The magnitude of mass transfer, preformation probability, and hence the SF half-lives gets significantly modified on switching from Model A to Model B. Further, a large amount of mass is transferred between the asymmetric fragments as compared to the symmetric ones. The SF half-lives are shown to depend strongly on the choice of classical models as well as on the cylindrical radius parameter, ${\alpha }_c$. The study infers the importance of classical models to spread further light in the understanding of the dynamical behavior of fragment formation in the fission process.

Visibility graphs (VGs), horizontal visibility graphs (HVGs) and the sandbox algorithm (SB) are applied for multifractal characterization of complex network systems that are converted from time series measurements, are used to characterize the fluctuations in pseudorapidity densities of singly charged particles produced in ${}^{16}$O–AgBr interactions at 60AGeV. The work presents the analysis of ring-like and jet-like events in terms of multifractality characterization of ${}^{16}$O–AgBr interactions at 60AGeV. We systematically compared the experimental events of both ring- and jet-like events with Monte Carlo (MC) simulated events. The investigation reveals that the multifractal spectrum for the jet-like events and ring-like events is different and can be distinguished. The ring-like events have its parameters slightly higher than that of jet-like events. Further analysis shows that the strength of the nonstatistical fluctuations is larger for ring-like events than those of jet-like events. The SB method presented here appears to be more useful than the conventional methods used for multifractal characterization.

By recasting the Klein–Gordon equation as an eigen-equation in the coupling parameter $v>0,$ the basic Klein–Gordon comparison theorem may be written $f_1\le f_2\Rightarrow G_1(E)\le G_2(E)$, where $f_1$ and $f_2$ are the monotone nondecreasing shapes of two central potentials $V_1(r)=v_1{f}_1(r)$ and $V_2(r)=v_2{f}_2(r)$ on $[0,\infty )$. Meanwhile, $v_1=G_1(E)$ and $v_2=G_2(E)$ are the corresponding coupling parameters that are functions of the energy $E\in (-m,m)$. We weaken the sufficient condition for the ground-state spectral ordering by proving (for example in $d=1$ dimension) that if ${\int }_0^x[f_2(t)-f_1(t)]{\phi }_i(t)dt\ge 0$, the couplings remain ordered $v_1\le v_2$, where $i=1\mathrm{\text{or}}2,$ and $\{{\phi }_1,{\phi }_2\}$ are the ground-states corresponding, respectively to the couplings $\{v_1,v_2\}$ for a given $E\in (-m,m).$. This result is extended to spherically symmetric radial potentials in $d>1$ dimensions.

Using HFB wave functions generated with a realistic KUO and an empirical JUNE45 effective two-body interactions, nuclear transition matrix elements (NTMEs) $M^{(K)}$ for the $0^{+}\to 0^{+}$ transition of neutrinoless double-$\beta$ decay of ${}^{76}$Ge isotope are calculated within mechanisms involving sterile neutrinos, Majorons and compositeness scenario. Uncertainties in nuclear transition matrix elements are estimated by calculating sets of 12 NTMEs with these two sets of wave functions, two alternative forms of finite size effects (FNS) and three different parametrizations of short range correlations (SRC). Uncertainties in NTMEs within mechanisms involving sterile neutrinos, Majorons and composite neutrinos turn out to be about 10%–36% depending on the mass of sterile neutrinos, 10% and 37%, respectively.

We analyze the charged-particle multiplicity distributions measured by the ALICE experiment, over a wide pseudorapidity range, for $pp$ collisions at $\sqrt{s}=8$, 7 and 2.76 TeV at the LHC. The analysis offers an understanding of particle production in high energy collisions in the purview of a new distribution, the shifted Gompertz distribution. Data are compared with the distribution and moments of the distributions are calculated. A modified version of the distribution is also proposed and used to improve the description of the data consisting of two different event classes: the inelastic and the nonsingle diffractive and their subsets in different windows of pseudorapidity, $\eta$. The distribution used to analyze the data has a wide range of applicability to processes in different fields and complements the analysis done by the ALICE collaboration in terms of various LHC event generators and IP-Glasma calculations.

A comparative study of $s$-wave and $p$-wave breakups in the ${}^{37}\mathrm{\text{Mg}}+{}^{208}\mathrm{\text{Pb}}$ reaction around the Coulomb barrier is presented. The elastic scattering, breakup and reaction cross-sections, corresponding to the three $3s_{1/2^{+}}$, $2p_{1/2^{-}}$ and $2p_{3/2^{-}}$ possible single-particle configurations in the ${}^{37}\mathrm{\text{Mg}}$ ground state, calculated with two different ${}^{37}\mathrm{\text{Mg}}$ ground-state binding energies, namely 0.22 and 0.49MeV are analyzed.

As in the breakup of other neutron-halo systems such as ${}^{11}\mathrm{\text{Be}}$, it is found that for all three ground-state configurations, couplings to the breakup channels suppress the Coulomb–nuclear interference peak in the elastic scattering cross-section. It is shown that the breakup through $s$-wave ground state is dominated by couplings to continuum $p$-waves, whereas the breakup through $p$-wave ground state, is largely dominated by couplings to continuum $s$-wave. Substantially larger $3s_{1/2^{+}}$ ground state total, Coulomb and nuclear breakup cross-sections than their $2p_{1/2^{-}}$ and $2p_{3/2^{-}}$ ground states counterparts are obtained. This is understood to mainly originate from a larger electric dipole response function of the transition from $3s_{1/2^{+}}$ ground state to the continuum, and from the fact that the Coulomb breakup cross-section is directly proportional to this function.

In conclusion, the breakup of ${}^{37}\mathrm{\text{Mg}}$ nucleus exhibits a similar breakup behavior as other one-neutron loosely bound systems. The results presented in this paper may provide some guidance for experimentalists to analyze possible future experimental data.