International Journal of Modern Physics E

The possible decay modes of even $A$ ${}^{238-250}$Cm parents have been analyzed to explore the relative emergence of various ground state emission mechanisms using the collective clusterization approach. Based on the collective availability of $\alpha -$, cluster and spontaneous fission (SF) experimental half-life data, we limit our study to isotopes of Cm. In view of this, the most probable decaying fragments from ${}^{238-250}$Cm are identified in different mass regions and a comprehensive analysis of the shell closure effect of the decay fragments corresponding to different mass domains is carried out within the methodology of Preformed Cluster Model (PCM). The isotopic analysis of the mass distributions and the related barrier characteristic quantities are investigated in view of ground state decay of ${}^{238-250}$Cm isotopes. The PCM calculated $\alpha$ and SF half-lives compare nicely with the experimental data and the predictions are made on cluster and heavy-cluster decay of Cm isotopes, where experimental data is not available. It will of further interest to validate these predictions by performing corresponding experiments.

In this work, the spectra of some even–even isotopes are studied by selecting core-cluster decomposition of the parent nucleus. The considered nuclei lie in the rare-earth and the transition metal regions. The Schrödinger equation can be solved using Bohr–Sommerfeld relation and the modified Woods–Saxon beside Coulomb potentials to reproduce the spectra of these isotopes with mass number $(154\le A\le 168)$. The theoretical calculations of the excitation energies of the ground state rotational band are compared to the experimental data. The cluster model calculations show a good agreement with the experimental data for the transitional and rotational nuclei more than the vibrational nuclei. Some negative parity bands of the chosen nuclei are studied. The core-cluster charge products are correlated with the transition probability $B(E2:2^{+}\to 0^{+})$.

The reaction ${}^{11}$Li($p,t$)⁹Li(gs) at an incident energy of 4.3MeV is interpreted in terms of a simplistic distorted-wave Born approximation, which assumes simultaneous transfer of the halo neutrons. The halo neutrons involved in the reaction is treated as either a di-neutron cluster or individual entities. Either of these approaches appears to be a good approximation of the reaction mechanism, as would be expected from earlier studies. The dominant contribution to the yield of the reaction comes from the known (2$s_{1/2}$)² neutron structure component of the ground state of ${}^{11}$Li. Furthermore, the cross-section angular distribution seems to be relatively insensitive to the fact that ${}^{11}$Li has an anomalously large radius due to its Borromean halo properties. Significantly this simple treatment of the reaction is in much better agreement with the experimental angular distribution than previous sophisticated calculations. The relevance and limitations of a more advanced theoretical treatment which includes coupled channel and sequential transfer are discussed in the context of the present results.

The one-proton emission, alpha decay and cluster decay using a Cubic Plus Proximity model with improved transfer-matrix method are executed for the first time for the study of decay properties of 368 isotopes of nuclei, far from the beta stability line and beyond the islands of stability $Z=130\text{–}144$ superheavy nuclei are studied within the range $290\le A\le 380$. The calculated decay half-lives are in good agreement with other theoretical approaches. The signature of neutron shell closure at $N=172,184,198,228,238$ and proton shell closure at $Z=138$ obtained from half-life curves for emission of different clusters pronounces the previous predictions. Investigation of competition between various decay modes brings out the dominant decay mode associated with an isotope; for a given $Z$ with increasing $A$ the dominant decay mode is seen to shift from proton decay to alpha decay and finally spontaneous fission. The decay modes and half-lives which are within the limit of experimental detection $10^{-6}s\le T_{1/2}\le 10^{30}s$ are presented.

The effect of diffuseness of nucleus–nucleus interaction potential is tested on the nuclear potential depth, barrier characteristics and fusion excitation functions by considering spherical+spherical and $\mathrm{\text{spherical}}+\mathrm{\text{deformed}}$ colliding partners. It is manifested from the calculations that fusion barrier height and fusion pocket depth get significantly modified with change in diffuseness parameter $(b)$ and deeper fusion pocket appears with an increase in the magnitude of diffuseness. We further observed that, depending on the value of $b$, the fusion pocket depth decreases more sharply for the reactions involving oblate target $({\beta }_2<0)$ as compared to prolate $({\beta }_2>0)$ systems, though the overall shift in the pocket (left or right) is almost equal i.e., $\sim$0.5fm for both cases. Furthermore, the effect of diffuseness on fusion cross-section is such that, on taking both spherical and/or deformed target-projectile combinations, lower strength of nuclear surface diffuseness (0.60fm) seems more suitable upto charge product $(Z_1{Z}_2)$ $\sim$200. However, for $200<Z_1{Z}_2\le 500$, higher value of diffuseness parameter (0.99fm) is desirable for systems with spherical as well as deformed target-projectile combinations. Finally, we have explored the effect of angle dependence on the nuclear surface diffuseness within ${}^{12}$C+${}^{159}$Tb reaction. The study reveals the significant contribution of angular diffuseness in fusion cross-section of reactions involving lanthanide target.

The Heavy-Ion Jet Interaction Generator (HIJING) Monte Carlo model was developed to simulate hadron production in proton–proton, proton–nucleus and nucleus–nucleus collisions. It has been updated recently with the latest parton distributions functions (PDFs) and new set of the parameters in the two-component mini-jet model that controls total $p+p$ cross-section and the central pseudorapidity density. We will discuss these new elements in the HIJING 2.0 model, derive the two-component model from the eikonal formalism of hadron–hadron collisions and review the hadron spectra and multiplicity distributions as compared to recent experimental data at the LHC energies. We will review in particular the data structure of the Monte Carlo program and discuss future improvements.

By using a nonrelativistic independent particle model, we investigate the mechanism promoting 34 as new magic number. We carried out Hartree–Fock plus Bardeen–Cooper–Schrieffer and Quasi-particle Random Phase Approximation calculations by consistently using the same finite-range interaction in all the three steps of our approach. We used four Gogny-like interactions, with and without tensor terms. We find that the shell closure for $N=34$ neutrons appears in isotones with $Z<26$ protons. The smaller the proton number, the more evident is the shell closure at $N=34$. An ideal nucleus to investigate this effect should be ${}^{48}$Si, as it has been recently suggested. However, some discrepancies occur between the results obtained with the four effective interactions we used concerning the position of the two-neutron drip line and, therefore, the existence of ${}^{48}$Si. The experimental identification of this nucleus could shed light about the shell evolution in nuclei far from the stability valley and put stringent tests on nuclear structure theories.

The well-known Grodzins product $B(E$2, 0${}_1^{+}\to$2${}_1^{+})\times E(2_1^{+})$ constancy rule was generalized to the Grodzins linearity relation in our recent work in the form of $B(E2)$ versus $[1/E(2_1^{+})]$ linear plots. In this form, besides testing the linear relation of $B(E2$) and kinetic moment of inertia, it also served as a tool for the study of the spectral details of the nuclei, and for the study of the variation of nuclear structure with $N$ and $Z.$ We now study its extension to the intra band $E$2 transition from the higher spins of the ground bands of even $Z$ even $N$ nuclei of the mid-mass region of Xe–Pt chain of isotopes. We use the plots of $B(E$2, $I\to I-2)$ versus $[1/E_{\gamma }(I\to I-2\left)\right]$ $(I^{\pi }=4^{+}$ and 6${}^{+})$ to test their linear relationship. There seems to be a good correlation of the two entities even at the higher spins for all the nuclei studied here. The deviations from linearity in specific cases can be used for studying the nuclear structures involved.

In this paper, we applied the method developed by Santhosh and Safoora in [Phys. Rev. C  94 (2016) 024623; 95 (2017) 064611] to theoretically investigate the fusion, evaporation-residue (ER) and fission cross-sections of the synthesis of the unknown superheavy ${}^{309,312}$126 nuclei produced by using the ${}^{58}$Ni + ${}^{251}$Cf and ${}^{64}$Zn + ${}^{248}$Cm combinations. The charge asymmetry, mass asymmetry and fissility of the DiNuclear System (DNS) in the synthesis of the mentioned combinations are also estimated. The calculated results show that the ER cross-sections for the synthesis of the ${}^{309-317}$126 nuclei are predicted to be much less than 1.0fb. In particular, it has been found that there may exist a valley of the ER cross-sections in the synthesis of a superheavy $Z=126$ element, which produces the ${}^{313}$126 isotope. Subsequently, a model for the mass dependence of the ER cross-section in the synthesis of the ${}^{307-320}$126 isotopes has been proposed for the first time. On the other hand, the quasi-fission process strongly dominates over the fusion in the two concerned interacting systems. The present results, together with those reported in the previous studies, indicate that the investigated projectile–target combinations are not capable for the synthesis of the ${}^{309,312}$126 isotopes due to tiny fusion cross-sections (about 2–3zb), which go beyond the limitations of available facilities. Further studies are thus recommended to search for alternative interacting systems. In conclusion, this work provides useful information for the synthesis of the gap isotopes ${}^{308-317}$126, which have not been well studied up to date.

This paper describes an atomic cascade model which is used to predict the absorption yields for a kaon at low orbits in ${}^{6,7}$Li,⁹Be,${}^{13}$C and ${}^{16}$O nuclei. The calculations show that most of the absorptions occur in $p$ and $d$ states so that their contribution adds up to 100% for ${}^{16}$O. However, for all of the targets, absorption in the other states is nearly zero. Also by increasing atomic number of target $Z$, the yield of $p$ states decreases while it increases for the $d$ states. The results also display a low sensitivity on the widths of 4$f$ state (0.1%), in which it is comparable with the natural width of the radiation transition $4f\to 3d$.