International Journal of Modern Physics E

In the presented review we discuss the problem of extracting the parameters of nuclear matter and charge distribution in stable and unstable isotopes. A substantial amount of information on the nuclear radii and other distribution parameters in light exotic nuclei has been obtained from experiments on intermediate-energy nucleus–nucleus collisions. The analyses of these experiments are usually performed with the help of the Glauber theory. We review the main assumptions of the Glauber theory and show how this theoretical approach is used to calculate reaction and interaction cross-sections. We also show how radii of nuclear matter can be obtained from the analysis of the experimental data on reaction cross-sections. In the provided analysis reaction cross-sections were calculated in optical and rigid approximations of the Glauber theory as well as using explicit expressions. Numerical calculations of Glauber's explicit expressions for reaction cross-sections were done using Monte Carlo technique. Recent results of the precise measurements of charge radii of light exotic nuclei which were done using the laser-spectroscopy technique as well as the method of the investigation of the nuclear matter distributions in proton elastic scattering experiments in inverse kinematics are also discussed.

In this paper, the tritium–tritium fusion reaction rate in a muonic molecular ion (μtt) is calculated by using a square-well nuclear potential as a complex for nuclear interaction between two tritones. The complex potential parameters are obtained by fitting process on fusion cross-section experimental data. The real and imaginary parts of the nuclear potential are calculated as U_r = -62531.87 (keV) and U_i = -165.63 (keV), respectively. A free parameter that is related to the radius of this potential is A = 0.004155. Also, considering the optical nuclear potential, the energy value of μtt muonic molecular ion is calculated. The fusion rate is calculated by liner combination of atomic orbital (LCAO) method. Finally, the reaction rate, λ, is obtained 0.28×10¹⁰s^-1 by calculating the transition probability through the potential barrier and the oscillation frequency of wave function.

Monopole shift in the proton states in odd neutron-rich F isotopes has been studied with neutron number changing from N = 10 to 20 for three different interactions. The variation of monopole shift point out towards appearance of shell closure at N = 14 and N = 16 and its disappearance at N = 20. Low lying states of odd F isotopes have also been calculated in the limited configuration space of sd shells for these interactions.

The experiments were performed to study excitation functions (EFs) of evaporation residues (ERs), i.e. ^103,102,101Ag, ^101,100,99Pd, ^101,100Rh, ⁹⁷Ru, ⁹⁶Tc, ⁹⁵Tc, ⁹⁴Tc, ⁹³Mo^m, ⁹²Nb^m populated in the reactions induced by ¹²C on ⁹³Nb for exploring the reaction dynamics involved at energies ≈ 47–75 MeV. The activation technique followed by offline γ-ray spectrometry has been employed to measure EFs. These measurements were simulated with other reported values available in literature as well as with theoretical predictions based on computer code PACE-2. The effect of variation of level density parameter involved in this code has also been studied. An excellent agreement was found between theoretical and experimental values in some of the fusion evaporation channels. However, significant enhancement of cross-section as observed in α-emission channels may be due to incomplete fusion (ICF) process and/or direct reaction process. To confirm the aforesaid reaction mechanism, Recoil Range Distributions (RRDs) of various ERs have been measured at ≈ 80 MeV. Moreover, an attempt is made to separate the percentage relative contributions of complete and incomplete fusion components from the analysis of the measured RRDs data. Further, the relative percentage ICF fraction, also estimated from EFs data, was found to be sensitive with the projectile energy.

Modifications in the energy–momentum dispersion laws due to a noncommutative geometry, have been considered in recent years. We examine the oscillations of extended objects in this perspective and find that there is now a "generation" of energy.

The characters of the angular distributions of quark-jets and gluon-jets with different flavors are carefully studied after introducing the cone-angle of jets. The quark-jets and gluon-jets are identified from the 3-jet events which are produced by Monte Carlo simulation Jetset7.4 in e⁺e^- collisions at GeV. It turns out that the ranges of angular distributions of gluon-jets are obviously wider than that of quark-jets at the same energies. The average cone-angles of gluon-jets are much larger than that of quark-jets. As the multiplicity or the transverse momentum increases, the cone-angle distribution without momentum weight of both the quark-jet and gluon-jet all increases, i.e. the positive linear correlation are present, but the cone-angle distribution with momentum weight decreases at first, then increases when n > 4 or p_t > 2 GeV. The characters of cone-angular distributions of gluon-jets produced by quarks with different flavors are the same, while there are obvious differences for that of the quark-jets with different flavors.

The ground state properties of light closed shell nuclei, i.e. ⁴He, ¹²C, ¹⁶O, ²⁸Si, ³²S, ⁴⁰Ca and ⁵⁶Ni are studied by using the channel-dependent effective two-body interactions (CDEI's). The CDEI's are generated through the lowest-order constrained variational (LOCV) calculation for asymmetric nuclear matter with the charge-dependent Av₁₈ bare nucleon–nucleon potential. The work is performed on the harmonic oscillator basis, and the local density approximation is applied to create the relative and the center of mass dependent effective two-body potential. Unlike nuclear matter, and similar to our previous calculations with the Reid68 interaction, while the Av₁₈ potential under binds above nuclei up J_max = 2 channel, it gives ground state binding energies closer to the experimental data with respect to the Δ- Reid68 and the Reid68 potentials. There are not much difference between the results of Av₁₈ interaction with J_max = 5, and those of Reid68Day potential which has been define up to J_max = 5. The different CDEI's up to J_max = 5 are discussed and the results of our calculations are compared with the other theoretical approaches and experimental data. Finally, it is shown that the contributions of higher partial waves (J>2) are not very important and the two-body kinetic energy in J = 1 channel is roughly twice as that of J = 0 which is not the case for the two-body potential energy.

Amongst iron regime nuclei, β-decay rates on titanium isotopes are considered to be important during the late phases of evolution of massive stars. The key β-decay isotopes during presupernova evolution were searched from available literature and a microscopic calculation of the decay rates were performed using the proton–neutron quasiparticle random phase approximation (pn-QRPA) theory. As per earlier simulation results, electron capture and β-decay on certain isotopes of titanium are considered to be important for the presupernova evolution of massive stars. Earlier the stellar electron capture rates and neutrino energy loss rates due to relevant titanium isotopes were presented. In this paper we finally present the β-decay rates of key titanium isotopes in stellar environment. The results are also compared against previous calculations. The pn-QRPA β-decay rates are bigger at high stellar temperatures and smaller at high stellar densities compared to the large scale shell model results. This study can prove useful for the core-collapse simulators.

Total reaction cross-sections of the two neutron halo nuclei ¹¹Li and ²²C elastic scattering from ¹²C target at E = 30–1000 MeV/nucleon have been analyzed using the eikonal phase shift based, for the first time, on the semi-phenomenological nucleon density. The obtained results reasonably agree with those of previous theoretical calculations as well as the corresponding experimental data.

A quantum theory of gravity, based upon a composite model of leptons and quarks, is presented. The model treats leptons and quarks as composites of three kinds of spin- particles (rishons) and/or their antiparticles. A strong color force, mediated by massless hypergluons, binds rishons and/or antirishons together to form colorless leptons or colored quarks, the fundamental particles of the Standard Model. The new model provides a qualitative understanding of the mass hierarchy of the three generations of leptons and quarks. An earlier conjecture that the residual interaction of the strong color force acting between any two colorless particles be identified with the corresponding gravitational interaction, is shown to lead approximately to Newton's law of gravitation.

A development has been made for the charged-particle-induced nonresonant reaction-rate equations. The forms of reaction-rate equations for nonresonant and resonant reactions have been united in a frame of Lorentzian-Function Approximation (LFA) mathematically. In the frame of LFA, the nonresonant reaction taken place within the Gamow window can be considered, in form, as a "resonance" reaction with a full width at half maximum (FWHM, Γ^nr) equal to the 1/e width (Δ) in a well-known Gaussian-Function Approximation (GFA).