This paper computationally explores some lesser-known results from the quantum scattering theory that gives the S-matrix in terms of the resolvent operator through the mediation of time-independent wave packets (TIWP). The S-matrix at a given energy is given by the ratio of the interacting and free TIWP’s evaluated at the corresponding on-shell momentum. This expression can also be expressed as the ratio of full and free resolvents at a given energy acting on the pre-collision wave packet. Another expression involves the ratio of the matrix elements of the interacting and free resolvents between post- and pre-collision wave packets. Computational implementations of these formal results involve the solution of the so-called TIWP form of the Lippmann–Schwinger equation (TIWP-LS). In the present contribution, the partial-wave TIWP-LS equation is solved using two schemes: (i) Direct numerical solution of the TIWP-LS equation via the quadrature discretization, and (ii) Construction of the resolvent operator by an expansion in Chebyshev polynomials of the scaled Hamiltonian. Computational performances of these procedures to compute the S-matrix are tested on a model potential for the p-wave case.
Isomeric yield ratios (IRs) of the fission products 130,132Sb, 131,133Te, 134,136I, 135Xe, and 138Cs were measured in the photofission of 232Th using bremsstrahlung end-point energies of 14 and 16 MeV. The experiments were performed at the 20 MeV ELBE electron linac (Helmholtz-Zentrum Dresden-Rossendorf), employing an off-line gamma-ray spectrometric technique. From the measured IR values, the average root-mean-square angular momenta (J RMS) of the primary fragments were deduced using a spin-dependent statistical model analysis. The results demonstrate that J RMS values of fission fragments with a spherical N = 82 shell are significantly lower than those for fragments without a closed neutron shell. Furthermore, the J RMS of odd-Z fission products were found to be higher than those of adjacent even-Z products, suggesting a distinct single particle effect. These findings highlight the significant influence of nuclear structure on the fission process. A comparison with literature data at different energies suggests that the excitation energy of the compound nucleus has a negligible effect on the fragment angular momentum within the studied energy range.
The photon flux-weighted average cross-sections of natGd(gamma,xn)151,153,159Gd reactions were measured at bremsstrahlung end-point energies of 30, 40, 50, and 60 MeV using a combination of activation techniques and off-line gamma-ray spectrometry. The measurements were conducted at the LUE-75 linear electron accelerator facility of the A.I. Alikhanyan National Science Laboratory (AANL) in Yerevan, Armenia. To complement the experimental data, theoretical calculations of the natGd(gamma,xn)151,153,159Gd reactions weighted average cross-section as a function of bremsstrahlung end-point energy were carried out using the TALYS 2.0 and EMPIRE 3.2 codes. The results from the experimental measurements were compared with the predictions from these models, as well as with available experimental data from the literature. For 151Gd, experimental data on the weighted average cross-section are reported for the first time, thereby providing new reference values for this isotope.Highlights
The quadrupole–quadrupole correlations are dominant in all nuclei with neutrons and protons outside magic closures. A subset among these shows features reminiscent of semiclassical rotors, i.e. J(J+1) spectra, and spectroscopic quadrupole moments and transition probabilities B(E2)’s consistent with the Bohr–Mottelson ansatz. But in the great majority of the cases the situation is not so clear. The Kumar–Cline invariants are an invaluable tool to decide to what extent the shape parameters β and γ are meaningful.
The annihilation and radiative decay widths of fully charmed hadrons are investigated using a non-relativistic phenomenological potential model. The wavefunctions and model parameters obtained by solving the non-relativistic Schrodinger equation are used to calculate the various decay widths. The annihilation decay widths of charmonium, radiative decay widths of charmonium and triply charmed baryons are evaluated. It is seen that the radiative decays of charmonium are dominated by E1 and M1 transitions, whereas for triply charmed baryons the radiative decays are dominated by E2 and M1 transitions.
