ELASTIC AND INELASTIC ALPHA TRANSFER IN THE 16O+12C SCATTERING

The elastic scattering cross section measured at energies $E\lesssim 10$ MeV/nucleon for some light heavy-ion systems having two identical cores like \oc exhibits an enhanced oscillatory pattern at the backward angles. Such a pattern is known to be due to the transfer of the valence nucleon or cluster between the two identical cores. In particular, the elastic $\alpha$ transfer has been shown to originate directly from the core-exchange symmetry in the elastic \oc scattering. Given the strong transition strength of the $2^+_1$ state of $^{12}$C and its large overlap with the $^{16}$O ground state, it is natural to expect a similar $\alpha$ transfer process (or inelastic $\alpha$ transfer) to take place in the inelastic \oc scattering. The present work provides a realistic coupled channel description of the $\alpha$ transfer in the inelastic \oc scattering at low energies. Based on the results of the 4 coupled reaction-channels calculation, we show a significant contribution of the $\alpha$ transfer to the inelastic \oc scattering cross section at the backward angles. These results suggest that the explicit coupling to the $\alpha$ transfer channels is crucial in the studies of the elastic and inelastic scattering of a nucleus-nucleus system with the core-exchange symmetry.\Keywords{optical potential, coupled reaction channels, inelastic $\alpha$ transfer

Elastic and Inelastic Alpha Transfer in the \(^{16}\)O+\(^{12}\)C Scattering

The elastic scattering cross section measured at energies \(E\lesssim 10\) MeV/nucleon for some light heavy-ion systems having two identical cores like \(^{16}\)O+\(^{12}\)C exhibits an enhanced oscillatory pattern at the backward angles. Such a pattern is known to be due to the transfer of the valence nucleon or cluster between the two identical cores. In particular, the elastic \(\alpha\) transfer has been shown to originate directly from the core-exchange symmetry in the elastic \(^{16}\)O+\(^{12}\)C scattering. Given the strong transition strength of the $2^+_1$ state of $^{12}$C and its large overlap with the $^{16}$O ground state, it is natural to expect a similar \(\alpha\) transfer process (or inelastic \(\alpha\) transfer) to take place in the inelastic \(^{16}\)O+\(^{12}\)C scattering. The present work provides a realistic coupled channel description of the \(\alpha\) transfer in the inelastic \(^{16}\)O+\(^{12}\)C scattering at low energies. Based on the results of the 4 coupled reaction-channels calculation, we show a significant contribution of the \(\alpha\) transfer to the inelastic \(^{16}\)O+\(^{12}\)C scattering cross section at the backward angles. These results suggest that the explicit coupling to the \(\alpha\) transfer channels is crucial in the studies of the elastic and inelastic scattering of a nucleus-nucleus system with the core-exchange symmetry.

What can we learn from the Interacting Boson Model in the limit of large boson numbers?

Over the years, studies of collective properties of medium and heavy mass nuclei in the framework of the Interacting Boson Approximation (IBA) model have focused on finite boson numbers, corresponding to valence nucleon pairs in specific nuclei. Attention to large boson numbers has been motivated by the study of shape/phase transitions from one limiting symmetry of IBA to another, which become sharper in the large boson number limit, revealing in parallel regularities previously unnoticed, although they survive to a large extent for finite boson numbers as well. Several of these regularities will be discussed. It will be shown that in all of the three limiting symmetries of the IBA [U(5), SU(3), and O(6)], energies of 0+ states grow linearly with their ordinal number. Furthermore, it will be proved that the narrow transition region separating the symmetry triangle of the IBA into a spherical and a deformed region is described quite well by the degeneracies E(0^+_2 ) = E(6^+_1 ), E(0^+_3 ) = E(10^+_1 ), E(0^+_4 ) = E(14^+_1 ), the energy ratio E(6^+_1 )/E(0^+_2 ) turning out to be a simple, empirical, easy-to-measure effective order parameter, distinguishing between first- and second-order transitions. The energies of 0+ states near the point of the first order shape/phase transition between U(5) and SU(3) will be shown to grow as n(n+3), where n is their ordinal number, in agreement with the rule dictated by the relevant critical point symmetries studied in the framework of special solutions of the Bohr Hamiltonian. The underlying dynamical and quasi-dynamical symmetries are also discussed.

Moments of inertia and B(E2;01+→21+)s in the NpNn scheme

We examine the collective nuclear structure of light and medium mass (Z = 50–82, N = 82–126) even–even nuclei using valence nucleon pair product (NpNn). We discuss the role of proton–neutron interaction in light mass nuclei and illustrate the variation of observables of collectivity and deformation (i.e., ground band moment of inertia) and B(E2) values with N and NpNn). The plot of these observables against NpNn vividly displays the formation of isotonic multiplets in quadrant I, strong dependence on NpNn in quadrant II and weak constancy with Z in quadrant III is illustrated.

The effect of the valence nucleons off the shells with Z = 82 and N = 126 on rotational characteristics of actinide nuclei

Our earlier results obtained for moments of inertia (M) in the case of 54 rotational level bands built on the ground state of actinide nuclei are taken for further analysis. In the current paper, resulting dynamic rotational characteristics, such as a 0, a 1, s 0 and the R 4/2 parameter, are studied from the standpoint of their dependence on the valence nucleon number product N p N n and on the variable P = N p N n/(N p + N n). New features of the nuclei deformation phenomenon in the actinide area arise when their dynamic rotational characteristics, mentioned above, are plotted in such a way as shown in the current work. The method of analysis presented here makes it possible to reveal nuclei with valence nucleon numbers for which the nuclear interactions are notable and those in which they are inconspicuous. E. g. when N p N n < 200 and P < 6 the strength of nuclear interaction gradually decreases with the increase of these variables. The strength of the nuclear interaction does not change significantly for N p N n > 200 and P > 6 — the rotational characteristics stabilise. Moreover, it is possible to establish the P variable as representing the effective number of interactions of each valence nucleon with those of the other type.