R.A. Broglia

Dynamics of the shell model

Abstract Many Fermi liquids are amenable to a shell-model description, where the particles move in an average potential. The coupling of the single-particle degrees of freedom to other modes of excitation strongly affects the properties of the shell-model potential. It is empirically found, however, that these couplings preserve the approximate validity of the shell model. Significant theoretical progress has recently been accomplished in the understanding of the resulting “dynamical shell model” in nuclear matter, normal liquid 3He, the electron gas and nuclei. The dominant modes which couple to the single-particle motion are particle-hole excitations in the case of nuclear matter, paramagnons in the case of 3He, phonons for electrons in metals and surface vibrations in the case of nuclei. For the latter, the dynamical shell model can be viewed as an extension of the optical model to encompass both positive and negative energies. It thus provides a unified description of scattering and of bound single-particle states. The associated potential is energy dependent. This feature is characterized by the nucleon effective mass. The theoretical and experimental evidence which testifies to the existence of a strong energy dependence of this effective mass around the Fermi energy and near the nuclear surface is the central subject of the present review.

Role of the nuclear surface in a unified description of the damping of single-particle states and giant resonances

Abstract The damping widths of single-particle states and of giant resonances are estimated in spherical nuclei, based on the excitation of surface modes. A Skyrme III interaction with an effective mass consistent with that resulting from infinite nuclear matter calculations with “realistic” forces (m ∗ /m = 0.76) , was utilized. The single-particle basis needed to construct the unperturbed nuclear response function for each multipolarity was obtained, treating this force in the Hartree-Fock approximation. Diagonalizing a schematic interaction in this basis, the surface modes were calculated. They are used to dress the single-particle and single-hole states and to renormalize the vertex interaction, taking into account the proper energy dependence of the couplings. The essential new feature of the present calculation as compared to the calculations reported in ref. 1 ) is that the energy dependence of the real and imaginary part of the self-energy is taken into account. This is done utilizing a strength function model. About 70 % of the damping widths arise from the coupling to specific intermediate states containing one low-lying collective surface vibration. The rest, from the coupling to many nonspecific states. Qualitative agreement is found with the experimental data for spherical nuclei throughout the mass table for both the single-particle states and the giant resonances. The model seems however to predict widths which are smaller than those experimentally observed.

Damping of the giant dipole resonance in hot, strongly rotating nuclei

Abstract The isovector dipole density-density response of hot rotating nuclei is calculated applying a cranked deformed Nilsson potential together with a separable dipole-dipole residual interaction. The transformation of the response function from the internal rotating coordinate frame to the laboratory frame is discussed and illustrated by classical results for a charged particle moving in a harmonic-oscillator potential. Calculations for 108 Sn, 152 Dy and 196 Pb are presented. For 108 Sn at high excitation energy thermal fluctuations of the shape gives rise to a rather structureless strength function with a considerable width. For 152 Dy and 196 Pb superdeformed minima of the potential surface are predicted. The coupling of the giant dipole resonance to the shape degrees of freedom of superdeformed nuclei can split the vibration by ≈ 10 MeV, the lowest peak being expected at an excitation energy of ≈ 7–8 MeV and carrying ≈ 30% of the energy-weighted sum rule.

Nuclear field theory

Abstract The nuclear spectrum is described in terms of elementary modes of excitation comprising pairing and surface vibrations and single-particle degrees of freedom. A unified theory of the mutual interweaving of these excitations which makes use of many-body field theoretical concepts is reviewed. The theory is illustrated through the study of the nuclear structure of 209 Bi.

Urea and Guanidinium Chloride Denature Protein L in Different Ways in Molecular Dynamics Simulations

In performing protein-denaturation experiments, it is common to employ different kinds of denaturants interchangeably. We make use of molecular dynamics simulations of Protein L in water, in urea, and in guanidinium chloride (GdmCl) to ascertain if there are any structural differences in the associated unfolding processes. The simulation of proteins in solutions of GdmCl is complicated by the large number of charges involved, making it difficult to set up a realistic force field. Furthermore, at high concentrations of this denaturant, the motion of the solvent slows considerably. The simulations show that the unfolding mechanism depends on the denaturing agent: in urea the beta-sheet is destabilized first, whereas in GdmCl, it is the alpha-helix. Moreover, whereas urea interacts with the protein accumulating in the first solvation shell, GdmCl displays a longer-range electrostatic effect that does not perturb the structure of the solvent close to the protein.

Semiclassical theory of heavy ion reactions

Abstract The application of the semiclassical theory [1] of direct reactions among heavy ions is discussed. Prescriptions are given to use this picture also for bombarding energies in which the nuclear forces play an important role in defining the trajectory of relative motion of the two colliding ions. The competition between different processes leading to the same final channel and the influence of channels which are strongly coupled to the final channel are discussed in the framework of the semiclassical coupled channel equations of motion. The possibility of including, within the semiclassical scheme, effects of antisymmetrization, recoil and non-orthogonality of the basis vectors are also discussed.

On the absorptive potential in heavy ion scattering

Abstract A preliminary investigation of the nuclear imaginary potential to be used for the analysis of elastic scattering data of heavy ions is presented. The derivation is carried out in the framework of the semiclassical description. The resulting potential is angular momentum independent and shows two components. A long range part due to transfer reactions and a short range part due to nuclear inelastic scattering. Coulomb excitation has not been taken into account. Simple closed expressions are derived for the transition amplitudes associated with the transfer and inelastic processes, including the Q -value dependence which can be used for the analysis of reaction data.

Damping of nuclear excitations at finite temperature

Abstract We calculate the damping of single-particle motion and of vibrational motion to lowest order in the coupling between the particles and the vibrations, using the finite temperature Matsubara formalism. The derived formulas have a complicated structure which however can be mostly understood in physical terms. We apply the theory to single-particle states in heavy nuclei, to the giant dipole vibration in 90Zr, and to the giant quadrupole vibration in 208Pb. Even at temperatures of the order of 3 MeV the main peak of the giant vibrations remains essentially unaffected although it acquires a long tail at the low-energy end.

Damping of rotational motion

Abstract The damping of rotational bands at high spin, based on few quasiparticle excitations, is directly related to the spread in the associated rotational frequencies, which leads to an I-dependent band mixing. The average properties of the continuum γ-ray spectrum can be parametrized in terms of the resulting spreading width Γrot↓ of the E2 rotational decay strength. For typical rare-earth nuclei this quantity is approximated by Γ rot ↓ (U) ∼- 0.13(I/40) U 1 4 MeV for U 1 , and by Γ rot ↓ (U) ∼ 0.22(t/40) 2 U −1 MeV for U > U 1 . The energy U1 can be approximated by 1.5(I/40) 4 5 MeV . A strong dependence of Γrot↓ (U) with mass number and deformation is found.

The role of the giant resonances in deep inelastic collisions between heavy ions

Abstract A unified description of heavy ion reactions which includes all the most important nuclear degrees of freedom in an average way is attempted, in terms of the semiclassical coupled equations.