Four-body distorted-wave theory for halo excitations in peripheral fragmentation reactions

A microscopic approach to breakup into the low-energy continuum of Borromean two-neutron-halo nuclei is developed by quantum mechanically taking into account both Coulomb and nuclear dissociation. The crucial role of both elastic and inelastic fragmentation is demonstrated for ⁶He breakup on C and Pb targets at intermediate energies in kinematically complete experiments. For the first time, recent GSI experimental data are analyzed quantitatively, and a rich and complex interplay of reaction mechanisms and low-lying halo excitations is revealed.     

Polarization potentials due to inelastic excitations

Dynamic polarization potentials generated by inelastic excitations of the projectile or target nuclei for three scattering systems are compared. Effects due to excitations to bound/unbound states as well as due to different multipolarities are studied. It is shown that the potentials exhibit similar radial dependence at large projectile-target separations; real parts change with the increased radius from repulsive to attractive while imaginary parts, close to zero or even emissive at the nuclear surface, are becoming absorptive at large distances. This general tendency is a consequence of the interplay between Coulomb and nuclear forces.     

Reactions with fast radioactive beams of neutron-rich nuclei

The neutron dripline has presently been reached only for the lightest nuclei up to the element oxygen. In this region of light neutron-rich nuclei, scattering experiments are feasible even for dripline nuclei by utilizing high-energy secondary beams produced by fragmentation. In the present article, reactions of high-energy radioactive beams will be exemplified using recent experimental results mainly derived from measurements of breakup reactions performed at the LAND and FRS facilities at GSI and at the S800 spectrometer at the NSCL. Nuclear and electromagnetically induced reactions allow probing different aspects of nuclear structure at the limits of stability related to the neutron-proton asymmetry and the weak binding close to the dripline. Properties of the valence-neutron wave functions are studied in the one-neutron knockout reaction, revealing the changes of shell structure when going from the beta-stability line to more asymmetric loosely bound neutron-rich systems. The vanishing of the N = 8 shell gap for neutron-rich systems like ¹¹Li and ¹²Be, or the new closed N = 14, 16 shells for the oxygen isotopes are examples. The continuum of weakly bound nuclei and halo states can be studied by inelastic scattering. The dipole response, for instance, is found to change dramatically when going away from the valley of stability. A redistribution of the dipole strength towards lower excitation energies is observed for neutron-rich nuclei, which partly might be due to a new collective excitation mode related to the neutron-proton asymmetry. Halo nuclei, in particular, show strong dipole transitions to the continuum at the threshold, being directly related to the ground-state properties of the projectile. Finally, an outlook on future experimental prospects is given.     

Direct processes in heavy ion collisions at E ⩽ 20 MeV/u

Elastic and inelastic scattering at projectile energies of E ? 20 MeV/u have been studied using a magnetic spectrometer. It is shown that nuclear rainbow scattering for ¹²C + ¹²C allows to extract information from small inter nuclear distances. The role of the collective inelastic excitations is studied and it is shown that they lead to a decomposition of the projectile (or target)if the threshold for particle emission is close to the excitation energy of low lying collective states. The origin of the continuous background in the study of high lying excitations in nuclei is studied and it is shown that it can be analysed quantitatively.     

Coupling effects of resonant and discretized non-resonant continuum states in 4He + 6Li scattering at 10 MeV/A

Alpha-particle scattering from the resonant (3 ₁ ⁺ ) and non-resonant continuum states of ⁶Li is studied at incident energy 10 MeV/A. The α + d breakup continuum part within the excitation energy E _ex = 1.475–2.475 MeV is discretized in two energy bins. Unlike the results at higher incident energies, here the coupled-channel calculations show significant breakup continuum coupling effects on the elastic and inelastic scattering. It is shown that even when the continuum-continuum coupling effects are strong, the experimental data of the ground state and the resonant as well as discretized non-resonant continuum states impose stringent constraint on the coupling strengths of the non-resonant continuum states.     

Coupling effects of resonant and discretized non-resonant continuum states in4He +6Li scattering at 10 MeV/A

Alpha- particle scattering from the resonant (3 ₁ ⁺ ) and non-resonant continuum states of⁶Li is studied at incident energy 10 MeV/A. Theα+d breakup continuum part within the excitation energyE _ex=1.475–2.475 MeV is discretized in two energy bins. Unlike the results at higher incident energies, here the coupled-channel calculations show significant breakup continuum coupling effects on the elastic and inelastic scattering. It is shown that even when the continuum-continuum coupling effects are strong, the experimental data of the ground state and the resonant as well as discretized non-resonant continuum states impose stringent constraint on the coupling strengths of the non-resonant continuum states.     

Excitation and decay of low-lying nuclear states in a dense plasma produced by a subpicosecond laser pulse

The excitation of low-lying nuclear levels in a hot, dense plasma, produced by a subpicosecond pulse with intensity exceeding 10¹⁶ W/cm², is investigated theoretically and experimentally. The basic channels of electronic (inelastic scattering and inverse internal electron convergence) and photon (photoexcitation) excitations of such states as well as the influence of the broadening of a nuclear level on the excitation efficiency and the presence of hot electronic component are examined. The experimental data from measurements of the decay kinetics of the low-lying nuclear level 6.238 keV of the stable isotope ¹⁸¹Ta, which were obtained on two experimental laser systems, are presented.     

Fragmentation processes in nuclear reactions

Fragmentation processes in nuclear collisions are reviewed. The main emphasis is put on light ion breakup at nonrelativistic energies. The post- and prior-form DWBA theories are discussed. The post-form DWBA, appropriate for the “spectator breakup” describes elastic as well as inelastic breakup modes. This theory can also account for the stripping to unbound states. The theoretical models are compared to typical experimental results to illustrate the various possible mechanisms. It is discussed, how breakup reactions can be used to study high-lying single particle strength in the continuum; how they can yield information about momentum distributions of fragments in the nucleus.     

0(+)(gs) --> 2(+)(1) excitations in the mirror nuclei 32Ar and 32Si

We measured the strength of the 0(+)(gs)-->2(+)(1) excitations in the radioactive mirror nuclei 32Ar and 32Si using the techniques of intermediate-energy Coulomb excitation for 32Ar and inelastic proton scattering in inverse kinematics for 32Si. The 32Ar measurement, taken together with previously existing Coulomb excitation data for 32Si, yields the isoscalar and isovector multipole matrix elements for the 0(+)(1)-->2(+)(1) transition between T = 2 states in the A = 32 system. The proton scattering measurement for 32Si, when combined with the Coulomb excitation data for this nucleus, yields a ratio of neutron and proton matrix elements, M(n)/M(p), for 32Si.     

Dipole states in the deuteron,other exotic nuclei,and “Schrödinger’s Cat”

The question whether the “soft giant dipole modes” in halo nuclei are resonances is discussed. It is argued that a resonance picture of these modes can be envisaged with a non Breit-Wigner line shape. The dipole Coulomb breakup of the deuteron is worked out as a specific example of such a picture. The “soft” and “hard” dipole modes of the more complex neutron-rich exotic nuclei are treated from this point of view. An interpretation of the coherent production of these modes in Coulomb excitation as a nuclear instance of Schrödinger cat state is advanced.     

The level structures of the nuclei232Th and238U

Time-of-flight gating techniques have been used to study the decay γ-rays from states excited by inelastic scattering of neutrons from²³²Th and²³⁸U. Neutron energies up to 1900 MeV have been used. From accurate determinations of the γ-ray energies, intensities and thresholds, detailed level and decay schemes have been obtained for²³²Th and²³⁸U. New levels in both nuclei are observed at larger excitations than before and the present work is incompatible with some previously accepted spin and collective band assignments derived from Coulomb excitation studies.     

Electromagnetic response and breakup of light weakly bound nuclei in a dicluster model

The light weakly bound nucleus ⁷Li is studied within a dicluster α + t picture. Different observables obtained within our simple model are compared with previous calculations and experiments showing good agreement. In particular, we calculate dipole and quadrupole electromagnetic response to the continuum. The energy distribution of B(Eλ) values are consistent with the energy-weighted molecular sum rule and display a sizable contribution of non-resonant character arising from the weak binding property. The corresponding form factors for excitations to the continuum are used in a semiclassical coupled-channel scheme to get estimates for the breakup cross-section in a heavy-ion reaction. The nuclear contribution is found to play an important role in the process for bombarding energies around the Coulomb barrier. The masses and charges ratios of the two clusters are shown to lead to features of the cluster halo that may significantly differ from the one usually associated with one-nucleon haloes.     

Fusion of weakly bound projectiles around the Coulomb barrier

The effect of breakup of weakly bound projectiles on fusion is studied using two approaches. The first approach based on the coupled discretised continuum channel (CDCC) formalism is used for ¹¹Be+²⁰⁸Pb, while the second one based on the two-centre shell model (TCSM) is used for ⁹Be+²⁰⁹Bi, ⁶⁴Zn. The CDCC approach describes the breakup in terms of inelastic excitations of the projectile to the continuum, while the breakup is described by molecular single-particle effects in the TCSM approach.     

Relativistic corrections to electron scattering: (II). Inelastic scattering

Relativistic corrections to inelastic electron scattering have been investigated using the results of a previous calculation on elastic scattering. A detailed discussion is made of the kinematics of inelastic scattering. Excitation of discrete states is treated in detail by two different methods, with particular attention paid to kinematical factors. Deuteron breakup is discussed and treated in a very similar manner to the discrete excitations. Comparison is made with analyses using plane wave final states and with previous work.     

Breakup excitation function at backward angles from α-spectra in the Li + Sm system

Breakup cross sections were obtained for the ⁶Li + ¹⁴⁴Sm system at energies above and below the Coulomb barrier from a detailed analysis of the data recorded at backward angles. These cross sections are compared with inelastic target excitations previously reported revealing a similar behavior as a function of the bombarding energy but a large absolute difference between them. Using kinematical considerations we have analyzed possible contributions from different breakup channels and we have extracted information on magnitudes such as the relative kinetic energies of the corresponding breakup fragments.     

Heavy ion reactions around the Coulomb barrier

The angular distributions of fission fragments for the ³²S+¹⁸⁴W reaction near Coulomb barrier energies are measured. The experimental fission excitation function is obtained. The measured fission cross sections are decomposed into fusion-fission, quasi-fission and fast fission contributions by the dinuclear system (DNS) model. The hindrance to completing fusion both at small and large collision energies is explained. The fusion excitation functions of ³²S+^90,96Zr in an energy range from above to below the Coulomb barrier are measured and analyzed within a semi-classical model. The obvious effect of positive Q-value multi-neutron transfers on the sub-barrier fusion enhancement is observed in the ³²S+⁹⁶Zr system. In addition, the excitation functions of quasi-elastic scattering at a backward angle have been measured with high precision for the systems of ¹⁶O + ²⁰⁸Pb, ¹⁹⁶Pt, ¹⁸⁴W, and ^154,152Sm at energies well below the Coulomb barrier. Considering the deformed coupling effects, the extracted diffuseness parameters are close to the values extracted from the systematic analysis of elastic and inelastic scattering data. The elastic scattering angular distribution of ¹⁷F+¹²C at 60 MeV is measured and calculated by using the continuum-discretized coupled-channels (CDCC) approach. It is found that the diffuseness parameter of the real part of core-target potential has to be increased by 20% to reproduce the experimental result, which corresponds to an increment of potential depth at the surface region. The breakup cross section and the coupling between breakup and elastic scattering are small.     

Evidence of correlation in spin excitations of few-electron quantum dots

We report inelastic light scattering measurements of spin and charge excitations in nanofabricated AlGaAs/GaAs quantum dots with few electrons. A narrow spin excitation peak is observed and assigned to the intershell triplet-to-singlet monopole mode of dots with four electrons. Configuration-interaction theory provides precise quantitative interpretations that uncover large correlation effects that are comparable to exchange Coulomb interactions.     

Effects of neutron skin on the excitation of isovector modes of neutron-rich nuclei

The existence of a neutron skin in neutron-rich nuclei is discussed in connection with the excitation of isovector dipole and quadrupole giant modes via isoscalar nuclear probes. In the case of large neutron excess, important contributions are obtained from the nuclear excitation, which may even become predominant according to proper kinematical conditions. At variance with the usual situation encountered in inelastic processes, constructive interference can be found between nuclear and Coulomb contributions.     

Coulomb and nuclear interactions in the dynamics of weakly-bound neutron-halo breakup on heavy target

Within our aim to clarify some aspects of the breakup dynamics of loosely-bound neutron-halo projectiles on a heavy target,we apply the continuum discretized coupled-channel formalism to investigate the beryllium¹¹Be breakup on a lead²⁰⁸Pb target atE_lab=140 MeV incident energy.By evidencing that the continuum–continuum couplings are much stronger in the nuclear breakup than in the Coulomb breakup,we conclude that the strength of these couplings in the total breakup is dominated by the nuclear contribution,with the diagonal monopole nuclear potential in the projectile–target center-of-mass having negligible effect on the total and nuclear breakup cross-sections.For this kind of reaction,we show that the condition for the total breakup to approach its dominant component in the absorption region is strongly dependent on the continuum–continuum couplings and the diagonal monopole nuclear potential.