Influence of breakup on elastic and α-production channels in the ~6Li+~(116)Sn reaction

The effects of breakup reactions on elastic and α-production channels for the ~6Li+~(116)Sn system have been investigated at energies below and near the Coulomb barrier. The angular distributions of α-particle production differential cross sections have been obtained at several projectile energies between 22 and 40 MeV. The measured breakup α-particle differential cross sections and elastic scattering angular distributions have been compared with the predictions of continuum-discretized coupled channels(CDCC) calculations. The influence of breakup coupling has also been investigated by extracting dynamic polarization potentials(DPP) from the CDCC calculations. From the predictions of CDCC calculations the relative importance of the nuclear, Coulomb, and total breakup contributions have also been investigated. The nuclear breakup couplings are observed to play an important role in comparison to the Coulomb breakup for the direct breakup mechanisms associated in the reaction of ~6Li projectile with ~(116)Sn target nuclei. The influence of strong nuclear breakup coupling exhibits suppression in the Coulomb-nuclear interference peak. The direct breakup cross sections from the CDCC calculations under-predict the measured α-particle differential cross sections at all energies. This suggests that the measured α particles may also have contributions from other possible breakup reaction channels.     

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.     

Finite Range Effects on Fusion and/or Breakup of ^6He^＋238U and ^11Li＋^208pb Systems

We have studied the effects of the finite range of the interaction between the fragments of the projectile on the fusion and/or breakup of ⁶He+²³⁸U and ¹¹Li+²⁰⁸Pb systems at near barrier energies within the framework of dynamic polarization potential approach. It has been found that at near barrier energies the maximum flux is lost to the breakup channel and at energies well above the Coulomb barrier the fusion coupled with the breakup channel opens up, initially with sharp rise and later becoming saturated at energy nearly twice of theCoulomb barrier. Further, it is found that the breakup cross section increases with the increasing range of the interaction between the fragments of the projectile while the fusion coupled with the breakup channel cross section decreases with the increasing range.     

Surface-integral formulation of scattering theory

We formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surface-integrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.     

Eikonal Reaction Theory for One- and Two-Neutron Removal Reactions

We present an accurate method of treating neutron removal reactions and it’s applications. According to the method, the nuclear and Coulomb breakup processes are consistently treated by the method of the continuum discretized coupled channels. This method is referred to as the eikonal reaction theory (ERT). We analyze the two types of removal reactions of ³¹Ne and ⁶He with ERT.     

Dynamic polarization potentials for <Superscript>6</Superscript>He + <Superscript>209</Superscript>Bi and <Superscript>11</Superscript>Li + <Superscript>208</Superscript>Pb systems at near-barrier energies

The Coulomb dipole induced dynamic polarization potentials for ⁶He + ²⁰⁹Bi and ¹¹Li + ²⁰⁸Pb systems within the framework of Feshbach’s formalism with a motive to ascertain the presence or absence of threshold anomaly have been studied. As a result of this study, the threshold anomaly has been found to be present for both systems. It has also been found that at deep sub-barrier energies the imaginary part either starts increasing or at least remains unchanged which indicates the presence of the breakup threshold anomaly. In addition, the Coulomb breakup transmission factors for both systems have been found to have maximum value below and near-barrier energies, but at very high energies due to closure of the breakup channel the breakup transmission coefficients quickly becomes zero.     

Role of nuclear couplings in the inelastic excitation of weakly bound neutron-rich nuclei

We study the breakup of weakly bound systems close to the neutron drip line in collisions with heavy-ions. The process is described in terms of inelastic excitations leading to states in the continuum. The nuclear and Coulomb multipole fields induced by the reaction partner are both included in the microscopic construction of the inelastic form factors. A fraction of the dissociation cross sections is triggered by the presence of resonances at high excitation energy. The largest probabilities for breakup result, however, from strongly coupled transitions to low-lying states in the continuum. Nuclear couplings associated with inelastic excitation to these states are found to extend to unusually large distances. As a consequence, the interplay of nuclear and Coulomb excitations differs from the ordinary situation encountered in heavy-ion inelastic processes involving systems close to the stability line.     

弱束缚弹核引起的熔合反应

⁶Li, ⁹Be为弱束缚核. 通过弱束缚弹核⁶Li, ⁹Be轰击靶²⁰⁸Pb,²⁰⁸Be的实验熔合激发函数与理论预言的比较, 讨论了弱束缚弹核破裂对熔合过程 的影响. 比较结果显示, 弱束缚弹核与重靶核的完全熔合截面在垒上能区 明显压低. 由部分熔合截面与完全熔合截面之和得到总熔合截面. 研究结果 表明, 破裂对总熔合截面几乎没有影响. 由此可见, 弱束缚核的部分熔合 可能发生在强吸收区域附近. 最后还给出了全熔合截面与部分熔合截面 之间的关系.     

Diffractive dissociation of deuterons and exotic nuclei <Superscript>6</Superscript>He and <Superscript>19</Superscript>C

A theory is developed for describing the diffractive dissociation of loosely bound two-cluster nuclei in the nuclear and Coulomb fields of nuclei having a diffuse boundary. The energy spectra of charged products of the breakup of ²H, ⁶He, and ¹⁹C nuclei are calculated on the basis of the proposed approach, and the results are found to be rather sensitive to nuclear structure. For some angles of neutron and proton emission from the reaction ¹²C(d, np)¹²C, the calculated cross sections are in satisfactory agreement with the results of kinematically complete experiments performed recently to study the breakup of intermediate-energy deuterons.     

Structure of light neutron-rich nuclei through coulomb dissociation

Coulomb breakup of neutron-rich nuclei around mass A ∼ 20 has been studied experimentally using secondary beams (∼ 500–600 MeV/u) of unstable nuclei produced at GSI. The spectroscopic factor deduced for the neutron occupying s _1/2 level in ¹⁵C ground state is consistent with the earlier reported value. The data analysis for Coulomb breakup of ¹⁷C shows that most of the cross section yields the ¹⁶C core in its excited state. For ^17–22O, the low-lying E1 strength amounts up to about 12% of the energy weighted dipole sum rule strength depending on neutron excess. The cluster sum rule limit with ¹⁶O as a core is almost exhausted for ^17,18O, while for more neutron rich isotopes the strength with respect to that limit decreases.     

Contribution of electric quadrupole and dipole-quadrupole interference terms in Coulomb breakup of 15C

The effects of electric quadrupole (E2) and dipole-quadrupole interference (E1–E2) terms in the Coulomb breakup of ¹⁵C have been investigated within the framework of eikonal approximation. The sensitivity of Coulomb breakup cross section, differential in relative energy and Longitudinal Momentum Distribution (LMD) of core fragments, towards these terms have been examined. A very small (1% of E1) contribution of E2 transition has been predicted in integrated Coulomb breakup cross section. Further it is also found that the inclusion of E2 and E1–E2 terms introduces a small asymmetry in the peak of relative energy spectrum and also increases the peak height of the spectrum. The contribution of dipole-quadrupole interference terms is clearly shown in LMD, as it introduces an asymmetry in the shape of LMD and enhances the matching between the data and predictions.     

Relativistic Shifted-l Expansion Technique for Dirac and Klein-Gordon Equations

The shifted-l expansion technique (SLET) is extended to solve for Dirac particle trapped in spherically symmetric scalar and/or kvector potentials. A parameter λ = 0, l is introduced in such a way that one can obtain the Klein-Gordon (KG) bound states from Dirac bound states. The 4-vector Coulomb, the scalar linear, and the equally mixed scalar and 4-vector power-law potentials are used in KG and Dirac equations. Exact numerical results are obtained for the Cvector Coulomb potential in both KG and Dirac equations. Highly accurate and fast converging results are obtained for the scalar linear and the equally mixed scalar and 4-vector power-law potentials.     

The hydrino and other unlikely states

We discuss the tightly bound (hydrino) solution of the Klein–Gordon equation for the Coulomb potential in 3 dimensions. We show that a similar tightly bound state occurs for the Dirac equation for the Coulomb potential in 2 dimensions. These states are unphysical since they disappear if the nuclear charge distribution is taken to have an arbitrarily small but non-zero radius.     

Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges

We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.     

Proton-induced deuteron breakup reaction2H(p,pp)n

The screening and renormalization approach allows for a mathematically correct incorporation, in three-body scattering theory, of the long-ranged Coulomb interaction between charged particles. It is based on first calculating the transition amplitudes using screened Coulomb potentials. Then, after renormalization the zero-screening limit, leading to the amplitudes pertaining to unscreened Coulomb potentials, is performed numerically. Within this formalism the proton-induced breakup of deuterons is investigated, with the Coulomb repulsion between the two protons taken into account. Kinematically complete differential cross sections in various kinematic configurations are calculated and compared with the results of an identical calculation but for the neutron-induced reaction. In this way information on the size of the Coulomb effects in the proton-deuteron reaction can be extracted. Comparison is made with experimental data at 13.0 MeV projectile energy. In addition, the quality of approximate ways of including the Coulomb interaction is studied.Dedicated to Prof. Werner Sandhas on the occasion of his 60th birthday     

Deuteron Breakup Differential Cross Sections and Analyzing Powers of {\overrightarrow{d} + p} Scattering at E d = 16 and 130 MeV

Deuteron breakup differential cross sections and analyzing powers for ${\overrightarrow{d} + p}$ scattering at E _d  = 16 and 130 MeV are examined using the energy-independent quark-model nucleon–nucleon interaction fss2. The Coulomb effect is incorporated by the sharp cut-off Coulomb force, acting between quarks, without the phase-shift renormalization for the breakup amplitudes. Our results are very similar to those by the meson-exchange potentials, including disagreement for some specific kinematical configurations. The accurate and systematic KVI data at E _d  = 130 MeV are reasonably reproduced by taking the Coulomb cut-off radius ρ ≥ 16 fm.     

Effects of E2 and El-E2 Interference on Coulomb Dissociation of 19C

We investigate the effects of higher order multipole transitions, in particular electric quadrupole （E2） and El-E2 interference, on the Coulomb dissociation of 19 C within the framework of the first order eikonal approximation. The sensitivity of the total Coulomb breakup cross section and the longitudinal momentum distribution of the core fragment to these effects are checked. The breakup occurs predominately through the dipole transition and the contribution of E2 transition to the total cross section is found to be within the range from 1 to 3% of that of El. It is further observed that the El-E2 interference term contributes nothing to the integrated cross section. On the other hand, the longitudinal momentum distribution is observed to be insensitive to the E2 transition while the El-E2 interference introduces a small asymmetry in its shape.     

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.     

The Li exclusive breakup on Si at 13 MeV

We have undertaken the study of ⁶Li breakup on a ²⁸Si target near the Coulomb barrier through an angular distribution measurement. Alpha particles were recorded in coincidence with deuterons in order to determine exclusively the breakup of lithium. The results are analysed and are discussed, in a continuum discretized coupled channel framework (CDCC).