Shape effects in heavy ion (Li) elastic scattering

The elastic scattering of aligned ⁶Li and ⁷Li on ⁵⁸Ni at E_cm = 12.7 MeV displays an “isotopic” effect which can be traced to the very different (mass) quadrupole moments of both isotopes. The elastic scattering of aligned ⁶Li and ⁷Li on ^12,13C at E_Li = 9 MeV displays large effects, but the angular dependence is much more complicated compared to the scattering on ⁵⁸Ni.     

Global optical model potentials for symmetrical lithium systems: 6Li+6Li, 7Li+7Li at Elab = 5–40 MeV

Angular distributions of ⁶Li+⁶Li elastic scattering were measured for E_lab = 5–40 MeV. An optical model analysis of these data together with older data of ⁷Li+⁷Li elastic scattering taken at E_lab = 8–17 MeV was performed with the aim to search for a “global” OM potential which describes elastic scattering in both LiLi systems in a broad energy range. Both surface and volume absorbing potentials can be found which fulfill this requirement if a linear energy dependence is assumed of the depths of the real as well as the imaginary potential. These depths, if fitted to individual angular distributions, are found to vary in a correlated manner with the beam energy. This is taken as indication of strong coupling between elastic, inelastic, and reaction channels. This is corroborated by the existence of resonances in reaction channels at these energies where the potential depths are most pronouncedly changing.     

Isotopic effects in the 7Li + 10, 11B elastic and inelastic scattering

Angular distributions of the ⁷Li + ¹⁰B elastic and inelastic scattering were measured at the energy E _lab (¹⁰B) = 51 MeV (21 MeV c.m.). These and previously measured ⁷Li + ¹⁰B elastic-scattering data known at the ⁷Li-beam energies 24 MeV (14.1 MeV c.m.) and 39 MeV (22.94 MeV c.m.) were analyzed within the optical model and coupled-reaction channels method to determine the energy dependence of the parameters of the scattering potential and find the difference of these parameters from that of ⁷Li + ¹¹B scattering. It was found that the ⁷Li + ¹¹B potential parameters fail to describe the ⁷Li + ¹⁰B scattering data. The biggest difference is observed between the depths of the imaginary potentials that describe these scatterings.     

Characteristics of elastic proton scattering from <Emphasis Type="Italic">A</Emphasis> = 9 Li,Be, and C isobars

Differential cross sections and analyzing powers (A _y ) for elastic proton scattering from ⁹Be at 220 MeV and 1.0 GeV and from ⁹Li and ⁹C at 60 and 700 MeV/nucleon are calculated in the context of the Glauber diffraction theory with the three-body wave functions for the ⁹Be, ⁹Li, and ⁹C nuclei described by the α + α + n, ⁷Li + n + n, and ⁷Be + p + p models. Comparison with the available experimental data is made, which allows some conclusions about the quality of the model wave functions.     

Comparison of 7Li , 7Be + 9Be elastic scattering in the coupled-reaction-channels approach

The data for the ⁷Li + ⁹Be and ⁷Be + ⁹Be elastic scattering at the energies E _lab(⁷Li) = 15.75 , 24, 30, 34, 63 and 130MeV and E _lab(⁷Be) = 17 , 19 and 21MeV were analyzed within the optical model and coupled-reaction-channels method. The elastic and inelastic scattering, reorientation of ⁷Li , ⁷Be and ⁹Be as well as most important transfer reactions were included in the coupled-channels scheme. The resulting ⁷Li and ⁷Be potentials are very similar and have the same energy dependence. The real potential for recently derived ⁸Be + ⁹Be scattering potentials is very similar to that for ⁷Li , ⁷Be but the imaginary part of the ⁸Be one has a much greater strength at longer range.     

Tensor interactions and polarization phenomena in heavy-ion scattering

Elastic and inelastic scattering of ⁷Li by ⁵⁸Ni at E_lab = 14.2 and 20.3 MeV is investigated theoretically, special emphasis being laid on polarization phenomena. A parameter-independent study shows second-rank tensor interactions to be the main origin of tensor analyzing powers for both elastic and inelastic scattering. Coupled-channel (CC) calculations using cluster-folding interactions which include the tensor terms are found to be successful in reproducing the data for cross sections and vector and tensor analyzing powers, when projectile excitation effects are sufficiently taken into account. Scattering of ⁶Li by ⁵⁸Ni at E_lab = 20.0 MeV is also investigated by the CC calculation, where successes similar to the ⁷Li case are obtained in understanding experimental data.     

A comparative analysis of the density distributions and the structure models of <Superscript>9</Superscript>Li

In the present study, we have analysed the elastic scattering cross-section data of ⁹Li + ¹²C system at E _lab = 540 MeV and ⁹Li + ²⁰⁸Pb system at E _c.m. = 28.3 MeV for some cluster models and various density distributions of the ⁹Li nucleus. First, we have obtained five different density distributions of the ⁹Li nucleus to generate real potentials with the help of double-folding model. For these densities, we have calculated the elastic scattering angular distributions. Secondly, using a simple approach, we have investigated some cluster models of the ⁹Li nucleus consisting of ⁶He + ³H and ⁸Li + n systems. We have presented the comparison of elastic scattering angular distributions for each system with each other as well as with the experimental data. Finally, we have given the cross-section values obtained from the theoretical calculations for all the systems studied in this paper.     

Channel coupling and exchange of an alpha-particle cluster in deuteron scattering on 6Li nuclei

Existing experimental data on elastic and inelastic deuteron scattering on ⁶Li nuclei in the energy range from 8 to 50 MeV were analyzed within the approach of coupled reaction channels. The coupling of elastic scattering and inelastic scattering accompanied by the transition to the 3⁺ state at E _x = 2.186 MeV and the mechanism involving the exchange of an alpha-particle cluster were taken into account in respective calculations. The phenomenological potentials obtained from the present analysis describe well experimental angular distributions at all energies and in full angular ranges. The depths of the real and imaginary parts of the potentials in question depend smoothly on energy at fixed values of the remaining parameters. The energy dependence of relevant volume integrals agrees well with similar data for the p + ⁶Li, ?? + ⁶Li, and ¹²C + ¹²C systems and with the predictions of a microscopic theory.     

Elastic and inelastic scattering of 6Li and 7Li by 54Fe at E = 36–50 MeV

Detailed angular distributions for the elastic and inelastic scattering of ⁷Li at E = 36, 42, and 48 MeV and of ⁶Li at E = 38, 44, and 50 MeV by ⁵⁴Fe have been measured. It is not possible to describe both sets of data with the same set of optical-model parameters. The ratio of $\text{U}\text{W}$ is 0.8 for ⁷Li and 1.4 for ⁶Li at the strong absorption radius, implying stronger absorption for ⁷Li than for ⁶Li. No energy dependence in the optical-model parameters was necessary for either ⁶Li or ⁷Li. The inelastic scattering from the ⁵⁴Fe 2⁺, 1.41 MeV state was well described by the DWBA and the extracted deformation length (βR = 0.62) was the same for both ⁶Li and ⁷Li scattering. It was not possible to describe the ⁷Li projectile excitation data with collective-model DWBA calculations showing that more detailed calculations for the projectile excitation are necessary.     

Scattering of radioactive nuclei 6He and 3H by protons: Effects of neutron skin and halo in 6He, 8He,and 11Li

In an experimental study of ⁶He+p and ³H+p collisions at ∼70 A MeV, the elastic scattering angular distributions were measured and the known excited state ⁶He_1.8¹ was observed. Comparative analysis of existing experimental data on proton elastic scattering by ⁴He, ⁶He, ⁶Li, ⁸He, ⁹Li, and ¹¹Li was performed. Effects of valence neutrons were investigated using the eikonal approach. A difference between ¹¹Li and ^6,8He was found.     

Elastic and inelastic proton scattering on 7Li nuclei within diffraction theory

On the basis of Glauber diffraction theory, the differential cross sections and analyzing powers are calculated for elastic and inelastic (to the $J^\pi = \frac{{1^ - }}{2}$ level at E ^* MeV) proton scattering on ⁷Li nuclei at E _p=0.2, 0.6, and 1.0 GeV. In this calculation, the ⁷Li wave function is taken in the αt model. The sensitivity of our results to variations in the parameters of the elementary pN and pα amplitudes is investigated. Effects induced by multiple scattering on the target-nucleus clusters are shown to play a significant role. Theoretical results are found to comply well with experimental data available only at E _p=0.2 GeV.     

Polarized deformed spin−32 projectile scattering and complex folded potentials

A formalism is presented where polarization observables of all ranks for deformed spin ?$\text{case3}\text{2}$ projectiles are calculated in a parameter-free fashion. Complex optical potentials for the available ⁷$\text{Li}$ + ⁵⁸Ni elastic scattering data at E_lab = 20.3 MeV are obtained from single folding calculations, taking the ⁷Li ground state to be an α + t cluster in relative p-state. The expansion of the hamiltonian in spin-space generates tensor terms of ranks 2 (T_R) and 3 (T₃) apart from the usual central and spin-orbit terms. The T_R potential fits the second-rank tensor analysing powers quite well without being able to resolve discrete ambiguities of input optical parameters. The T₃ term generates a J · L contribution, making the spin-orbit interaction three-component. The ⁷Li vector analysing power so obtained is negative, but the magnitude is not fully reproduced. Modification of parameters to account for absorption modes not included in the superposition model indicates the need for properly handling dynamical polarization effects due in particular to the low-lying first excited state of ⁷Li.     

Double folding model analysis of 7Li scattering

Elastic scattering angular distributions have been measured for the scattering of ⁷Li by ⁴⁴Ca, ⁵⁶Fe and ^{58, 60}Ni at $\text{E(}{}^7\text{Li}\text{) = 34}\text{MeV}$. These data are well described by the optical model using volume Woods-Saxon potentials. These and previously measured ⁷Li scattering data also have been analyzed with a double-folding real potential which employs the nucleon-nucleon potential of Bertsch et al. The overall best fit to the experimental data down to σ/σ_R ~ 10^?3 is obtained when the DF potential is multiplied by approximately 0.6. However, the best fit for the peripheral data alone (σ/σ_R ～ 10^?1 is obtained without any renonnalization.     

Study of the 8Be first T = 2 state with 4He + α and 7Li + p initiated excitation functions

In a high resolution study of the ⁴He + α initiated excitation functions in the region of the ⁸Be first T = 2 state, weak resonance excursions have been observed in some reaction channels yielding the total width Γ = 14.7 ± 4.0 keV. No resonance excursion has been observed in the ⁴He + α elastic scattering yielding the branching ratio Γ_α/Γ ≦ 0.003 for the decay of the ⁸Be first T = 2 state into two α-particles. For the decay to the low-lying states of ⁶Li and ⁷Li lower limits of the branching ratio are given. The reinvestigation of the ⁷Li+p initiated excitation functions revealed no resonance anomaly in the region of the ⁸Be first T = 2 state. The upper limit Γ_p/Γ ≦ 0.023 has been derived for the proton decay to the ⁷Li_g.s.. The results are compared with previous measurements and with shell-model calculations.     

Search for solar axions emitted in an <Emphasis Type="Italic">M</Emphasis>1 transition in <Superscript>7</Superscript>Li* nuclei

The resonance absorption of solar axions by ⁷Li nuclei, which is accompanied by the excitation of the first nuclear level of lithium a + ⁷Li → ⁷Li* → ⁷Li + γ, is sought. To this end, the energy spectrum has been measured by an HPGe detector that is surrounded by a LiOH layer. A new upper limit m_a ≤ 16 keV (at 90% C.L.) has been determined for the mass of the hadron axion.     

Scattering and transfer reactions for 6, 7Li + 90, 91Zr

Elastic scattering data have been measured for the ⁷Li + ⁹⁰Zr, ⁶Li + ⁹⁰Zr, and ⁶Li + ⁹¹Zr systems at E(Li) = 34 MeV. Inelastic scattering data for the ⁷Li + ⁹⁰Zr and ⁶Li + ⁹⁰Zr systems were also measured for the 2⁺(2.18 MeV) and 3^?(2.75 MeV) states in ⁹⁰Zr and the $\text{1}\text{2}{}^{\mathrm{?}}\text{(0.48}\text{MeV}\text{)}$ state in ⁷Li. Optical model analyses of the elastic scattering data and DWBA analyses for the states in ⁹⁰Zr were performed. The deduced deformation lengths for the 2⁺ state agreed with those extracted in other studies but the deformation length for the 3^? state was smaller. The ⁹⁰Zr(⁷Li, ⁶Li)⁹¹Zr angular distributions were measured for the 1.21 and 2.03 MeV states and the 2.19 MeV doublet in ⁹¹Zr. Also, ⁹⁰Zr(⁷Li, ⁶He)⁹¹Nb angular distributions were measured for the ground states, 0.10, 3.41 and 4.82 MeV states in ⁹¹Nb. The transitions well matched in angular momentum were described by finite-range DWBA calculations, while other transitions displayed the same phase problems seen with heavier ions. The extracted spectroscopic information was consistent with the results of other reaction studies. At the present energy, it was not possible to determine whether the l = 1 phase problem that occurs for heavy-ion single-nucleon transfer reactions on 2s-1d shell nuclei occurs in ⁹¹Zr also.     

Sub- and above-barrier fusion of loosely bound 6Li with 28Si

Fusion excitation functions are measured for the system ⁶Li + ²⁸Si using the characteristic $ \gamma$ -ray method, encompassing both the sub-barrier and above-barrier regions, viz, E _lab = 7-24 MeV. Two separate experiments were performed, one for the above-barrier region ( E _lab = 11-24 MeV) and another for the below-barrier region ( E _lab = 7-10 MeV). The results were compared with our previously measured fusion cross-section for the ⁷Li + ²⁸Si system. We observed the enhancement of the fusion cross-section at sub-barrier regions for both ⁶Li and ⁷Li , but the yield was substantially larger for ⁶Li . However, for well-above-barrier regions, a similar type of suppression was identified for both the systems.     

Dynamic deformation of light nuclei in excited states

An important property—the dynamic deformation of B* light aligned nuclei—is investigated for the nuclear reactions A(x, y)B* → γ + B ₀ by measuring the y-γ correlations. Dynamic deformation is determined from the orientation tensors of multipolar moments. Normalization constants of the contributions from even-rank orientation tensors are determined from the condition of coincidence between dynamic and static deformations of the B* nucleus for θ _y = 0°. Experimental dynamic deformations of ¹²C(2⁺) nuclei caused by the inelastic scattering of α particles and deuterons are determined, along with the ¹⁰Be(2⁺) nuclei formed in reaction ⁹Be(d, p)¹⁰Be(2⁺). It is shown that the dynamic deformation of the aligned nuclei depends on how they are formed and their structure, and evolves substantially when the angle θ _y is varied.