The influence of the spectroscopic deformation of Li-isotopes on their interaction with51V

The energy dependence of the total reaction cross sectionσ ^r and its tensor analyzing powerT ₂₀ ^r was measured for the⁷Li?⁵¹V interaction in the energy rangeE _Li=10–20 MeV using two different experimental methods. Reaction residues were observed directly by their characteristicγ-emission, and the elastic scattering of⁷Li from⁵¹V was investigated. Additionally, the elastic scattering of⁶Li from⁵¹V was measured at 9.8, 12 and 14 MeV. The tensor analyzing power data can be interpreted as being caused by the spectroscopic mass deformation of the Li-ions. The energy dependence of σr andT ₂₀ ^r above the Coulomb barrier can be described in terms of the classical sharp-cutoff model.     

On the nuclear interaction potential in the reactions with heavy ions

The interaction potential of heavy ions⁴He,⁶Li,¹²C and¹⁶O is constructed in the folding model. The density distribution of nuclear matter for these nuclei is calculated in the framework of the hyperspherical function method. For the calculation of the folding potentials we have employed the Skyrme nucleon-nucleon forces. The influence of several effects on the results of calculations is studied: the role of the three-body forces of the nucleon-nucleon interaction, dependence of the folding potential on the mass numbers of the colliding nuclei and the possibility of observing the monopole resonance in the ion inelastic scattering. Using our folding potential as a real part of the optical potential we have calculated the differential cross section of elastic scattering of⁶Li from¹²C at laboratory energy of lithium ionsT _L =90.0 MeV. Reasonable agreement with experiment is obtained.     

On the tensor term in the deuteron optical potential nearE d =20 MeV

The elastic scattering of vector and tensor polarized deuterons near 20 MeV has been analyzed in terms of the phenomenological optical potential including a complex tensor term ofT _R -type. In comparison with folding potentials we find a strong reduction of the real part of theT _R -potential with increasing mass number, the contribution of coupling to vibrational excitations is discussed.     

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.     

Puzzle of the <Superscript>6</Superscript>Li quadrupole moment: Steps toward solving it

The problem of the origin of the quadrupole deformation in the ⁶Li ground state is investigated with allowance for the three-deuteron component of the ⁶Li wave function. Two long-standing puzzles related to the tensor interaction in the ⁶Li nucleus are known: that of an anomalous smallness of the ⁶Li quadrupole moment (being negative, it is smaller in magnitude than the ⁷Li quadrupole moment by a factor of 5) and that of an anomalous behavior of the tensor analyzing power T_2q in the scattering of polarized ⁶Li nuclei on various targets. It is shown that a large (in magnitude) negative exchange contribution to the ⁶Li quadrupole moment from the three-deuteron configuration cancels almost completely the “direct” positive contribution due to the αd folding potential. As a result, the total quadrupole moment proves to be close to zero and highly sensitive to fine details of the tensor nucleon-nucleon interaction in the ⁴He nucleus and of its wave function.     

Elastic scattering of 56 MeV polarized deuterons on 4He

The differential cross section and the vector and tensor analyzing powers A_y, A_xx, A_yy and A_xz were measured for the d-⁴He elastic scattering at 56 MeV. The measurement of A_xz was performed using a deuteron beam polarized in the horizontal plane. An optical-model analysis of the experimental data was carried out. The magnitude of the tensor analyzing powers could not be reproduced without the tensor potential. By including the T_R type tensor potential, the optical-model calculations give a reasonable reproduction of the experimental data at θ_c.m. < 120°. The obtained T_R tensor potential was much stronger than that predicted by the folding model. The strength of the real T_R potential was roughly in accordance with that obtained from the optical-model analysis of d-⁴He elastic scattering at 20.2 MeV.     

Precision measurement of the muonic 5-4 transitions in Pb and 4-3 transitions in ba as a test for the validity of QED

The real parts of the optical model potentials for 104 MeV alpha-particle and 156 MeV⁶Li ion scattering from^{40, 48}Ca are calculated in terms of folding model approaches. The validity of different procedures is tested by comparing the differential cross section predictions with experimental data measured with high angular accuracy. It is found that a refined folding potential accounting for density dependence of an effective nucleon-nucleon interaction is appropriate for alpha particle scattering without any parameter adjustment. However, for⁶Li ion scattering renormalization of the depth of the real potential is necessary.     

Thed(7Li,p)8Li cross section nearE cm=0.61 MeV

The absolute cross sectionσ of thed(⁷Li,p)⁸Li reaction near theE _cm=0.61 MeV resonance has been measured using a⁷Li ion beam and a windowless gas target system filled with D₂ gas. The proton yield of the reaction and theβ-delayedα-activity of the residual nuclides⁸Li were observed both concurrently with the elastic scattering yield, relatingσ to the Rutherford scattering cross sectionσ _R. The resulting values,σ (fromp)=143.6±8.9 mb andσ (from⁸Li)=151±20 mb, lead to a weighted mean value ofσ=153±6 mb (x ²=2.26) including all available values andσ=146±5 mb (x ²=0.05) removing some values from the data set. The consequences for the expected flux of high-energy solar neutrinos are discussed.     

The interaction of aligned 7Li with 58Ni

Elastic and inelastic scattering of aligned ⁷Li on ⁵⁸Ni was studied experimentally for several energies between 14 and 22 MeV. Complete sets of second-rank tensor analyzing powers were measured for two energies, 14.2 and 22.0 MeV. The shape-effect model has been used for a qualitative interpretation of the data. The success of this model indicates the spectroscopic deformation of ⁷Li to be the main source of the observed second-rank tensor analyzing powers. The result enters the formulation of the diffraction as well as the optical model both of which are used to improve the analysis of the data. Besides the parameters which determine the central interaction the spectroscopic deformation was the only adjustable parameter. The deformation was found to be negative, in agreement with the oblate shape of ⁷Li. However the extracted value of the deformation varies within a factor of two when comparing different experiments and/or analyses with different models. The second-rank tensor analyzing powers for projectile excitation are roughly explained by the assumption that the angular momentum transfer is perpendicular to the momentum transfer.     

Fusion of aligned deformed heavy ions calculated in the surface friction model

The surface friction model for heavy ion induced fusion is extended to cover collisions of aligned deformed nuclei taking into account dynamic quadrupole and octupole vibrations and rotations of the reaction partners. Calculated fusion cross sections for unpolarized beam and the tensor analyzing powerT ₂₀ for fusion of²³Na +²³Na are compared with data. The analyzing power is found to be sensitive to variations of the tangential friction strength.     

Analysis of proton transfer in polarized 7Li scattering by 208Pb at 33 MeV

Angular distributions of the differential cross section and the second-rank tensor analysing power T₂₀ have been measured for the one-proton transfer reaction induced by polarized ⁷Li on ²⁰⁸Pb at 33 MeV leading to several states in ²⁰⁹Bi. The experimental data were analysed simultaneously with data for elastic and inelastic scattering of ⁷Li by means of CCBA and CRC calculations. The spectroscopic factors for ²⁰⁹Bi states are obtained.     

Tensor interaction in heavy-ion scattering: (I). The turning-point model

The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power $\text{T}{}_{\mathrm{2q}}$ have certain relations with each other for each type of tensor interaction (T_R, T_P and T_L types). The predicted relations between the $\text{T}{}_{\mathrm{2q}}$ are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for ⁷Li and ²³Na elastic scattering from ⁵⁸Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a T_P? or T_L-type tensor interaction in polarized heavy-ion scattering. The presence of a T_P-type tensor interaction is suggested by measured $\text{T}{}_{20}\text{/}\text{T}{}_{22}$ ratios for ⁷Li+⁵⁸Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail.     

Seniority-three yrast states in theN=82 nucleus147Tb

Firm spin-parity assignments for the high-spin states up to 3.5 MeV in the one-proton nucleus¹⁴⁷Tb were obtained from¹⁴⁴Sm(⁶Li, 3n) in-beamγ-ray and conversion electron measurements. The energies of these two-particle one-hole excitations were calculated from the shell model with empirical nucleon-nucleon interaction energies. The calculated energy splittings agree well with experiment, whereas the theoretical excitation energies disagree by ?1 MeV if recently measured ground state masses are used.     

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.     

Energy dependence of tensor analyzing powers in deuteron elastic scattering from 208Pb

Differential cross section and all four analyzing powers iT₁₁, T₂₀, T₃₁ and T₂₂ have been measured for deuteron elastic scattering from ²⁰⁸Pb at incident energies from 10 to 23 MeV. The energy dependence of the tensor analyzing powers was investigated. A considerable deviation of the data from optical-model calculations including a T_r-type tensor potential is found near the Coulomb barrier.     

Energy dependence of nucleon-deuteron elastic scattering observables and its bearing on the3 P J nucleon-nucleon interactions

The energy dependence of neutron-deuteron elastic scattering observables has been calculated from 5 to 45 MeV via rigorous three-nucleon calculations using the Bonn B nucleon-nucleon interaction. The goal of these calculations was to identify energy and angular regions that may be investigated experimentally to study the question of charge-symmetry breaking in the³ P _J nucleon-nucleon forces and/or Coulomb interactions. It was found that the measurement of the neutron-deuteron elastic analyzing power at 16 and 22.7 MeV and its comparison to proton-deuteron data obtained at the same incident energy is the most promising case for studying the issue of charge-symmetry breaking in the³ P _J nucleon-nucleon forces and/or Coulomb interactions.     

Scattering of polarized 7Li by 120Sn and projectile-target spin-dependent interactions

Scattering of ⁷Li by ¹²⁰Sn targets at E_lab = 44 MeV is investigated in the coupled-channel frame by taking account of the projectile virtual excitations to the lowest three excited states. Calculations are performed by the cluster-folding (CF) interactions and the double-folding (DF) one. Both interactions reproduce very well the experimental data on the cross section, the vector analyzing power, the second-rank tensor ones and the third-rank tensor one in elastic and projectile inelastic scattering, although some differences are found between the CF results and the DF ones. In the calculation, the virtual excitations of the projectile are important for most of the analyzing powers and the spin-orbit interaction is indispensable for the vector analyzing power. These features are in contrast to those in ⁷Li-⁵⁸Ni scattering at 20 MeV and are interpreted as over-Coulomb-barrier effects. The scattering amplitudes and the analyzing powers are investigated by the invariant amplitude method, which provides a key connecting the spin-dependent interactions to the analyzing powers. The method proposes an important relationship between the tensor analyzing powers, which is useful in analyses of both theoretical and experimental results. Finally, it is found that in the elastic scattering the second-rank tensor analyzing powers are proportional to the strength of the second-rank tensor interaction and the vector and third-rank tensor analyzing powers to the square or cube of the strength of this interaction, while in the inelastic scattering the cross section is proportional to the square of the strength of the tensor interaction, other quantities being weakly dependent on the strength.     

Approximation of the microscopic effective pairing interaction by the off-shell T matrix for free nucleon-nucleon scattering

The effective pairing interaction in the ¹ S ₀ channel as calculated microscopically within the Brueckner method for a planar slab of nuclear matter by using the separable version of the Paris nucleon-nucleon potential is investigated. The effective interaction is determined for the model space including all negative-energy single-particle states. An analysis is performed for two values of the chemical potential, μ=?8 and ?4 MeV. It is shown that, to a high precision, the effective interaction can be approximated by the off-shell T matrix for free nucleon-nucleon interaction, the T matrix in question being taken at a negative value of the total energy of two nucleons E=2μ.