The excitation functions of complete and incomplete fusion reactions of 6Li with Pt nuclei

Experimental results from measuring the energy dependences of cross sections of fusion and transfer reactions for ⁶Li beams and Pt targets are presented. The experiments were performed using the MSP-144 magnetic analyzer; stacks of platinum foils were installed at the focal plane of this analyzer. In the energy range 22.5–42.5 MeV, the energy resolution of the beam hitting the target stack was not worse than 0.25 MeV and that of the transmitted beam was not worse than 0.40 MeV. The yields of products of neutron and deuteron transfer reaction on target nuclei were measured using the γ activity induced in the platinum targets. Thus, excitation functions for transfer reactions were obtained in a wide energy range, including near the Coulomb barrier. It was shown that the basic reaction channel is the deuteron capture from ⁶Li. In this case, the maximum of the excitation function for ⁶Li breakup and subsequent deuteron capture lies near the Coulomb barrier of the reaction.     

Electric and magnetic response to the continuum for A = 7 isobars in a dicluster model

The mirror isobars ⁷Li and ⁷Be are investigated in a dicluster model. The magnetic dipole moments and the magnetic dipole response to the continuum are calculated in this framework. The magnetic contribution is found to be small with respect to electric dipole and quadrupole excitations even at astrophysical energies, at a variance with the case of the deuteron. Energy-weighted molecular sum rules are evaluated and a formula for the molecular magnetic dipole sum rule is found which matches the numerical calculations. Cross-sections for photo-dissociation and radiative capture as well as the S -factor for reactions of astrophysical significance are calculated with good agreement with known experimental data.     

Deuteron stripping to the single particle states of 17O

Angular distributions for deuteron-¹⁶O elastic scattering and the ¹⁶O(d, p)¹⁷O reaction leading to levels with E_x = 0.0, 0.87, and 5.08 MeV have been measured at energies of 25.4, 36.0 and 63.2 MeV. The elastic deuteron data have been fit with a standard spin one optical model potential to obtain parameters for use in a DWBA analysis of the (d, p) data. The potential found in the search is shown to be consistent with other data taken in the range from 25 to 82 MeV. In addition to this deuteron optical potential, an adiabatic deuteron potential, which includes the effects of deuteron breakup, was used in the DWBA analysis. The neutron form factor was selected independent of the width of any state. The mean square radius, a single particle property, is used to find the well parameters and it determines the width of the single particle state. The spectroscopic factors obtained for the ground and first excited states are between 0.8 and 1.0 and are consistent with a large single particle parentage for these states and lower energy data. The width extracted from the DWBA analysis of the 5.08 MeV unbound state was 20% less than that obtained from elastic neutron scattering to the same state, possibly pointing up some difficulties with DWBA procedures commonly used. The adiabatic deuteron potential yields spectroscopic factors that are energy independent to 20% and gives satisfactory calculated angular distribution shapes for angles less than 40°. The conventional deuteron potential gives less satisfactory calculated shapes with the consequent introduction of some ambiguity in the derived spectroscopic factors.     

ON THE CONTRACTION AND DEFORMATION OF DEUTERON CLUSTER IN 6Li

The ground state of ⁶Li is investigated by means of the projected variational method for double well-cluster shell model. The results of the variational calculation show that the root-mean-square radius of d-cluster in the ground state of ⁶Li is smaller than that of free deuteron and as the mean distance between the α-cluster and the d-cluster decreases there are two effects on the d-cluster, namely contraction effect in which the d-cluster contracts first and then makes a bit extension and deformation effect in which the d-cluster makes oblation first and then streteches.It is also demonstrated by the calculation that the repulsive component of the odd sytate of N-N force and the pauli exchange of the nucleons between the clusters play an important role not only on the cluster structure in the ground state of ⁶Li but also on the contraction and the deformation of d-cluster in ⁶Li.     

The deuteron and its magnetic moment the effects of non-local nuclear forces and of unitary transformations

The deuteron theory is renewed and completed for non-local Hamiltonians. A method to calculate deuteron wave functions is given. The formula for the current density and the magnetic dipole moment of a non-local potential is derived, and applied to the GCT, GT, and HJ-potential. The effects of a unitary transformation on the deuteron data — electric quadrupole moment, magnetic dipole moment, and radius — are shown. For the numerical calculations the Ristig-Kistler transformation and the HJ-potential were used. It is shown that an overall fit cannot be reached.     

Deuteron exchange mechanism for the6Li(n, α) reaction at low energies

It is proposed that the major part of the low energy (l/v)⁶Li(n, α)³H cross section may be explained as being due to a direct deuteron exchange mechanism. This proposal is in agreement with recent experimental data on the spin-dependent⁶Li(n, α) cross section; it may be used to extract information on the⁶Li-αd vertex constant. The importance of the assumption of ad-exchange process for the⁶Li(n, α) angular distribution is discussed in the framework ofS-matrix theory.     

Charge form factor and cluster structure of the 6Li nucleus

The charge form factor of the 6Li nucleus is considered on the basis of its cluster structure. The charge density of ⁶Li is presented as a superposition of two terms. One of them is a folded density and the second one is a sum of the ⁴He and deuteron densities. Using the available experimental data for ⁴He and deuteron charge form factors, a satisfactory agreement of the calculations within the suggested scheme is obtained with the experimental data for the charge form factor of ⁶Li, including those in the region of large transferred momenta.      

The deuteron wave function at short range and the triton

It is shown that if one assumes something between zero and the prediction of the scaling model with dipole fit for the neutron electric form factor, then a variety of short-range behaviour for the deuteron wave function is consistent with existing experimental data on the deuteron electric form factor. This still relatively wide latitude for the inner deuteron wave function, consistent with existing experimental electromagnetic data, gives rise to an off-shell variation of approximately 1.2 MeV in the triton binding energy with a fixed ¹S₀ interaction and a P_D varying from 4.5 to 6.5 %. Interactions with greater densities of matter at short range bind the triton more strongly and closer to the experimental value. An off-shell variation of 0.7 MeV is obtained with a fixed p_d and singlet interaction. However, a single measurement of the deuteron tensor polarization at about q² = 20 fm^?2 would severely restrict this variation.     

Quasi-elastic electron scattering (e,e′p) and (e,e′d) from 6Li in a coincidence experiment

Coincidence cross sections for the reactions ⁶Li(e, e′p) and ⁶Li(e, e′d) have been measured in the region of quasi-elastic scattering. Using incident electrons of 2.5 and 2.7 GeV, the four-momentum transfers to the proton were 6.6 fm^?2, 10.0 fm^?2 and 11.6 fm^?2. The proton coincidence data agree with shell-model distributions assuming a Woods-Saxon potential and including short-range nucleon-nucleon correlations. The best fit to the deuteron coincidence data is obtained with a cluster wave function for the p-nucleons and a harmonic oscillator wave function for the s-nucleons taking into account the deuteron yield from the s-shell. The ratio of the deuteron cross section from ⁶Li divided by the elastic e-d scattering cross section depends only slightly on the four-momentum transfer and has a value of ≈ 2.     

Photodisintegration of Light Nuclei

The first microscopic calculation of inelastic reactions on nuclei with mass number A = 6 is presented. In particular, we consider the total photoabsorption cross section of ⁶He and ⁶Li. It is shown that the halo nucleus ⁶He exhibits two types of dipole resonances, the normal giant dipole resonance and a low-energy soft dipole resonance associated with the excitation of the outer neutrons. Comparing our results with available experimental data we note the role of P-wave interaction. Calculations are performed using the Lorentz integral transform (LIT) method and the effective interaction in the hyperspherical harmonics formalism (EIHH).     

Spin-dipole excitations of6Li in charged pion photoproduction

In the framework of bound shell model we have calculated the photoproduction of charged pions on⁶Li when spin-isospin dipole resonance is excited. It is shown that the transition strength concentrates in several energy regions. Such a gross-structure of the excitation spectrum is governed by the configurational splitting of the resonance. The excitation spectrum in⁶Li(γ, τ)-reaction is compared with the⁶Li(τ, γ), (e, e′) and (n, p)-reaction spectra where spin-isospin transitions are dominating too.     

Nature of halo in light nuclei

A feature peculiar to light neutron-rich nuclei is that their lowest decay thresholds are only slightly above their ground states. Among them, ⁶He and ¹¹Li are two most striking examples. The energy needed to break ⁶He (¹¹Li) into an alpha particle (⁹Li) and two neutrons is about 1 MeV (300 keV). So small a value prompts one to construct their theory by analogy with the zero-range-nuclear-force approximation previously applied to the deuteron. A more detailed analysis shows, however, that the simple version of this approximation applied to systems that decay through a three-particle channel does not take into account some important features of these systems and requires significant improvements. First, with increasing distance between three particles, the potential energy decreases, in contrast to what is observed for binary systems, in inverse proportion to the hyperradius cubed. Second, the Pauli exclusion principle adds complexity even in the asymptotic domain, and we meet its demands in constructing the ⁶He and ¹¹Li wave functions in the continuum. An approach is proposed to analyze weakly bound three-cluster systems that takes into account the aforementioned features and which describes correctly the experimentally observed structure of bound and unbound states above the threshold for three-particle decay.     

Folding model analysis of pion elastic and inelastic scattering from 6Li and 12C

π ^±-Nucleus scattering cross sections are calculated applying the Watanabe superposition model with a phenomenological Woods-Saxon potential. The phenomenological potential parameters are searched for π ^± scattering from ⁶Li and ¹²C to reproduce not only differential elastic cross sections but also inelastic and total and reaction cross sections at pion kinetic energies from 50 to 672 MeV. The optical potentials of ⁶Li and ¹²C are calculated in terms of the alpha particle and deuteron optical potentials. Inelastic scattering has been analyzed using the distorted waves from elastic-scattering data. The values of deformation lengths thus obtained compare very well with the ones reported earlier.     

A search for the effects of nuclear matter in backward pion-deuteron quasielastic scattering by 6Li

Results of a kinematically complete experiment on backward π^? d quasielastic scattering by ⁶Li are presented. The experiment was carried out at the ITEP 3-m magnetic spectrometer with pion beams of momenta 0.72, 0.88, and 1.28 GeV/c. The Fermi-motion parameters of a quasideuteron cluster and the effective number of quasideuterons in ⁶Li are determined for the ⁶Li(π^?, π^? d)⁴He reaction. These values agree well with the proton-and electron-beam measurements. The possibility of observation of the effects of deuteron wave-function modification in nuclear matter is discussed for this reaction.     

Soft dipole mode in the 11Li nucleus within the asymptotic-potential approximation

A soft dipole mode in the ¹¹Li nucleus treated within the microscopic three-cluster model is studied in the asymptotic-potential approximation. The model faithfully reproduces the energy and the root-means-quare radius of the ground state and the behavior of the effective photodisintegration cross section at low energies above the threshold for ¹¹Li breakup, suggesting the existence of two resonance states in this region.     

Effect of the deuteron anisotropy: Longitudinal and transverse components of the electric dipole polarizability

The anisotropy effect of the electric polarization (stretching) of the deuteron in the Coulomb field, caused by the tensor character of the nuclear force, is investigated. The values of the longitudinal (with the major axis, or the spin of the deuteron, directed along the electric field), and transverse components of the deuteron electric dipole polarizability that correspond to the low-energy n-p data, are predicted to be α₆ = 0.669 fm³ and α_⊥ = 0.555 fm³ (the potential YYm). The values of the major and minor semi-axes of the deuteron are calculated.     

The 6Li(e,e′α) and 6Li(e,e′d) reactions at 520 MeV

The reactions ⁶Li(e,e′α) and ⁶Li(e,e′d) have been studied at T₀ ≈ 520 MeV and q ≈ 1.4 fm^?1, by coincidence measurements. The angular dependence of the cross sections is interpreted in the plane wave impulse approximation to obtain the momentum distribution of α-particle and deuteron clusters in ⁶Li. The amount of clustering of ⁶Li is also discussed.     

Deuteron scattering on <Superscript>6</Superscript>Li at an energy of 25 MeV

At an energy of 25 MeV and in the angular range 7°−175° in the laboratory frame, angular distributions were measured for elastic deuteron scattering on ⁶Li nuclei and for the respective inelastic-scattering processes accompanied by the transitions to the ground state (1+) of the ⁶Li nucleus and to its excited state at E _x = 2.186 MeV (J ^π = 3⁺). The resulting data were analyzed on the basis of the optical model of the nucleus and the coupled-reaction-channel method with allowance for the mechanism of alpha-particle-cluster exchange. It is shown that only upon including, in the analysis, channel coupling and the exchange mechanism can the experimental cross sections for elastic and inelastic scattering be reproduced over the entire range of angles.     

Further study and analysis of the <Superscript>7</Superscript>Li on <Superscript>56</Superscript>Fe reaction at 50 MeV incident energy

We present deuteron and triton spectra measured at 12 laboratory angles from the reaction of 50 MeV ⁷Li on ⁵⁶Fe together with evaporative components as modeled by CASCADE and fitted to the backward angle data. The deuteron and triton “break-up” spectra obtained by subtracting the evaporative components from the measured spectra are also presented. The break-up of the ⁷Li projectile near the surface occurs with high probability and the major fraction of the break-up cross-section is taken by (⁷Li,α) transfer process. A crude estimate of the fraction of the total cross-section is found to be of the same order of magnitude as the overall spectroscopic factor determined by the diffraction model. The value of the estimated fraction of total cross section at 50 MeV incident energy is compared to that at 68 MeV incident energy for the same reaction. However, these values of estimated fraction of total cross section are found very much consistent with the measured yields at both incident energies. The importance of the level density parameter in locating the maximum of excitation energy is indicated in the diffraction model.