Elastic scattering of 33 MeV tritons and isospin dependence of mass-3 optical potential

Differential cross section data are presented for the elastic scattering of 33 MeV tritons from a range of nuclei from ¹²C to ²³²Th. These data have been analysed using a phenomenological optical model. Parameters are presented for three families of the real potential. A comparison of the triton optical model potential with those from a re-analysis of ³He scattering from fp shell nuclei has allowed the isospin dependence of the optical model potential for mass-3 projectiles to be obtained in this mass region.     

Optical-model analysis of the elastic scattering of 100 MeV protons from Mg and Si

Elastic scattering differential cross sections for the interaction of 100 MeV protons with ²⁴Mg and ²⁸Si have been measured using a high-resolution Ge(Li) spectrometer to resolve the inelastic scattering contribution to the elastic peak. The results have been analysed using the conventional optical model, and the experimental differential cross sections and total reaction cross section are excellently reproduced. The results agree with previous analyses of the elastic scattering of 100 MeV protons on 1p shell nuclei in that no set of geometric parameters can provide a quantitative fit to both nuclei. It is observed, however, that the fluctuations of the optical-model parameters for optimum fits are decreased over the fluctuations observed for the 1p shell nuclei. The present results combined with previous optical-model analyses on ²⁴Mg and ²⁸Si at 50 MeV and 40 MeV respectively, are found to be consistent with an energy dependence of dV/dE ≈ −0.3 for the depth of the real central potential in agreement with other, more extensive, investigations of the energy dependence for protons elastically scattered from ¹⁶O and ⁴⁰Ca.     

3He-scattering from the stable even Sm-isotopes atE τ=40.9 MeV

Differential cross sections of the scattering of³He-particles were measured from^{144, 148, 150, 152, 154}Sm nuclei atE _τ=40.9 MeV. The elastic scattering data were analysed with the simple optical model. The ambiguities of the real central potential and some trends depending on the target mass in the optical potential parameters are discussed.     

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.     

Neutron-induced charged-particle reactions in 6Li and 9Be

Angular distributions of tritons from the ⁶Li(n, t)⁴He reaction were measured at E_n = 7.25, 6.77, 6.57, 5.24 and 4.71 MeV. Angular distributions of douterons from respectively, the ⁶Li(n, d)⁵He two-body breakup reaction were measured at E_n = 6.77 and 6.57 MeV, and of protons from the ⁶Li(n, p)⁶He reaction at E_n = 6.77, 5.24 and 4.71 MeV. All these reactions in ⁶Li were analyzed as direct interaction in the formalism of the distorted wave Born approximation. The optical model for the nuclear interaction was found to apply reasonably well to nuclei as light as ⁴He, ⁵He, ⁶He and ⁶Li. In addition, ⁶Li as an alpha-deuteron cluster gives the best bound-state wave function to describe the experimental angular distribution of tritons. The excitation functions at forward angles of the ⁶Li(n, t)⁴He, ⁶Li(n, d)⁵He and ⁶Li(n, p)⁶He reactions were measured for incident neutron energies between 4.4 and 7.3 MeV. It is found that the ⁶Li(n, d)⁵He two-body breakup reaction has a threshold at about E_n = 5.3 MeV. Angular distributions at E_n = 18.3 MeV for tritons and protons from the ⁹Be(n, t)⁷Li and ⁹Be(n, p)⁹Li, respectively, were also measured.     

Effective nucleon-nucleon forces and interaction of light exotic nuclei with stable nuclei at low energies

The effect of the density dependence of effective nucleon-nucleon forces on the folded potential of the interactions of the light exotic nuclei ⁶He, ¹¹Li, ¹¹Be, and ⁸B with the stable nucleus ¹²C is studied, and the corresponding experimental data on the total reaction cross sections and on elastic scattering are analyzed. A semimicroscopic double-folding model featuring various density-dependent forces based on the M3Y interaction is used together with the nucleon densities as calculated within the density-functional method by using a unified set of parameters for all the above nuclei. It is shown that the angular distributions recently measured for elastic ⁶He scattering on ¹²C at an energy of 41.6 MeV per projectile nucleon and for elastic ¹¹Be scattering on ¹²C at an energy of 49.3 MeV per projectile nucleon can be described satisfactorily if the real part of the optical folded potential is supplemented with a surface term mimicking the contribution of the dynamical polarization potential.     

Experimental investigation of highly excited states of the 5,6He and 5,6Li nuclei in the (6Li, 7Be) and (6Li, 7Li) one-nucleon pickup reactions

The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions on ⁶Li and ⁷Li nuclei were investigated in the angular interval 0°–20° in the laboratory system at a ⁶Li energy of 93 MeV. In addition to low-lying states of the ^5,6He and ^5,6Li nuclei, broad structures were observed near the t(³He)+d and t(³He)+t thresholds at the excitation energies of 16.75 (3/2⁺) and ～20 MeV (for ⁵He), 16.66 (3/2⁺) and ～20 MeV (⁵Li), 14.0 and 25 MeV (⁶He), and ～20 MeV (⁶Li). The angular distributions measured in the ⁷Li(⁶Li, ⁷Be)⁶He reaction for transitions to the ground state (0⁺) and excited states at E _x=1.8 MeV (2⁺) and 14.0 MeV of the ⁶He nucleus were analyzed by the finite-range distorted-wave method assuming the 1p-and 1s-proton pickup mechanism. The (⁶Li, ⁷Be) and (⁶Li, ⁷Li) reactions were shown to proceed predominantly through the one-step pickup mechanism, and the broad structures observed at high excitation energies are considered as quasimolecular states of the t(³He)+d and t(³He)+t types.     

Momentum distributions of <Superscript>4</Superscript>He nuclei from the <Superscript>6</Superscript>He and <Superscript>6</Superscript>Li breakup

Experimental data on the momentum distributions of ⁴He nuclei originating from ⁶He and ⁶Li breakup on various targets are presented over a wide beam energy range. The experiment with ⁶He was performed at the DRIBs accelerator complex for radioactive beams at the Joint Institute for Nuclear Research (JINR, Dubna). The intensity of the ⁶He beam used was 5 × 10⁶ particles per second and its energy was 10 MeV per nucleon. The momentum distributions of breakup products were measured by means of the MSP-144 magnetic spectrometer. The distribution width was shown to be virtually independent of the target mass. A small value of this width, σ ～ 28 MeV/c, confirms the presence of a halo in ⁶He. The measurements performed with ⁶Li beams of energy 18 and 46 MeV per nucleon at the U-400M accelerator yielded a width value of σ ～ 50 MeV/c for the momentum distributions of ⁴He nuclei, which is intermediate between that for ⁶He and those for stable nuclei. A compilation of the widths of the momentum distributions of fragments originating from the breakup of various nuclei is presented versus the binding energy of one or two neutrons in these nuclei, the target mass and the projectile energy.     

Four-nucleon pickup reaction on 12 ⩽ A ⩽ 94 nuclei

The differential cross sections for the (d, ⁶Li) reaction on targets of ¹²C, ¹⁶O, ²⁴Mg, ⁴⁰Ca, ⁵⁸Ni and ⁹⁴Mo have been measured at E_d = 54.2 MeV. The measured angular distributions have been analyzed by finite-range DWBA calculations, and spectroscopic factors for an α-cluster transfer have been extracted. In the DWBA analysis using an optical model with a phenomenological Woods-Saxon potential, the spin-orbit part of the deuteron optical potential played a significant role in reproducing the measured angular distributions but the spin-orbit part of the ⁶Li optical potential had a minor effect. Relative spectroscopic factors extracted from the present data were compared with theoretical predictions together with the results from the (p, pα) reaction. The relative spectroscopic factors for 1p-shell nuclei were in quantitative agreement with theoretical predictions. However, there were certain discrepancies between the spectroscopic factors extracted from the (d, ⁶Li) reaction and those from the (p, pα) reaction, and the discrepancies increased with target mass number.     

Optical model analysis of 14 to 40 MeV neutron elastic scattering from 27Al, 28Si and 32S

An optical model analysis of 14 to 40 MeV neutrons elastic scattering from 2s-1d shell nuclei ²⁷Al, ²⁸Si and ³²S is described. A set of spherical optical model parameters is presented for each nucleus. A regional neutron optical model, valid for nuclei near the center of the 2s-1d shell, is proposed. A comparison between neutron and relevant proton data, which entailed the analysis of the latter, confirms earlier determinations of the Coulomb correction term to the real potential and of the strength of the real isospin potential.     

Elastic 3He scattering from even Ar isotopes and backward-angle anomalies in the systematics of elastic 3He scattering

Angular distributions have been measured for ³He elastic scattering from ^{36, 38, 40}Ar at 26.5 MeV and from ³⁶Ar and ⁴⁰Ca at energies between 24.5 and 28 MeV. This scattering clearly shows features of “anomalous” backward-angle scattering, which is discussed in the systematics of ³He scattering from heavier target nuclei. The data for “anomalous” scattering can be described by optical potentials which show features significantly different from those of “normal” scattering. These features are smaller radius parameters for the real optical potential and a strongly reduced volume integral for the imaginary potential.     

Measurement of the excitation function for the <Superscript>7</Superscript>Li(t,p)<Superscript>9</Superscript>Li reaction using detection of delayed neutrons

The excitation function for the ⁷Li(t, p)⁹Li reaction is measured at the EGP-10 electrostatic tandem accelerator (VNIIEF) at the incident triton energies E _t = 5–11.3 MeV. The measurements were based on detection of delayed neutrons resulting from the decay of ⁹Li nuclei. The neutrons were detected by the 4π detector consisting of ³He counters enclosed in a polyethylene moderator. A pulsed mode was used for irradiating the LiF target (210 μg cm^?2) of natural isotopic composition on the tantalum backing. Absolutization of the excitation function was performed against the ⁷Li(p, n) reaction cross sections.     

Energy dependence of the optical model parameters for 3He ions scattered from 40Ca and 58Ni

The differential cross sections for the elastic scattering of ³He ions on targets of ⁴⁰Ca and ⁵⁸Ni have been measured at incident energies of 27.7, 51.4, 73.2 and 83.5 MeV. The results of optical model analyses showed that only one unique potential (J_R ≈ 330 MeV · fm³) with a surface absorptive term can provide acceptable fits to the large angle elastic scattering cross sections at 83.5 MeV. The particular geometrical set found at 83.5 MeV could not, however, give an adequate fit to the data with energy less than 40 MeV. Subsequent analyses indicated that a break in the energy dependence of the real potential is observed for the low energy data. Explicit energy dependent terms were obtained by fitting all the data simultaneously. These phenomenological potentials were also compared with the folded nucleon-nucleus potential. The influence of the α-particle channels on the elastic scattering of ³He ions at 83.5 MeV was also examined.     

The (d, 6Li) reaction on 12C, 16O, 24Mg, 40Ca and 58Ni at 54.25 MeV

The (d, ⁶Li) reaction was studied at E_d = 54.25 MeV on the target nuclei ¹²C, ¹⁶O, ²⁴Mg, ⁴⁰Ca and ⁵⁸Ni. The data were analyzed with finite-range DWBA calculations. The absolute values of the α-cluster spectroscopic factors and the target mass dependence of the relative S_α were in agreement with those in the (p, pα) reaction at E_p = 100 and 157 MeV. The theoretical calculations of the relative S_α were in better agreement with the experimental data at higher energy than at the lower energies.     

One-nucleon spectroscopy of light nuclei

The capabilities and limitations of the conventional many-particle shell model and modern potential cluster models are discussed. New revaluated and more accurate calculations of one-nucleon spectroscopic characteristics of the light nuclei of 1p shell are presented. In many-particle shell model for nuclei with A = 7, 9, 11, 13, and 15 nucleon partial widths of highly excited states with the isotopic spin T = 3/2 were calculated both for “allowed” and “forbidden” transitions. One-nucleon spectroscopic factors were calculated in threebody multicluster models of ⁶Li{αnp}, ⁸Li{αtn}, and ⁹Be{ααn} nuclei. For isobar-analogue nuclei ⁷Li and ⁷Be, the spectroscopic proton S _p and neutron S _n factors for transitions to the ground and excited states of corresponding residue nuclei of the triplet ⁶Li-⁶He-⁶Be were calculated in the framework of binary potential αtand ατ models. Integral, differential and polarization characteristics of photonuclear processes ⁷Li(γ, n ₀)⁶Li, ⁶He(p, γ_{0 + 1})⁷Li, ⁷Li(γ, p ₀)⁶He, and ⁹Be(γ, p _{0 + 1})⁸Li were calculated in this approach.     

Total cross sections for 4,6He + 28Si reactions measured at 10–28 MeV/A

New results on the energy dependence of the total cross section (σ _R) for ⁶He scattering on ²⁸Si in the incident energy range 10–28 MeV/A are obtained. The α-particle-production cross sections for the ²⁸Si(⁶He, ⁴He)X channel are measured as well. The secondary beam of ⁶He with an intensity of up to 5×10⁴ particle/s was generated by bombarding a thick beryllium target with ～32-MeV/A ⁷Li ions. In the energy region below 17 MeV/A, σ _R increases sharply. The experimental dependences of the total cross sections are compared with the results of σ _R calculations using the double-folding potential within the optical model. The energy dependence of σ _R for ⁶He differs from that for the neighboring nuclei, which can be associated with the structural features of the former nucleus. The energy spectra of α particles produced in the ⁶He interactions with silicon indicate two mechanisms of their production: transfer reaction and ⁶He breakup in the field of the ²⁸Si nucleus.     

Angular distribution of 6He+p elastic scattering

The angular distribution of ¹H(⁶He,p)⁶He elastic scattering has been measured at E_c.m.=4.3 MeV by using a thick-target inverse kinematic method. The experimental differential cross sections are reproduced by the distorted-wave Born approximation calculation utilizing the CH89 global optical potential parameter set. The real part of CH89 is reduced comparing with other potentials, which may be attributed to the couplings necessary for the weakly bound nuclei.     

The elastic scattering of 3He on 4He at medium energies

The differential cross section of the elastic scattering ³He(⁴He, ⁴He)³He has been measured at center of mass energies E_c.m. between 28 and 44 MeV and in the c.m. angular range of 20° to 160°. The ³He polarization P at E_c.m. = 42 MeV and θ_c.m. = 132° was determined in a double scattering experiment. The analysis of the cross section data with the optical and the cluster model has been described previously. The phase shifts obtained in the cluster model calculations were used as starting values in a phase shift analysis. The resulting final real phase shifts and elasticity parameters give good fits to the cross section data. At 44 MeV the elasticity parameters show a pronounced odd-even dependence on angular momentum which had been found already in the case of the real phase shifts. The result of the polarization experiment |P| < 0.22 is consistent with cluster model predictions.     

Correlation investigations of the low-energy 10He spectrum

The spectrum of low-lying states in the ¹⁰He nucleus is investigated for the two-neutron transfer reaction ³H(⁸He, p)¹⁰He. The secondary beam of ⁸He nuclei with the energy 21.5 MeV/nucleon and a cryogenic tritium target are used in the experiment. The ¹⁰He ground state is observed in the missing mass spectrum at the energy of 2.1 MeV (Γ ～ 2 MeV) above the decay threshold. Analysis of the angular correlations of the ¹⁰He decay products yields the spin and parity of two excited ¹⁰He states, J ^π = 1^? in the energy range from 4 to 6 MeV and J ^π = 2⁺ at energies above 6 MeV.     

Highly excited 8Be core in the configuration of the 12C and 11B ground states

Angular distributions of the ¹²C(d, ⁶Li)⁸Be reaction at E_lab = 78.0 MeV and the ¹¹B(³He, ⁶Li)⁸Be reaction at E_lab = 71.8 MeV were measured. Transitions leading to ⁸Be in the ground state and the 3.04, 16.63, 16.92, 17.64 and 18.15 MeV excited states were observed. A DWBA analysis was performed regarding the (d, ⁶Li) and (³He, ⁶Li) reactions as direct α particle or triton transfers, respectively.