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.     

Study of the <Superscript>12</Superscript>C (<Superscript>8</Superscript>B, <Superscript>7</Superscript>Be)<Emphasis Type="Italic">X</Emphasis> knockout reaction at intermediate energies

The breakup reactions of ⁸B on a ¹²C target at 142, 285, 790, and 936MeV/nucleon have been studied. One-proton-removal cross sections, leading to the production of ⁷Be fragments in the ground and first excited states (at 0.429MeV), and the longitudinal momentum distributions of the ⁷Be fragments are obtained in the Eikonal approximation of the Glauber Model. The results of the calculations including the contribution of the ⁷Be to the ground and first excited states of ⁸B are compared with the available experimental data. One-proton-removal cross section for the ¹²C(⁸B, ⁷Be)X knockout reaction at 142, 285, 790, and 936 MeV/nucleon energy has been calculated. ⁸B and ⁷Be cross sections and momentum distribution are in a good agreement with available data.     

dd → 3 Hen Reaction at Intermediate Energies

The dd → ³ Hen reaction is considered at the energies between 200 and 520?MeV. The Alt–Grassberger–Sandhas equations are iterated up to the lowest order terms over the nucleon–nucleon t-matrix. The parameterized ³ He wave function including five components is used. The angular dependence of the differential cross section and energy dependence of tensor analyzing power T ₂₀ at the zero scattering angle are presented in comparison with the experimental data.     

Alpha-nucleus elastic scattering at intermediate energies

Elastic scattering of 288,340,480 and 699 MeV Alpha-particles was measured on ²⁰⁸Pb, ¹¹⁶Sn and ⁵⁸Ni. The data were analysed in terms of a phenomenological optical model. The optical potentials obtained were found to vary consistently with the target nucleus and the incident energy. The radial zone where the potentials are well determined was studied in detail. The data for ²⁰⁸Pb were also analysed with a folding model. The energy dependence of the strong-absorption radius and of the reaction cross section shows that the nuclear surface becomes slightly transparent for incident energies above 150 MeV per nucleon.     

Surface and volume contributions to real and imaginary parts of the heavy-ion optical potential

Starting from the Feshbach expression for the optical potential, explicit formulae for the real and the imaginary parts of the optical potential between two heavy ions (HI's) are obtained. They are each composed of a volume and a surface term. The contributions to the volume term are calculated in two nuclear Fermi liquids which flow through each other starting from the realistic Reid soft core nucleon-nucleon (NN) interaction. Since the Fermi surface is formed by two spheres one obtains a complex Brueckner reaction matrix which is approximated by a complex, effective local interaction. It is used in a fully antisymmetrized double folding procedure to obtain the volume terms of the optical potential between the two HI's. The surface contributions are directly calculated in the collision of the two finite HI's. The collective surface vibrations (3^? octupole state and 2⁺, 4⁺ (T = 0) giant resonances for the ¹⁶O?¹⁶O collision) are included as intermediate states. This yields especially an imaginary contribution at the surface which reduces the transparency found with the volume terms alone. The method is applied to ¹⁶O?¹⁶O scattering at 83 and 332 MeV laboratory energy. The local approximations to the real and imaginary parts obtained in this way agree well with phenomenological fits. The surface terms improve the agreement of the differential cross section at 80 MeV where experimental data are available.     

Production of heavy nuclei in the interaction of <Superscript>7</Superscript>Li ions with copper nuclei at an energy of 35 MeV per nucleon

The absolute values of the cross sections for the production of target fragments in the interaction of copper with ⁷Li ions at an energy of 35 MeV per nucleon were measured. The measurements were performed by recording the yields of radioactive nuclear residues with the aid of a semiconductor detector from ultrapure germanium. The charge and isobaric distributions in the mass-number range 22–69 amu were used to deduce the mass yield of reaction products and to calculate the total interaction cross section. The results are presented that were derived from a comparison with data obtained for ¹²C + Cu reactions and with estimates based on theoretical models.     

Energy dependence of 12C+12C single-neutron transfer cross sections

The one-neutron transfer reaction induced by 25, 35 and 50 MeV/nucleon ¹²C beams on a ¹²C target has been studied. The observed angular distributions for the ¹³C_g.s-¹¹C_g.s. final state agree in shape and magnitude with predictions of the exact finite- range distorted wave Born approximation. Above roughly 30 MeV/nucleon, the angel integrated cross section falls off with an approximately exponential slope in accordance with the expectations of the reaction dynamics at high bombarding energies.     

Peculiarities in total cross sections of reactions with weakly bound nuclei <Superscript>6</Superscript>He, <Superscript>9</Superscript>Li

The energy dependence of the total cross sections for the ⁶He + Si and ⁹Li + Si reactions was measured at beam energies between 5 and 20 MeV per nucleon. The results agree with experimental data published for the ⁶He + Si reaction. New data are obtained for the ⁹Li + Si reaction in the vicinity of a local enhancement of the total cross section. A theoretical analysis of the possible reasons behind the appearance of this peculiarity in the case of collisions of ⁶He and ⁹Li nuclei with silicon target nuclei is performed. In particular, the enhancement may owe its origin to the effect of loosely bound projectile nucleons.     

Incomplete deep-inelastic heavy-ion collisions

A phenomenological two-step reaction model is proposed, in which a direct projectile fragmentation in the initial stage is succeeded by a binary dissipative interaction between the heavy projectile fragment and the target in the final state. Multi-differential cross sections are estimated by folding the fragmentation cross section given in the local plane-wave Born approximation with the cross section for deep-inelastic collisions calculated within the classical friction model, including statistical fluctuations and mass transfer. For forward angles satisfactory results are obtained in comparison with the experimental data on inclusive spectra, angular distributions, angular correlations, γ-multipliciites, and element distributions in ²⁰Ne-induced reactions for bombarding energies of 10–20 MeV/nucleon.     

Study of the γD → ppπ− reaction in the Δ(1236) region for well defined kinematical conditions

The γD → ppπ^? reaction cross section, in the Δ(1236) region, is measured in a counter experiment with high statistical accuracy. Particular emphasis is put on the accurate determination of the complete kinematics. For low values of the undetected nucleon momentum (p_r, ≈ 50 MeV/c), the validity of the spectator nucleon model is experimentally checked and the γn → pπ^? elementary reaction cross section is extracted and compared with other experimental data. When the recoiling nucleon momentum increases (p_r ≈ 150 MeV/c), significant departures from the spectator nucleon model are found. Presumably they are the signature of final state interaction effects.     

Production cross sections of multiply charged fragments in heavy ion interactions at 150–200 MeV/nucleon

A total of 1720 ¹⁶O-emulsion nucleus interactions at 150–200 MeV/nucleon have been investigated. Production cross sections of multiply charged projectile fragments are given. It is found that the cross section for the production of N, C, B and Be projectile fragments in ¹⁶O-nucleus interactions is similar at 0.2 and 2 GeV/nucleon. The fragmentation cross sections for Li and He are larger at 0.2 than at 2 GeV/nucleon.     

Delta-isobar configurations in 12C and 16O nuclei

The differential yield of the reaction ¹⁶O(γ, π ⁺ p) at the maximum photon energy of 450 MeV was measured in the region of high momentum transfers to the residual nuclear system. The experimental results obtained for the ¹⁶O nucleus and the cross section measured earlier for the reaction ¹²C(γ, π ⁺ p) were analyzed on the basis of a model that takes into account the admixture of isobar states in the nuclear wave function. The probabilities for the delta-isobar configurations in the ground states of the carbon and oxygen nuclei per nucleon were estimated empirically at 0.012 ± 0.003 ± 0.002 and 0.019 ± 0.003 ± 0.003, respectively.     

Δ(3, 3) excitations and effective three-nucleon forces in finite nuclei

Contributions from three-body terms with intermediate Δ(3,3) isobar excitations to the ground state energies of nuclei are investigated. These terms can either be understood as three-body clusters in a many-body theory including isobar excitations explicitly or as contributions to an effective three-nucleon force. For the example ¹⁶O the resulting contribution is attractive and its value is typically about ?0.5 MeV per nucleon. This is smaller than the typical values of 1 MeV per nucleon repulsion obtained from the modifications of the effective two-body nucleon-nucleon interaction in nuclei due to intermediate Δ(3, 3) configurations. The gain in energy from the three-body terms including Δ(3,3) configurations, however, is of the same importance as the contribution from three-body terms including nucleons only.     

Energy dependence of the total cross section for the reaction of 4He ions with silicon nuclei

Directly measured data on the total cross section for the reaction of projectile ⁴He ions with silicon nuclei at energies below 25 MeV/nucleon are presented. The energy dependence of the parameters of a semimicroscopic potential is determined from the measured values of this cross section. This investigation was performed at the Flerov Laboratory of Nuclear Reactions at the Joint Institute for Nuclear Research (Dubna, Russia) and at the Department of Physics at the University of Jyväskylä (Finland).     

质子滴线核12N在28Si靶上的核反应总截面测量

描述了50.4MeV/u的¹²N和42.3MeV/u的¹³N次级放射性束在²⁸Si靶上引起的核反应总截面σ_r实验研究,结果发现¹²N的反应总截面σ_r比其相邻同位素核¹³N有着异常的增大.这可能是核形变及核子对效应造成的,试验中的测量误差也不可忽视.利用微观Glauber模型计算了¹²N在²⁸Si靶上的核反应总截面,并与实验结果做了比较,发现理论计算与实验结果拟合较好 关键词： 质子晕 反应截面     

The reaction mechanism of heavy ion scattering at intermediate energies

The contribution to the real and imaginary nucleus-nucleus (N-N) optical potential from nucleon-nucleon scattering in the medium is calculated in a local density approximation from a two Fermi sphere nuclear matter picture for the N-N collision. This reaction mechanism is shown to be dominant for ¹²C + ¹²C scattering at all considered energies (160 MeV < E_lab < 2250 MeV) giving a weakly energy dependent reaction cross section of about 900 mb. Inclusion of the collective 2⁺, 3^? excitations in a coupled channel calculations gives good agreement for both the measured elastic and inelastic 2⁺ cross section at E_lab = 1016 MeV. This fully microscopic parameter free calculation indicates that the energy dependence of the reaction cross section for this system is mostly due to the decrease of the collective contribution with increasing energy contrary to current theoretical models.     

Mass yield distributions of target fragments from the reactions of iron with 135 MeV/nucleon 12C and 80 MeV/nucleon 16O ions

Cross sections for the production of target fragments in the reactions of iron with 135 MeV/nucleon ¹²C and 80 MeV/nucleon ¹⁶O ions have been measured by off-line γ-ray spectroscopy. Through these data, the mass yield distributions have been obtained. The result of the experiment for the reaction with 135 MeV/nucleon ¹²C ions is compared with theoretical calculations using the fusion-fragmentation model and the GEMINI code for sequential binary decay, following a calculation with the fireball model. Reveived: 24 March 1999 / Revised version: 16 July 1999     

Heavy ion induced transfer reactions on 148Nd

Transfer reactions induced by ¹⁶O and ¹⁸O beams on ¹⁴⁸Nd were measured with a time-of-flight setup at 72 MeV incident energy. The angular distributions are bell shapes having their maxima at angles somewhat below the grazing angle. The excitation in the final nuclei takes place (if possible) near the optimum Q-value and is spread over 5 MeV for the one-particle transfer reactions and up to 10 MeV for the multiparticle transfers. The cross sections for the individual channels are explained mostly by Q-window considerations. In spite of the differences in the individual channels the total transfer cross section integrated over excitation energy, angle, and all channels turns out to be the same same for both ¹⁶O and ¹⁸O beams. This cross section amounts to 20 % of the total reaction cross section and nicely fills the gap between the measured fusion cross section and the total reaction cross section obtained from optical model calculations based on elastic scattering data.     

Fragmentation of stable and neutron-rich 12-16C into boron fragments at approximately 240 MeV/nucleon

The elemental fragmentation cross sections of boron fragments produced by stable and neutron-rich^12-16C beams with a carbon target were systematically measured at an incident beam energy of approximately 240 MeV/nucleon.The measured cross sections were found to increase as the projectile mass number increases.The observed feature is explained qualitatively based on the abrasion-ablation two-stage reaction model and is compared quantitatively with predictions from various reaction models,including empirical and statistical models.All models agree with the measured cross sections within a factor of 2.     

Near threshold production of neutral pions by complex particles

Cross sections for the inclusive neutral pion production cross section have been measured for near threshold energy ³He particles on complex nuclei. The results of these measurements are of order 10^?36 cm²/sr · MeV. The neutral pion cross section for 710 MeV ⁴He on ¹²C has been found to be comparable to the production cross section for nucleons, 10^?30 cm²/sr · MeV. Comparisons are made with a naive model relating complex particle production to nucleon production of pions.