Large-angle quasi-free scattering in 6Li(p,pd)4He at 670 MeV

The ⁶Li(p, pd)⁴He reaction was investigated at 670 MeV by a coincidence experiment with a large-angle scattering geometry. The energy sharing and angular correlation of the reaction products were measured and the momentum distribution of the recoil nucleus was determined for transitions leading to residual nuclei in the ground and excited states. Results were analysed in terms of a simplified distorted-wave impulse approximation using cluster-model and three-body wave functions. The observed momentum distribution of the p-n pair in the p-shell of ⁶Li is in agreement with three-body calculations, while the spectroscopic factor is larger than predicted by theory. Transitions to breakup states of the α-particle also have the characteristics of quasi-free scattering on deuteron clusters.     

Four-body calculations of 3He(p,pp)d and 3He(p,pd)p break-up reactions

We calculate the differential cross sections at various angles for reactions ³He(p, pp)d and ³He(p, pd)p at 35 MeV and 45 MeV incident proton laboratory energy, solving the integral equations of four-body theory with separable, S-wave, spin-dependent two body forces.     

Quasi-free scattering in the 6Li(d,dα)2H reaction at 52 MeV

In order to study the momentum distribution of an α-cluster in ⁶Li we have investigated the quasi-free scattering of deuterons in the ⁶Li(d, dα)²H reaction, using 52 MeV deuterons. The α-particle detector was kept at a fixed position of 30° and the second detector scanned over a range of coplanar angles. The α-cluster momentum distribution has been extracted by means of the plane-wave impulse approximation, using both the energy-sharing method and the angular correlation method. The momentum distributions so obtained are in good agreement with those obtained from other reactions such as (p, pα) and (α, 2α), and are compared with the spectator model. The reasons why the model works well are discussed. For the first time, to our knowledge, quasi-free scattering of deuterons on an α-cluster of a nucleus has been measured and analysed.     

The reaction 3He + p → p + p + d studied with BOL at 69 MeV 3He incoming energy

The proton-induced ³He breakup into p and d has been studied in a kinematically complete way at 69 MeV ³He-incoming (23 MeV p-incoming) lab energy, using the spherical multi-detector array BOL.The four-dimensional cross-section data cover most of the three-body final-state phase space. By slicing and integrating the data, they have been brought into suitable one- and two-dimensional representations to reveal different aspects of the reaction process. Based on these, this paper presents information on the interplay between the different reaction modes occurring in the p³He breakup process. In particular, pp final-state interaction, pp and pd quasi-free scattering and nucléon transfer have been studied here.Anomalous effects, probably due to interference between these processes, show up in the data.     

Mass 2 and 3 cluster structure study with quasi-free reactions induced by 58 MeV protons on 9Be, 12C and 14N

Cross sections for (p, pd) and (p,p³He) reactions at 58 MeV have been measured for ⁹Be, ¹²C and ¹⁴N targets. An energy resolution of about 400 keV permitted identification of several excited states in the different residual nuclei. The experimental results are presented and analysed in the framework of the distorted-wave impulse approximation. Spectroscopic and mechanism information is discussed. Some additional quasi-free reactions involving t, ³He and α structure of ⁹Be have been observed and are also reported.     

Prior-form DWBA analysis of (3He,pd) elastic breakup at 90 MeV

Proton-deuteron coincident cross sections in ¹²C,⁵¹V,⁹⁰Zr(³He,pd) elastic breakup at 90 MeV have been calculated within the framework of the prior-form distorted-wave Born approximation (DWBA). Sufficient convergence of the calculations was obtained by including the pd relative angular momenta up to l = 4. The calculations reproduced the general trend of the coincident energy spectra and the angular correlation data, though deficiencies of the calculations were seen at some angles. The peripheral feature of the (³He, pd) elastic breakup is discussed from the angular momentum dependence of the transition amplitude.     

DWIA calculations of proton momentum distributions in 12C and 16O(e,e'p) reactions

The DWIA analysis of the quasi-free (e, e'p) process on ¹²C and ¹⁶O has been performed within the framework of the single-particle shell model. The spherical Hartree-Fock wave functions for the effective Skyrme forces are used in describing the ground-state properties of these nuclei. The competition between the structure effects and the final proton-nucleus interaction in forming the momentum distributions of outgoing protons is studied in a wide range of recoil momenta (up to 3 fm^?1). The distorting optical potential has been calculated on the basis of the Watson multiple scattering theory. The results of the analysis are compared with the new data obtained at Saclay.     

A microscopic multi-channel calculation for the reactions 7Li(p,p)7Li and7Li(p,n)7Be

Based on a refined resonating group method a microscopic multi-channel calculation for the reactions ⁷Li(p, p)⁷Li and ⁷Li(p, n)⁷Be has been performed. Diagonal S-matrix elements and differential cross sections are presented from the ⁷Li-p threshold up to E = 2.5 MeV c.m. and compared with experimental data.     

Comparison of the noncoplanar 6Li(p,pd)4He reactions at 120 and 200 MeV

The ⁶Li(p, pd)⁴He reaction was studied at 200.2 MeV, at the quasi-free angle pair (θ_p, θ_d) = (54°, ?48.9°), for noncoplanarity angles φ from 0° to 28°. ⁶Li αd spectroscopic factors of 0.84 and 0.76 are deduced from our coplanar data at this energy and 120 MeV, respectively, for ground-state 2S Woods-Saxon wave functions. A recent microscopic three-body calculation predicts spectroscopic factors from 0.70 to 0.75; using the ground-state wave functions from this study, we deduce a factor of 0.76 from the 200 MeV data. DWIA calculations fit the measured integrated cross sections versus φ for spectator momenta P_α ? 100 MeV/c at both bombarding energies, but underpredict them for larger P_α. Momentum form factors were better reproduced with 1S αd cluster wave functions for a soft-core bound-state potential than with the 2S Woods-Saxon wave functions, but the former wave functions generate unphysically large (～1.25) spectroscopic factors.     

The 2H(p, 2p)n reaction at Einc = 45 MeV and its sensitivity to various separable S-wave N-N potentials

This paper presents and analyses the data for the ²H(p, pp)n reaction at E_inc = 44.9 MeV. Kinematic conditions including the quasi-free scattering region and the regions far from quasi-two-body processes are considered. The experimental results are compared with the predictions of several separable S-wave models of the N-N interaction. Potential models that differ only off-shell, as well as models that predict different N-N scattering results are included to help to isolate aspects of the break-up reaction sensitive to off-shell and on-shell differences. The regions far from quasi-free scattering are generally much more sensitive to the off-shell features of the interaction than are quasi-free scattering results. On-shell differences in the potential affect predictions in all regions of phase space with the potentials best representing the free N-N data giving the best overall fit to the data over most regions of phase space.     

The reaction mechanism of the 7Li(n,tα)n reaction at En = 14.4 MeV

The correlation spectra of the three-body break-up of the n+⁷Li system have been studied at a neutron energy of 14.4 MeV. The analysis of the data reveals the predominant role of sequential processes. The Phillips-Griffy-Biedenharn theory has been applied to fit the data. The contribution of quasi-free scattering has also been observed and analysed in the frame of the PWIA.     

Cross section of the reaction 6Li(p, γ)7Be

The cross section of the reaction ⁶Li(p, γ)⁷Be has been measured using Ge(Li) γ-ray spectrometers for proton bombarding energies E_p from 200 keV to 1200 keV. At E_p = 800 keV, the total (p, γ) integrated cross section is found to be 3.1 ± 0.4 μb. The cross section adopted from consideration of this and previous measurements is in good agreement with that predicted from the known thermal neutron cross section for ⁶Li(n, γ)⁷Li on the assumption that properties of mirror direct capture reactions can be well described by optical potentials that use the same parmeter values for the two reactions.     

Spin assignments from the 142Nd(7Li, 6He)143Pm and 144Sm(7Li, 6He)145Eu reactions at 52 MeV

Angular distributions have been measured for transitions to low-lying states in ¹⁴³Pm and ¹⁴⁵Eu populated by the ¹⁴²Nd(⁷Li, ⁶He)¹⁴³ and the ¹⁴⁴Sm(⁷Li, ⁶He)¹⁴⁵Eu reactions at $\text{E(}{}^7\text{Li}\text{) = 52}$ MeV. Elastic scattering of ⁷Li at 52 MeV on ¹⁴²Nd and ¹⁴⁴Sm, and ⁶Li at 46 MeV on ¹⁴²Nd and at 45 MeV on ¹⁴⁴Sm, were measured. Optical-model parameters extracted from fits to the scattering data were used in a finite-range DWBA analysis of the angular distributions for levels below 1.40 MeV excitation energy in ¹⁴³Pm and 1.84 MeV in ¹⁴⁵Eu. The reaction cross sections forward of 6° c.m. allow unambiguous distinction to be made between 2d_{$\text{5}\text{2}$} and 2d_{$\text{3}\text{2}$} final states. Final-state spins have been assigned to d-states in ¹⁴³Pm at 1.40 MeV($\text{3}\text{2}$⁺)and in ¹⁴⁵Eu at 1.042 MeV ($\text{3}\text{2}$⁺). Existing assignments to other levels in both residual nuclei have been confirmed.     

Li(p,pd)He reaction at 100 MeV

An angular correlation experiment of the ⁶Li(p, pd)⁴He reaction at 100 MeV has been performed using a symmetric and coplanar geometry and covering an angular range from 45.5 to 57°. In addition to the conventional ΔE-E telescope systems for the detection of both protons and deuterons, a 14° analyzing magnet was employed to select deuterons of a given momentum range. The results for the ground state transition are consistent with those obtained at other incident energies. The angular distribution for the transition to the 20 MeV excited state of the recoiling α-particle was also obtained and the overall magnitude of the differential cross section is at least an order of magnitude smaller than that of the ground state transition. The plane wave impulse approximation (PWIA) was used to analyze the experimental results. A form factor was generated using the Saxon-Woods potential as the d-α inter-cluster potential. Satisfactory agreement between theory and experiment was obtained. A value of 0.45 ±0.08 was extracted for the deuteron clustering probability on ⁶Li. The exchange and the optical distortion effects were also discussed.     

Quasi-free (p,pα) scattering on 24Mg, 28Si, 40Ca and 58Ni at 157 MeV

Sixfold energy spectra have been measured for the (p, pα) reaction at 157 MeV on ²⁴Mg, ²⁸Si, ⁴⁰Ca and ⁵⁸Ni around quasi-free kinematic conditions. For the three s-d shell nuclei the experiment covered a map ranging from 0 to 220 MeV/c in recoil momentum and from 0 to 20 MeV in excitation energy of the final nucleus. Recoil momentum distributions have been obtained for the 0⁺ ground state and the 2⁺ first excited state of ²⁰Ne, ²⁴Mg and ³⁶Ar, and also for the states around 4.4 MeV (mainly 4⁺) of ³⁶Ar. The a spectroscopic factors extracted by a DWIA analysis are about three times larger than those predicted by the SU(3) model; however, they agree quite well in relative magnitude for a number of cases. The disagreement in shape between experiment and theory observed at low recoil momentum for the 2⁺ states might result from another reaction mechanism. The cross sections for ⁵⁸Ni are about a factor often smaller than those for ⁴⁰Ca. The ⁵⁸Ni(p, pα)⁵⁴Fe reaction seems to lead mainly to excited states of the final nucleus.     

12C(7Li,t)16O和20Ne(d,6Li)16O反应的研究

本文把用于处理重离子引起的单粒子转移反应的Goldfarb-Buttle方法推广到多粒子转移反应。计算了¹²C(⁷Li,t)¹⁶O和²⁰Ne(d,⁶Li)¹⁶O反应,用了¹⁶O的全相干波函数,考虑了某些反冲因素,并将结果与实验作了比较。     

Correlation and polarization characteristics of the 40Ca(p, dπ+)39K reaction

The ⁴⁰Ca(p, dπ⁺)³⁹K reaction was studied theoretically at a proton energy of 650 MeV within the distorted wave impulse approximation (DWIA) and under the assumption of a quasi-free mechanism of the elementary process pp → dπ⁺ of pion production. The peripheral nature of the reaction on the nucleus was shown. The influence of the effects of distortions in the initial and final states of the reaction on the differential cross section and other spin-dependent characteristics are discussed.     

A microscopical DWBA description of the charge-exchange reactions (7Li, 7Be)

The charge-exchange reaction (⁷Li, ⁷Be is described in the frame of a microscopical DWBA with central effective forces. The transition density for ⁷Li-⁷Be is calculated in two ways: with a one-particle model and with a cluster model, taking full account of recoil effects. The formalism is used for the cases of (⁷Li, ⁷Be reactions with ⁶Li and ⁴⁰Ca. Further cross sections for reactions on ¹²C and ¹⁶O with $\text{E(}{}^7\text{Li) = 78 MeV}$ and excitation energies around 4.5 and 6.2 MeV, respectively, are compared to new data obtained at the Kurchatov Institute. Here particle-hole states in an oscillator model were used to characterize the heavy system. Angular distributions are well reproduced, but absolute cross sections are 6–7 times too small. This indicates that the assumption of a direct one-step process is correct, but that tensor forces should be included as a component of the effective nucleon-nucleon force.     

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.