Nuclear Physics A 641 (1998) 3120Alpha spectroscopic factors for6Li,7Li,9Be and12C from the (~p,pα) reaction at 296 MeVT. Yoshimuraa, A. Okihanab, R.E. Warnerc, N.S. Chantd, P.G. Roosd,C. Samantae,S.Kakigia,N.Koorif, M. Fujiwarag, N. Matsuokag,K. Tamurag, E. Kubob,K.UshirobaInstitute for Chemical Research, Kyoto University, Uji, Kyoto 611, JapanbKyoto University of Education, Kyoto 612, JapancDepartment of Physics, Oberlin College, Oberlin, OH 44074, USAdDepartment of Physics and Astronomy, University of Maryland, College Park, MD 20742, USAeSaha Institute of Nuclear Physics, Calcutta 700064, IndiafDepartment of Mathematical and Natural Sciences, Tokushima University, Tokushima 770, JapangResearch Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567, JapanReceived 28 May 1998; accepted 1 July 1998AbstractThree-body breakup cross sections and analyzing powers for the6Li,7Li,9Be and12C(~p,pα)reactions were measured at an incident energy of 296 MeV. Data were analyzed using the planewave impulse approximation (PWIA) and the distorted wave impulse approximation (DWIA)and compared with previous studies. DWIA calculations reproduce shapes of projected spectraand analyzing power distributions fairly well with the exception of the12C(~p,pα)8Be reactions.Extracted spectroscopic factors for6Li,9Be and12C are larger than those found in the previousstudies. In contrast, extracted spectroscopic factors for7Li agree with the previous work. Thiswork suggests that the spectroscopic factor for6Li is ∼ 0.8, independent of incident energies andreaction types.c 1998 Elsevier Science B.V.Keywords: NUCLEAR REACTION6Li,7Li,9Be,12C(~p, pα), E = 296 MeV; measured σ(θp,θα,Ep), Ay;deduced alpha spectroscopic factor. Projected energy spectrum, analyzing power distribution, quasifreescattering, distorted wave impulse approximation.1. IntroductionThe cluster structure of light nuclei has been the subject of experimental and theo-retical studies for many years. In particular, it appears that alpha cluster structures areoften found in the ground-state wave functions of light nuclei, a result at least partially0375-9474/98/$ - see front matterc 1998 Elsevier Science B.V. All rights reserved.PII S0375-9474( 98)00432-1NUPHA 41884 T. Yoshimura et al. / Nuclear Physics A 641 (1998) 3120due to the alpha particle’s large binding energy and stability. The nuclear ground-statewave function may be projected onto a two-body cluster structure, in which the alphaparticle is bound to the residual nucleus; the cluster structures are then characterized byspectroscopic factors and momentum distributions of the bound alpha particles relativeto the residual core. Specifically, the spectroscopic factor is defined as the square of thenormalization of the overlap amplitude between the target ground state and the residualsystem comprising the alpha particle and the core.Historically, quasifree scattering (QFS) and transfer reactions have been used toinvestigate alpha cluster structures. If we ignore initial and final state interactions, theQFS process involves a projectile which interacts directly with an alpha particle withouttransferring any momentum to the core, i.e. the core remains a spectator. Spectator modeldescriptions such as the plane wave impulse approximation (PWIA) or distorted waveimpulse approximation (DWIA) have had some success in describing cluster knockoutreactions. Using these approaches spectroscopic factors, relative momentum distributionsand spin observables of the elementary two-body processes can be extracted.The nucleus6Li has the simplest alpha cluster structure in which an alpha particleis loosely bound to a deuteron or a p1n pair. The alpha cluster structure for thisnucleus has been studied extensively. According to recent theoretical studies, the three-body (α + N + N) models predict spectroscopic factors Sα=0.6510.75 [1,2] forα + d clustering whereas microscopic and some resonating group theory models givelarger values, Sα=0.9211.04 [31 7]. Experimentally, spectroscopic factors for6Li wereextracted from the (p, pα) data at 100 MeV [8],the(α, 2α) data at 771120 MeV [9],the (p, pd) data at 120 [11] and 200 MeV [11],andthe(e, e0d) data at 480 MeV [13]using the DWIA theory. These experimental spectroscopic factors are plotted versusincident energy in Fig. 1. The spectroscopic factors are roughly divided into two groups;one near 0.8 extracted from deuteron knockout (p, pd) and (e, e0d) reactions, and asecond group between 0.4 and 0.6 extracted from alpha particle knockout. In addition,one notes a tendency for the spectroscopic factors to be larger at the higher incidentenergy. Theoretically, the spectroscopic factor should remain constant and independent0.40.50.60.70.80.91.01.190100 200 300 400 500(p,pα)(α,2α)(e,e'd)(p,pd)SαdINCIDENT ENERGY(MeV)present workMicroThree-bodyFig. 1. Spectroscopic factors for6Li versus incident energy.T. Yoshimura et al. / Nuclear Physics A 641 (1998) 3120 5of incident energy or reaction type. The origin of the variation in the spectroscopicfactors extracted from data is not yet clear. To investigate this problem, measurements atdifferent incident energies are needed, especially at higher incident energies where thereaction mechanism description should be more reliable. For a measurement at around300 MeV, which is easily accessible with the RCNP cyclotron, no data are currentlyavailable.It is also well known that7Li,9Be and12C have large overlap with alpha clusterstructures. For example, the7Li ground state has a large overlap with a bound two-cluster description consisting of an alpha particle and a triton. In this case, the relativeangular momentum of the bound alpha cluster is L = 1, which leads to minimum in theQFS cross section at a kinematical condition where the residual triton has zero recoilmomentum. According to Roos et al. [8], DWIA calculations reproduce reasonably theshapes of energy sharing distributions (differential cross sections plotted as a functionof detected proton energy) in the7Li(p, pα)3H reaction at 100 MeV. However, theseauthors note that the predictions are slightly too broad, perhaps due to inaccuracies inthe bound-state wave function or optical potentials. A value of Sα=0.94 for the7Liground-state spectroscopic factor was obtained from the (p, pα) data at 100 MeV [8]which agrees with Sα=1.12 from simple LS coupling shell model calculations bySmirnov et al. [14]. However, the spectroscopic factor obtained