Fukunaga, Kiyoji

Kakigi, Shigeru

Okihana, Akira

Sekioka, Tuguhisa

Kyoto University Research Information Repository

Title Quasifree Scattering in the ³He([→p], 2p)²H and ³He([→p],pd)¹H Reactions at 64.9 MeVAuthor(s)Kakigi, Shigeru; Fukunaga, Kiyoji; Okihana, Akira; Sekioka,TuguhisaCitationBulletin of the Institute for Chemical Research, KyotoUniversity (1995), 73(1): 19-26Issue Date1995-03-31URL http://hdl.handle.net/2433/77601RightType Departmental Bulletin PaperTextversionpublisherKyoto UniversityBull. Inst. Chem. Res., Kyoto Univ., Vol. 73, No. 1, 1995   Quasifree Scattering in the  3He(p, 2p)2H and 3He(1i, pd)1H                  Reactions at 64.9 MeV                       Shigeru KAKuGi*, Kiyoji FUKUNAGA**,                     Akira OKIHANAt and TuguhisaSEKtoKAtt                                Received January26, 1995    The 3He(1i, 2p)2H and 3He(Ji, pd)'H reactions at 64.9 MeV were investigated in the quasifree scattering region. The cross sections and the analyzing powers were measured at several coincidence angle pairs. They were compared with the calculation i the plane-wave impulse approximation a d a modified one taking account of double scattering effect.    KEY WORDS : (i, 2p), (~, pd) Reactions/ Quasifree Scattering/ Few-Nucleon System                           1. INTRODUCTION    In recent years, the quasifree scattering (QFS) for few-nucleon systems have been studied. The QFS cross sections are calculated in the plane-wave impulse approximation (PWIA) on the spectator model usually used for the QFS process. Shapes of the energy spectra are well reproduced by the PWIA calculation but absolute values of the PWIA cross sections are larger than experimental values. The latter fact can be ascribed to multiple-scattering (MS) effects, which are measured with a MS factor°.    For the 3He(p, 2p)2H reaction, the ratio of the cross section measured to that calculated in the PWIA has been well reproduced by the MS calculation taking account of the single and double scatterings2'3). In the present study, the MS effect in the QFS region is investigated for the 3He(1i, 2p)2H reaction in the kinematical condition other than that for the previous one and for the 3He(p, pd)'H reaction in which the deuteron is the scattering partner in the QFS process, not the spectator as in the (1i, 2p) QFS reaction.                     2. EXPERIMENTAL PROCEDURE    A 64.5 MeV polarized proton beam was obtained from the AVF cyclotron of the Research Center for Nuclear Physics (RCNP) of Osaka University. The ion source was tuned to provide the maximum polarization of the beam. The polarization axis was adjusted perpendicular to the reaction plane. The spin direction of the beam was periodically changed. The beam polarization was monitored with a polarimeter set at the upper stream from a scattering chamber. The polarimeter was composed of a polyethylene target and two NaI (Tl) scintillation detectors * i$* 1 G : Institute for Chemical Research, Kyoto University, Uji, Kyoto 611. ** IM* : Yamagata University, Yamagata 990. t iLPi : Kyoto University of Education, Kyoto 612. tt ~guJ~ : Himeji Institute of Technology, Himeji 671-22. ( 19 )                      S. KAKIGI, K. FUKUNAGA, A. OKIHANA and T. SEKIOKA placed symmetrically at 47.5° with respect to the beam direction. The analyzing power for the  p+12C elastic scattering at 64.5 MeV was 0.975±0.0094). The beam polarization was stable within a range from 0.85 to 0.86 during the experiment. The beam spot was about 2 mm in diameter at the center of the scattering chamber and the beam current was about 150 nA. A 13 cm diameter gas chamber with 10 pm Havar windows containing 3He gas (isotopic purity 99.98%) was set at the center of the scattering chamber. The gas pressure, monitored with a gage, was 3 atm at room temperature.    Charged particles from reaction on the target were detected with four AE-E counter telescopes. Two of them (A and B) placed 10° apart were set on one side of the beam and two others (C and D) placed 10° apart on the other side of the beam. Each counter telescope consisted of a totally depleted Si surface barrier AE detector and a 25.4 mm thick NaI(T1) scintillation E detector. The thicknesses of the AE detectors were 200 pm for the telescopes A 01 02 N                 1.5 - 38.5, 45.0° 0.30 - 41.8°, 41.8° 0.29 1.0 - /}C -             }                       48.4°, 35.0° 0.31 51.7°, 31.5° 0.26 E 1.0 - 11-       /T 1+         0.5 - /{}~ {I\  - /++ } -aa +447+}         13 / V'+4...4,+/+r + 0                      53.0°, 30.0° 0.23 57.4°, 25.0° 0.16 1.0 - 0.5-}f_i4\ A1.*•4              0 '1 ++++,±+}'44'++4.4+             0 20 40 60 0 20 40 60 E1 (MeV)          Fig. 1. Coincidence nergy spectrafor the 3He(p, 2p)2H reaction at 64.9 MeV.                 Solid lines represent he PWIA values multipliedby factors N. (20)            Quasifree Scattering in the  3HeV,  2p)2H and 3He(ji, pd) `H Reactions and C, and 150fum and 100pm for the telescopes B and D, respectively.    Double slit systems made of 10 mm thick lead were used to define the target volume and solid angles of the detectors. For each coincidence pair, one slit system (for the detector A or B) defined the target volume, which was contained in the umbra of the other (for the detector C or D), its front slit serving only as a buffer. For coincidence measurements, one of the detector pairs (A—C, A—D, B—C and B—D) was choosen with taking into account the energy of detected particles and the thickness of the AE counter. Coincidence angle pairs are shown in Tables I and II.    Signals from the counter telescopes were analyzed through a fast-slow coincidence circuit. Signals (LIE, E, timing, coincidence pair and beam spin direction) were stored on a magnetic tape through the RCNP RAW DATA PROCESSOR-PDP11 system. Data were analyzed off-line with the FACOM M-380Q system at the Institute for Chemical Research of Kyoto University. ep ed N                     1.5 34.4°, 60.00 0.23 41.4°,55.0° 0.27 1.0 -           If , I        0.5 -1T -P~• 44 4 N y+~~i0+ff                  0  •Mf~14f}•4....1-'t•4_..i.  57.4°, 45.0° 0.44 74.6°,35.0° 0.70 E 1.0 --        G                      -100.5-             ,f}-}~            0+~fi.._./iri                             94,6°, 25.0° 0.76 106.6°, 20.0° 0.68 1.0 --          0.5 - ,10\                                                                      - 1{1 1 S        0W.I /!~.1             0 20 40 60 0 20 4060 Ep (MeV )          Fig. 2. Coincidence nergy spectra for the 3Hej, pd) IH reaction at 64.9 MeV.                 Solid lines represent the PWIA values multiplied by factorsN. (21 )                                        S. KAKIGI, K. FUKUNAGA, A.  OKIHANA and T. SEKIOKA             Two-dimensional energy spectra were obtained after particle identification and subtraction of               random coincidence events.                                 3. RESULTS AND DISCUSSION                 In two-dimensional coincidence spectra,yields were localized along kinematical oci of the             three-body processes. The yields were projected on the proton energyaxis. Figs. I and 2 show             energy spectra of protons from the 3He(pi, 2p)2H and 3He(p, pd)'H reactions, respectively, plotted             with solid circles. Error bars include only statistical uncertainty. Peaks are observed at the             energies, indicated by arrows, corresponding to zero of the unobserved particle energy in the             laboratory system. Thus the peaks can be attributed to the QFS processwith the unobserved              particle as a spectator. •                The measured cross sections were compaired with the PWIA calculations based on the             spectator model. A three-body reaction a + A-' 1+2+3 is considered, where the particle a is             the projectile and the particle A the target nucleus assumed to consist of particles b and c             bounded, A= (bc). The PWIA differential cross section is given as                                   Table I. Cross sections and analyzingpowers for the                                         QFS process in the 3He(ti, 2p)2H reactionat                                          64.9 MeV. 01 02 d6/dEldn1d122A,                                (deg) (mb/Mevsr2)                               25.0 57.4 0.51±0.05 -0.013±0.079                                30.0 53.0 0.77±0.09 -0.051±0.050                               31.6 51.5 0.84±0.05 +0.047±0.032                                33.9 49.4 0.90±0.09                              35.0 48.4 0.99±0.06 -0.021±0.046                               38.5 45.0 1.09±0.07 -0.026±0.033                               41.8 41.8 1.11±0.06 -0.002±0.038                                  Table II. Cross sections and analyzingpowersforthe                                        QFS process in the 3He(ii, pd)'H reactionat                                            64.9 MeV.                     Opad d6/dEpdDpdUdA,                               (deg) (mb/Mev sr2)                                29.7 62.2 1.38±0.12 +0.085±0.058                                34.1 59.6 1.15±0.08 -0.063±0.049                                              35.0 58.4-0.025±0.045                                41.4 55.0 0.94±0.08 -0.010±0.053                    45.0 51.4-0.070±0.054                                57.4 45.0 0.62±0.07 -0.277±0.061                               60.0 44.4 0.66±0.06 -0.309±0.052                               74.6 35.0 0.59±0.06 -0.385±0.061                               94.6 25.0 0.40±0.05 -0.395±0.060                               106.6 20.0 0.34±0.05 -0.220±0.076                                        ( 22 )                  Quasifree Scattering in the 3He(p', 2p)2H and  3He(p,  pd)'H Reactions (d6/dt21dD2dE1)PwsA=KXSX (d6/dD)12X I ocp3)I2,(1)      where K is the kinetic factor given'nby/p/,           K= [M122P/P22E3/(paES)]/[P2 (E2 +E3)E2(p2+C3)P2/p2],     with            Es=(p32+9,42)1/2      and S is the spectroscopic factor, S=1/2 for 3He target. (d6/dn)12 is the half-off energy shell      differential cross section for the 1+2 scattering in the (12) center of mass system. These were      replaced approximately by the on-shell values in the post collision prescription, which were      obtained from the data for pp scattering5l and for pd scattering6'7'8'91 through interpolation. 4/(62 I2 is the momentum density,given~by           C(p)I2=[ai3(a+'P)3]/[2r(a2+p2)(P2+p2)]2.      Thus                                         (a) 10 - 5 -                    a   0.5  0.2 - (b) >, 0 ------------------------- ft                                   -0 .2 -0 - 1III 1                  0 3060 90 120 150 180 epc (deg)                 Fig. 3 Two-body pp cross sections deduced from observed QFS cross sections                      using the PWIA formula (a) and pp-QFS analyzing powers (b) for the 3He(p-, 2p)2H reaction at 64.9 MeV. Solid lines represent the pp elastic                       scattering cross section and analyzing power, and dashed line the elastic                       cross section multiplied by the MS factor. (23)                       S.  KAKIGI, K. FUKUNAGA, A. OKIHANA and T. SEKIOKA      I O(0)12= [(a+/3)l (aP]3/n2. The parameters (a, f) in fm— I are (0.4201, 1.202) for 3He(pd) 1°l. Thus 10(0)12=0.437 X 10-6 MeV-3. In Figs. 1 and 2, solid lines represent the PWIA cross sections multiplied by factors N shown in the figures. Shapes of the energy spectra are well reproduced by the PWIA calculation but N< 1, the absolute values being not reproduced.    Next the differential cross sections at the QFS points (T3=0) were obtained and listed in Tables I and II for the 3He(p, 2p)2H and 3He(fi,pd)1H reactions, respectively. Two-body scattering cross sections (do cli2)12 were deduced from the QFS ones using eq. (1) and are shown in the upper parts of Figs. 3 and 4 with solid circles as a function of the angle B1cm in the (12) center of mass system. The relative kinetic energy T1-2 is constant of 26.6 MeV for the (p, 2p) reaction and 37.5 MeV for the (p, pd) reaction. The deduced cross sections are compared with                                      (a)                      50 -                N           E 10- \\         °- 5- \\       E.)t\ \\       1\ _ 0.5 -~.~T                                        i 0.4-(b) 0 ------------------- -0.4 - 0 30 60 90 120 150 180 Bpm (deg)           Fig. 4. Two-body pd cross sections deduced from observed QFS cross sections                using the PWIA formula (a) and pd-QFS analyzing powers (b) for the 3He(h., pd)1 H reaction at 64.9 MeV. Solid lines represent the pd elastic                  scattering cross section and analyzing power, and dashed and dash-dotted                 lines the elastic cross section multiplied by the MS factors for the pd                  singlet and quartet states, respectively. ( 2 4 )             Quasifree Scattering in the  3He(¢, 2p)2H and 3He(fi, pd)'H Reactions the elastic scattering ones, represented with solid lines in the figures. The absolute values diminish in the QFS process.    This fact can be attributed to the multiple scattering effect. The transition operator U is approximated as U=t12—t23Got12`t13Got12, where t11 is the two-body transition operator through the ij pair interaction and Go is the free space propagator. The first term corresponds to the transition in the impulse approximation (IA) and the second and third terms contribute to the multiple scattering effect, as a correction to the IA term. The interaction between the projectile proton and the deuteron in 3He contributes to the correction term in the (p, 2p) QFS process and however it plays the leading part in the (p, pd) QFS process. A separable form is assumed for the two-body transition matrix and its parameters (a, A in fm-1 are (-0.1112, 1.20), (0.420, 1.20) and (0.094, 1.20) for the pp singlet, pd doublet and pd quartet states, respectively2). The MS factor is calculated and the PWIA cross sections were multiplied by 17712, (do/d12) ms = (d6/d-0)free X 17712, shown in Fig. 3 with dashed line and in Fig. 4 with dashed and dash-dotted lines for the pd-QFS in the doublet and quartet states, respectively.    The lower parts of Figs. 3 and 4 show the QFS analyzing powers by solid circles. Also are shown with solid lines those for the corresponding elastic scatterings, obtained from the data for pp5) and pd7'$'11,12) scatterings through interpolation. As seen from the figures, the QFS analyzing powers are similar those for the corresponding elastic scatterings.     In conclusion, the double scattering effect can be considered as a correction to the single scattering calculation of the cross section for the QFS region. The calculation including the double scattering well reproduces the experimental cross sections. The result is the same as that for the 3He(p, 2p)2H reaction obtained in different geometries. For the analyzing power, on the other hand, the double scattering seems to be an effect of higher order because the observed values do not differ so much from those for the elastic scattering.     This experiment was performed under the program number 23A03.                             REFERENCES (1) K. Fukunaga, S. Kakigi, T. Ohsawa and A. Okihana, J. Phys. Soc. Jpn., 52, 69 (1983). (2) S. Kakigi, K. Fukunaga, T. Ohsawa, A. Okihana, T. Sekioka, H. Nakamura-Yokota, S. Tanaka and S.     Kato, Nucl. Phys., A473, 31 (1987). (3) S. Kakigi, K. Fukunaga, A. Okihana and T. Sekioka, Bull. Inst. Chem. Res., Kyoto Univ., 68, 103 (1990). (4) S. Kato, K. Okada, M. Kondo, A. Shimizu, K. Hosono, T. Saito, N. Matsuoka, S. Nagamachi, K.     Nisimura, N. Tamura, K. Imai, K. Egawa, M. Nakamura, T. Noro, H. Shimizu,K. Ogino and Y.     Kadota, Nucl. Inst. and Meth., 169, 589 (1980). (5) R. Wilson, The Nucleon-Nucleon Interaction (Interscience Publisher, New York, 1963) p. 177. (6) T.A. Cahill, J. Greenwood, H. Willmes and D.J. Shadoan, Phys. Rev., C4, 1499 (1971). (7) N. Bunker, J.M. Cameron, R.F. Carlson, J. Reginald Richardson, P. Tomas, W.T.H. van Oers and     J.W. Verba, Nucl. Phys., A113, 461 (1968). (8) H. Shimizu, K. Imai, N. Tamura, K. Nisimura, K. Hatanaka, T. Saito, Y. Koike and Y. Taguchi, Nucl.    Phys., A382, 242 (1982). (9) K. Hatanaka, N. Matsuoka, H. Sakai, T. Saito, K. Hosono, Y. Koike, M. Kondo, K. Imai, H. Shimizu, ( 2 5 )                       S. KAKIGI, K. FUKUNAGA, A. OKIHANA and T. SEKIOKA    T. Ichihara, K. Nisimura and A. Okihana,  Nucl. Phys., A426, 77 (1984). (10) I. Slaus, R.G. Alias, L.A. Beach, R.O. Bondelid, E.L. Petersen, J.M. Lambert, P.A. Treado and R.A.    Moyle, Nucl. Phys., A286, 67 (1977). (11) N.S.P. King, J.L. Romero, J. Ullmann, H.E. Conzett, R.M. Larimer and R. Roy, Phys. Lett., 69B,    151(1977). (12) J.C. Faivre, D. Garreta, J. Jungerman, A. Papineau, J. Sura and A. Tarrats, Nucl. Phys., Al27, 169    (1969). ( 26 )

Quasifree Scattering in the ³He([→p], 2p)²H and ³He([→p], pd)¹H Reactions at 64.9 MeV

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Quasifree Scattering in the ³He([→p], 2p)²H and ³He([→p], pd)¹H Reactions at 64.9 MeV

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