3He(d,p)4He reaction at intermediate energies and impulse picture of the (d,p) reactions

Physics Letters B 533 (2002) 1–7 www.elsevier.com/locate/npe

3 He(d, p)4He

reaction at intermediate energies and impulse picture of the (d, p) reactions

T. Uesaka a,∗ , J. Nishikawa a , H. Okamura a , K. Suda a , H. Sakai b , A. Tamii b , K. Sekiguchi b , K. Yako b , S. Sakoda b,1 , H. Kato b,2 , M. Hatano b , Y. Maeda b , T. Saito b , N. Uchigashima b , N. Sakamoto c , Y. Satou c,3 , T. Ohnishi c , T. Wakui c , T. Wakasa d , K. Itoh e,4 a Department of Physics, Saitama University, Saitama, 338-8570, Japan b Department of Physics, University of Tokyo, Bunkyo, Tokyo 113-0033, Japan c RIKEN (The Institute of Physical and Chemical Research), Saitama 351-0198, Japan d Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, Japan e Tandem Accelerator Center, University of Tsukuba, Ibaraki 305-8577, Japan

Received 24 January 2002; received in revised form 7 March 2002; accepted 8 March 2002 Editor: J.P. Schiffer

Abstract Cross section, tensor analyzing power T20 , and vector polarization correlation coefficient Cy,y for the 3 He(d, p)4 He reaction have been measured at 0◦ and Ed = 140, 200, and 270 MeV. The data are compared with a calculation based on an impulse approximation taking the D-state admixtures in deuteron, 3 He, and 4 He explicitly into account. The reasonable agreement with the data is understood as a consequence of a close connection between the 3 He(d, p)4 He reaction and the d + N backward scattering.  2002 Elsevier Science B.V. All rights reserved. PACS: 25.45.Hi; 29.25.Pj; 29.27.Hj; 29.30.Aj Keywords: (d, p) reaction; Polarized deuteron beam; Polarized 3 He target; Deuteron structure; Impulse approximation

* Corresponding author.

E-mail address: [email protected] (T. Uesaka). 1 Present address: Fujitsu corporation, Tokyo 140-8508, Japan. 2 Present address: Dai-ichi Kangyo Bank, Tokyo 100-0011,

Japan. 3 Present address: Center for Nuclear Study, University of Tokyo, Saitama 351-0198, Japan. 4 Present address: Tohoku University, Miyagi 980-8577, Japan.

Though they are made of more fundamental particles, quarks and gluons, we can safely treat nucleons as structure-less particles to explain nuclear phenomena in the low energy region. On the other hand, intermediate and high-energy reactions which occur in a regime where the high-momentum component of nuclear wave function plays a primary role can be affected by the substructures of nucleon. This is the case in the elastic electron–deuteron scattering at large mo-

0370-2693/02/$ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 0 - 2 6 9 3 ( 0 2 ) 0 1 5 6 5 - 4

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T. Uesaka et al. / Physics Letters B 533 (2002) 1–7

mentum transfer [1] and the one nucleon transfer reactions induced by high-energy deuteron beams [2]. Recent data from Thomas-Jefferson Laboratory showed that the tensor polarization t20 for the ed elastic scattering can be reproduced quite well at Q2 < 1.7 (GeV/c)2 without contributions from nonnucleonic degrees of freedom [1]. However, this does not necessarily mean that explicit quark degrees of freedom are unimportant in deuteron. As Glozman claims in Ref. [3], the destructive interference of the s 6 and s 4 p2 quark configurations in deuteron makes the ed elastic scattering observables less sensitive to the quark structure of deuteron and it is crucial for the purpose to extract an information on quark-structure of deuteron to carry out measurements of exclusive processes, such as the 2 H(e, e p)N ∗ reaction. There are polarization data of the 2 H(e, e p) reaction, which again are consistent with calculations without nonnucleonic contribution, but only at low momentum region of k < 0.7 fm−1 [4]. The proton momentum distribution in a deuteron obtained through the deuteron inclusive breakup reaction on carbon [5] has been the first data to arouse a suspicion of our conventional understandings about the deuteron structure. Though it is consistent with the calculation using Paris nucleon–nucleon potential at kpn < 1 fm−1 , where kpn denotes a proton momentum in the deuteron rest system, the momentum distribution deviates substantially from the calculation in the region kpn = 1–2.2 fm−1 . Similar deviation in the momentum distribution has been also observed for the d + p backward scattering [6]. This observations triggered off subsequent measurements of polarization observables, tensor analyzing power T20 and polarization transfer coefficient κ0 , by using high-energy polarized deuteron beams at SATURNE and JINR [7, 8]. These data are analyzed in terms of one-nucleon exchange (ONE) approximation [9], which is a naive model for the nucleon transfer reactions, incorporating additional corrections, such as, multiple scattering effects [10], relativistic effects [11], and dynamical ∆ excitation in the intermediate channel [6]. While these models cannot give a sufficient description of the data when used with conventional wave functions of deuteron, a multiple-scattering calculation based on quark structures of deuteron has succeeded in reproducing the polarization observables for the deuteron inclusive breakup reactions quite well [12]. However,

there have not been any theory which can explain polarization observables for the d + p backward scattering and the deuteron inclusive breakup simultaneously. One of the outstanding differences between data for these two processes appears at k ∼ 0.4 GeV/c, where a strange structure is observed in T20 data of the d + p backward scattering, which is missing in those of the deuteron inclusive breakup. It is of crucial importance to understand what, reaction mechanisms and/or exotic components in deuteron, are responsible for the difference in the deuteron inclusive breakup and the d + p backward scattering. Possible experimental approach along this line is to measure data which provides an information complementary to those from the previously obtained. Recently, we have pointed out the polarization correlation coefficient, C// , for the 3 He(d, p)4 He reaction may be a unique probe to the D-state admixture in deuteron [13]. The usefulness of this observable to investigate the D-state admixture is attributed to the strong spin-selectivity in the neutron capture process by 3 He nucleus, i.e., spins of transferred neutron and 3 He must be anti-parallel to each other in order to form 4 He in the final state. In the ONE expression, C// is proportional to the D-state fraction in deuteron as 2 C// = 94 u2w+w2 , where u and w are the S- and D-state wave functions of deuteron in momentum space. This is a marked contrast to T20 and κ0 which include an S- and D-state interference term (uw-term) together with a w2 -term. It is thus expected that C// may be a candidate to provide an information on the deuteron structure complementary to those from T20 and κ0 . The first data of C// together with other polarization observables was measured at RIKEN at θlab = 4 ◦ and Ed = 270 MeV [13]. However, the data were found to be at variance with distorted-wave Born approximation calculations. It was not possible, at that time, to judge what is responsible for the discrepancy between the data and the calculation because the experimental data are limited, i.e., only at one deuteron energy and only at one finite angle. One may claim that an intrinsic complexity of the reaction, such as, contributions from the D-state admixtures in 3 He and 4 He may smear out the deuteron D-state effect, while other may claim that the framework of Born approximation is not appropriate for a description of the reaction with light nuclei. To clarify the situation, it is important to measure data at different energies and at 0◦ , where a

T. Uesaka et al. / Physics Letters B 533 (2002) 1–7

space symmetry minimizes complicating effects, such as spin-orbit force effects. In this Letter, we report experimental data of cross section, tensor analyzing power T20 , vector polarization correlation coefficient Cy,y for the 3 He(d, p)4 He reaction at 0◦ and at three incident deuteron energies of 140, 200, and 270 MeV. The data are analyzed in terms of a model based on an impulse approximation [14] which may be an alternative method to the Born approximation in analyzing the (d, p) reaction at intermediate and high energies. The experiment was carried out at RIKEN Accelerator Research Facility. Polarized deuteron beams used in this experiment were generated by an atomic-beam type polarized ion source [15]. The beam polarization was measured with an in-beam polarimeter after acceleration in the Ring cyclotron. The analyzing reaction was the d + p elastic scattering, observed at θcm = 110◦, 82.5◦, and 87.5◦ at Ed = 140, 200 [16], and 270 MeV [17], respectively. The beam polarizations were about 70% of the ideal values and almost constant of time. Two different targets were used depending on observables to be measured. In the cross-section and tensor analyzing power measurements, we employed a cryogenic gas target, where 3 He gas was cooled down to ∼ 11 K in a copper container contacted to a refrigerator. The geometrical length of the container was 10 mm (20 mm) at the Ed = 140 and 200 MeV (270 MeV) measurements. The density of the 3 He gas was 6.6 × 1020 cm−3 . Entrance and exit windows of 6-µm thick Havar foils separate the 3 He gas from vacuum. In the polarization correlation measurements, on the other hand, a spin-exchange type polarized 3 He target was bombarded by deuteron beams. The target had a so-called “double-cell” structure [18] consisting of a target cell and an optical-pumping cell, where two cells were connected to one another through a pipe with an inner diameter of 8 mm. The whole target was made of Borosilicate glass, Corning 7056 which has an only weak relaxing effect to polarized 3 He gas. The target cell whose size was 5 cm in diameter and 10 cm in length along the beam path contained 3 He gas with a density of 7.0 × 1019 atoms/cm3 together with a small amount of N2 gas and Rb vapor. Absolute value of the 3 He polarization was calibrated by mean of the frequency shift of Rb electron-spin-resonance (ESR) in the vicinity of polarized 3 He gas [19,20]. Typical

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target polarization was approximately 0.15 and its uncertainty P /P was 8% which mostly came from the variation seen in the ESR data and an uncertainty in the gas density. Scattered protons from the 3 He gas target was detected with the QQD-QD type magnetic spectrograph SMART [21]. It should be noted that, in the polarization correlation measurement, the polarized 3 He target was placed between the first dipole magnet and the third quadrupole magnet, and therefore following QD magnets alone were used for momentum-analysis of scattered protons. The focal-plane detectors consisted of three plastic scintillation counters and an eight-plane multi-wire drift chamber (MWDC). Signals from the scintillation counters generated a trigger to a data acquisition system [22]. The pulse height information, corresponding to an energy loss of the particle incident on the focal plane, was also used to identify the particle. Huge background events of lowenergy deuterons were rejected by means of this pulse height information. Trajectory of the particle was provided by the timing signals from the MWDC. The proton momentum and scattered angle were reconstructed from the trajectory with the help of ion-optical data sets of SMART measured beforehand. Typical proton energy spectra obtained for both targets are shown in Fig. 1. In each case, a peak due to the 3 He(d, p)4 He reaction at Ex = 0 MeV is well separated from other peaks due to the (d, p) reactions from Haver foils or a glass cell. Experimental results are listed in Table 1. Uncertainties in Table 1 are statistical ones only. Systematic uncertainties for dσ/dΩ, T20 , Cy,y are estimated to be 5%, 2%, and 8%, respectively. The last one is dominated by the uncertainty in the 3 He polarization. Fig. 2 presents the data as a function of the incident deuteron energy. In panel (b), data of the tensor analyzing power for the d + p backward scattering [8,16] are also shown with open circles. It is found that both data of T20 are negative and their magnitude increase with the deuteron energy. These features are naturally explained by the different signs of S- and D-state wave functions of deuteron in momentum space and the increasing magnitude of the D/S state ratio with kpn because T20 is dominated by the S- and D-state interference term in the region considered. In addition, one can relate T20 for the 3 He(d, p)4 He reaction to that for the d + p backward scattering by shifting the incident

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T. Uesaka et al. / Physics Letters B 533 (2002) 1–7

Table 1 Measured cross sections and polarization observables at 0◦ . Uncertainties are statistical ones only Ed (MeV)

140

200

270

dσ/dΩ (mb/sr) T20 Cy,y

2.88±0.025 −0.294±0.013 −0.635±0.018

1.92±0.012 −0.428±0.024 −0.661±0.025

0.845±0.006 −0.557±0.035 −0.664±0.032

Fig. 1. Typical proton energy spectra obtained for the cryogenic gas target and the polarized target. A peak at Ex = 0 MeV corresponds to protons from the 3 He(d, p)4 He reaction in each case.

energy by approximately +70 MeV, which may be attributed a Fermi-motion effect in the target as shown later. These observations encourage one to analyze the present data in the light of an impulse approximation which relates the d + A scattering amplitudes to those for the d + N scattering. In the following, we follow the approach conceptually based on the model in Ref. [14]. The model assumes that the incident deuteron (d) interacts with one nucleon (N ) in the target (3 He) and the other two nu˜ are left as spectators as shown in Fig. 3. cleons (d) The d–N scattering amplitudes (τ dN ) are approximated with those for the free d–N scattering. After the d–N scattering, the recoiled two nucleon (d  ) and the spectator d˜ merge into an alpha particle in the final state. This model has succeeded in reproducing the vector analyzing power for the 3 He(d, p)4 He reaction

Fig. 2. (a) Cross section, (b) tensor analyzing power T20 , and two polarization correlation coefficients (c) Cy,y for the 3 He(d, p)4 He reaction at 0◦ (filled circles). T20 for the d + p backward scattering is also shown with open circles in panel (b). Solid and broken lines in panel (a) represent calculation with two different assumption on the momentum dependence of d  wave function. Solid lines in panel (b) and (c) represent calculation with the d–N scattering amplitudes at the off-shell (thick lines) and on-shell (thin lines) energies, respectively. Dotted lines are calculations with the d + N scattering amplitudes at the off-shell energy without D-state admixtures in 3 He and 4 He.

Fig. 3. Graph of the 3 He(d, p)4 He reaction. Relative momenta between d˜ and N (d  ) in 3 He (4 He) are denoted by Kh (Kα ).

T. Uesaka et al. / Physics Letters B 533 (2002) 1–7

reasonably well [14]. In the present calculation, we take the Fermi motion of a participant nucleon N in the target into account while Ref. [14] supposes that N has a fixed momentum in the target. It is assumed that the Fermi momentum of the nucleon is so small compared with the incident deuteron momentum that we can use the d + N scattering amplitudes at 0◦ . The Dstate admixtures of 3 He and 4 He are also taken into account explicitly. The transition matrix elements are given as Tνp ;νh νd
 ˜   Ψ d,d (K α )τνdN = pν ˜ (N,d)

d  ;νN νd

 ˜  (EdN )Ψνd,N (K h )ϕνd h (1)

τ dN

where is the free d–N scattering amplitude. A subscript ν represents a spin projection of each particle on the beam axis. The internal momentum in 4 He, K α , and the total energy of three nucleons in their center-of-mass system, EdN , are functions of momentum of the participant nucleon K h . The ˜ clustering in summation is taken over possible (N, d) 3 3 the He nucleus. Wave functions of He and 4 He are written as     ˜ d,N h ) Ψν = 1 s ˜ νN ν ˜  1 νh uh (Kh )Y 0 (K 2 d

h

+

0

d 2


 1



3 2 sd˜ νN νd˜ 2 νN

+ νd˜



σ

 1  σ   × 2 2νN + νd˜ σ 2 νh wh (Kh )Y2 (Kh ) χN χd˜ , 3

(2)

 Ψ

˜  d,d

α ) = sd˜ sd  νd˜ νd  |00uα (Kα )Y00 (K +


sd˜ sd  νd˜ νd  |2νd˜ + νd   σ



α ) χ ˜ χd  , × 22νd˜ + νd  σ |00wα (Kα )Y2σ (K d (3) where χN , χd˜ , and χd  are the spin wave functions ˜ and d  , respectively. The radial wave funcof N , d, tions u and w for d–p and d–d clusterings are taken from Ref. [23]. For other clusterings, N –(pN)singlet in 3 He and (pN)singlet –(nN)singlet in 4 He, we use the

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same S-state wave functions. This approximation does not affect the following arguments, because details of 3 He and 4 He wave functions have little influence on the results as shown later. In this Letter, ONE approximation [9] is applied for the d–N scattering amplitudes instead of using exact Faddeev amplitudes employed in Ref. [14]. This can be justified on the ground that the higher order effect is less important at forward angles, especially at 0◦ as demonstrated in Ref. [14]. It allows us to approximate the transition amplitudes as
(EdN ) = t Ψd  |χνn χνN  χνn χνp |ϕνd  τνdN p ν  ;νN νd d

∼t




 11

νn

     2 2 νn νN sd νd χνn χνp |ϕνd ,

(4)

νn

where t and t  are spin-independent factors. Wave functions of deuteron and d  are denoted by ϕνd and Ψd  , respectively. In the latter part of Eq. (4), the d  wave function is assumed to be independent of the internal momentum. The reason for this is that Ψd  is dominated by scattering states of two nucleons and therefore it is expected to depend on the internal momentum only weakly. A spin dependence of Ψd  is designated by a Clebsch–Gordan coefficient in Eq. (4). Deuteron wave functions are calculated by using CDBonn potential [24]. After spin-algebraic calculations, we obtain  1 Tνp ;νh νd = d 3 K h F (K h )(−1)νh− 2 δνh ,−νn √    × 12 12 νn νp 1νd (ud + 5 12νd 0|1νd wd ). (5) Here F (K h ) depends on the S- and D-state radial h wave functions of 3 He and 4 He, and depends on K only slightly. It should be emphasized that F (K h ) is spin-independent and the spin selectivity in neutron capture process by 3 He survives as δνh ,−νn although we have taken the D-state admixture in 3 He and 4 He into account explicitly. Thus, spin dependences of the integrand in Eq. (5) are due to this spin selectivity and the deuteron wave function alone. The transition amplitudes Tνp ;νh νd depend on D-state admixture in 3 He and 4 He only weakly through F (K ). In the h energy region considered, the largest contribution to the integral in Eq. (5) comes from where the participant nucleon moves in the opposite direction to

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T. Uesaka et al. / Physics Letters B 533 (2002) 1–7

of the incident deuteron with a momentum of Kh ∼ 0.3 fm−1 . This value of Fermi momentum corresponds to an increase of a deuteron energy of +70 MeV in the rest frame of the participant nucleon. This is consistent with the previously mentioned relation between tensor analyzing powers for the 3 He(d, p)4 He reaction and the d + p backward scattering in Fig. 2(b). The results of calculation are compared with the experimental data in Fig. 2. The solid line in Fig. 2(a) represents the calculation of cross section, where its absolute value is normalized to reproduce the data. Energy dependence of the measured cross section is well reproduced by the calculation. If the momentum dependence of the d  wave function is similar to that of deuteron, the calculated cross section behaves as the broken line in Fig. 2(a) which is too steep to reproduce the data. Thus it is reasonable to assume that the d  wave function depends on the internal momentum only weakly. Thick solid lines in the Fig. 2(b) and (c) represent the calculation with the d–N amplitudes at the offshell energy, i.e., taking the spectator d˜ on the energy shell. On the other hand, thin solid lines represent calculation with the d–N amplitudes at the on-shell energy, taking the d + N system on the energy shell. Both calculations reproduce the data reasonably well, though the calculation with the d–N amplitudes at the on-shell energy deviates from the data at the highest energy. Large negative value of Cy,y (Fig. 2(c)) together with its modest energy dependence is also well reproduced by the calculations. Calculations with different nucleon–nucleon potentials, Nijmegen-I [25] and Argonne v18 [26] are found to give less than 3% changes to the polarization observables in the energy region considered. Calculations without D-state admixtures in 3 He and 4 He which is denoted by dottedlines in the figure do not give noticeably different results. This is because the 3 He and 4 He wave functions affect the polarization observables only through the spin-independent factor, F (K h ) in Eq. (5). Fig. 4 shows the data of polarization correlation co1 T20 + 32 Cy,y for the reaction efficient, C// = 1 − √ 2 2 as a function of the deuteron energy. The solid line represents the calculation with the d–N amplitudes at the off-shell energy. The small positive value of the data is again consistent with the calculation. This small value of C// is a consequence of a small D-state contribution in the energy region. The contribution is expected

Fig. 4. Polarization correlation coefficient C// as a function of the deuteron energy. Error bars include Solid line represents the calculation with the d–N amplitudes at the off-shell energy.

to reach a maximum and C// have a value of 94 at Ed ∼ 1.5 GeV where the S-state contribution vanishes. The impulse model calculation is found to give a reasonable description of the data. This reasonable agreement is understood as a consequence of the close connection between the 3 He(d, p)4 He reaction and the d + N backward scattering. We can thus expect that the 3 He(d, p)4 He reaction can be a good probe to the high-momentum spin structure of deuteron at the d + p backward scattering. It is important to note that this conclusion is independent of our choice of 3 He and 4 He wave functions and the polarization observables are mainly sensitive to the D-state admixture in deuteron. However, it is necessary to test the validity of this model more extensively. For that purpose, angular distributions of the cross section and the polarization observables are considered to be useful. In summary, we have measured cross section, tensor analyzing power T20 , and vector polarization correlation coefficient Cy,y for the 3 He(d, p)4 He reaction at 0◦ by using polarized deuteron beams of Ed = 140, 200, and 270 MeV. The data are compared with the impulse model where the scattering amplitudes of the incident deuteron and a nucleon in the target 3 He nucleus are approximated by the free d–N scattering amplitudes. We have designated that energy dependence of cross section, tensor analyzing power, and polarization correlation coefficients are reproduced well by the calculation with standard wave functions of deuteron, 3 He, and 4 He and even with ONE approximation in the d–N scattering amplitudes. This may indicate that the 3 He(d, p)4 He reaction is closely connected to the d + N backward scattering. In addition, it

T. Uesaka et al. / Physics Letters B 533 (2002) 1–7

is important to note that the sensitivity of the polarization observables to the D-state admixture in deuteron is found not to be affected much by the choice of wave functions of 3 He and 4 He. We plan to extend the present investigation to higher energies, for example by using Ed
12 GeV polarized deuteron beam from Nuclotron at JINR.

Acknowledgements The authors would like to express their gratitude to all the staff of RIKEN Accelerator Research Facility. They are also indebted to S. Yamamoto for her help in a preparation of the polarized 3 He target. One of the authors (T.U.) would like to acknowledge the financial support of the Special Researcher’s Basic Science Program of RIKEN.

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