- Email: [email protected]
Tensor analyzing power of the (d, 2He) reaction at 270 MeV
2 February 1995 PHYSICS
LETTERS
B
Physics Letters B 345 ( 1995) l-5
Tensor analyzing power of the (d, 2He) reaction at 270 MeV H. Okamura a*1, S. Fujitaa, Y. Hara b, K. Hatanaka *, T. IchiharaC, S. Ishida a, K. Katoh b, T. Niizeki b, H. Ohnuma b, H. Otsu a, H. Sakai a, N. Sakamoto a, Y. Satou a, T. Uesaka a, T. Wakasaa, T. Yamashita b a Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan b Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152, Japan ’ The Institute of Physical and Chemical Research (RKEN), Wako, Saitama 351-01, Japan d Research Center for Nuclear Physics, Osaka Universi& Ibaraki. Osaka 567, Japan
Received 10 November 1994 Editor: R.H. Siemssen
Abstract The tensor analyzing power of the (d, ‘He) reaction has been measured at 270 MeV. Its usefulness for spectroscopic studies, particularly in identifying the J” of spin-flipdipole states, is demonstratedfor a i*C target. The data are reasonably well reproduced in terms of the distorted-waveBorn approximationtheory for the three-body reaction.
Recently the charge exchange (d, pp) reaction with the emitted protons coupled to the singlet S state was successfully measured at intermediate energies, taking advantage of the simple one-step reaction mechanism for the interpretation of the data and of the high efficiency for the detection of the two protons [ 1,2]. The ejectile system, though it is unbound, is commonly referred to as *He. Compared with the (n, p) reaction, it is characterized by the selective excitation of the spin-flip modes. In addition, it is theoretically shown [ 31 that the tensor analyzing powers are sensitive to J* of the residual nucleus and provide essentially the same nuclear information as the polarization transfer observables of the (II, p) reaction, the measurement of which is not feasible. The simplicity of the measurement of tensor analyzing powers should make the (d, *He) reaction a promising tool for nuclear spectroscopy.
An application of interest is the study of spin-flip dipole states. The (n,p)-type reaction has the advantage that the background Gamow-Teller transition (L = 0) is Pat&blocked due to the neutron-excess of heavy nuclei. A broad structure characterized by a L = 1 angular distributions is commonly observed in the intermediate energy (p, n) spectra for mediumheavy nuclei. Its width of about 10 MeV is believed to be caused by a superposition of the spin-dipole states (2-, 1-, and O- levels for a O+ target). However, the strength distribution of each .F, which is fundamental for the understanding of the particle-hole residualinteraction, has not been clearly determined [4]. It would be fascinating to know if the O- collective states were enhanced through its coupling to the pionic degrees of freedom in the nucleus. The usefulness of the tensor analyzing power in identifying P, however, has not been experimentally established. In this letter, we present the tensor an-
’ E-mail: [email protected]. 0370-2693/95/$09.50 @ t995 Elsevier Science B.V. All rights reserved SSDIO370-2693(94)01607-O
2
H. Okamuru et ul. /Physics
alyzing powers, A, and A,,, of the (d,*He) reaction at 270 MeV on the ‘*C target, the structure of which is well understood. This is the first measurement for well separated levels with various J” of the residual nucleus. The cross section and the vector analyzing power A, are also presented. The quality of the data is good enough to allow detailed discussions of the reaction mechanism. An analysis based on the distorted-wave Born approximation (DWBA) theory is presented. The experiment was performed at the RIKEN Accelerator Research Facility utilizing the newly constructed polarized ion source [ 5,6]. The polarization axis was rotated with a Wien filter downstream of the ion source so that it lay on the normal (sideway) direction of the scattering plane for the measurement of A, and A, (A,,). The beam polarization was monitored by using the d+p scattering at 270 MeV and it was 70-75% of the ideal value throughout the experiment. The natural carbon target with a thickness of 9.76 mg/cm* was bombarded withe a beam intensity of 0.1-2 nA. The *He is efficiently measured by the coincidence detection of the two protons emitted in close geometries. The protons are momentum-analyzed and detected at the first focal plane of the SMART spectrograph. Details of the experimental procedure are described in the previous publications [ 2,7]. It should be noted that the energy and angular resolutions have been significantly improved owing to the newly constructed detector system (Fig. 1) . The (d, *He) cross section is defined by da zi=Y?
Ema. ..-.
1 ss
d3u
dflza,d&,,dednppd’
’
477 lmin
where the p-p relative energy is denoted by E. The factor i arises from the indistinguishability of two protons. The integration limits of emin = 0 and E- = 1 MeV are set considering that the P-wave contribution is not negligible at E greater than 1 MeV according to the analysis of the ‘H(d, *He)n reaction at 200 and 350 MeV [lo]. The overall uncertainty of the cross section is estimated to be 20%, mainly caused by the uncertainty of the efficiency in resolving the trajectories of two protons. The ‘H( d, *He)n reaction was measured with a CH:! target as a crosscheck. The invariant cross section at 0’ was obtained to be du/dt =
Letters B 345 (1995) 1-5
12C(cL2He) E, = 270 MeV
e,,=4-100
I T
0.5
”
II.............
0.0 ,!I
1III
0
III1
5
“B Excitation
IIII
10
IIII
15
IIkI
20
25
Energy (MeV)
Fig. 1. Typical excitation energy spectra of the cross section and A,* with the result of gaussian peak-fitting. The overall energy resolution is 460 keV (FWHM) .
73 mb/(GeV/c)2 which is consistent with the data at 200 and 350 MeV [ lo]. Fig. 1 shows excitation energy spectra of the cross section and A, at the mean center-of-mass angles of 0.5” and 7”, where the Gamow-Teller and dipole states are relatively enhanced, respectively. Some discrete levels, 1: (ground), 2: (0.95 MeV), and 1; (2.62 MeV), are clearly seen to be excited as well as the broad structures at 4.5 and 7.5 MeV. A striking feature is the conspicuously large A,, observed at the energies corresponding to the 2: and 1, states, which agrees with the prediction of the plane-wave impulse approximation (PWIA) theory [ 31 where the A,, becomes close to +l for natural-parity states. The broad structures, on the other hand, show a moderate A,, consistent with the continuum at high excitation-energies. It should be noted that, in the (~,n)-type reaction,
3
H. Okamura et al. /Physics Letters B 345 (19951 l-5
though they are clearly characterized by the L values. The vector analyzing power is close to zero for all states which again agrees with the PWIA prediction. The uncertainty of the analyzing powers arising from the estimate of background does not have influence on the following argument since the analysing powers of the background are quite similar to those extracted for the peaks at 4.5 and 7.5 MeV. The data have been analyzed with the the priorformalism of the DWBA theory for the three-body reaction [ 111. The T-matrix element is expressed as TDwBA= (&&&‘A=
0
5
10
15
20
ecrn (ded
Fig. 2. Angular distributions of the cross section. The result of DWBA analysis is also presented normalized by the factor indicated for each state. For the ground state, the dotted curve represents the calculation without including the tensor part of the effective interaction. For the peak at 4.5 MeV, contributions from the 2; and 4; states and their incoherent sum are separately shown by dashed, dotted, and solid curves, respectively. For the peak at 7.5 MeV, the sums of the 2;. 2;. and 2; states and of the 1;. l;, and 1; states are shown by dashed and dotted curves, respectively.
the isobaric analog 1; of “N is not clearly observed since its width is broad [ 81. The yield for each state has been obtained by gaussian peak-fitting (Fig. 1) . The continuum background is estimated with the semiphenomenological parameterization of the quasi-free scattering [ 91. The angular distributions of the cross section and the analyzing powers thus obtained are shown in Figs. 2 and 3, respectively. An interesting feature is the rich structures of A, and Axx, while the cross sections show monotonous distributions al-
IV(x~)spZJ’.4) 9
where the projectile wave functions of the incidentand exit-channels are denoted by Q(r) and I,&,( E; r), the target wave functions by UA( X) and *A* (x), and the distorted wave functions by xy’(R) and X&~(R), respectively. The effective interaction between the nucleons in the projectile and in the target is denoted by V(R-x+r/2). For the simplicity of the calculation, ,&2 is assumed to be independent of r and E [ 111. Also $& and I,& are assumed to be in pure 3S1 and *& states, respectively, so that the integration over r can be carried out separately. ppdis represented by the Paris deuteron wave function [ 121 and the unbound +zHeis obtained from the Reid soft-core plus Coulomb potential [ 131 at each E. The orthogonality between pd and $2~~ is satisfied by the spin parts of them and the choice of the radial components has negligible influence on the result of the calculation. The remaining part of the Tmatrix is calculated by an ordinary two-body DWBA code. The program TWOFNR [ 141 was used for the present calculation. The effective two-body interaction is taken from the central and tensor parts of the t-matrix parameter&ion at 140 MeV by Franey and Love [ 151. The effect of the single-nucleon knock-on exchange is included by a short-range approximation for the central part [ 161. The one-body density matrices of the target are calculated by using the wave functions of Cohen and Kurath [ 171 and of Millener and Kurath [ 181 for the positive- and negative-parity final states, respectively. The optical potential for the incident-channel was determined by the preliminary data of elastic scattering measured at RIKEN [ 191. The parameters are listed in Table 1. The results of the calculation are shown in Figs. 2 and 3. Reasonable agreement with the data is obtained
H. Okamuru et al. /Physics
0
5 10 15
0
5 10 15
0
Letters B 345 (1995) 1-5
5 10 15 8,
0
5 10 15
0
5 10 15
0
5 10 15
(deg)
Fig. 3.
Angular distributions of the analyzing powers with the result of DWBA analysis. For the curves, see the caption of Fig. 2. The DWBA prediction for the 0: state (& = 14 MeV) is also presented for comparison. Table 1 Parameters of the deuteron optical-potential used in the calculation. V
W
(MeV) ;fm) 15.52
VLS
;?fm) (MeV) ;‘fm) Tim) (MeV) 1::)
1.60 0.66
8.11
1.59 0.62
3.65
Tk)
0.87 0.91
both for the cross section and for the analyzing powers. The relative normalization factors of the cross section for the 2:, 2,, and 4, states with respect to the ground state are consistent with those in the analysis of the intermediate energy (p, n) and (n,p) reactions [ 20-22 1. However, the origin of the overall normalization factor, 0.6, is not understood. It may be attributed to the defect in describing the exit-channel distorted wave function [ 231. In the present calculation, the parameters of the 2He optical-potential are chosen to be the same as those for the deuteron, except for the depth of the imaginary part ( W) which is modified to 25 MeV to improve the fit of A,. But A, is also sensitive to the spin-orbit part of the deuteron optical-potential and the choice of W has influence on the amplitude of the cross section by as much as 50%. The 2He distorted wave should be determined by a more advanced three-body theory, such as the adiabatic approximation [ 241.
In spite of this uncertainty, the DWBA calculation clearly demonstrates the usefulness of the tensor analyzing powers for the spectroscopic study. The A, and A,, are weakly influenced by the choice of the optical potentials, as far as the present calculation is concerned, and show a distinctively different behavior depending only on J”. Particularly the O- state can be unambiguously identified since the A, is exactly equal to + 1 (Fig. 3) due to the parity conservation [ 251. In the present data, however, no significant concentration of the O- strength has been observed up to the excitation energy of 30 MeV. It is worth noting that the large A,, arises mainly from the tensor part of the effective interaction, as can be seen from the difference between the solid and dotted curves for the 1;” state in Fig. 3. This feature is a consequence of the selection rule on spin-transfer and contrasts with ordinary deuteron-induced reactions where the large tensor analyzing powers are caused only through the higher-order effect of the spin-orbit potential or the D-state of the deuteron wave function. Finally the structure of the peak at 7.5 MeV is briefly discussed. Several shell-model states are predicted around this excitation energy [ 181. According to the DWBA calculation, the sums of 2- states and l- states form the main contributions with the same order of magnitude. Although the shape of the differ-
H. Okamuru et al. /Physics
ential cross section shows the slightly better agreement with that of the l- states (Fig. 2), it is largely influenced by the distorted waves and by the subtraction of the continuum background, making the estimate of the relative contribution to be ambiguous. A clear conclusion, on the other hand, is drawn from the tensor analyzing powers. Both the A, and A,, strongly suggest the dominant contribution from 2- states rather than from 1 - states (Fig. 3). This result disagrees with that of the intermediate energy (p, n) reactions where the dominance of the l- states is suggested [ 21,221. But it is derived from the small difference of the shapes of the cross section and largely relys on the shell-model prediction. The discrepancy between the two reactions may be attributed also to the different selectivities on the spin-transfer. The non-spin-flip lstates, the strength of which is also predicted to concentrate at similar excitation energies, can be excited in the (p, n) reaction. In summary, the t*C( d, *He) ‘*B reaction has been measured at 270 MeV with the emphasis laid on the tensor analyzing powers. The A, and A,, exhibit a the distinctively different behaviour depending on J” of the residual i*B. This feature is confirmed by the DWBA calculation which reproduces the data reasonably well. The present success of the prior-form DWBA theory is encouraging. The development of a more realistic but simple description is expected, which will allow the extensive application of the (d, *He) reaction. The further measurement on heavy nuclei is currently underway and will hopefully provide the definitive understanding on the spin-dipole state. The authors are grateful to the staff of RIKFN Accelerator Research Facility, particularly to Y. Yano,
Letters B 345 (1995) l-5
5
A. Goto, and M. Kase, for their invaluable assistance during the experiment. They also thank K. Ikegami, J. Fuji@ N. Inabe, and T. Kubo for their work in constructing the polarized ion source. References [l] C. Ellegaard et al., Phys. Rev. Lett. 59 (1987) 974; Phys. Lett. B 231 (1989) 365. [2] H. Ohnuma et al., Phys. Rev. C 47 ( 1993) 648. [3] D.V. Bugg and C. Wilkin, Nucl. Phys. A 467 (1987) 575; C. Wiiin and D.V. Bugg, Phys. Lett. B 154 ( 1985) 243. [4] F. Osterfeld, Rev. Mod. Phys. 64 ( 1992) 491, and references therein. [5] H. Okamura et al., AIP Conf. Proc. 293 ( 1994) 84. [6] H. Okamura et al., Nucl. Phys. A 577 ( 1994) 89~. [7] T. lchihara et al., Nucl. Phys. A 569 (1994) 287~. [ 81 W.A. Sterrenburg, M.N. Harakeh, S.Y. van der Wed and A. van der Woude, Nucl. Phys. A 405 (1983) 109. [9] K.J. Raywood et al., Phys. Rev. C 41 (1990) 2836. [ 101 S. Kox et al., Nucl. Phys. A 556 ( 1993) 621. [ 11) G. Baur and D. Trautmann, Phys. Rep. 25 (1976) 293. [ 121 M. Lacombe et al., Phys. Lett. B 101 (1981) 139. [13] R.V. Reid, Jr., Ann. Phys. (N.Y.) 50 (1968) 411. [ 141 M. Igarashi, program TWOFNR, unpublished. [ 151 M.A. Franey and WC. Love, Phys. Rev. C 31 (1985) 488. [16] M. Golin, E Petrovich and D. Robson, Phys. Lett. B 64 (1976) 253. [ 171 S. Cohen and D. Kurath, Nucl. Phys. 73 (1965) 1. [ 181 D.J. Millener and D. Kurath, Nucl. Phys. A 255 ( 1975) 3 15. [ 191 T. Uesaka et al., RIKEN Accel. Prog. Rep. 27 (1993) 40. [20] J. Rapaport et al., Phys. Rev. C 24 ( 1981) 335. [21] C. Garde et al., Nucl. Phys. A 422 (1984) 189. 1221 X. Yang et al., Phys. Rev. C 48 (1993) 1158. [23] N. Austem, Phys. Rev. C 30 (1984) 1130. [24] M. Yahiro, J.A. Tostevin and R.C. Johnson, Phys. Rev. Lett. 62 (1989) 133. [25] M. Simonius, in: Polarization Nuclear Physics, edited by D. Fick, Lecture Notes in Physics Vol. 30 (Springer, 1974).
LETTERS
B
Physics Letters B 345 ( 1995) l-5
Tensor analyzing power of the (d, 2He) reaction at 270 MeV H. Okamura a*1, S. Fujitaa, Y. Hara b, K. Hatanaka *, T. IchiharaC, S. Ishida a, K. Katoh b, T. Niizeki b, H. Ohnuma b, H. Otsu a, H. Sakai a, N. Sakamoto a, Y. Satou a, T. Uesaka a, T. Wakasaa, T. Yamashita b a Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan b Department of Physics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo 152, Japan ’ The Institute of Physical and Chemical Research (RKEN), Wako, Saitama 351-01, Japan d Research Center for Nuclear Physics, Osaka Universi& Ibaraki. Osaka 567, Japan
Received 10 November 1994 Editor: R.H. Siemssen
Abstract The tensor analyzing power of the (d, ‘He) reaction has been measured at 270 MeV. Its usefulness for spectroscopic studies, particularly in identifying the J” of spin-flipdipole states, is demonstratedfor a i*C target. The data are reasonably well reproduced in terms of the distorted-waveBorn approximationtheory for the three-body reaction.
Recently the charge exchange (d, pp) reaction with the emitted protons coupled to the singlet S state was successfully measured at intermediate energies, taking advantage of the simple one-step reaction mechanism for the interpretation of the data and of the high efficiency for the detection of the two protons [ 1,2]. The ejectile system, though it is unbound, is commonly referred to as *He. Compared with the (n, p) reaction, it is characterized by the selective excitation of the spin-flip modes. In addition, it is theoretically shown [ 31 that the tensor analyzing powers are sensitive to J* of the residual nucleus and provide essentially the same nuclear information as the polarization transfer observables of the (II, p) reaction, the measurement of which is not feasible. The simplicity of the measurement of tensor analyzing powers should make the (d, *He) reaction a promising tool for nuclear spectroscopy.
An application of interest is the study of spin-flip dipole states. The (n,p)-type reaction has the advantage that the background Gamow-Teller transition (L = 0) is Pat&blocked due to the neutron-excess of heavy nuclei. A broad structure characterized by a L = 1 angular distributions is commonly observed in the intermediate energy (p, n) spectra for mediumheavy nuclei. Its width of about 10 MeV is believed to be caused by a superposition of the spin-dipole states (2-, 1-, and O- levels for a O+ target). However, the strength distribution of each .F, which is fundamental for the understanding of the particle-hole residualinteraction, has not been clearly determined [4]. It would be fascinating to know if the O- collective states were enhanced through its coupling to the pionic degrees of freedom in the nucleus. The usefulness of the tensor analyzing power in identifying P, however, has not been experimentally established. In this letter, we present the tensor an-
’ E-mail: [email protected]. 0370-2693/95/$09.50 @ t995 Elsevier Science B.V. All rights reserved SSDIO370-2693(94)01607-O
2
H. Okamuru et ul. /Physics
alyzing powers, A, and A,,, of the (d,*He) reaction at 270 MeV on the ‘*C target, the structure of which is well understood. This is the first measurement for well separated levels with various J” of the residual nucleus. The cross section and the vector analyzing power A, are also presented. The quality of the data is good enough to allow detailed discussions of the reaction mechanism. An analysis based on the distorted-wave Born approximation (DWBA) theory is presented. The experiment was performed at the RIKEN Accelerator Research Facility utilizing the newly constructed polarized ion source [ 5,6]. The polarization axis was rotated with a Wien filter downstream of the ion source so that it lay on the normal (sideway) direction of the scattering plane for the measurement of A, and A, (A,,). The beam polarization was monitored by using the d+p scattering at 270 MeV and it was 70-75% of the ideal value throughout the experiment. The natural carbon target with a thickness of 9.76 mg/cm* was bombarded withe a beam intensity of 0.1-2 nA. The *He is efficiently measured by the coincidence detection of the two protons emitted in close geometries. The protons are momentum-analyzed and detected at the first focal plane of the SMART spectrograph. Details of the experimental procedure are described in the previous publications [ 2,7]. It should be noted that the energy and angular resolutions have been significantly improved owing to the newly constructed detector system (Fig. 1) . The (d, *He) cross section is defined by da zi=Y?
Ema. ..-.
1 ss
d3u
dflza,d&,,dednppd’
’
477 lmin
where the p-p relative energy is denoted by E. The factor i arises from the indistinguishability of two protons. The integration limits of emin = 0 and E- = 1 MeV are set considering that the P-wave contribution is not negligible at E greater than 1 MeV according to the analysis of the ‘H(d, *He)n reaction at 200 and 350 MeV [lo]. The overall uncertainty of the cross section is estimated to be 20%, mainly caused by the uncertainty of the efficiency in resolving the trajectories of two protons. The ‘H( d, *He)n reaction was measured with a CH:! target as a crosscheck. The invariant cross section at 0’ was obtained to be du/dt =
Letters B 345 (1995) 1-5
12C(cL2He) E, = 270 MeV
e,,=4-100
I T
0.5
”
II.............
0.0 ,!I
1III
0
III1
5
“B Excitation
IIII
10
IIII
15
IIkI
20
25
Energy (MeV)
Fig. 1. Typical excitation energy spectra of the cross section and A,* with the result of gaussian peak-fitting. The overall energy resolution is 460 keV (FWHM) .
73 mb/(GeV/c)2 which is consistent with the data at 200 and 350 MeV [ lo]. Fig. 1 shows excitation energy spectra of the cross section and A, at the mean center-of-mass angles of 0.5” and 7”, where the Gamow-Teller and dipole states are relatively enhanced, respectively. Some discrete levels, 1: (ground), 2: (0.95 MeV), and 1; (2.62 MeV), are clearly seen to be excited as well as the broad structures at 4.5 and 7.5 MeV. A striking feature is the conspicuously large A,, observed at the energies corresponding to the 2: and 1, states, which agrees with the prediction of the plane-wave impulse approximation (PWIA) theory [ 31 where the A,, becomes close to +l for natural-parity states. The broad structures, on the other hand, show a moderate A,, consistent with the continuum at high excitation-energies. It should be noted that, in the (~,n)-type reaction,
3
H. Okamura et al. /Physics Letters B 345 (19951 l-5
though they are clearly characterized by the L values. The vector analyzing power is close to zero for all states which again agrees with the PWIA prediction. The uncertainty of the analyzing powers arising from the estimate of background does not have influence on the following argument since the analysing powers of the background are quite similar to those extracted for the peaks at 4.5 and 7.5 MeV. The data have been analyzed with the the priorformalism of the DWBA theory for the three-body reaction [ 111. The T-matrix element is expressed as TDwBA= (&&&‘A=
0
5
10
15
20
ecrn (ded
Fig. 2. Angular distributions of the cross section. The result of DWBA analysis is also presented normalized by the factor indicated for each state. For the ground state, the dotted curve represents the calculation without including the tensor part of the effective interaction. For the peak at 4.5 MeV, contributions from the 2; and 4; states and their incoherent sum are separately shown by dashed, dotted, and solid curves, respectively. For the peak at 7.5 MeV, the sums of the 2;. 2;. and 2; states and of the 1;. l;, and 1; states are shown by dashed and dotted curves, respectively.
the isobaric analog 1; of “N is not clearly observed since its width is broad [ 81. The yield for each state has been obtained by gaussian peak-fitting (Fig. 1) . The continuum background is estimated with the semiphenomenological parameterization of the quasi-free scattering [ 91. The angular distributions of the cross section and the analyzing powers thus obtained are shown in Figs. 2 and 3, respectively. An interesting feature is the rich structures of A, and Axx, while the cross sections show monotonous distributions al-
IV(x~)spZJ’.4) 9
where the projectile wave functions of the incidentand exit-channels are denoted by Q(r) and I,&,( E; r), the target wave functions by UA( X) and *A* (x), and the distorted wave functions by xy’(R) and X&~(R), respectively. The effective interaction between the nucleons in the projectile and in the target is denoted by V(R-x+r/2). For the simplicity of the calculation, ,&2 is assumed to be independent of r and E [ 111. Also $& and I,& are assumed to be in pure 3S1 and *& states, respectively, so that the integration over r can be carried out separately. ppdis represented by the Paris deuteron wave function [ 121 and the unbound +zHeis obtained from the Reid soft-core plus Coulomb potential [ 131 at each E. The orthogonality between pd and $2~~ is satisfied by the spin parts of them and the choice of the radial components has negligible influence on the result of the calculation. The remaining part of the Tmatrix is calculated by an ordinary two-body DWBA code. The program TWOFNR [ 141 was used for the present calculation. The effective two-body interaction is taken from the central and tensor parts of the t-matrix parameter&ion at 140 MeV by Franey and Love [ 151. The effect of the single-nucleon knock-on exchange is included by a short-range approximation for the central part [ 161. The one-body density matrices of the target are calculated by using the wave functions of Cohen and Kurath [ 171 and of Millener and Kurath [ 181 for the positive- and negative-parity final states, respectively. The optical potential for the incident-channel was determined by the preliminary data of elastic scattering measured at RIKEN [ 191. The parameters are listed in Table 1. The results of the calculation are shown in Figs. 2 and 3. Reasonable agreement with the data is obtained
H. Okamuru et al. /Physics
0
5 10 15
0
5 10 15
0
Letters B 345 (1995) 1-5
5 10 15 8,
0
5 10 15
0
5 10 15
0
5 10 15
(deg)
Fig. 3.
Angular distributions of the analyzing powers with the result of DWBA analysis. For the curves, see the caption of Fig. 2. The DWBA prediction for the 0: state (& = 14 MeV) is also presented for comparison. Table 1 Parameters of the deuteron optical-potential used in the calculation. V
W
(MeV) ;fm) 15.52
VLS
;?fm) (MeV) ;‘fm) Tim) (MeV) 1::)
1.60 0.66
8.11
1.59 0.62
3.65
Tk)
0.87 0.91
both for the cross section and for the analyzing powers. The relative normalization factors of the cross section for the 2:, 2,, and 4, states with respect to the ground state are consistent with those in the analysis of the intermediate energy (p, n) and (n,p) reactions [ 20-22 1. However, the origin of the overall normalization factor, 0.6, is not understood. It may be attributed to the defect in describing the exit-channel distorted wave function [ 231. In the present calculation, the parameters of the 2He optical-potential are chosen to be the same as those for the deuteron, except for the depth of the imaginary part ( W) which is modified to 25 MeV to improve the fit of A,. But A, is also sensitive to the spin-orbit part of the deuteron optical-potential and the choice of W has influence on the amplitude of the cross section by as much as 50%. The 2He distorted wave should be determined by a more advanced three-body theory, such as the adiabatic approximation [ 241.
In spite of this uncertainty, the DWBA calculation clearly demonstrates the usefulness of the tensor analyzing powers for the spectroscopic study. The A, and A,, are weakly influenced by the choice of the optical potentials, as far as the present calculation is concerned, and show a distinctively different behavior depending only on J”. Particularly the O- state can be unambiguously identified since the A, is exactly equal to + 1 (Fig. 3) due to the parity conservation [ 251. In the present data, however, no significant concentration of the O- strength has been observed up to the excitation energy of 30 MeV. It is worth noting that the large A,, arises mainly from the tensor part of the effective interaction, as can be seen from the difference between the solid and dotted curves for the 1;” state in Fig. 3. This feature is a consequence of the selection rule on spin-transfer and contrasts with ordinary deuteron-induced reactions where the large tensor analyzing powers are caused only through the higher-order effect of the spin-orbit potential or the D-state of the deuteron wave function. Finally the structure of the peak at 7.5 MeV is briefly discussed. Several shell-model states are predicted around this excitation energy [ 181. According to the DWBA calculation, the sums of 2- states and l- states form the main contributions with the same order of magnitude. Although the shape of the differ-
H. Okamuru et al. /Physics
ential cross section shows the slightly better agreement with that of the l- states (Fig. 2), it is largely influenced by the distorted waves and by the subtraction of the continuum background, making the estimate of the relative contribution to be ambiguous. A clear conclusion, on the other hand, is drawn from the tensor analyzing powers. Both the A, and A,, strongly suggest the dominant contribution from 2- states rather than from 1 - states (Fig. 3). This result disagrees with that of the intermediate energy (p, n) reactions where the dominance of the l- states is suggested [ 21,221. But it is derived from the small difference of the shapes of the cross section and largely relys on the shell-model prediction. The discrepancy between the two reactions may be attributed also to the different selectivities on the spin-transfer. The non-spin-flip lstates, the strength of which is also predicted to concentrate at similar excitation energies, can be excited in the (p, n) reaction. In summary, the t*C( d, *He) ‘*B reaction has been measured at 270 MeV with the emphasis laid on the tensor analyzing powers. The A, and A,, exhibit a the distinctively different behaviour depending on J” of the residual i*B. This feature is confirmed by the DWBA calculation which reproduces the data reasonably well. The present success of the prior-form DWBA theory is encouraging. The development of a more realistic but simple description is expected, which will allow the extensive application of the (d, *He) reaction. The further measurement on heavy nuclei is currently underway and will hopefully provide the definitive understanding on the spin-dipole state. The authors are grateful to the staff of RIKFN Accelerator Research Facility, particularly to Y. Yano,
Letters B 345 (1995) l-5
5
A. Goto, and M. Kase, for their invaluable assistance during the experiment. They also thank K. Ikegami, J. Fuji@ N. Inabe, and T. Kubo for their work in constructing the polarized ion source. References [l] C. Ellegaard et al., Phys. Rev. Lett. 59 (1987) 974; Phys. Lett. B 231 (1989) 365. [2] H. Ohnuma et al., Phys. Rev. C 47 ( 1993) 648. [3] D.V. Bugg and C. Wilkin, Nucl. Phys. A 467 (1987) 575; C. Wiiin and D.V. Bugg, Phys. Lett. B 154 ( 1985) 243. [4] F. Osterfeld, Rev. Mod. Phys. 64 ( 1992) 491, and references therein. [5] H. Okamura et al., AIP Conf. Proc. 293 ( 1994) 84. [6] H. Okamura et al., Nucl. Phys. A 577 ( 1994) 89~. [7] T. lchihara et al., Nucl. Phys. A 569 (1994) 287~. [ 81 W.A. Sterrenburg, M.N. Harakeh, S.Y. van der Wed and A. van der Woude, Nucl. Phys. A 405 (1983) 109. [9] K.J. Raywood et al., Phys. Rev. C 41 (1990) 2836. [ 101 S. Kox et al., Nucl. Phys. A 556 ( 1993) 621. [ 11) G. Baur and D. Trautmann, Phys. Rep. 25 (1976) 293. [ 121 M. Lacombe et al., Phys. Lett. B 101 (1981) 139. [13] R.V. Reid, Jr., Ann. Phys. (N.Y.) 50 (1968) 411. [ 141 M. Igarashi, program TWOFNR, unpublished. [ 151 M.A. Franey and WC. Love, Phys. Rev. C 31 (1985) 488. [16] M. Golin, E Petrovich and D. Robson, Phys. Lett. B 64 (1976) 253. [ 171 S. Cohen and D. Kurath, Nucl. Phys. 73 (1965) 1. [ 181 D.J. Millener and D. Kurath, Nucl. Phys. A 255 ( 1975) 3 15. [ 191 T. Uesaka et al., RIKEN Accel. Prog. Rep. 27 (1993) 40. [20] J. Rapaport et al., Phys. Rev. C 24 ( 1981) 335. [21] C. Garde et al., Nucl. Phys. A 422 (1984) 189. 1221 X. Yang et al., Phys. Rev. C 48 (1993) 1158. [23] N. Austem, Phys. Rev. C 30 (1984) 1130. [24] M. Yahiro, J.A. Tostevin and R.C. Johnson, Phys. Rev. Lett. 62 (1989) 133. [25] M. Simonius, in: Polarization Nuclear Physics, edited by D. Fick, Lecture Notes in Physics Vol. 30 (Springer, 1974).