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Deuteron D-state effects on the vector polarization observables in (d, p) reactions at 55.4 MeV
Volume
127B, number
PHYSICS
6
LETTERS
DEUTERON D-STATE EFFECTS ON THE VECTOR POLARIZATION
11 August
1983
OBSERVABLES
IN (d, p) REACTIONS AT 55.4 MeV T. KUBO Institute ofphysical
and Chemical Research (RIKEN),
Hirosaw,
Wako-shi, Saitama 351, Japan
H. OHNUMA, T. KISHIMOTO, M.A. BRENNAN, Y. YOSHIDA Department
ofphysics,
Tokyo Institute of Technology,
Oh-okayama, Meguro, Tokyo, Japan
M .SUGITANI Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo, Japan
and T. SUEHIRO Department Received
of Physics, Tohoku Institute of Technology,
Nagamachi, Sendai, Japan
19 April 1983
The vector analyzing power Ay and polarization Py have been measured for the In = 0 transitions ’ I6 Sn(d, p)’ ’ 7Sn(gs) Sn(gs) at Ed = 55.4 MeV to obtain the quantities Sp = 2py - Uy and Sd = 3Ay - 2Py. The deuteron and 117Sn(d,p)“8 D-state effects which are clearly observed for Sd are found to arise prlm~ily from contributions quadratic in the D-state amplitude.
Since the early papers by Johnson and Santos [l] and Delic and Robson [2], the effects of the deuteron D-state on direct (d, p) and (p, d) reactions have been the subject of many experimental and theoretical studies. The D-state has been shown to play an important role in determining reaction observables at very high incident energies [3], where large momentum transfers are involved. At low incident energies, although the D-state has only small effects on differential cross sections, it has been also shown to be important to describe tensor polarization observables such as tensor analyzing powers [4], polarization transfer coefficients [S] and the polarization of the residual state [6]. Recently Cadmus and Haeberli [7] and Ohnuma et al. [S] first observed large D-state effects on vector polarization observables in the reaction l16Sn(d, p)l17Sn(gs, l/2+ at Ed = 8.22 and 22 MeV, respectively. They measured the vector analyzing 0 03 l-9163/83/OOOO-0000/S
03.00 0 1983 North-Holland
powerAy and the proton polarization P,, to obtain the quantities S =2P,, -2A,andSd=3Ay -pY. Their analyses sRow that the fit to sd is considerably improved by the inclusion of the D-state. The quantities Sp and sd were first introduced for En = 0 (d, p) transitions by Johnson [9] to approximately separate the spin-orbit distortion effects in proton and deuteron channels from each other in the absence of the D-state. The modifications due to the inclusion of the D&ate were also made by Johnson [ 10,7], and are given as follows S, = $P(p, SS) - 2P(p, SD) + P(DD),
& =P(d,ss)+ ~P(~,sD)+P(~,sD)
-:P(DD).
(1)
Here the notation is the same as in refs. [7,10], Without the D-state, only the first terms remain in the expressions (I), and then the separation of the spinorbit distortion effects is achieved. 403
Volume
127B, number
6
PHYSICS
Cadmus and Haeberli [7 ] showed that the large Dstate effects observed at Ed = 8.22 MeV, arose primarily from the terms P(DD) and -iP(DD) in the expressions (1). These two terms are quadratic in the Dstate amplitude and independent of the spin-orbit distortions in the two channels. We further analyzed the 22 MeV data, and also found that such quadratic D-state terms had large magnitude. These results are surprising because of the importance of the spin-orbit distortions, especially that of the proton channel, to reproduce the observed A, and Pv [8] . It is important to test the general validity of these results at higher energies, where the D-state effects are known to be more significant. In the present work we have measured the differential cross sections du/dQ and the vector analyzing powers A, for the I,, = 0 reactions I16Sn(d, p)l17Sn(gs, l/2+) and 117Sn(d,p)118Sn(gs, O+) at Ed = 55.4 MeV. The polarization of outgoing protons Pv has been measured indirectly through the measurements of the analysing powers for the inverse (p, d) reactions at E = 60.8 MeV. The quantities S, and S, have been caPculated from the measured A, and Py . The results obtained have been compared with the exact-finite-range (EFR)-distorted-wave Born approximation (DWBA) calculations with and without the deuteron D-state. The measurements were made using vector-polarized deuteron and proton beams from the AVF cyclotron at the Research Center for Nuclear Physics (RCNP), Osaka University. The beam intensity was typically 60 nA on target, The beam polarization, monitored by using a carbon polarimeter, amounted to about 45% for deuterons and 80% for protons. The targets used were self-supporting foils of enriched isotopes. Scattered particles were analyzed by the magnetic spectrometer RAIDEN [l l] and detected in a focal plane counter system [ 121. Experimental results are shown in figs. 1,2 together with calculations. The results of do/dR,A, and Py for the reaction 1 1 7 Sn(d, p) 1 18 Sn are similar to those for the reaction 1 l6 Sn(d, p)l 1 7Sn. The calculation was performed using the code DWUCKS [ 131. The proton distorting potential parameters are those which reproduce the cross section for elastic scattering of 61.4 MeV protons on ’ 16Sn [lh]. The deuteron parameters are those of an adiabatic potential [15] constructed from the neutron 404
LETTERS
11 August
“% Y
t
0”
30”
/
0” 6c.m.
I
/
30”
1983
1 60”
Fig. 1. Cross section, analyzing power and polarization for the r ’ 6Sn(d, p)’ r 7Sn(gs, l/2+) transition at Ed = 55.4 MeV compared with the EFR-DWBA calculations with (solid line) and without (dashed line) the D-state effects.
0”
30”
0” 8 c.m.
30”
60”
Fig. 2. Experimentally determined Sp and Sd for the r ’ 6Sn(d, p) r 1 7 Sn (left) and ” 7Sn(d, p)’ ’ * Sn (right) transitions compared with the EFR-DWBA calculations. See caption for fig. 1.
PHYSICS LETTERS
Volume 127B, number 6
of Becchetti and Greenlees [I 61. The Reid soft-core potential [ 171 was used for the n-p interaction to describe the transfer of a neutron and to generate the deuteron internal wave function. Solid and dashed lines in figs. 1,2 show the calculations with and without the D-state, respectively. The cross sections are well reproduced and found not much affected by the inclusion of the D&ate. The analyzing powers A, and the polarizations Pu are also well reproduced except at small angles where the calculated curves are slightly shifted forward. The inclusion of the D-state decreases the oscillation amplitude of calculated A, and Pv , in better agreement with the data. The results for S, clearly show the importance of the D-state effects. The fit to S, is considerably improved by the inclusion of the D-state. The experimental S, values are negative and large at most angles, while the calculations without the Dstate give only small S, . The results for S, also show the importance of the D&ate effects, although they are not as clear as for Sd. Each term in the expressions (1) has been calculated to see if the large D-state effects arise primarily from the quadratic D&ate terms also at this energy. Fig. 3 shows the results for the reaction l16Sn(d, p)ll7Sn. The quadratic D-state terms, P(DD) and -:P(DD), were calculated by switching and proton
potentials
11 August 1983
off the spin-orbit potentials in both channels, and the quadratic S-state terms, $P(p, SS) and P(d, SS), by omitting the D&ate. The linear D&ate terms, -2P(p, SD) and 3P(p, SD) + P(d, SD), are those remaining after the subtraction of the above two terms from the calculations in which all the contributions are included. Fig. 3 shows that the quadratic D-state terms in both S, and sd are the largest of all, indicating that the D-state effects primarily arise from such terms in agreement with the results at lower energies. The quadratic S-state terms represent the spinorbit distortion effects. This term in S, is much larger than that in sd, showing that the spin-orbit distortion effects arise primarily from the proton channel. The quadratic S-state term in S, gives a partial account of S, , while this term in sd plays a minor role (see fig. 2). The spin-orbit distortion effects are mostly removed in sd. Thus the D-state effects are more clearly seen in Sd than in S,. The linear D-state terms, although they tend to cancel the quadratic Dstate terms, are small. The D-state effects for A, and Pv are not as large as those for Sp and Sd . The reason for this can be understood from the expressions for A, and Py : A, = $P(p, SS) + P(d, SS) + P(p, SD) + P(d, SD) - :P(DD) , Py = P(p, SS) + P(d, SS) f P(d, SD) + $P(DD) .
0
C -I
0”
30”
0”
3o”
60’
0c.m. Fig. 3. Contributions of separate terms in the expressions (1) and (2) for the reaction 116Sn(d,p)’ 1 ‘Sn (see text).
(2)
It is immediately found that the quadratic D-state terms in A, and Pv are four or five times smaller than those in S, and Sd . The calculations of each term in the expressions (2) are also shown in fig. 3 _ The P(p, SS) terms are dominant in both A, and Pr. Thus A, and Py are mainly determined by the spinorbit distortion effects in the proton channel. In summary, both A, and Py have been measured for the I,, = 0 transitions l16Sn(d, p)l17Sn(gs, l/2+) and 1 17Sn(d, p) ’ 18Sn(gs, 0’) at Ed = 55.4 MeV in the present work. The vector polarization observables s, and sd have been obtained from the measured A, and Py. The large D-state effects have been clearly observed for sd and to a lesser degree for S,. The D-state effects are found to arise primarily from contributions which are quadratic in the D-state amplitude. On the other hand, A, and P,, are mainly determined by the spin-orbit distortion effects. 40.5
Volume
127B. number
6
PHYSICS
This experiment was performed at RCNP, Osaka University; under Program Numbers 12A07 and 13A17. The authors thank the members of RCNP for their hospitality and help throughout the experiment. Special thanks are to Professor K. Nishimura, Dr. K. Imai and Dr. H. Shimizu for the production of polarized beams, to Dr. K. Hatanaka and the cyclotron crew for the operation of polarized ion source and cyclotron, and to Professor H. Ikegami, Professor K. Hosono, Professor S. Morinobu, Dr. M. Fujiwara and Dr. Y. Fujita for their help in the use of RAIDEN and its data taking system. References [l]
R.C. Johnson and FD. Santos, Phys. Rev. Lett. 19 (1967) 364. [2] G. Delic and B.A. Robson, Nucl. Phys. Al56 (1970)
406
97.
LETTERS
11 August
1983
[3] E. Rost and J.R. Shepard, Phys. Lett. 59B (1975) 413. [4] L.D. Knutson, E.J. Stephenson, N. Rohrig and W. Haeberli, Phys. Rev. Lett. 31 (1973) 392; R.C. Johnson et al., Nucl. Phys. A208 (1973) 221. [5] A.K. Bask et al., Nucl. Phys. A275 (1977) 381. [6] H. Ohnuma et al, Phys. Rev. Lett. 46 (1981) 310. [7] R.R. Cadmus and W. Haeberli, Nucl. Phys. A349 (1980) 103. [S] H, Ohnuma et al., Phys. Lett. 97B (1980) 192. [9] R.C. Johnson, Nucl. Phys. 35 (1962) 654. [lo] R.C. Johnson, Nucl. Phys. A90 (1967) 289. [ 1l] H. Ikegami et al., Nucl. Instrum. Methods 175 (1980) 335. [12] Y. Fujitaet al., Nucl. Instrum. Methods 173 (1980) 265. [13] P.D. Kunz, unpublished. [ 141 G.B. Fulmer, J.B. Ball, A. Scott and M.L. Whiten, Phys. Rev. 181 (1969) 1565. [15] JD. Harvey and R.C. Johnson, Phys. Rev. C3 (1971) 636. [ 161 F.D. Becchetti and G.W. Greenlees, Phys. Rev. 182 (1969) 1190. [17] R.V. Reid, Ann. Phys. (NY) 50 (1968) 411.
127B, number
PHYSICS
6
LETTERS
DEUTERON D-STATE EFFECTS ON THE VECTOR POLARIZATION
11 August
1983
OBSERVABLES
IN (d, p) REACTIONS AT 55.4 MeV T. KUBO Institute ofphysical
and Chemical Research (RIKEN),
Hirosaw,
Wako-shi, Saitama 351, Japan
H. OHNUMA, T. KISHIMOTO, M.A. BRENNAN, Y. YOSHIDA Department
ofphysics,
Tokyo Institute of Technology,
Oh-okayama, Meguro, Tokyo, Japan
M .SUGITANI Institute for Nuclear Study, University of Tokyo, Tanashi, Tokyo, Japan
and T. SUEHIRO Department Received
of Physics, Tohoku Institute of Technology,
Nagamachi, Sendai, Japan
19 April 1983
The vector analyzing power Ay and polarization Py have been measured for the In = 0 transitions ’ I6 Sn(d, p)’ ’ 7Sn(gs) Sn(gs) at Ed = 55.4 MeV to obtain the quantities Sp = 2py - Uy and Sd = 3Ay - 2Py. The deuteron and 117Sn(d,p)“8 D-state effects which are clearly observed for Sd are found to arise prlm~ily from contributions quadratic in the D-state amplitude.
Since the early papers by Johnson and Santos [l] and Delic and Robson [2], the effects of the deuteron D-state on direct (d, p) and (p, d) reactions have been the subject of many experimental and theoretical studies. The D-state has been shown to play an important role in determining reaction observables at very high incident energies [3], where large momentum transfers are involved. At low incident energies, although the D-state has only small effects on differential cross sections, it has been also shown to be important to describe tensor polarization observables such as tensor analyzing powers [4], polarization transfer coefficients [S] and the polarization of the residual state [6]. Recently Cadmus and Haeberli [7] and Ohnuma et al. [S] first observed large D-state effects on vector polarization observables in the reaction l16Sn(d, p)l17Sn(gs, l/2+ at Ed = 8.22 and 22 MeV, respectively. They measured the vector analyzing 0 03 l-9163/83/OOOO-0000/S
03.00 0 1983 North-Holland
powerAy and the proton polarization P,, to obtain the quantities S =2P,, -2A,andSd=3Ay -pY. Their analyses sRow that the fit to sd is considerably improved by the inclusion of the D-state. The quantities Sp and sd were first introduced for En = 0 (d, p) transitions by Johnson [9] to approximately separate the spin-orbit distortion effects in proton and deuteron channels from each other in the absence of the D-state. The modifications due to the inclusion of the D&ate were also made by Johnson [ 10,7], and are given as follows S, = $P(p, SS) - 2P(p, SD) + P(DD),
& =P(d,ss)+ ~P(~,sD)+P(~,sD)
-:P(DD).
(1)
Here the notation is the same as in refs. [7,10], Without the D-state, only the first terms remain in the expressions (I), and then the separation of the spinorbit distortion effects is achieved. 403
Volume
127B, number
6
PHYSICS
Cadmus and Haeberli [7 ] showed that the large Dstate effects observed at Ed = 8.22 MeV, arose primarily from the terms P(DD) and -iP(DD) in the expressions (1). These two terms are quadratic in the Dstate amplitude and independent of the spin-orbit distortions in the two channels. We further analyzed the 22 MeV data, and also found that such quadratic D-state terms had large magnitude. These results are surprising because of the importance of the spin-orbit distortions, especially that of the proton channel, to reproduce the observed A, and Pv [8] . It is important to test the general validity of these results at higher energies, where the D-state effects are known to be more significant. In the present work we have measured the differential cross sections du/dQ and the vector analyzing powers A, for the I,, = 0 reactions I16Sn(d, p)l17Sn(gs, l/2+) and 117Sn(d,p)118Sn(gs, O+) at Ed = 55.4 MeV. The polarization of outgoing protons Pv has been measured indirectly through the measurements of the analysing powers for the inverse (p, d) reactions at E = 60.8 MeV. The quantities S, and S, have been caPculated from the measured A, and Py . The results obtained have been compared with the exact-finite-range (EFR)-distorted-wave Born approximation (DWBA) calculations with and without the deuteron D-state. The measurements were made using vector-polarized deuteron and proton beams from the AVF cyclotron at the Research Center for Nuclear Physics (RCNP), Osaka University. The beam intensity was typically 60 nA on target, The beam polarization, monitored by using a carbon polarimeter, amounted to about 45% for deuterons and 80% for protons. The targets used were self-supporting foils of enriched isotopes. Scattered particles were analyzed by the magnetic spectrometer RAIDEN [l l] and detected in a focal plane counter system [ 121. Experimental results are shown in figs. 1,2 together with calculations. The results of do/dR,A, and Py for the reaction 1 1 7 Sn(d, p) 1 18 Sn are similar to those for the reaction 1 l6 Sn(d, p)l 1 7Sn. The calculation was performed using the code DWUCKS [ 131. The proton distorting potential parameters are those which reproduce the cross section for elastic scattering of 61.4 MeV protons on ’ 16Sn [lh]. The deuteron parameters are those of an adiabatic potential [15] constructed from the neutron 404
LETTERS
11 August
“% Y
t
0”
30”
/
0” 6c.m.
I
/
30”
1983
1 60”
Fig. 1. Cross section, analyzing power and polarization for the r ’ 6Sn(d, p)’ r 7Sn(gs, l/2+) transition at Ed = 55.4 MeV compared with the EFR-DWBA calculations with (solid line) and without (dashed line) the D-state effects.
0”
30”
0” 8 c.m.
30”
60”
Fig. 2. Experimentally determined Sp and Sd for the r ’ 6Sn(d, p) r 1 7 Sn (left) and ” 7Sn(d, p)’ ’ * Sn (right) transitions compared with the EFR-DWBA calculations. See caption for fig. 1.
PHYSICS LETTERS
Volume 127B, number 6
of Becchetti and Greenlees [I 61. The Reid soft-core potential [ 171 was used for the n-p interaction to describe the transfer of a neutron and to generate the deuteron internal wave function. Solid and dashed lines in figs. 1,2 show the calculations with and without the D-state, respectively. The cross sections are well reproduced and found not much affected by the inclusion of the D&ate. The analyzing powers A, and the polarizations Pu are also well reproduced except at small angles where the calculated curves are slightly shifted forward. The inclusion of the D-state decreases the oscillation amplitude of calculated A, and Pv , in better agreement with the data. The results for S, clearly show the importance of the D-state effects. The fit to S, is considerably improved by the inclusion of the D-state. The experimental S, values are negative and large at most angles, while the calculations without the Dstate give only small S, . The results for S, also show the importance of the D&ate effects, although they are not as clear as for Sd. Each term in the expressions (1) has been calculated to see if the large D-state effects arise primarily from the quadratic D&ate terms also at this energy. Fig. 3 shows the results for the reaction l16Sn(d, p)ll7Sn. The quadratic D-state terms, P(DD) and -:P(DD), were calculated by switching and proton
potentials
11 August 1983
off the spin-orbit potentials in both channels, and the quadratic S-state terms, $P(p, SS) and P(d, SS), by omitting the D&ate. The linear D&ate terms, -2P(p, SD) and 3P(p, SD) + P(d, SD), are those remaining after the subtraction of the above two terms from the calculations in which all the contributions are included. Fig. 3 shows that the quadratic D-state terms in both S, and sd are the largest of all, indicating that the D-state effects primarily arise from such terms in agreement with the results at lower energies. The quadratic S-state terms represent the spinorbit distortion effects. This term in S, is much larger than that in sd, showing that the spin-orbit distortion effects arise primarily from the proton channel. The quadratic S-state term in S, gives a partial account of S, , while this term in sd plays a minor role (see fig. 2). The spin-orbit distortion effects are mostly removed in sd. Thus the D-state effects are more clearly seen in Sd than in S,. The linear D-state terms, although they tend to cancel the quadratic Dstate terms, are small. The D-state effects for A, and Pv are not as large as those for Sp and Sd . The reason for this can be understood from the expressions for A, and Py : A, = $P(p, SS) + P(d, SS) + P(p, SD) + P(d, SD) - :P(DD) , Py = P(p, SS) + P(d, SS) f P(d, SD) + $P(DD) .
0
C -I
0”
30”
0”
3o”
60’
0c.m. Fig. 3. Contributions of separate terms in the expressions (1) and (2) for the reaction 116Sn(d,p)’ 1 ‘Sn (see text).
(2)
It is immediately found that the quadratic D-state terms in A, and Pv are four or five times smaller than those in S, and Sd . The calculations of each term in the expressions (2) are also shown in fig. 3 _ The P(p, SS) terms are dominant in both A, and Pr. Thus A, and Py are mainly determined by the spinorbit distortion effects in the proton channel. In summary, both A, and Py have been measured for the I,, = 0 transitions l16Sn(d, p)l17Sn(gs, l/2+) and 1 17Sn(d, p) ’ 18Sn(gs, 0’) at Ed = 55.4 MeV in the present work. The vector polarization observables s, and sd have been obtained from the measured A, and Py. The large D-state effects have been clearly observed for sd and to a lesser degree for S,. The D-state effects are found to arise primarily from contributions which are quadratic in the D-state amplitude. On the other hand, A, and P,, are mainly determined by the spin-orbit distortion effects. 40.5
Volume
127B. number
6
PHYSICS
This experiment was performed at RCNP, Osaka University; under Program Numbers 12A07 and 13A17. The authors thank the members of RCNP for their hospitality and help throughout the experiment. Special thanks are to Professor K. Nishimura, Dr. K. Imai and Dr. H. Shimizu for the production of polarized beams, to Dr. K. Hatanaka and the cyclotron crew for the operation of polarized ion source and cyclotron, and to Professor H. Ikegami, Professor K. Hosono, Professor S. Morinobu, Dr. M. Fujiwara and Dr. Y. Fujita for their help in the use of RAIDEN and its data taking system. References [l]
R.C. Johnson and FD. Santos, Phys. Rev. Lett. 19 (1967) 364. [2] G. Delic and B.A. Robson, Nucl. Phys. Al56 (1970)
406
97.
LETTERS
11 August
1983
[3] E. Rost and J.R. Shepard, Phys. Lett. 59B (1975) 413. [4] L.D. Knutson, E.J. Stephenson, N. Rohrig and W. Haeberli, Phys. Rev. Lett. 31 (1973) 392; R.C. Johnson et al., Nucl. Phys. A208 (1973) 221. [5] A.K. Bask et al., Nucl. Phys. A275 (1977) 381. [6] H. Ohnuma et al, Phys. Rev. Lett. 46 (1981) 310. [7] R.R. Cadmus and W. Haeberli, Nucl. Phys. A349 (1980) 103. [S] H, Ohnuma et al., Phys. Lett. 97B (1980) 192. [9] R.C. Johnson, Nucl. Phys. 35 (1962) 654. [lo] R.C. Johnson, Nucl. Phys. A90 (1967) 289. [ 1l] H. Ikegami et al., Nucl. Instrum. Methods 175 (1980) 335. [12] Y. Fujitaet al., Nucl. Instrum. Methods 173 (1980) 265. [13] P.D. Kunz, unpublished. [ 141 G.B. Fulmer, J.B. Ball, A. Scott and M.L. Whiten, Phys. Rev. 181 (1969) 1565. [15] JD. Harvey and R.C. Johnson, Phys. Rev. C3 (1971) 636. [ 161 F.D. Becchetti and G.W. Greenlees, Phys. Rev. 182 (1969) 1190. [17] R.V. Reid, Ann. Phys. (NY) 50 (1968) 411.