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Evidence for pion exchange currents in the analysis of the 4He (p, d)3He reaction at intermediate energies
Volume 89B, number 1
PHYSICS LETTERS
31 December 1979
EVIDENCE FOR PION EXCHANGE CURRENTS IN THE ANALYSIS OF THE 4He (p, d) 3He REACTION AT INTERMEDIATE ENERGIES J.R. SHEPARD, E. ROST and G .R. SMITH
Nuclear Physics Laboratory 1, University of Colorado, Boulder, CO 80309, USA Received 27 September 1979 Revised manuscript received 22 October 1979
Previous unsuccessful analyses of 4He (p, d)aHe at intermediate energies have employed densities based directly on the measured e- + 4He elastic scattering. When the effects of pion exchange currents are removed, the resulting DWBAanalysis is in qualitative agreement with the experimental data.
In an earlier paper [1], the 4He (p,d) 3He data [2] at Tp = 770 MeV were analyzed using the exact-finiterange, distorted-wave Born approximation. It was found that the calculations failed to describe the data in that they gave an unobserved minimum in the angular distribution and exceeded the data by a factor of ~ 2.5 at larger angles. In addition, the calculations could not describe the energy dependence by comparison to the Tp = 434 MeV data [3]. It was suggested in ref. [1 ] that pion emission and reabsorption processes [4] might be important; however, it was difficult to understand how these would cancel the simple nucleon transfer process so as to reduce the larger angle predictions. A key element in the earlier analysis was the bound state n-3He wavefunction which was generated from the charge density in 4He. This density was obtained from the electron scattering charge form factor taken directly from the experimental data [5]: Fc(q2) = [(do/d~2)/(do/d~)point ] 1/2.
(1)
This form factor exhibits a deep minimum near q2 = 10 fm -2 and the resulting n-3He momentum space wavefunction has a corresponding minimum at q ~- 2.2 fm -1. The 4He(p, d)3He DWBA cross section at Tp = 770 MeV (and to a lesser extent at Tp = 434 MeV) is sensitive to this part of the n-3He wavefunction. 1 Work supported in part by the U.S. Department of Energy.
In recent years several calculations of pion-exchange-current contributions to elastic electron scattering on 4He have been performed. Although some differences in detail exist between the different calculational procedures they all predict the same qualitative effects near the first minimum of Fc(q 2) where the meson exchange mechanisms contribute so as to shift the minimum ofFc(q2 ) to lower q2 and greatly increase the second maximum (fig. 1). Thus in constructing a true 4He nucleon density from electron scattering data we should subtract the pion exchange contributions from the charge form factor. Instead we adopted the simpler procedure of fitting the model calculation of Gari et al. [6] which used a Reid soft core potential [8] (other two-body potential models gave essentially identical results). The model calculation is reasonably fitted with a functional form [5] Fc(q2) = [ 1 - (a2q2) N] exp(-/~2q2),
(2)
with a = 0.280, ~ = 0.681 a n d N = 6. This is to be com. pared with the fit to the experimental data [5] with = 0.316 also shown in fig. 1. The calculation of the n-3He wavefunction from the charge form factor proceeds as in ref. [1]. First the matter density in 4He is obtained from a Fourier transform of Fc, correcting for the proton finite size. Next the interior part of the n-3He wavefunction is extraqted by a simple coordinate transformation as13
Volume 89B, number 1
PHYSICS LETTERS
1.0
lated to the empirical p + 4 H e potential by two similar scaling procedures. The existence of new p + 3He elastic scattering data for Tp = 415 MeV [10] allows a somewhat more direct procedure. We take the T d 800 MeV deuteron potential to be the phenomenological potential obtained from fitting the 415 MeV p+3He data with the depths doubled. For the analysis of the Tp = 434 MeV 4He (p, d) 3He reaction we chose to scale the 770 MeV potential depths using the KMT [ 11 ] multiple scattering theory and n u c l e o n nucleon data [12] to obtain the relative complex well depths. Comparison of the DWBA calculations with the data at Tp = 770 MeV is shown in fig. 2. It is seen that the cross sections with the meson exchange term removed are smaller and that the minimum at 0 ~ 150 has disappeared. The calculations at forward angles are below the data by a factor 2 - 3 . It is possible that this discrepancy could be accounted for by including
e- + 4He
OI
I Fc o. ol
o.ool
I
i
2
I
_
I
4
i
31 December 1979
I
6
•
(a)
q(fm-') Fig. 1. Charge form factors for 4He. The solid points represent the measured elastic e-+ 4He scattering data [5], and the dotted line through these points is the fit of eq. (2). The open circles and solid line represent the meson-exchange subtracted pseudodata (ref. [6] ) and resulting fit. suming a (ls) 4 configuration. Finally the exterior wavefunction is obtained by matching the correct asymptotic form at the point (r ~ 3.5 fm) where the logarithmic derivatives are the same. The most striking effect of using the meson-exchange corrected version o f F c is observed in the momentum space n-3He wavefunction where the magnitude of the second maximum is greatly reduced as a direct consequence of a similar reduction in F c as shown in fig. 1. Distortions of the p-4He system at 770 MeV were obtained from an optical model search to the 720 MeV elastic scattering data of Verbeck et al. [9]. A noteworthy feature of the resulting potential is the small diffusivity (a <~ 0.3 fm) required. This result was checked using data [10] at 1050 MeV and a very similar potential with small diffusivity was also found. The lack of deuteron elastic scattering data in this energy region hampers determination of a deuteron distorting potential. In ref. [1 ], this potential was re14
'~°'~'~"
'4He (P'd')~He '1
i.o
I \',?'.,,? ~L
io
(b) I00
r~
=L
7~\ ' - l~,~
20
30
"He (p,d):He T p = 4 5 4 MeV"
I0
i
i
i
20
40
60
~.
8c.m.(degrees)
Fig. 2. (a) The Tp = 770 MeV 4He (p, d) 3He data is compared to exact finite-range DWBA predictions with (solid
line) and without (dashed line) the corrections due to meson exchange; (b) the same comparison is made to the Tp = 434 MeV 4He (p, d) 3He data.
Volume 89B, number 1
PHYSICS LETTERS
more terms (e.g. pion emission and reabsorption [4] ) than the simple one-nucleon pickup term. Calculations are also compared with the Tp = 434 MeV data in fig. 2. Once again the unsatisfactory large angle behavior observed using an uncorrected Fc(q) disappears when a meson-exchange-corrected Fc(q) is used. The effect in calculations compared with the Tp = 156 MeV data of Bernas et al. [13] is small since at this energy the reaction does not sample sensitively the bound state wavefunction at momenta o f q ~ > 2 fm -1. Cross sections for 4He(p, d) 3He at 01ab = 22.50 (0cm ~ 340) have been measured by K~/llne et al. [14] for 200 < Tp < 500 MeV. This (p, d) excitation function is shown in fig. 3 and compared to distorted wave calculations using meson-exchange corrected and uncorrected n- 3He wavefunctions. The distorting poten-
4He(p,d)3He 10 3
"-C t~ .c~
0
10 2
o
Cuj MCM
"XNN\
[0 I
\\
b~ ,~h~
%o
i0°
I
0
I
200
I
I
I
400
I
600
I
I
800
Tp(MeV)
Fig. 3. The excitation function at 01ab = 22.50 for the 4He (p, d) 3He data is compared to the predictions of the exact finite-range DWBAwith (solid line) and without (dashed line) the corrections due to meson exchange. Data from refs. [2, 3,13] (open circles) are included with the data of ref. [14] (solid points).
31 December 1979
tials were determined by using the same depth scaling procedure as for the Tp = 434 MeV calculation. Once again, the results using the corrected F c (q) are superior to those using the uncorrected one. Specifically, the dashed curve in fig. 3 shows a large enhancement of the cross section at Tp ~, 600 MeV which is directly attributable to the large secondary maximum in the uncorrected F c (q). Only with the reduced secondary maximum in the corrected F c (q) is qualitative agreement with data achieved. In summary, the 4He(p, d)3He reaction at Tp = 434 and 770 MeV is qualitatively understandable in a onenucleon transfer model using quasi-phenomenological distortions obtained from proton elastic scattering experiments. The crucial difference from the earlier failure [ 1] is the construction of the n-3 He wave function from electron scattering data with pion-exchange effects subtracted from the measured charge form factors so as to give a "true" nucleon density. Other mechanisms such as pion emission and reabsorption [4] may be needed for quantitative agreement with experiment and such calculations are underway [15]. These calculations also involve an n-3He vertex which should be constructed from the "true" density as well. Regardless of the reaction mechanism considered, effects of distortion are crucial [1] and must be included. Direct measurement of d + 3He (or d + t) elastic scattering cross sections at the appropriate energies would help to eliminate some of the uncertainty in describing the deuteron distortion. Polarization or analyzing power measurements for the 4He(p, d) reaction in the energy range 200 < Tp < 800 MeV might be useful in untangling effects due to distortion from those due to reaction modes other than the one-nucleon process treated here. It would also be interesting to apply the present technique to the (p, d) reaction on other light nuclei. However, the present case might be optimal for seeing the effect of meson-exchange processes. This is because (1) these processes are particularly important for electron scattering on 4He, compared, for example, to 160 [6] and (2) the relation between the single particle wavefunction and the nuclear structure is especially simple for 4He. In any case, the present work has demonstrated that the intermediate energy (p, d) reaction can be used to explore meson exchange effects.
15
Volume 89B, number 1
PHYSICS LETTERS
References [1] E. Rost, J.R. Shepard and D.A. Sparrow, Phys. Rev. C17 (1978) 1513. [2] T. Bauer et al., Phys. Lett. 67B (1977) 265. [3] J. Berger et al., Lett. Nuovo Cimento 19 (1977) 287. [4] N.S. Craigie and C. Wilkin, NucL Phys. B14 (1969) 477, [5] R.L. Frosch et al., Phys. Rev. 160 (1967) 874; R.G. Arnold et al., Phys. Rev. L~tt. 40 (1978) 1429. [6] M. Gari, H. Hyuga and Z.G. Zabolitzky, Nucl. Phys. A271 (1976) 365. [7] M. Radomski and D.O. Riska, Nuel. Phys. A274 (1976) 428.
16
31 December 1979
[8] R.V. Roid, Ann. Phys. 50 (1968) 411. [9] S.L. Verbeck et al., Phys. Lett. 59B (1975) 339. [10] G. Bruge, Saclay internal report DPh-N/ME/78-1, unpublished. [11 ] A.K. Kerman, H. McManusand R.M. Thaler, Ann. Phys. 8 (1959) 551; H. Feshbach, A. Gal and J. Hiifner, Ann. Phys. 66 (1971) 20. [12| R.A. Arndt, R.H. Hackman and L.D. Roper, Phys. Rev. C!5 (1977) 1002 and 1o~ tit. [13] M, Bernas et aL, Nucl. Phys. A156 (1970) 289. [14] J. K/illne et al., Phys. Rev. Lett. 41 (1978) 1638. [15] W.S. Pong, private communication.
PHYSICS LETTERS
31 December 1979
EVIDENCE FOR PION EXCHANGE CURRENTS IN THE ANALYSIS OF THE 4He (p, d) 3He REACTION AT INTERMEDIATE ENERGIES J.R. SHEPARD, E. ROST and G .R. SMITH
Nuclear Physics Laboratory 1, University of Colorado, Boulder, CO 80309, USA Received 27 September 1979 Revised manuscript received 22 October 1979
Previous unsuccessful analyses of 4He (p, d)aHe at intermediate energies have employed densities based directly on the measured e- + 4He elastic scattering. When the effects of pion exchange currents are removed, the resulting DWBAanalysis is in qualitative agreement with the experimental data.
In an earlier paper [1], the 4He (p,d) 3He data [2] at Tp = 770 MeV were analyzed using the exact-finiterange, distorted-wave Born approximation. It was found that the calculations failed to describe the data in that they gave an unobserved minimum in the angular distribution and exceeded the data by a factor of ~ 2.5 at larger angles. In addition, the calculations could not describe the energy dependence by comparison to the Tp = 434 MeV data [3]. It was suggested in ref. [1 ] that pion emission and reabsorption processes [4] might be important; however, it was difficult to understand how these would cancel the simple nucleon transfer process so as to reduce the larger angle predictions. A key element in the earlier analysis was the bound state n-3He wavefunction which was generated from the charge density in 4He. This density was obtained from the electron scattering charge form factor taken directly from the experimental data [5]: Fc(q2) = [(do/d~2)/(do/d~)point ] 1/2.
(1)
This form factor exhibits a deep minimum near q2 = 10 fm -2 and the resulting n-3He momentum space wavefunction has a corresponding minimum at q ~- 2.2 fm -1. The 4He(p, d)3He DWBA cross section at Tp = 770 MeV (and to a lesser extent at Tp = 434 MeV) is sensitive to this part of the n-3He wavefunction. 1 Work supported in part by the U.S. Department of Energy.
In recent years several calculations of pion-exchange-current contributions to elastic electron scattering on 4He have been performed. Although some differences in detail exist between the different calculational procedures they all predict the same qualitative effects near the first minimum of Fc(q 2) where the meson exchange mechanisms contribute so as to shift the minimum ofFc(q2 ) to lower q2 and greatly increase the second maximum (fig. 1). Thus in constructing a true 4He nucleon density from electron scattering data we should subtract the pion exchange contributions from the charge form factor. Instead we adopted the simpler procedure of fitting the model calculation of Gari et al. [6] which used a Reid soft core potential [8] (other two-body potential models gave essentially identical results). The model calculation is reasonably fitted with a functional form [5] Fc(q2) = [ 1 - (a2q2) N] exp(-/~2q2),
(2)
with a = 0.280, ~ = 0.681 a n d N = 6. This is to be com. pared with the fit to the experimental data [5] with = 0.316 also shown in fig. 1. The calculation of the n-3He wavefunction from the charge form factor proceeds as in ref. [1]. First the matter density in 4He is obtained from a Fourier transform of Fc, correcting for the proton finite size. Next the interior part of the n-3He wavefunction is extraqted by a simple coordinate transformation as13
Volume 89B, number 1
PHYSICS LETTERS
1.0
lated to the empirical p + 4 H e potential by two similar scaling procedures. The existence of new p + 3He elastic scattering data for Tp = 415 MeV [10] allows a somewhat more direct procedure. We take the T d 800 MeV deuteron potential to be the phenomenological potential obtained from fitting the 415 MeV p+3He data with the depths doubled. For the analysis of the Tp = 434 MeV 4He (p, d) 3He reaction we chose to scale the 770 MeV potential depths using the KMT [ 11 ] multiple scattering theory and n u c l e o n nucleon data [12] to obtain the relative complex well depths. Comparison of the DWBA calculations with the data at Tp = 770 MeV is shown in fig. 2. It is seen that the cross sections with the meson exchange term removed are smaller and that the minimum at 0 ~ 150 has disappeared. The calculations at forward angles are below the data by a factor 2 - 3 . It is possible that this discrepancy could be accounted for by including
e- + 4He
OI
I Fc o. ol
o.ool
I
i
2
I
_
I
4
i
31 December 1979
I
6
•
(a)
q(fm-') Fig. 1. Charge form factors for 4He. The solid points represent the measured elastic e-+ 4He scattering data [5], and the dotted line through these points is the fit of eq. (2). The open circles and solid line represent the meson-exchange subtracted pseudodata (ref. [6] ) and resulting fit. suming a (ls) 4 configuration. Finally the exterior wavefunction is obtained by matching the correct asymptotic form at the point (r ~ 3.5 fm) where the logarithmic derivatives are the same. The most striking effect of using the meson-exchange corrected version o f F c is observed in the momentum space n-3He wavefunction where the magnitude of the second maximum is greatly reduced as a direct consequence of a similar reduction in F c as shown in fig. 1. Distortions of the p-4He system at 770 MeV were obtained from an optical model search to the 720 MeV elastic scattering data of Verbeck et al. [9]. A noteworthy feature of the resulting potential is the small diffusivity (a <~ 0.3 fm) required. This result was checked using data [10] at 1050 MeV and a very similar potential with small diffusivity was also found. The lack of deuteron elastic scattering data in this energy region hampers determination of a deuteron distorting potential. In ref. [1 ], this potential was re14
'~°'~'~"
'4He (P'd')~He '1
i.o
I \',?'.,,? ~L
io
(b) I00
r~
=L
7~\ ' - l~,~
20
30
"He (p,d):He T p = 4 5 4 MeV"
I0
i
i
i
20
40
60
~.
8c.m.(degrees)
Fig. 2. (a) The Tp = 770 MeV 4He (p, d) 3He data is compared to exact finite-range DWBA predictions with (solid
line) and without (dashed line) the corrections due to meson exchange; (b) the same comparison is made to the Tp = 434 MeV 4He (p, d) 3He data.
Volume 89B, number 1
PHYSICS LETTERS
more terms (e.g. pion emission and reabsorption [4] ) than the simple one-nucleon pickup term. Calculations are also compared with the Tp = 434 MeV data in fig. 2. Once again the unsatisfactory large angle behavior observed using an uncorrected Fc(q) disappears when a meson-exchange-corrected Fc(q) is used. The effect in calculations compared with the Tp = 156 MeV data of Bernas et al. [13] is small since at this energy the reaction does not sample sensitively the bound state wavefunction at momenta o f q ~ > 2 fm -1. Cross sections for 4He(p, d) 3He at 01ab = 22.50 (0cm ~ 340) have been measured by K~/llne et al. [14] for 200 < Tp < 500 MeV. This (p, d) excitation function is shown in fig. 3 and compared to distorted wave calculations using meson-exchange corrected and uncorrected n- 3He wavefunctions. The distorting poten-
4He(p,d)3He 10 3
"-C t~ .c~
0
10 2
o
Cuj MCM
"XNN\
[0 I
\\
b~ ,~h~
%o
i0°
I
0
I
200
I
I
I
400
I
600
I
I
800
Tp(MeV)
Fig. 3. The excitation function at 01ab = 22.50 for the 4He (p, d) 3He data is compared to the predictions of the exact finite-range DWBAwith (solid line) and without (dashed line) the corrections due to meson exchange. Data from refs. [2, 3,13] (open circles) are included with the data of ref. [14] (solid points).
31 December 1979
tials were determined by using the same depth scaling procedure as for the Tp = 434 MeV calculation. Once again, the results using the corrected F c (q) are superior to those using the uncorrected one. Specifically, the dashed curve in fig. 3 shows a large enhancement of the cross section at Tp ~, 600 MeV which is directly attributable to the large secondary maximum in the uncorrected F c (q). Only with the reduced secondary maximum in the corrected F c (q) is qualitative agreement with data achieved. In summary, the 4He(p, d)3He reaction at Tp = 434 and 770 MeV is qualitatively understandable in a onenucleon transfer model using quasi-phenomenological distortions obtained from proton elastic scattering experiments. The crucial difference from the earlier failure [ 1] is the construction of the n-3 He wave function from electron scattering data with pion-exchange effects subtracted from the measured charge form factors so as to give a "true" nucleon density. Other mechanisms such as pion emission and reabsorption [4] may be needed for quantitative agreement with experiment and such calculations are underway [15]. These calculations also involve an n-3He vertex which should be constructed from the "true" density as well. Regardless of the reaction mechanism considered, effects of distortion are crucial [1] and must be included. Direct measurement of d + 3He (or d + t) elastic scattering cross sections at the appropriate energies would help to eliminate some of the uncertainty in describing the deuteron distortion. Polarization or analyzing power measurements for the 4He(p, d) reaction in the energy range 200 < Tp < 800 MeV might be useful in untangling effects due to distortion from those due to reaction modes other than the one-nucleon process treated here. It would also be interesting to apply the present technique to the (p, d) reaction on other light nuclei. However, the present case might be optimal for seeing the effect of meson-exchange processes. This is because (1) these processes are particularly important for electron scattering on 4He, compared, for example, to 160 [6] and (2) the relation between the single particle wavefunction and the nuclear structure is especially simple for 4He. In any case, the present work has demonstrated that the intermediate energy (p, d) reaction can be used to explore meson exchange effects.
15
Volume 89B, number 1
PHYSICS LETTERS
References [1] E. Rost, J.R. Shepard and D.A. Sparrow, Phys. Rev. C17 (1978) 1513. [2] T. Bauer et al., Phys. Lett. 67B (1977) 265. [3] J. Berger et al., Lett. Nuovo Cimento 19 (1977) 287. [4] N.S. Craigie and C. Wilkin, NucL Phys. B14 (1969) 477, [5] R.L. Frosch et al., Phys. Rev. 160 (1967) 874; R.G. Arnold et al., Phys. Rev. L~tt. 40 (1978) 1429. [6] M. Gari, H. Hyuga and Z.G. Zabolitzky, Nucl. Phys. A271 (1976) 365. [7] M. Radomski and D.O. Riska, Nuel. Phys. A274 (1976) 428.
16
31 December 1979
[8] R.V. Roid, Ann. Phys. 50 (1968) 411. [9] S.L. Verbeck et al., Phys. Lett. 59B (1975) 339. [10] G. Bruge, Saclay internal report DPh-N/ME/78-1, unpublished. [11 ] A.K. Kerman, H. McManusand R.M. Thaler, Ann. Phys. 8 (1959) 551; H. Feshbach, A. Gal and J. Hiifner, Ann. Phys. 66 (1971) 20. [12| R.A. Arndt, R.H. Hackman and L.D. Roper, Phys. Rev. C!5 (1977) 1002 and 1o~ tit. [13] M, Bernas et aL, Nucl. Phys. A156 (1970) 289. [14] J. K/illne et al., Phys. Rev. Lett. 41 (1978) 1638. [15] W.S. Pong, private communication.