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The 14N(γ, π+)14Cg.s. reaction through the delta resonance region
Physics Letters B 271 (1991) 47-51 North-Holland
PHYSIC S LETTERS B
The 14N (~/, g + ), 4Cg.s reaction through the delta resonance region J.H.J. D i s t e l b r i n k a,b W. C l a y t o n a L. G h e d i r a a,,, T. K o b a y a s h i ~, D. Myers a,2 j. Shaw a, P. Stoler a, E.J. W i n h o l d " a n d M. Y a m a z a k i a.3 Physics Department, Rensselaer Poh,technic Institute Troy, N Y 12180, USA b Laboratoo, for Nuclear Science, Massachusetts Institute oJ'Technolo~)', Cambridge, MA 02139, US,4
Received 7 June 1991
The pion angular distribution for 14N('}', ~+ )14Cg.s has been measured at a photon energy of 400 MeV. The energy dependence of the cross section through the delta region, and the apparent strength of the resonance contribution, as determined by the present measurement together with earlier lower energy measurements, cannot be accounted for by any current theory, Calculations which use the delta-hole model in the resonance channel overestimate the present results by a factor of over two.
C h a r g e d p i o n p h o t o p r o d u c t i o n at energies t h r o u g h the delta region has two i m p o r t a n t c o m p o n e n t s , o n e i n v o l v i n g delta e x c i t a t i o n s a n d the o t h e r i n v o l v i n g c o n t r i b u t i o n s f r o m the n o n - r e s o n a n t Born t e r m s in the p r o d u c t i o n o p e r a t o r . Fig. 1 shows that for the ele m e n t a r y p(?', rc+ )n process, the delta c o n t r i b u t i o n , while i m p o r t a n t , n e v e r d o m i n a t e s . T h e Born contrib u t i o n is d o m i n a n t n e a r t h r e s h o l d and r e m a i n s c o m parable to the resonance c o n t r i b u t i o n e v e n at the delta peak. T h i s b e h a v i o r is in c o n t r a s t to the (7, n°) process at the peak w h e r e delta e x c i t a t i o n is d o m i n a n t . In c o m p l e x nuclei, we e x p e c t charged p i o n p h o t o p r o d u c t i o n to reflect this e l e m e n t a r y process, but we expect the e x c i t a t i o n and p r o p a g a t i o n o f deltas to be significantly a f f e c t e d by n u c l e a r m e d i u m effects. As the e x c i t a t i o n energy is v a r i e d t h r o u g h the delta region, there should be a varying interplay between nonr e s o n a n t a n d r e s o n a n t excitations. In a t t e m p t i n g to u n d e r s t a n d that i n t e r p l a y and its d e p e n d e n c e on nuclear m e d i u m effects, we h a v e focused on the ~4N (y, = + )14Cg.s" transition. T h i s M 1 t r a n s i t i o n is an i m p o r t a n t special case because o f the n e a r - v a n i s h i n g o f the a l l o w e d G a m o w K Present address: CAEN France, 2 Chemin Lateral, F-94290 Villeneuve le Roi, France. 2 Present address: Physics Department, United States Air Force Academy, Colorado Springs, CO 80840, USA. 3 Present address: Mitsubishi Electric Corporation, 2-20-11 NisiGotanda, Shinagawa, Tokyo 141, Japan.
~" a00 aa ~ e60 .~ ~ e°°l
+
p(7,,~ )n
/
\
\ \ ~ O "~ ;~ .~
z6o zoo
/\ ................. /
50
..... I .... I .... I .... o 150 200 250 300 zoo P h o t o n E n e r g y (MeV)
I .... 350
400
Fig. 1. The p(y, ~+ )n cross section, as calculated by Laget [ 1]. The solid curve, which fits experiment well, is the full cross section, including both delta and non-resonant terms, while the dashed curve is due only to the non-resonant Born diagrams.
Teller m a t r i x e l e m e n t between the 14N and HC g r o u n d states ( w h i c h gives rise to the a n o m a l o u s l y long 13decay l i f e t i m e o f '4C). As a result, there is a suppression o f the n o r m a l l y d o m i n a n t n o n - r e s o n a n t t e r m in the p h o t o p r o d u c t i o n o p e r a t o r w h i c h is p r o p o r t i o n a l to ~r.E ( w h e r e ~ is the n u c l e o n spin o p e r a t o r and e is the p h o t o n p o l a r i z a t i o n ) . Because o f this suppression, the delta t e r m in the p h o t o p r o d u c t i o n o p e r a t o r is e x p e c t e d to play a m o r e d o m i n a n t role as corn-
0370-2693/91/$ 03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
47
Volume 271, number 1,2
PHYSICS LETTERS B
pared to the non-resonant Born terms than is usually the case in (7, ~+ ) reactions. The present ~4N (Y, ~+ )14Cgs angular distribution measurement at 400 MeV follows on our earlier lower energy studies [ 2 - 4 ] at energies of 200, 230, 260, and 320 MeV, and a Mainz measurement at 173 MeV [ 5 ]. This is the first such study for l p-shell nuclei on the high energy side of the delta. All these measurements taken together now provide information on the energy dependence o f the cross section through the delta region. We find that this overall energy d e p e n d e n c e and the apparent strength of the resonance contribution over this energy range cannot be accounted for by any current theory. M o m e n t u m - s p a c e calculations based on the distorted wave impulse a p p r o x i m a t i o n ( D W I A ) [ 2 , 5 8] described the earlier low energy data at 173 and 200 MeV d a t a very well. However, at higher energies in the delta resonance region, the calculated D W I A values fell well below the data. More recently, several groups [9,10] have p e r f o r m e d i m p r o v e d calculations which use the d e l t a - h o l e model to include med i u m modifications o f the delta. In their calculations, Suzuki et al. [9] and T i a t o r et al. [10] treat the resonant a m p l i t u d e in the d e l t a - h o l e model while retaining a D W I A treatment o f the non-resonant background amplitude. At 320 MeV both calculations agree within about 10% and fall below experiment by about 25%. Thus these calculations do much better than the D W I A in the delta region, showing the i m p o r t a n c e of m e d i u m effects for delta excitations. We now find, however, that serious difficulties appear with these calculations when confronted by the present results. The calculations cannot account for the cross section energy dependence through the delta. The e x p e r i m e n t was p e r f o r m e d at the M I T - B a t e s Linear Accelerator Center. A 400 MeV electron beam with m o m e n t u m spread o f _+0.15% was incident on a 365 m g / c m 2 Be3N2 sintered target disc. Positive pions emitted from the target at an angle 0~ were mom e n t u m - a n a l y z e d and detected by the Bates Med i u m Energy Pion Spectrometer ( M E P S ) [11]. Measurements were m a d e at five different angles 0~ ranging from 23 ° to 56 °. For the forward angle points at 0~=23 ° and 27 ° , MEPS had to be m o v e d 50 cm back from its normal position. At these two angles, two separate sets of data-taking runs were m a d e at different times, with different effective solid angles 48
14 November 1991
o f 1.9 and 3.0 msr respectively. For 0~>~ 35 °, a 20 msr collimator was used for all runs, and a single measurement was m a d e at each angle. Optical calculations of the solid angle-efficiency product for MEPS used the codes T R A N S P O R T [12] and T U R T L E [ 13 ], and were experimentally verified by (e, e' ) optics studies in the backward mode. These studies showed that the focal plane efficiency was flat to within + 5% over the full m o m e n t u m acceptance of 20%. The absolute system efficiency was checked by making H (7, rr+ ) runs using a polyethylene target and comparing the extracted cross sections to the world data. The experimental arrangement and the analysis procedures have been described previously [3]. Briefly, a pair o f crossed vertical drift chambers in the focal plane yielded m o m e n t u m information. A set o f four scintillators and a (~erenkov detector prov i d e d the system trigger. The silica aerogel Cerenkov detector, in anticoincidence with the scintillators, rejected the large positron background from pair production in the target. The data analysis included corrections for pion decay, pion scattering and absorption in the detector array, count rate losses, and other spectrometer inefficiencies. The resulting spectrum is mainly pions but is still c o n t a m i n a t e d with positrons and muons. A p o l y n o m i a l fit through the positron background appearing beyond the ground state end point was extended linearly through the ground state region to remove the positrons from the data. The shape and magnitude of the muon contribution to the ground state region was then calculated with a Monte Carlo technique [ 3 ] using the experimental p i o n - m u o n spectrum and an iterative procedure. The resulting corrected spectrum (fig. 2) was fit with an effective photon spectrum containing real bremsstrahlung [14] and virtual photon [15] contributions. The differential cross sections obtained at five angles are plotted versus 0~ in fig. 3. The error bars are statistical only. The data points at 23 ° and 27 ° combine the results o f the two i n d e p e n d e n t measurements at each angle, which were consistent within their statistical uncertainties. Systematic errors, mainly caused by normalization uncertainties and fit inaccuracies, are estimated to be 15%. The curves in fig. 3 are the result of calculations by Tiator et al. [ 10 ] which split the p h o t o p r o d u c t i o n a m p l i t u d e into a
Volume 271, number 1,2
'
'
I
. . . .
PtPFSICS LETTERS B
I
. . . .
I
. . . .
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©
,
,
I
. . . .
100
I
. . . .
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120
.
.
.
140
.
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Channel n u m b e r Fig. 2. Typical experimental spectrum corrected for positron background and decay muons as described in the text. The pion yield is in arbitrary units. The ground state end point is at channel 129. The muon correction in the ground state region is at the 20% level.
'"N (>.+)~4C
0 o 0 5")
40
O t. (..)
"~ .,.a =
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Scattering Angle (CM) Fig. 3. The experimental differential cross section values at 400 MeV plotted against pion angle 0~. Error bars are statistical. The solid curve is the full calculation of Tiator et al. [ 10], while the dashed curve is their calculation using the resonance amplitude only. resonance piece treated in the delta-hole model and a background non-resonant amplitude treated in nonlocal DWIA. Two-step processes involving rc° production followed by charge exchange are included, but do not play a major role. This calculation significantly disagrees with the data, yielding calculated cross sections two to three times the experiment. As fig. 3 shows, the calculation gives a resonance cross section which is only one third the full cross sec-
14 November 1991
tion. Hence the n o n - r e s o n a n t contribution dominates the calculated cross section, as expected at this energy. We conclude that the disagreement between theory and experiment at 400 MeV is caused at least in part by problems with the calculated non-resonant part, which appears to be substantially overestimated. This disagreement is in striking contrast to the situation at lower energies, below and near the delta peak. At 230 MeV, the calculations agree well with our earlier data, while at 260 and 320 MeV they are about 25% below the data. To clarify the energy dependence of these effects, we plot in fig. 4 excitation functions for several mom e n t u m transfer values, showing our present results at 400 MeV together with our earlier lower energy cross sections. In addition we show the calculations of Tiator et al. [10], giving the results of their full calculation and that using the resonance amplitude only. According to their results, the resonance part contributes about half the cross section in the delta region near 300 MeV, and is less important at higher energies. An e x a m i n a t i o n of fig. 4 reveals some significant new problems. The experimental data at fixed q show a p r o m i n e n t peaking near 260 MeV, strongly suggesting the importance of delta excitation. However, the calculated resonance cross section appears to be too small to yield this strong peaking. Probably as a result, the overall calculated shape does not resemble the data. It is much less peaked, lying about 25% below experiment at 260 and 320 MeV, but substantially above it at 400 MeV. The calculation appears to have too large a ratio of non-resonant to resonant cross sections in the delta region. Independently of calculation, however, the resonance-to-background ratio in fig. 4 appears to be much larger than for the elementary process (fig. 1 ), and the cross section falls to a much lower relative value at 400 MeV than does that for the proton. Tiator et al. use the phenomenological H1 1p-shell wave functions of Huffman et al. [ 16,17 ] in both their delta-hole and DWIA calculations. In contrast to earlier model wave functions, those wave functions fit both elastic and inelastic electron scattering data well, over the range of m o m e n t u m transfer between 1 and 1.5 fm ~ which is of primary interest in the present experiment. The good overall D W l A fits of Tiator et al. to (3', =+ ) at 173 and 200 MeV are only 49
Volume 27 l, number 1,2
1.25
i , i t
PHYSICS LETTERS B
l l l l
r i l l
La=o.19~!,
I
I~1
'm
r r , ,
We conclude that presently available theoretical treatments of JaN (7,/I;+ )I 4Cg.s. are inadequate. In the hybrid calculations o f T i a t o r et al. [ 10], both the resonant and non-resonant parts a p p e a r to need improvements. One limitation of these calculations is that the resonant and non-resonant parts are not treated on an equal footing. As a consequence, interference effects between them may not be evaluated correctly. In addition, m e d i u m effects are not properly treated for the non-resonant part, which is calculated in DW1A. Finally, the non-resonant calculation does not satisfy unitarity [ 10]. In summary, the pion angular distribution for ~4N (y, rt + )14Cg.s has been measured at a photon energy o f 400 MeV, and is not well fit by current theoretical treatments based on hybrid models which use the d e l t a - h o l e model for the resonance and DW1A for the non-resonant part. The present experimental results, together with earlier lower energy data, demonstrate that these theoretical treatments o f photoproduction in 14N a r e incomplete and require further refinements. Their failure to account for the overall shape o f the cross section energy dependence in the delta region and for the apparent strength of the resonance contribution is the most striking result of this study. This result is quite unexpected, coming as it does after a long period of experimental and theoretical development, and after the a p p a r e n t earlier successes o f these models had led to the view that the i m p o r t a n t processes involved here were now well understood.
I
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. . . .
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e
(~ 25
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,,,I .... i .... ) .... m~,~,
z25., . . . . . . . I . . . . I . . . . . . . . ~ : t.18 tm-t
I....
I00
50 25 150
~,~ 200
Photon
250
300
-
350
400
14 November 1991
-
450
Energy (MeV)
Fig. 4. Excitation functions for taN (y,/I: + ) 14Cg.s for several values of momentum transfer. The points at 400 MeV are our present results, while the lower energy points are earlier results [25]. The solid curve is the full calculation of Tiator et al. [10] while the dashed curve is their calculation using the resonance amplitude only.
We thank Dr. L. T i a t o r for supplying us with the results o f calculations before publication, and the Bates accelerator staff for their help during the experiment. This work was supported in part by the National Science F o u n d a t i o n through G r a n t No. PHY89-05162 and by the D e p a r t m e n t o f Energy through Contract No. DE-AC02-76ER03069.
References
achieved with these wave functions. This suggests that the nuclear structure input is under good control in these calculations. (Still, we should note that the inelastic form factor data above 1.7 fm ~ is not well described [17 ], and A m o s et al. [18 ] have criticized these wave functions on other grounds. ) 50
[ 1 ] J.M. Lager, Phys. Rep. 69 ( 1981 ) 1. [2] B.H. CoUman el al., Phys. Rev. Lett. 55 (1985) 684. [3] L. Ghediraet al., Phys. Rev. C 41 (1990) 653. [4] P.K. Teng et al., Phys. Lett. B 177 (1986) 25. [ 5 ] K. R~Shrich et al., Phys. Lett. B 153 ( 1985 ) 203: Nucl. Phys. A475 (1987) 761.
Volume 271, number 1,2
PHYSICS LETTERS B
[6] L. Tiator and L.E. Wright, Phys. Rev. C 30 (1984) 989. [7] R. Wittman and N.C. Mukhopadhyay, Phys. Rev. Lett. 57 (1986) 1113. [8] R.A. Eramzhyan, M. Gmitro and S.S. Kamalov, Phys. Rev, C41 (1990) 2865. [ 9 ] T . Suzuki, T. Takaki and J.H. Koch, Nucl. Phys. A 460 (1986) 607. [10] L. Tiator, J. Vesper, D. Drechsel, N. Ohtsuka and L.E, Wright, Nucl. Phys, A 4 8 5 (1988) 565. [ I I ] J . A . Nelson, M.S. thesis, Massachusetts Institute of Technology ( 1986 ), unpublished. [ 12] K.L. Brown and S.K. Howry, computer code T R A N S P O R T / 360, Stanford Linear Accelerator Center Report SLAC-91 (1970).
14 November 1991
[13] D.C. Carey, K.L. Brown and Ch. Iselin, computer code DECAY TURTLE, Stanford Linear Accelerator Center Report SLAC-246 (1982). [ 14 ] J.L. Matthews and R.O. Owens, Nucl. Instrum. Methods I I 1 (1973) 157. [15] k. T i a t o r a n d L.E. Wright, Nucl. Phys. A 379 (1982) 407. [16] R.L. Huffman et al., Phys. Lett. B 139 (1984) 249. [ 17 ] R.L. Huffman et al., Phys. Rev. C 35 ( 1987 ) 1. [18] K. Amos, D. Koetsier and D. Kurath, Phys. Rev. C 40 (1989) 374.
51
PHYSIC S LETTERS B
The 14N (~/, g + ), 4Cg.s reaction through the delta resonance region J.H.J. D i s t e l b r i n k a,b W. C l a y t o n a L. G h e d i r a a,,, T. K o b a y a s h i ~, D. Myers a,2 j. Shaw a, P. Stoler a, E.J. W i n h o l d " a n d M. Y a m a z a k i a.3 Physics Department, Rensselaer Poh,technic Institute Troy, N Y 12180, USA b Laboratoo, for Nuclear Science, Massachusetts Institute oJ'Technolo~)', Cambridge, MA 02139, US,4
Received 7 June 1991
The pion angular distribution for 14N('}', ~+ )14Cg.s has been measured at a photon energy of 400 MeV. The energy dependence of the cross section through the delta region, and the apparent strength of the resonance contribution, as determined by the present measurement together with earlier lower energy measurements, cannot be accounted for by any current theory, Calculations which use the delta-hole model in the resonance channel overestimate the present results by a factor of over two.
C h a r g e d p i o n p h o t o p r o d u c t i o n at energies t h r o u g h the delta region has two i m p o r t a n t c o m p o n e n t s , o n e i n v o l v i n g delta e x c i t a t i o n s a n d the o t h e r i n v o l v i n g c o n t r i b u t i o n s f r o m the n o n - r e s o n a n t Born t e r m s in the p r o d u c t i o n o p e r a t o r . Fig. 1 shows that for the ele m e n t a r y p(?', rc+ )n process, the delta c o n t r i b u t i o n , while i m p o r t a n t , n e v e r d o m i n a t e s . T h e Born contrib u t i o n is d o m i n a n t n e a r t h r e s h o l d and r e m a i n s c o m parable to the resonance c o n t r i b u t i o n e v e n at the delta peak. T h i s b e h a v i o r is in c o n t r a s t to the (7, n°) process at the peak w h e r e delta e x c i t a t i o n is d o m i n a n t . In c o m p l e x nuclei, we e x p e c t charged p i o n p h o t o p r o d u c t i o n to reflect this e l e m e n t a r y process, but we expect the e x c i t a t i o n and p r o p a g a t i o n o f deltas to be significantly a f f e c t e d by n u c l e a r m e d i u m effects. As the e x c i t a t i o n energy is v a r i e d t h r o u g h the delta region, there should be a varying interplay between nonr e s o n a n t a n d r e s o n a n t excitations. In a t t e m p t i n g to u n d e r s t a n d that i n t e r p l a y and its d e p e n d e n c e on nuclear m e d i u m effects, we h a v e focused on the ~4N (y, = + )14Cg.s" transition. T h i s M 1 t r a n s i t i o n is an i m p o r t a n t special case because o f the n e a r - v a n i s h i n g o f the a l l o w e d G a m o w K Present address: CAEN France, 2 Chemin Lateral, F-94290 Villeneuve le Roi, France. 2 Present address: Physics Department, United States Air Force Academy, Colorado Springs, CO 80840, USA. 3 Present address: Mitsubishi Electric Corporation, 2-20-11 NisiGotanda, Shinagawa, Tokyo 141, Japan.
~" a00 aa ~ e60 .~ ~ e°°l
+
p(7,,~ )n
/
\
\ \ ~ O "~ ;~ .~
z6o zoo
/\ ................. /
50
..... I .... I .... I .... o 150 200 250 300 zoo P h o t o n E n e r g y (MeV)
I .... 350
400
Fig. 1. The p(y, ~+ )n cross section, as calculated by Laget [ 1]. The solid curve, which fits experiment well, is the full cross section, including both delta and non-resonant terms, while the dashed curve is due only to the non-resonant Born diagrams.
Teller m a t r i x e l e m e n t between the 14N and HC g r o u n d states ( w h i c h gives rise to the a n o m a l o u s l y long 13decay l i f e t i m e o f '4C). As a result, there is a suppression o f the n o r m a l l y d o m i n a n t n o n - r e s o n a n t t e r m in the p h o t o p r o d u c t i o n o p e r a t o r w h i c h is p r o p o r t i o n a l to ~r.E ( w h e r e ~ is the n u c l e o n spin o p e r a t o r and e is the p h o t o n p o l a r i z a t i o n ) . Because o f this suppression, the delta t e r m in the p h o t o p r o d u c t i o n o p e r a t o r is e x p e c t e d to play a m o r e d o m i n a n t role as corn-
0370-2693/91/$ 03.50 © 1991 Elsevier Science Publishers B.V. All rights reserved.
47
Volume 271, number 1,2
PHYSICS LETTERS B
pared to the non-resonant Born terms than is usually the case in (7, ~+ ) reactions. The present ~4N (Y, ~+ )14Cgs angular distribution measurement at 400 MeV follows on our earlier lower energy studies [ 2 - 4 ] at energies of 200, 230, 260, and 320 MeV, and a Mainz measurement at 173 MeV [ 5 ]. This is the first such study for l p-shell nuclei on the high energy side of the delta. All these measurements taken together now provide information on the energy dependence o f the cross section through the delta region. We find that this overall energy d e p e n d e n c e and the apparent strength of the resonance contribution over this energy range cannot be accounted for by any current theory. M o m e n t u m - s p a c e calculations based on the distorted wave impulse a p p r o x i m a t i o n ( D W I A ) [ 2 , 5 8] described the earlier low energy data at 173 and 200 MeV d a t a very well. However, at higher energies in the delta resonance region, the calculated D W I A values fell well below the data. More recently, several groups [9,10] have p e r f o r m e d i m p r o v e d calculations which use the d e l t a - h o l e model to include med i u m modifications o f the delta. In their calculations, Suzuki et al. [9] and T i a t o r et al. [10] treat the resonant a m p l i t u d e in the d e l t a - h o l e model while retaining a D W I A treatment o f the non-resonant background amplitude. At 320 MeV both calculations agree within about 10% and fall below experiment by about 25%. Thus these calculations do much better than the D W I A in the delta region, showing the i m p o r t a n c e of m e d i u m effects for delta excitations. We now find, however, that serious difficulties appear with these calculations when confronted by the present results. The calculations cannot account for the cross section energy dependence through the delta. The e x p e r i m e n t was p e r f o r m e d at the M I T - B a t e s Linear Accelerator Center. A 400 MeV electron beam with m o m e n t u m spread o f _+0.15% was incident on a 365 m g / c m 2 Be3N2 sintered target disc. Positive pions emitted from the target at an angle 0~ were mom e n t u m - a n a l y z e d and detected by the Bates Med i u m Energy Pion Spectrometer ( M E P S ) [11]. Measurements were m a d e at five different angles 0~ ranging from 23 ° to 56 °. For the forward angle points at 0~=23 ° and 27 ° , MEPS had to be m o v e d 50 cm back from its normal position. At these two angles, two separate sets of data-taking runs were m a d e at different times, with different effective solid angles 48
14 November 1991
o f 1.9 and 3.0 msr respectively. For 0~>~ 35 °, a 20 msr collimator was used for all runs, and a single measurement was m a d e at each angle. Optical calculations of the solid angle-efficiency product for MEPS used the codes T R A N S P O R T [12] and T U R T L E [ 13 ], and were experimentally verified by (e, e' ) optics studies in the backward mode. These studies showed that the focal plane efficiency was flat to within + 5% over the full m o m e n t u m acceptance of 20%. The absolute system efficiency was checked by making H (7, rr+ ) runs using a polyethylene target and comparing the extracted cross sections to the world data. The experimental arrangement and the analysis procedures have been described previously [3]. Briefly, a pair o f crossed vertical drift chambers in the focal plane yielded m o m e n t u m information. A set o f four scintillators and a (~erenkov detector prov i d e d the system trigger. The silica aerogel Cerenkov detector, in anticoincidence with the scintillators, rejected the large positron background from pair production in the target. The data analysis included corrections for pion decay, pion scattering and absorption in the detector array, count rate losses, and other spectrometer inefficiencies. The resulting spectrum is mainly pions but is still c o n t a m i n a t e d with positrons and muons. A p o l y n o m i a l fit through the positron background appearing beyond the ground state end point was extended linearly through the ground state region to remove the positrons from the data. The shape and magnitude of the muon contribution to the ground state region was then calculated with a Monte Carlo technique [ 3 ] using the experimental p i o n - m u o n spectrum and an iterative procedure. The resulting corrected spectrum (fig. 2) was fit with an effective photon spectrum containing real bremsstrahlung [14] and virtual photon [15] contributions. The differential cross sections obtained at five angles are plotted versus 0~ in fig. 3. The error bars are statistical only. The data points at 23 ° and 27 ° combine the results o f the two i n d e p e n d e n t measurements at each angle, which were consistent within their statistical uncertainties. Systematic errors, mainly caused by normalization uncertainties and fit inaccuracies, are estimated to be 15%. The curves in fig. 3 are the result of calculations by Tiator et al. [ 10 ] which split the p h o t o p r o d u c t i o n a m p l i t u d e into a
Volume 271, number 1,2
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'
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. . . .
PtPFSICS LETTERS B
I
. . . .
I
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I
©
,
,
I
. . . .
100
I
. . . .
f
120
.
.
.
140
.
160
Channel n u m b e r Fig. 2. Typical experimental spectrum corrected for positron background and decay muons as described in the text. The pion yield is in arbitrary units. The ground state end point is at channel 129. The muon correction in the ground state region is at the 20% level.
'"N (>.+)~4C
0 o 0 5")
40
O t. (..)
"~ .,.a =
2o ./-
k, ¢D
//
-x
0
20
40
60
80
log
Scattering Angle (CM) Fig. 3. The experimental differential cross section values at 400 MeV plotted against pion angle 0~. Error bars are statistical. The solid curve is the full calculation of Tiator et al. [ 10], while the dashed curve is their calculation using the resonance amplitude only. resonance piece treated in the delta-hole model and a background non-resonant amplitude treated in nonlocal DWIA. Two-step processes involving rc° production followed by charge exchange are included, but do not play a major role. This calculation significantly disagrees with the data, yielding calculated cross sections two to three times the experiment. As fig. 3 shows, the calculation gives a resonance cross section which is only one third the full cross sec-
14 November 1991
tion. Hence the n o n - r e s o n a n t contribution dominates the calculated cross section, as expected at this energy. We conclude that the disagreement between theory and experiment at 400 MeV is caused at least in part by problems with the calculated non-resonant part, which appears to be substantially overestimated. This disagreement is in striking contrast to the situation at lower energies, below and near the delta peak. At 230 MeV, the calculations agree well with our earlier data, while at 260 and 320 MeV they are about 25% below the data. To clarify the energy dependence of these effects, we plot in fig. 4 excitation functions for several mom e n t u m transfer values, showing our present results at 400 MeV together with our earlier lower energy cross sections. In addition we show the calculations of Tiator et al. [10], giving the results of their full calculation and that using the resonance amplitude only. According to their results, the resonance part contributes about half the cross section in the delta region near 300 MeV, and is less important at higher energies. An e x a m i n a t i o n of fig. 4 reveals some significant new problems. The experimental data at fixed q show a p r o m i n e n t peaking near 260 MeV, strongly suggesting the importance of delta excitation. However, the calculated resonance cross section appears to be too small to yield this strong peaking. Probably as a result, the overall calculated shape does not resemble the data. It is much less peaked, lying about 25% below experiment at 260 and 320 MeV, but substantially above it at 400 MeV. The calculation appears to have too large a ratio of non-resonant to resonant cross sections in the delta region. Independently of calculation, however, the resonance-to-background ratio in fig. 4 appears to be much larger than for the elementary process (fig. 1 ), and the cross section falls to a much lower relative value at 400 MeV than does that for the proton. Tiator et al. use the phenomenological H1 1p-shell wave functions of Huffman et al. [ 16,17 ] in both their delta-hole and DWIA calculations. In contrast to earlier model wave functions, those wave functions fit both elastic and inelastic electron scattering data well, over the range of m o m e n t u m transfer between 1 and 1.5 fm ~ which is of primary interest in the present experiment. The good overall D W l A fits of Tiator et al. to (3', =+ ) at 173 and 200 MeV are only 49
Volume 27 l, number 1,2
1.25
i , i t
PHYSICS LETTERS B
l l l l
r i l l
La=o.19~!,
I
I~1
'm
r r , ,
We conclude that presently available theoretical treatments of JaN (7,/I;+ )I 4Cg.s. are inadequate. In the hybrid calculations o f T i a t o r et al. [ 10], both the resonant and non-resonant parts a p p e a r to need improvements. One limitation of these calculations is that the resonant and non-resonant parts are not treated on an equal footing. As a consequence, interference effects between them may not be evaluated correctly. In addition, m e d i u m effects are not properly treated for the non-resonant part, which is calculated in DW1A. Finally, the non-resonant calculation does not satisfy unitarity [ 10]. In summary, the pion angular distribution for ~4N (y, rt + )14Cg.s has been measured at a photon energy o f 400 MeV, and is not well fit by current theoretical treatments based on hybrid models which use the d e l t a - h o l e model for the resonance and DW1A for the non-resonant part. The present experimental results, together with earlier lower energy data, demonstrate that these theoretical treatments o f photoproduction in 14N a r e incomplete and require further refinements. Their failure to account for the overall shape o f the cross section energy dependence in the delta region and for the apparent strength of the resonance contribution is the most striking result of this study. This result is quite unexpected, coming as it does after a long period of experimental and theoretical development, and after the a p p a r e n t earlier successes o f these models had led to the view that the i m p o r t a n t processes involved here were now well understood.
I
100
75 50 25
,P,,I . . . . I . . . . I . . . . I . . . . 1
0 ¢ ~ . t25
....
Gq ~100
I ....
I ....
I ....
I ....
I
'
xt=t'2 f m t
75 50
"
f
O 25L_~ •~...¢
o U3
"~-
"--
/
,,,( .... I
I . . . . 1. . . . I
. . . .
t25 ..... }. . . . I . . . . I . . . . I . . . .
I
r./'l 100 ~.q=l.5 ~ - t O'l " 0
7s so
e
(~ 25
o (I)
~0
~---.
,,,I .... i .... ) .... m~,~,
z25., . . . . . . . I . . . . I . . . . . . . . ~ : t.18 tm-t
I....
I00
50 25 150
~,~ 200
Photon
250
300
-
350
400
14 November 1991
-
450
Energy (MeV)
Fig. 4. Excitation functions for taN (y,/I: + ) 14Cg.s for several values of momentum transfer. The points at 400 MeV are our present results, while the lower energy points are earlier results [25]. The solid curve is the full calculation of Tiator et al. [10] while the dashed curve is their calculation using the resonance amplitude only.
We thank Dr. L. T i a t o r for supplying us with the results o f calculations before publication, and the Bates accelerator staff for their help during the experiment. This work was supported in part by the National Science F o u n d a t i o n through G r a n t No. PHY89-05162 and by the D e p a r t m e n t o f Energy through Contract No. DE-AC02-76ER03069.
References
achieved with these wave functions. This suggests that the nuclear structure input is under good control in these calculations. (Still, we should note that the inelastic form factor data above 1.7 fm ~ is not well described [17 ], and A m o s et al. [18 ] have criticized these wave functions on other grounds. ) 50
[ 1 ] J.M. Lager, Phys. Rep. 69 ( 1981 ) 1. [2] B.H. CoUman el al., Phys. Rev. Lett. 55 (1985) 684. [3] L. Ghediraet al., Phys. Rev. C 41 (1990) 653. [4] P.K. Teng et al., Phys. Lett. B 177 (1986) 25. [ 5 ] K. R~Shrich et al., Phys. Lett. B 153 ( 1985 ) 203: Nucl. Phys. A475 (1987) 761.
Volume 271, number 1,2
PHYSICS LETTERS B
[6] L. Tiator and L.E. Wright, Phys. Rev. C 30 (1984) 989. [7] R. Wittman and N.C. Mukhopadhyay, Phys. Rev. Lett. 57 (1986) 1113. [8] R.A. Eramzhyan, M. Gmitro and S.S. Kamalov, Phys. Rev, C41 (1990) 2865. [ 9 ] T . Suzuki, T. Takaki and J.H. Koch, Nucl. Phys. A 460 (1986) 607. [10] L. Tiator, J. Vesper, D. Drechsel, N. Ohtsuka and L.E, Wright, Nucl. Phys, A 4 8 5 (1988) 565. [ I I ] J . A . Nelson, M.S. thesis, Massachusetts Institute of Technology ( 1986 ), unpublished. [ 12] K.L. Brown and S.K. Howry, computer code T R A N S P O R T / 360, Stanford Linear Accelerator Center Report SLAC-91 (1970).
14 November 1991
[13] D.C. Carey, K.L. Brown and Ch. Iselin, computer code DECAY TURTLE, Stanford Linear Accelerator Center Report SLAC-246 (1982). [ 14 ] J.L. Matthews and R.O. Owens, Nucl. Instrum. Methods I I 1 (1973) 157. [15] k. T i a t o r a n d L.E. Wright, Nucl. Phys. A 379 (1982) 407. [16] R.L. Huffman et al., Phys. Lett. B 139 (1984) 249. [ 17 ] R.L. Huffman et al., Phys. Rev. C 35 ( 1987 ) 1. [18] K. Amos, D. Koetsier and D. Kurath, Phys. Rev. C 40 (1989) 374.
51