The forward, backward and 90° deuteron photodisintegration between 7 and 19 MeV photon energy

Nuclear Physics A530 (1991) 420-436 North-Holland

E

N ' DEUT T BETWEEN 7 AN 19 TN ENERGY*

eV

A. DE GRAEVE', A. ZIEGER2 , R. VAN DE VYVER', C. VAN DEN ABEELE', H. FERDINANDE', L. VAN HOOREBEKE', D. RYCKBOSCH', F. DE SMET' and B. ZIEGLER2 ' Nuclear Ikysics Laboratom; RUG, Ghent, Belgium = Abteilung Kernphysik, Mat-Planck-Institut fcir Chemie, Mainz, Germany Received 28 December 1990 (Revised 18 March 1991) A

E

, The 0° and 180°, as well as the 90® differential cross sections for the 2 H(y, p)n reaction have been measured at lab photon energies between 7 and 19 MeV. Special attention was paid to the accuracy, in particular by measuring the forward Compton electron yield. For the extreme angles, the statistical error on our results amounts to 4-5%® (0°) and 7-8%® (180°), respectively, while the systematic uncertainty is at most 3% . The data confirm the existence of a minimum in the forward cross section and indicate beyond any doubt that the fore/aft ratio is larger than unity. Comparison shows reasonable agreement with the results from recent "conventional" theoretical approaches, including meson exchange and relativistic corrections, although the description of the c-coefficient, appearing in the Partovi expansion of the differential cross section, remains unsatisfactory. A possible source for this discrepancy could be the inadequate description of the El and/or the E2 transition operator .

I

NUCLEAR REACTIONS 2 H(y, p), E = 7-19 MeV; measured Q(6) .

l. Introduction For some time now the deuteron photodisintegration reaction process has received substantial attention, especially at the extreme angles where effects become perceptible which remain concealed at other angles. In 1984 Cambi and collaborators ' ) suggested that the discrepancy between the results of the non-relativistic impulse approximation calculation by fartovi 2) (hereafter called the "standard" approach) and the data from the timely experiment at 0° by Hughes et W) could be ascribed to relativistic effects, specifically to the spin-orbit part in the transition operator. Later on, a number of independent calculations 4-8 ) affirmed this finding, while experimental confirmations for the forward cross section were provided by some * Supported in part by the Deutsche Forschungsgemeinschaft, SFB 201 . 0375-9474/91/$03 .50 © 1991 - Elsevier Science Publishers B.V . (North-Holland)

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421

measurements 9- "). Although the concurrence of theory and experiment is not yet perfect in detail, they do seem to converge at the higher energies (60-120 MeV). As far as the low-energy region (i.e. below 20 MeV) for the forward cross section is concerned, the situation is not very clear. On the one hand, accurate experimental data are scarce: leaving out of consideration the (from finite angles) extrapolated ones - which are considered less reliable - only one directly measured value '2) existed at 10 MeV until 1986, while recently a data point was obtained at 15 eV from neutron-proton capture studies '3), showing however a °/® uncertainty. On the other hand, the various theoretical results differ markedly, especially in predicting the position and depth of the minimum in the forward cross section. In the more recent (so-called conventional) calculations, the major effect on the magnitude and shape of the forward cross section in this energy range stems from the inclusion of meson exchange currents (MEC). This effect increases the calculated cross section at about 10 MeV - where in the standard calculation a mini u occurs - from roughly 5 pb/sr to 5.5 pb/sr and at the same time shifts the dip - 11 MeV. The inclusion of the relativistic spin-orbit effects is hardly visible at these energies and only leads to a minor lowering ofthe cross section. However, comparing the different theoretical approaches, including spin-orbit and even meson exchange of relativistic order, some differences cannot be overlooked. The behaviour of the calculated cross section at low energies ranges from no minimum 'a), to a sharp minimum at -7 MeV [ref. 's)] over a shallow one around 11-12 MeV [refs. ")] or at about 15 MeV [ref. `6)]. It should be pointed out here that some ofthe criticism 8 °' 5) on the methods applied in the conventional theoretical approaches, has recently been refuted by the Mainz-Florence collaboration "). A similar observation holds for the backward cross section : at 180` analogous relativistic effects are expected to play a role. At the low-energy side a striking difference between the standard and the relativistic results appears: the rather pronounced classical minimum vanishes almost entirely in the more complete relativistic calculations . However, no experimental results are yet available. The directly measured results existing in the higher energy interval between 30 and 50 MeV are furthermore conflicting: at equal energy, a backward cross section was found higher than the forward one 9). Traditionally, the differential cross section (in the CM system) is written in terms of the Partovi expansion 2) : d d,2(0) - a + b sin e ®+ c oos O+ d sine 0 cos 0 + e sin 4 ® ,

with 0 the c .m . proton emission angle. The "Partovi coefficients" a to e contain information about the EM multipolarity of the transition(s) involved. The expressions for the cross section at extreme angles then are

422

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Graeve et al. / Deuteron photodisintegration

owing the magnitude of the forward and backward cross section at the same energy, the coefficients a and c can be extracted. The coefficient a is the constant (i.e. angle independent) term referring to pure 1 and El transitions, whereas c contains e El/ Ml and 1/E2 interference amplitudes. An interesting point here is that, in order to explain the unexpected behaviour of the experimental results, obtained at Argvnne '8) for the ratio of the differential cross sections, adjimichael et a ") suggested that a 1-. :.!,s conventional treatment ofthe E2 transitions (containing ingredients of which the origin is as yet unclear) in this reaction might result in other c-values, completely different from what is generally expected. In this paper, accurate measurements ofthe 0® and 180® 2 (y, p) differential cross section in the low-energy region (7-19 eV) are discussed. Some of the data have 20,21 ). Special emphasis is put on the already been briefly discussed elsewhere accuracy of the method of deriving absolute cross section values, which was checked by measuring the forward Compton electron cross section, the result of which can e well-known theoretical value . In addition, the 90° t y compared ' cross section was measure simultaneously during all forward and backward riments. Sect. 2 of is paper focuses on the experimental set-up, the transmission of the ctrometer d the data taking of the forward and backward measurements. tails about the method of analysis are given in sect. 3. An essential part is contained in sect. dealing with the overall accuracy o the experiments. Sect. 5 presents the results and a comparison with theory; conclusions are drawn in sect. 6, in which also suggestions for future experiments are made.

2.1 . SETUP

e experiments were performed with a bremsstrahlung photon beam produced either at the 90 eV (0.1% duty cycle) or -in the case of the forward 7.5 MeV measurements - at the 12 eV (2°/® duty cycle) linac of the Ghent State University. e collimation of the photon beam was adjusted in each experiment to the specific needs of the set-up, resulting in a beam spot at the target of 12 mm diameter and of 10 m diameter in the forward 7.51VIeV runs. The actual targets were deuterated polyethylene foils, while the background was measured with non deuterated polyethylene having almost the same thickness : a CD2 foil has a weight of (4 .88 :E 0.09) mg/cm2 , a CH2 foil is (4.56--+0 .03) g/c 2 thick (see table 1 and ref. 12)). e magnetic spectrometer, needed to deflect the forward or backward going protons out of the beam line, consists of two dipole magnets (a = 53.5°, p = 35 cm) placed in a non-dispersive, translational mode. In order to confine the protons to a small cone around 0° (or 180°) a circular collimator (with an inner radius of 10 m) is positioned at 45.65 cm behind the targets and 37 .22 cm in front of the

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423

TABLE 1

The experimental parameters for the different measurements (with (E,,) the mean photon energy, T_ the bremsstrahlung endpoint energy and Bo the magnetic induction)

(E,,)

(MeV)

T_ (MeV)

BO (kG)

Target thickness (mg/cm2) CD2/CH2

9 = 0®

7.5 10 14.7

12 18 20

6.65 8.11 10.98

4.88/4.56 9.76/9 .12 9.76/9 .12

10 12 12

3 3

0 =180°

12 14.5

18 19

8.11 9.39

9.76/9 .12 9.76/9 .12

12 12

3 3

9 = 90°

7-20

all

-

4.88/4.56

<20 mm

Beamspot at target (mm 0)

Surface barrier det ctor thickn ss/area pm/2 pm/2 2 mm/ 2

2

mm2 mm2

;;m/2 0 mM2 m/ 000 mm2 2 mm/ 12

MM2

entrance of the first magnet . This leads to a solid angle of 1.51 sr in the e f an ideal point source. In between both magnets an additional rectangular colli t r helps to restrict the proton beam, and to reduce the possible background ca by scattering of the particles on the chamber walls. The dipole magnets are co e e to two independent power supplies . The stability and reproducibility of the magnetic fields was better than 10 -4. The equal setting of each magnetic field was achieved and controlled by NMR probes, using an original technique developed at the ax-Planck-Institut/Mainz 22) . The arrangement of these two dipole magnets in translational mode results in an achromatic system for those particles having the nominal momentum; however, for particles with a different momentum, the corresponding images are but located close to the central trajectory and do not coincide (i.e. the system is not fully achromatic). The detector was placed at this (approximate) spatial focus. Its lateral position and size were chosen in such a way that the largest possible number of protons was registered . Furthermore, an appropriate choice for the thickness of the detector as a function of the specific conditions for the experiment (mainly the proton energy range to be detected), allows the use of the spectroscopic information supplied by the solid state detector effectively . The set-up for the 180° experiments is schematically represented in fig. 1, while the experimental parameters for the different measurements, including the thickness of the used detectors, are also summarized in table 1 . Note that in most cases a Si detector with an area of 2000 mm2 and a thickness of 300 pm was used, which suffices to stop 6.2 eV protons. However, in the case of the forward 15 eV measurement, a thicker detector (2 mm/ 12_`0 w-n 2 ) was mounted. ®n the other hand, in the backward 15 MeV experiment, the original (thin) detector was kept which led to a distortion of the measured photoproton spectrum at the high energy side, the effect of which was taken into account in the analysis procedure (see further) .

,~, De tJraev-e et ai. / Deuteron püotoc~isintegration

P2

Fig. 1. S4he atic dr~v~~in~ of the e.~peri~nental $et-up fir the DSO® measurements. the dipole m.°~gnets.

1 and

2 represent

z ( y, p) lso in ic to in fig. 1 is the set-up to si ultaneously measure the 9 ° cr SS Se~t2on. is ex ri ant was schedule in t e first place to check the systematic e accuracy of t e ex rimants since is cross section is fairly well known `) . reaction cha bar was installed behind (0® set-up) or in front of (1 g0° set-up) t e rst agnat, respectively . e detector was positioned about 40 cm underneath t e target, e ping a solid angly of °~.6~ msr. is detector has an area of 1250 mm2 an a t ickness of ? e 90° c. . cross section was simultaneously determined ring any 0° or 1~0° ex eri ant, for each endpoint energy of the bremsstra lung. ?.? . °T

NS

iSSI®~3 PR®PERTIES DE ï"I-iE SPECTR®

ETER

he knowledge of the "geo attic" e ciency of a detection system (here defined as the e active solid angle spanned by the entire detection apparatus) is of key i portance in every experiment . In our case, this geometric e ciency is primarily ate ine by the transmission function of the spectrometer - the solid state detector being 1 %® ei~~cient to detect the protons. e transmission curve as a function of o entu , was calculated using a ray tracing code, taking also into account the behaviour of the magnetic fringing fields . This ray tracing code was embedded in a orate Carlo programme to simulate the random starting position and angle of the emitted proton at the target, the latter not being a point source. ®n the other hand, the transmission curve was measured with the help of an absolutely calibrated `zg~h ~-source . After transforming the a-energy scale to relative momentum ( p/p° , with p® the central momentum), the whole transmission curve can be scanned by measuring the c~-spectra at appropriate different magnet settings . A comparison between the calculated and measured geometric eihciency (i.e. transmission curve converted to ei~ective solid angle) is made in fig. 2 for the 1g0° set-up . (An example of such a comparison for the forward set-up can be found in ref. 2°) .) The agreement

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425

0 a

cot v

Fig. 2. Comparison between the measured (open dots) and the calculated (solid line) transmission (or geometric efficiency) as a function of the relative momentum (plpo, with p® the central momentum) r the lg®° set-up . The dashed curve shows this same calculated quantity for the Ct° set-up .

is excellent ; some minor deviations in the slopes can be attributed to the i ite knowledge of the fringing field shapes. Consequently, the transmission of t e spectrometer for protons was determined using the same onte Carlo code. 2.3. DATA TAKING

All subruns of an experiment were summed, and normalized to the amount of charge - or photon energy - collected by the 1$S- 2 chamber 24), taking into account air pressure and ambient temperature for each roan. e energy calibration a-source, of the surface barrier detector was performed with the help of a 2228 _yielding peaks with energies between 5 .4 and 8 .8 eV. Fig. 3 shows a representative example of a raw recorded summed spectrum for the forward 15 MeV experiment . The data points represent the proton counts from the CD2 target, the histogram the background from the 01-12 foil. Note that no scaling whatsoever has been carried out to the spectra. The vertical dashed lines indicate the transmission region, extending roughly from 5 to 10.2 eV proton energy, which can be clearly distinguished from the low energetic background . In this tow-energy interval, both the C132 and 01-12 spectra perfectly coincide . This can be understood by the fact that this exponentially decreasing background mainly . e stems from Compton electrons and/or photons randomly reaching the detector fl 2C( a ) y, background in the transmission region mainly originates from the reaction 25 ) taking place in the target . In order to obtain the net counts from the 2 1-I(y, p) reaction only, the C 2 background can thus simply be subtracted from the CD2 spectrum, without any further correction, since both targets have the same effective thickness for the production of photo-alpha particles (i .e. the thickness of the targets being of such magnitude that a-partiicles produced at the beam entrance

426

A.

Graeve et aL / Deuteron photodisintegration

00

7.0

9.0

11.0

P®PtocleEnergy 1 MeV) o~

Fig. 3. Semi-log plot of the measured normalized particle spectra for the forward 15 MeV experiment. The solid dots are obtained with the CD, target, while the histogram stems from the CH2 measurement. The transmission region is indicated by the vertical dashed lines.

side, lose too much energy and are no longer accepted by the spectrometer; consequently, only a fraction ofboth CD, and CH2 targets contributes to the transmitted cr-spectrum, yielding a nearly identical background). 3. Method of analysis For the analysis of the data a Monte Carlo simulation of the entire process was performed. Evidently, the starting position is the target, of which the knowledge of the exact thickness and ofthe deuteration percentage (94.2%) is required (for details of the target composition see ref. `2) ). The precise depth at which the photonuclear reaction is to take place, as well as its position are randomly chosen (and uniformly distributed over the beam spot size of the target ; this is justified as the photon collimator has an opening angle much smaller than the average angle of emission of the bremsstrahlung) . The calculation is performed as follows : for a certain photon energy (e.g. E,, _ 10 MeV) the relevant energy interval covering at least the transmission region, is determined. This interval is divided in bins of 100 keV. In each bin the absolute number of photons is calculated based on the Schiff integrated-over-angles (IOA) bremsstrahlung formula - taking into account the appropriate beam hardener and normalizing the total area of the Schiff spectrum (integrated over energy) to the total photon flux measured with the NBS-I'2 chamber. In a second part the number of protons is determined that has to be followed through the detection system. Here the number of target nuclei, the number of photons as just calculated for that energy

A. De Graeve et al. / Deuteron photodisintegration

427

and the theoretical deuteron photodisintegration cross section for that photon energy are taken into account. In such a way the absolute number of protons is found for that 100 keV wide photon energy bin. The energy dependence of the cross section and the angular distribution (around 0° or 180°) is given by theoretical results from ref.'). In fact four different simulations were performed to probe the influence of the theoretical input on the final results: a standard cross section (based on the Paris and Bonn potentials) and a relativistic one (idem). The differences on the deduced cross section values were in any case smaller than 1 .5%. Further important "processes" to be taken into account are the energy loss an processes related to it, multiple scattering allowing protons with a dishitegratic angle of up to 11° to leave the target in the forward direction. Therefore, the u the of the full Partovi expression for the differential cross section is required b sin' 0 term is non-negligible. The energy loss is calculated over the remainder target layer by a range-energy formula and is of the order of roughly 0.5 e but can be as large as 15% of the initial energy, while the determination of the multiple erman 26). e scattering is based on the concepts developed by Marion and Zi proton with this resulting energy and angle is followed through the spectrometer. The discussed procedure is applied for a large number of protons in each energy bin and results in an absolute proton spectrum at the detector position. e effect of multiple scattering convoluted with the angular distribution on the cross section value is of the order of 1% (180°/ 15 MeV) to 3% (0°/ 10 MeV). The comparison of the simulated spectrum with the net measured one directly yields the absolute cross section value. Fig. 4 displays the net measured spectrum as data points and the simulated spectrum as a histogram forthe forward 15 MeV experiments. The theoreti.ie .i . . . .0 . . . . . . .eef .e . . . . . . .

. . . . . . . .

0

5

'

J~

o 2

U

1-1

5.0

8.0 9.0 6.0 7.0 Detected proton energy (MeV)

10.0

Fig. 4. Comparison between the net measured spectrum (data points) for the forward 15 MeV experiment and the Monte Carlo simulation (histogram) as described in the text .

.A. De Graeue et al. / Deuteron Photodisintegration 1 cross section put in is the relativistic calculation using the Paris potential from ref. e correction for the effect of multiple scattering on the deduced cross section for the 0® measurements is negligible (<0.3%) . Furthermore, the energy loss of the protons is smaller than at extreme angles since the targets are only 4.88 mg/cm2 (CD,) and 4.56 mg/cm'- (C 2) thick.

xperintental accuracy The possible sources of systematic errors or uncertainties are the following: (a) the bremsstrablung shape, which is assumed to be correctly described by the Schiff-1 .{ß.A. spectrum, (b) the beam monitoring or the collection of the total (integrated) charge by the BS-P2 chamber, (c) the thickness, and more importantly, the composition of the target foils CD, and CH,, especially the amount of deuterons resent, (d) the transmission or geometric efficiency of the experimental et-up and (e), the method of analysis (energy loss, multiple scattering, . . .). stringent test for the overall accuracy of the experiments at extreme angles without having to check all possible sources of uncertainties separately - is the measurement of the forward Compton electron yield. The 0® cross section (differen tial with respect to the Compton electron solid angle) for this process is exactly known from the Klein- ishina formula and amounts to 1 .678 b/sr at a photon energy of 10 eV. e experimental set-up used is nearly identical to the 0° proton lay-out: identical targets, photon beam endpoint, spectrometer arrangement (collimators, magnets) and detector position were used. The only differences were (a) the intensity of the photon beam, which was lowered by about a factor of 100 to avoid pulse pile-up, (b) a thick Si-detector (2 mm) with an area of 1250 mm2 was employed and (c), a much lower magnetic field (-I kG) was necessary to focus electrons with kinetic energies (Ej between 7 and 15 eV. In order to eliminate the pair electrons, which also contribute to the measured forward electron yield, the pair positrons were measured by reversing the magnetic field. In total, four series of runs constitute one cycle of a measurement at a certain energy: namely (i) electrons from the CD2 target, eT, (ii) electrons from an empty target holder, e~, (iii) positrons from the CD2 target, eT, and (iv) positrons from an empty target holder, eÉ . The net Compton electron yield is en,, =(e-r-e-) -(eT-e')

An example of such a net energy loss spectrum is given in fig. 5 for E,, =15 MeV. The solid curve represents a calculated shape of the recorded spectrum. This is based on the computation of the energy loss of electrons in silicon as proposed by lunck and Leisegang 27), leading to an improved, i.e. broader Landau spectrum. Furthermore, a factor was included in the calculation, taking into account a broadening due to the unknown electron-energy resolution of the detector.

A. De Graeve et al. / Deuteron photodisintegration

:5 O U

429

0 400

600

800 1000 DEe(kéV) in Si

1200

1400

Fig. 5. An example of a net Compton electron energy loss spectrum with the spectrometer set for 15 eV z~) photon energy. The solid line depicts the theoretical shape as predicted by 8lunck and Leise ng (see text).

In order to establish the overall systematic uncertainty of the experiments, the integral of the measured spectrum has to be compared to the theoretical result. latter is determined from a Monte Carlo simulation (as for the photoproton ex ments) starting from the Klein-Nishina cross section values, including the energy dependence and the angular distribution ofthe cross section and taking into account the multiple scattering of the electrons in the target. The difference between the integral of this resulting spectrum and the measured one directly gives the accuracy. This turns out to be about 3% which, incidentally, is also the accuracy of the 24) of the NBS-P2 ionization chamber which was used as the calibration constant primary tool for the determination of absolute cross sections; this implicitly proves that the bremsstrahlung shape is correctly described by the Schiff IOA expression for our geometry .

esults and discussion 5.1 . THE 0=0* RESULTS

The absolute c.m. values for the forward 2H(y, p) cross section are reported in 2°'21) . A compilatable 2. Some of these data have been discussed previously in refs. tion of our data in the low energy region is given in fig. 6. (Note that here more data points are shown than listed in table 2; in the figure we plotted all deduced cross section values resulting from an analysis wherein the transmission region 2°,21), while the table only contains those was split up in several energy bins values corresponding to the plateau region of the transmission curve.) Some "16) are also indicated. Comparison with theory leads to several theoretical results 2''15 observations .

~ t raeve et al. / Deuteroaa photodisirttegration

.

3®

TABLE 2

Elbsolute c.m. cross section values for the 2I-i(y, psu reaction at extreme angles and at 90° c .m, as a function of lab photon energy (with ®E,, = half width of the transmission region) E,, ( ev)

c~E~

do'/d~l (0°) (wb/sr)

0.9

5.89 ~0.28

1.2

5.38 ~0.20

eV)

(

7 7.5 8 9 10 11 12 13 14 .5 14.3 15 16 17 i8 19

6.11 ~ 0.29

d~/d!l (90°) (wbAsr) 237.39 ~ 1.27

4.32~ 0.35

1.3 2.0 1.6

dQ/d~t (180°) (wblsr)

4.18 ~0.29

208.47 ~ 1. 184 .18 ~ 1.28 1 .86~ 1.17 149 .27 ~ 1.24 135 .33 ~ 1.64 122 .93 ~ 1 .39 111 .60 ~ 1 .00 102.22 f0.81 94.81 ~0.84 85.91 ~ 1 .78 82.17~ 1 .25 78.69 ~ 1.72

10

4

8 12 Lab Photon Energy

16 (MeV)

20

Fig. 6. ®ur measured forward 21-1(y, p)n absolute cross sections in the low energy region : dots: ref. Z° )~ triangles : ref. 2') . 1'he curves represent the result of various theoretical calculations : full line: ref.') long-dashed line: ref. 2); dash-dotted line: ref. '6) ; dotted line: ref. 's) . For the interpretation of these curves, see text.

431

A. De Cïraeve et al. / Deuteron photodisintegration

First of all, the minimum in the cross section, predicted by almost all of them 14)), is confirmed. Although the exact (an exception is the calculation by Lucio et al. position of the minimum ca not unambiguously be determined, it can hbe concluded that it is not located below 9 eV. Secondly, the standard calculation by artovi 2) does not suffice to describe the absolute magnitude of the measured cross section. At these low energies, this is primarily due to the effect of meson exchange but on the other hand it seems that also (the method of) including relativistic effects as an influence. Thirdly, the measured cross section values around 15 eV are surprisingly e when compared to the standard and conventional relativistic calculations . 15), describing these poin Lorentz- and gauge-invariant approach by hiagornyi et aL the closest has to be rejected (see also ref. 17)), when examining the very low-ener range, i.e. below 9 eV. Another calculation ruled out by these measurements is e the diagrammatical approach by Laget 16), predicting the minimum at 1 owever, it is noteworthy to mention here the results of a similar but improve approach by Levchook 28), who obtains remarkable agreement it experiment. 5.2. THE ® = 1so® RESULTS

Table 2 also contains the cross section values for the backward reaction at =12 eV and 14.5 eV. The last value corresponds to a rather large energy bin. This is due to the fact that all data in the transmission region were used, without being able to rely on the spectroscopic information we normally have from the solid state detector (see sect. 2.1). Fig. 7 contains the backward cross section values and 2'4'6) . For this backward angle, the comparison of a. set of theoretical calculations experiment with theory reveals no problems : apart from the calculation by Pandey

6

10

26 36 46

50

60

70

80

90

100

Lab Photon Energy (MeV) triangles: ref. 9). For Fig. 7. The backward absolute 2 (,y, p)n cross section: solid points: our data ; dashes : ref. 2); comparison the result of various theoretical calculadons is shown: full line: ref. 4); long paper) . in this results the various short-dashed line : ref. 6) (representative example from

A. De tiraeve et al. / Deuteron photodisintegration

432 et

l.

6 ), all theoretical calculations describe the new data points very well. It is

interesting to note that the minimum (if any) in this case seems to be much less pronounced than in the forward cross section ; the data point at E,, = 38.2 MeV is questionable 9), as this backward cross section value is larger than the forward one. 5.3. THE 0 =90° RESULTS

Fig. 8 displays the (centre-of-mass) differential cross section at ®c_,. = 90° In the energy region 7-19 eV (see also table 2) . These values are the weighted mean of all the measurements of this cross section, performed simultaneously with the experiments at extreme angles. Shown as a dashed line in fig. 8 is the fit to the world 23). In this fit, special attention was given to the low energy region; its accuracy data is believed to be not better than 2-3%. The result of a relativistic theoretical calculation 7) is indicated by a full line . e influence of the relativistic effects on the cross section is almost negligible at this angle: a standard calculation would not be distinguishable from the relativistic one. conclusion here is that the new 90® values agree with the existing data within about 3%, and furthermore correspond extremely well with theory. It also shows that the experimental parameters in our experiments were well under control, giving an enhanced credibility to our cross section values at extreme angles, especially at the backward angle, where the Compton electron yield cannot be measured and one has to rely solely on the 2 ionisation chamber. 5.4. DEDUCED VARIABLES

Combining our data at extreme angles, the values of a and c can be unambiguously determined, as was pointed out in the Introruction. Table 3 compares the experimental a- and c-coefficients at 12 MeV (using an interpolated 0° value) and at 250 200 :~_ 150C:

100 -

b

`J 50 5

10

15

Photon energy (Me\i )

20

Fig. 8. The absolute c.m. cross section at 90° c.m. in the energy region 7-19 MeV, as determined from our experiments . The dashed line is the result ofa fit to the world data 23), while the solid curve represents the theoretical prediction 7 ).

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433

TABLE 3

Comparison of the experimental a- and c-coefficients with a number of theoretical values (S= Standard, R = Relativistic) EY (1VleV)

This work (ILb/sr)

S/Paris 2)

S+MEC 4)

R/Paris 7)

R/Bonn 7)

R/RSC 4)

a

12 14.5

5.00 :E0.23 5.15 :1:0.21

4.66 4.89

5.17 5.23

4.91 5.01

4.75 4.85

5 4.99

c

12 14.5

u.68 :1:0.23 0.97+0 .21

0.52 0.63

0.46 0.55

0.49 0.60

0.47 0.57

0 0.55

Coefficient

14.5 MeV with several theoretical results. Note first of all that the c-values are definitely positive, which terminates a controversy 9) about its sign. e a- e cie t compares well (within one standard deviation) with theory, if at least es exchanges are included (columns 5-8). Here again, it is clear that at these 1 energies the major effect is not of relativistic origin, but is due to the inclusion f meson exchange . When considering different potentials (columns 6 and 7), one the impression that the Paris potential leads to a better description of the data than the Bonn potential, the latter giving results for a which are more than one standard deviation lower than the experiment. As for the c-coefficient, the situation is not so obvious. The experimental values agree reasonably well with the theoretical ones at E,, =12 MeV, whereas at 14.5 eV this is only the case within two standard deviations . All theoretical values of c at 14.5 MeV are lower than 0.65 wb/sr (the highest value being found for the standard calculation) . Since the c-coefficient primarily contains E1-E2 interference terms, one can possibly locate the source of the problem in either the calculation of the E l or of the E2 transition amplitude. In order to obtain good agreement with the results of the measurements for the ratio of the differential cross sections for the 2 H(y, n)p reaction at 45°, 135° and ts), adjimic ael et 155° to that at 90°, performed at Argonne National Laboratory '9) al suggested recently a modification (possibly originating from non-nucleonic degrees of freedom or from changes in the long range part ofthe NN wave functions) to the E2 transition amplitude, which has a direct impact on the c-, d- and ecoefficients . From a fit to the Argonne data they arrive at c-coefficients which, in the relevant energy range, are significantly higher than those obtained i the conventional E1-Ml approximation (in the language of ref. '9)) ; moreover, this coefficient now shows a descending trend as a function of the photon energy. Although may be not too much importance should be attached to the absolute magnitude of the deduced coefficients, the values of the resulting c-coefficient, however, seem to e unacceptably high (at 121VIeV it equals 2.95 p,b/sr, and at 15 eV it still amounts t o 2.35 ~Lb/sr) and are in clear disagreement with our experimental data. Finally, these fitted coefficients lead to a completely unrealistic forward/ backward cross

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section ratio, (in`,olving the coefficients a and c), showing that only a direct measurement of this quantity will lead to an unambiguous conclusion . . Summary

conclusions

In this paper we described the measurement and analysis ofthe absolute 2H(y, p)n cross sections at extreme angles at the energies 7.5, 10, 12 and around 14.5 MeV. Simultaneously the differential cross section at 90° lab angle was measured as well. For the first time the differential cross section values at these energies have been obtained with a systematic uncertainty of at most 3%. This was determined by measuring the forward Comp- on electron yield, using the same target, spectrometer and detector. A further result is that our high-accuracy 90° cross section values 23) . confirm the evaluated data set In figs. 6 and 7, the new results at extreme angles were compared with theory. It can be concluded that the minimum in the forward cross section lies between 9 and 11 eV photon energy while, considering all available data, the backward cross section does not seem to show a pronounced dip (see sect . 5 .2). At these lower energies especially the effect of meson exchange plays an important role. Furthermore, several theoretical calculations can be rejected '5 '6), based on the experimental values at extreme angles: Nagornyi et al. ), Laget Pandey and Rustgi 6), the standard calculation by Partovi 2) and also the recent interpretation by Hadjimichael et al. '9) of the Argonne data . Comparing the results of two calculations using identical methods but different NN potentials with the measured values, indicates a slight preference for the Paris potential over the Bonn potential. In fig. 9 the existing forward cross section values below pion threshold are compared with three theoretical results [by Jaus et aL 5 ), Friar et aL 4) and 'S Nagornyi )], and for completeness, also a standard calculation using the Paris potential 2) is shown. The rather high value of the cross section at 14.7 MeV cannot satisfactorily be reproduced by theory. Examining in more detail the Partovi coefficients a and c at 12 and 14.5 eV (table 3), the deviation between theory and experiment can be located in the c-coefficient. The fact that the a-coefficient agrees well with the different theoretical approaches indicates that meson exchanges are taken into account correctly. It seems, however, that still more consistency in the treatment of the reaction, modifying the E l and/or the E2 transition operator, is nec ssary. A final remark concerns the adjacent energy region (20-50 MeV). As can be seen in fig. 9, the recent calculations still overshoot the existing experimental values in this range. It seems worthwhile and interesting to perform some additional experiments. At the PI/ ainz such measurements are in progress for the outgoing protons at 0° as well as at 180' in order to obtain the fore/aft ratio. e acknowledge the financial support lent by the Interuniversity Institute for Nuclear Science (III ) and by the National Fund for Scientific Research (NFWQ)

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A. De Graeve et al. / Deuteron photodisintegration 10 -! 9 ~~

0=o'

8 ~,

r

E5 4

b 3-v `11 2 0

i

0

I

10

T

20 30 40 50 60 70 80

90 100 110 120

Lab Photon Energy (MeV)

Fig. 9. Overview of all existing experimental data below pion threshold for the forward 2H(y, p)n reaction cross section: solid dots : our values ; open circle : ref. 12 ); full squares: ref. 3) ; open diamonds: ref.'); solid triangle: ref."). The curves are a representative set of recent theoretical results. (a) A standard approach: long-dashed line 2), (b) relativistic calculations : full line : ref. 4); dash-dotted line: ref. 5); ls). dotted line : ref.

Brussels, Belgium. We are grateful to the ax-Planck-Institut für C e ie (Abteilung Kernphysik) for making almost the entire experimental equipment used in these measurements available to us. We also wish to express our gratitude to the linac crew of the Nuclear Physics Lab (Gent) for the many hours of smooth beam time. e ere c 1) 2) 3) 4) 5) 6) 7) 8) 9)

10) 11)

12) 13) 14)

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