Determination of the n-n scattering length from the2H(n, np)n reaction at bombarding energies between 17 MeV and 27 MeV

Nuclear Physics A329 (1979) 141-156: © North-Holland PublishGep Co ., Amsterdam Not to be eeproduced by photoprint or microfm without written permission from the publisher

DETERMINATION OF THE n-n SCATTERING LENGTH FROM THE =H(n, np)n REACTION AT BOMBARDING ENERGIES BETWEEN 17 MeV AND 27 MeV W. VON WITSCH, B . GÓMEZ MORENO, W . ROSENSTOCK und K. ETTLING t

Institut für Strahlen- und Kernphysik der Universität Bonn, D5300 Bonn, Germany and J . BRUINSMA rt

Natuurkundg Laboratorium, Vrye Unioersiteit, Amsterdam, The Netherlmds Received 23 March 1979 Abstract : The n-n final-state interaction has been investigated in a kinematically complete experiment with high statistical accuracy via the 2H(n, np)n reaction . An intense neutron beam with a continuous energy spectrum up to 27 MeV was used and protons and neutrons were detected in coincidence, probing a region of phase space not investigated before at these energies. The Monte Carlo analysis with exact, charge dependent three-body calculations with S:wave rank-one. separable potentials and exponential form factors yields a. = -16.9 f 0.6 fm for the n-n scattering length . A comparison with calculations by P . Doleschall including P- and D-waves as well as a tensor force suggests that the theoretical error is much smaller than the experimental uncertainty .

E

NUCLEAR REACTIONS 'H(n, np)n, 17 MeV 91 E ;5 27 MeV ; measured o(E., n-p coin . Deduced n-n scattering length . CD, target.

Ed,

1. Introtlot:tion Numerous attempts have been made t) to determine the neutron-neutron scattering length since Wong and Noyes 2) suggested in 1962 that measurement of a., by way of comparison with the Coulomb-corrected proton-proton scattering length app, would provide a very sensitive test of charge symmetry in the strong interaction. However, for a long time the result ofjust one such experiment could be considered experimentally accurate as well as reliable from a theoretical point of view, namely the kinematically complete measurement 2 H(n - , 2n)y by Haddock et al. s) who obtained am = -16.7 f 1 .3 fm [ref. 4 )] . In all other reactions at least one additional nucleon was present in the final state whose interaction with the two neutrons could not be treated in a dynamically exact way. This situation was changed some years t Now at Dornia AG, Frieçfrichshafen, Germany . tt Now, at Hydraulic Division of the Delta Department, The Hague, The Netherlands.

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ago when numerical solutions to the Faddeev equations became available s) which could be used for the analysis of break-up spectra from the ZH(n, 2n)p reaction . Nevertheless, only three experiments have been reported 6-a) until now in which kinematically complete measurements were performed t and where exact Faddeev calculations were employed to extract the n-n scattering length . From these, done at 14 MeV [refs. 6, e)] and at 18.4 MeV [ref. ')], a weighted mean value of a. = -16.2 f 0.7 fm can be deduced, with an additional theoretical uncertainty of the order of ±0.5 fm [ref. 9 )] . On the other hand, Alder et al. 11) obtained a. = -18.3 f0.5 fm from a very careful and precise measurement of the y-spectrum from the 2 H(n- , y)2n reaction which is considerably smaller than the hitherto accepted value of about -16.3 fm [ref. 9)] . In this paper, a kinematically complete measurement of the 2H(n, np)n reaction is described which extends the earlier ones 6-e) to higher bombarding energies and employs a different geometry . High statistical accuracy was obtained by use ofan intense neutron beam of continuous energy up to 27 .1 MeV. The analysis was performed with Monte Carlo simulations using exact, fully charge depenent threebody calculations with S-wave rank-one separable potentials and exponential form factors 12). The dependence of the extracted value for the n-n scattering length upon higher partial waves and tensor forces is investigated . 2. Kinematical considerations The present experiment differs from previous ones mainly in two respects ; Protons and neutrons were detected at nearly equal angles on opposite sides of the beam, corresponding to a kinematical situation where n-n and n-p final-state interactions (FSI) appear symmetrically in the same spectrum together with contributions from n-p quasi-free scattering (QFS) as depicted in fig. 1 . Since a continuous range of bombarding energies was used the break-up events populate an extended region in the EòEp plane, bounded by the kinematical locus for the highest energy, in which the FSI and QFS produce "mountain ridges". Eventual counts from the 12C(n, np)11B reaction on carbon contained in the CD2 target cannot contaminate the n-n FSI region of interest ; the same is true for elastically scattered deuterons which might have falsely been identified as protons. Because the n-n FSI enhancement occurs at high proton energies and runs nearly parallel to the EP axis a fairly thick target could be used without introducing undue broadening of the n-n peak . On the other hand, the n-p FSI which is characterized by low proton energies is then completely smeared out and cannot be observed as a peak. This was, however, considered a tolerable price to be paid for higher statistical accuracy in the n-n FSI region, especially since a direct comparison t Kinematically incomplete experiments in which only the proton is detected at forward angles in the laboratory system are plagued by serious experimental and additional theoretical diíriculties 6) and give inconsistent results '-'°) .

=H(n, np)n

143

18 18 14 12 a

w

10 8 8 4 2 '24681012141616

En [MOI

Fig. 1. Kinematics of the 'H(% np)n reaction at 0. - 50° and 0. = -4g° for bombarding energies Eo between 17 MeV and 27 MeV. 'Me minimum relative energy in the two FSl regions is zero, the lowest spectator energy is approximately 0.5 MeV . Also shown are the locus for the "C(n, np) 1 `B reaction at Eo = 27 MeV (dashed curve) and for elastic n-d coincidences (dash-dotted line), some of which can reach the detectors due to multiple scattering .

of the two interactions in the 'So state is not. possible anyhow due to the IS, admixture in the n-p force.. 3. Experimental set-up and procedure The experiment was carried out at the isochronous cyclotron of the University of Bonn in three separate runs. The experimental arrangement is shown in fig. 2. The primary neutron beam was produced via the d+d reaction in a Wavily shielded, LNZ cooled target cell filled with deuterium gas to a pressure of 90 bar [ref. 13)] which was bombarded with 28 MeV deuterons of 10 AA average intensity. Neutrons emitted in forward direction were collimated to produce a beam of 22 mm diameter with an intensity of 1 .65 x 106 neutrons/MeV . cm2 - s on the target for the highest energies . The energy distribution of the neutron beam was monitored with a proton recoil telescope positioned just downstream from the reaction target (fig . 3). The target consisted of a CD z foil of50 mg/CMZ thickness in the first, and of30. mg/cm' in the second and third part of the experiment . It was mounted perpendicular to the axis ofthe proton arm in a small, thin-walled scattering chamber with beam entrance and exit windows made from 30. .um thick Ti foils to minimize the amount of background-producing materials in the immediate target vicinity . The target had the form ofan ellipse with half-axes of 15 mm and 10 mm, respectively, so that it appeared as a circular disc to the beam, with a diameter slightly smaller than the mouth of the

W . VON WITSCH et al.

144

CONCRETE ~~ w1 84C NEUTRON Pb 1-'-_ PARAFFIN ä ; ; ; PARAFFIN 41 2 CO 3 i

BEAM NEUTRON DETECTOR WITH COLLIMATOR AND, SHIELDING

CD2-TARGET and SCINTILLATION FOIL DET. Cu -COLLIMATOR ^?Y-MONITOR

Fig . 2 . Experimental arrangement .

r Z

m W Z Z U W d N 2

10

20 30 E .[MWI Fig. 3 . The continuous spectrum of the neutron beam as recorded with the proton recoil telescope for energies above 10 MeV .

'H(n, np)n

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collimator. The target was positioned by means of a self-portrait of the neutron beam obtained in a 2 min exposure by placing X-ray film in the target plane preceded by a 0.3 mm polyethylene converter. In the first run, break-up protons were detected at 48° with a NE104 plastic scintillator of 110 mm diameter which was replaced in the last two runs by an arrangement of six 450 mm' Si surface-barrier detectors mounted in two vertical rows at47° and 49°, respectively, in each ofwhich the three detectors were electronically treated as one. On their way from the target to the proton detector the charged particles had to pass through a thin (ca. 1 .5 mg/cmz) scintillation foil detector i4) positioned close to the CDZ target in order to produce the start signals for the timeof-flight (TOF) measurements. Neutrons were detected at 50° on the opposite side of the beam with a 76 mm thick NE213 plastic scintillator of 127 mm diameter . It was well shielded and equipped with a double-truncated conical collimator made from a mixture of Li2 C03 and paraffin and designed following the prescription of Glasgow et al. ") to minimize accidental as well as time-correlated background from neutrons scattered in the throat area or from the surface of the collimator walls. Pulse shape discrimination was employed to distinguish neutrons from y-rays while the TOF together with the pulse height in the proton arm served to reject recoil deuterons and heavier charged particles. In addition to the pulse height and TOF spectra of the reaction products, the TOF of the bombarding particles was determined by recording the time difference between signals from the scintillation foil detector and the r.f. signals from the cyclotron which overdetermines the kinematics, helping to reduce accidental background. Six parameters were thus recorded in coincidence and stored on magnetic tape for subsequent off-line analysis : pulse height and TOF in both the neutron and proton arm, the pulse shape signal from the neutron detector, and the TOF of the incoming neutron. A simplified diagram of the electronic set-up is shown in fig. 4. In the neutron detector, the dynode pulses were electronically limited so that a higher gain could be utilized for the smaller pulses . This made possible the use of a threshold below 50 keV equivalent èlectron energy in the presence of high energy neutrons, providing a useful dynamic range in excess of 250 :1 as well as a relatively high detection efficiency which is slowly varying with energy down to Eo x 1 MeV . For pulse shape analysis the anode rather than the dynode pulses were used resulting in a much improved n-y discrimination at the lowest energies (fig . 5) . The zero points of the time scales in the neutron and proton arm and the relative timing between the two arms were set by means of coincident y-rays from a "Na source and with a's from "'Am. Additional calibration points were provided by small prompt y-peaks appearing in the TOF spectra of the two detectors. The zero points were adjusted to lie in the middle of the time scales so that the tpt,, plane was divided into four sectors, three of which contained only accidental coincidences which could then be subtracted in the off-line anaysis. The time resolution was measured for each detector combination as a function of energy and found to be typically 1 ns. The

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relative stability of the r.f. signal from the cyclotron was monitored with a tiny plastic scintillator plàced close to the gas target, detecting v-rays produced by the deuteron pulses in the beam stop and measuring their time of arrival in relation to the r.f. signal. Details of the methods used for the calibrations of the various time and energy scales are given elsewhere 16).

Fig. 4. Simplified block diagram of

The relative efficiency of the neutron detector was calculated with the Monte Carlo program HYCALC ") and checked with neutrons from the 3H(p, n)3He and IH(d, n)"He reactions.*For use in the Monte Carlo simulations, the differential efficiency across theface of the detector wasmeasured at E, = 4 MeV and at 6 .5 MeV, as were the resolution and the response of the proton scintillation detector as a function ofenergy. The efficiency of the scintillation foil detector was also measured and found to be close to 100 l up to 20 MeV [ref. '°)]. The singles count rates were approximately 1 .7 x 10' s-1 in the proton scintillator, 800 s - ' in each of the two sets of surface-barrier detectors, 1 .6x 104 s -1 in the neutron detector, and 101 s- ' in the scintillation foil detector. The total experimental running time was 26 d, resulting in more than 30 000 true coincidences in the n-n FSI region for bombarding energies above 15 MeV.

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Fig. 5 . Pulso-ehape discrimination versus pulse height for a threshold of 50 keV equivalent electron energy. The peaks at maximum pulse heights are due to the electronic limiting of the dynode pulses as explained in the main text .

4. Data red~ and aoatysis 4.1 . EXPERIMENTAL RESULTS

The raw experimental data had to be reduced for the analysis in order to eliminate background and to bring the data into a form suitable for comparison with theory . The main contributions to the background came from y-rays and from deuterons scattered into the proton detector, some of which were in true coincidence with neutrons because the two detectors were positioned close to the recoil axes for n-d (and n-p) elastic scattering, an advantage for calibration purposes 16). The y-rays were removed by a two-dimensional window applid to the pulse shape versus pulse height spectrum of the neutron detector (fig . 5) while an EP mass-analysis was performed to separate protons from deuterons.

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Background was further reduced by use of the measured energy (TOF) of the incoming neutrons. For each event, a nominal bombarding energy Eó was calculated from three-body kinematics for point geometry and compared with the measured one. If the two differed by more than twice the experimental uncertainty due to finite geometry, resolution, and target thickness the event was rejected. After this kinematical restraint had been applied there were still some accidental coincidences left which were investigated by moving the zero points of the time axes into the regions of negative TOF and repeating the analysis under otherwise identical conditions . The situation is somewhat complicated by the fact that most, but not all, accidental coincidences are correlated in two of the three detectors. However, with deuterons and y-rays removed beforehand, the relative number of accidentals remaining in the region of interest, i .e. for EP z 6.5 MeV, was merely 2 % which were subtracted from the data. A detailed description of this procedure is given in ref. '6). The statistical accuracy obtained in the present experiment was still not sufficient for a direct, i.e. three-dimensional, analysis (fig. 6). Consequently, a way had to be found of condensing the data before comparison with theoretical predictions. The procedure chosen is based on a method first described by Schram et al. ' e). In the momentum plane, for fixed scattering angles Bo and Bp, events belonging to different bombarding energies Eo fall on kinematical ellipses of equal excentricity . When the co-ordinate system is rotated through 45° and its origin shifted into the centre of the respective ellipse an angle a is obtained which defines, together with Eo, the kinematics of the event completely. The big advantage ofthis parametrisation is illustrated in fig. 7 : the same value of a corresponds to the same kinematical situation - e.g. a = 43° for the n-n FSI - for all bombarding energies t9), thus

Fig . 6 . Isometric presentation of the experimental results for bombarding energies above 14 MeV. The n-n FSI appears as a high mountain ridge in the right hand corner .

2H(n, np)n

149

V C O

â â

Fig . 7. Kinematical ellipses in the momentum plane. Any particular kinematical situation such as, e .g ., the n-n FSI occurs at the same value of the projection angle a irrespective of the bombarding energy .

providing a convenient means of compressing the data into two-dimensional spectra without loss of resolution . The dependence on 0 is weak so that the data from the two rows of proton detectors at 47° and 49° could also be added up. For the analysis, all counts falling within a given energy bin AE; were then projected onto the a-axis. However, it should be emphasized that due to the finite resolution and target thickness the value of Eó calculated for each event from the measured energies Eo and EP could differ appreciably from the actual bombarding energy Eo as demonstrated in fig. 8 . A mass spectrographic analysis performed on the deuterated polyethylene target indicated a.hydrogen content of 1 %. A background run was therefore made with the CDZ target replaced by a CHZ foil of equal thickness revealing that some elastic n-p events did reach thedetectors through multiple scattering, forming a narrow peak in the QFS region near a = -15°. While this "true" background (which was subtracted from the data) amounted to approximately 5 % in the maximum of the hydrogen peak it was flat and smaller than 0.3 % for a z 0°, proving that no appreciable number of n-p coincidences from any background producing reactions were present in the n-n FSl region of interest. 4s . THEORETICAL SPECTRA

For the analysis, the experiment was simulated by Monte Carlo calculations described in detail in ref. 19) and sketched briefly in the following.

w. VON

150

WITSCH er

m.

W z z V K W

n. z

o c>

17

19

21

E, [MeV]

23

25

27

Fig. 8 . Monte Carlo spectrum of the bombarding energies Eo which contribute within the indicated range of energies Eo which are the fictitious bombarding energies calculated from the memwed energies Fb and Ev neglecting energy loss and finite resolution .

First, a bombarding energy was selected according to the measured distribution (fig . 3). Random numbers were then chosen to determine the reaction point in the target, a point in the neutron detector and on the face of one of the proton detectors. After a correction for multiple scattering in the proton arm the relevant kinematical quantities and the phase space factor were calculated using relativistic kinematics . In order to find the "measured" quantities En, EP, and Eé the specific experimental conditions were now taken into account, viz. the energy loss and the energy straggling of the protons, the energy and TOF resolution in the proton and neutron detector, respectively, and the conversion of the neutron TOF into energy using an average flight path. After this, the relative weight factor was calculated regarding the efficiency of the neutron detector and the energy dependent loss of neutrons due to interactions in the target and other materials. Since in the n-n FSI both neutrons are travelling together with low relative energy so that the probability is rather high for both of them to hit the detector the resultant increase of detection efficiency was also taken into account. To obtain the theoretical cross sections the Faddeev equations were solved beforehand, using an improved version of the Ebenhöh-Bruinsma-Stuivenberg (EBS) code '- ") with fully charge dependent S-wave rank-one separable potentials and exponential form factors. These calculations were performed for 7 values of

2Wn, np)n

151

the n-n scattering length between a. . = -13 fm and a m = -19 fm, in steps of 1 fm, . and for 15 bombarding energies from Eo = 14 MeV to Eo = 28 MeV, in steps of 1 MeV; the effective range was kept fixed at r o , m = 2.8 fm. In the EBS code the calculated amplitudes are fitted with a function whose parameters constituted part of the input for the MC program. The matrix element for any value of Eo could then be obtained by linear interpolation, thereby introducing an error in the cross section calculation which was shown to be smaller than 0.1 % in any case . Because the wide range of energies necessitated the simulation of a unusually large number of events every effort was made to speed the MC program up, e.g. by avoiding the very time-consuming use of subroutines and the simulation of events which ire not actually observable in the experiment, and by incorporating pre-calculated tables whereever practicable 19). Thus the timeneeded for the complete simulation of one event was only 2 ms (CPU) on the University's IBM 370/168 computer while the calculation of the matrix elements at the two energies needed for theinterpolation took 5 ms (CPU) which is five timesfaster than the earlierversion of the EBS code 7); only after this improvement was its use in the present case feasible . Since the experimental data below Eó = 17 MeV were considered less reliable due to various experimental reasons (mainly the low energies of the detected particles) only the data above 17 MeV were included in the final analysis in order to save computer time; this corresponds to the flat, high-energy part of the neutron spectrum shown in fig. 3. For each value of a nn, and for each of the different experimental arrangements, 106 events were simulated to produce the desired statistical accuracy. Finally, the MC data falling within given energy bins AEó were projected onto the a-axis in exactly the same way as the experimental data. 4.3 . DATA ANALYSIS

The projected MC spectra were normalized to the experimental data in the region of strong n-n final-state interaction. The n-n scattering length was then deduced from X2 fits to the shape of the n-n peak alone using am as a free parameter. As can be seen from figs. 9 and 10, the overall fit to the data is good for Eó 5 21 MeV while for higher bombarding energies the theory more and more overestimates the contributions from n-p QFS relative to the n-n FSI. Since the FSI is sitting on the tail ofthe QFSpeak it might be argued that the extracted value of a. can be trusted only if the theory describes the whole spectrum correctly. Excluding therefore the data above Eó = 21 MeV (fig . 9) a best-fit value of a .=

-16.9f0.6fm

was obtained where the error corresponds to Xmin+ 1 and includes statistical and other experimental uncertainties as detailed below. If, on the other hand, only the data above Eó = 21 MeV are used (fig . 10) the result is a. . = -17.0f 0 .5 fm indicating that the shape of the n-n FSI peak and, consequently, the value of am extracted from

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W Z Z S

174 E ; 4 21 [ MeV] a  .-17.0 fm . é.nn 2 .9 f m

200

150

Z W

a.

Z

100

0

50

-40°

-20°

00

PROJECTION

20 °

ANGLE

40 ° '

a [DEG1

60 0

Fig. 9. Projected coincidence spectrum of the data taken with the 30 mg/cm 2 target, for Eo from 17 MeV to 21 MeV corresponding to actual bombarding energies between approximately 18 MeV and 23 MeV (see fig. 8) . The curve is the result of Monte Carlo simulations with a = -17 fm and r,, .. = 2 .8 fm, normalized to the data between a = 25° and a = 60° (full line) .

it are not influenced very much by the presence of the background from n-p QFS even when its relative magnitude is predicted incorrectly by the theory . A similar disagreement between theory and experiment in the QFS region was found by Bovet et al. Z1 ) for the case where the energy of the spectator proton remains several

too Z

300

200

100

-40°

-20° 0° PROJECTION

20°

ANGLE

40°

600

a[DEG1

Fig . 10 . Same as fig . 9 but for 21 < Eo --5 27 MeV.

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'H(n, np)n TABLE 1

Influence of experimental uncertain ties on the deduced value of a-- for the data below Eo = 21 MeV Source of error

da-- (fm)

statistics (experiment) statistics (Monte Carlo) e-(±O .I- ) ep(t O.I-) relative efficiency of neutron detector time resolution of neutron detector neutron loss due to interactions and scattering energy loss of protons (f 10 %) multiple scattering of protons

0.50 0.10 0.10 0.10 0.15 0.10 0.15 0.10 0.05

total

0.60

hundred keV above zero throughout as in the present experiment . More detailed examinations of these effects have been made in several experiments using-proton probes, a review of which is given, e.g., in ref. 31). The influence of various experimental uncertainties on the best-fit value of am has been carefully investigated by means of extensive MC simulations; the important effects are listed in table 1 for the data below Eó = 21 MeV. The influence oftherelative neutron detection efficiency was tested by variation of the experimental input parameters in HYCALC, and by comparison with the analytical program DETEFF zZ) . The number of neutrons not reaching the detector due to interactions in the target and other material was estimated using cross section data taken from the literature . The main uncertainties here stem from the fact that most of the neutron cross sections depend rather strongly on the energy, and that some ofthe lost neutrons are replaced by others with different energies which are scattered into the detector instead. Although these effects are relatively small in the present case they can become appreciable in experiments using thicker targets. The sensitivity of the fits to the effective range is weak ; changing its value by ±0.5 fm does not alter the deduced value of a m by more than 0.05 fm. A precise determination of the effective range from the present experiment is not possible : since the cross section in the n-n peak depends to about the same extent on ro, m and on a. . the uncertainty of 0 .6 fm in the scattering length would cause an equally large error in ro, m even if absolute cross sections were measured with high accuracy. An effort is presently being made to determine ro, o in a continuation of this experiment where n-n and n-p QFS are measured under nearly identical conditions. In order to probe the reliability of the theory which necessarily must work with simplified nucleon-nucleon interactions several calculations were performed with different form factors and potentials. Since it was impossible to repeat the Monte

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Carlo simulations for each theoretical model the following procedure was adopted: for a given set of parameters (usually a. = -17 fm and ro . . = 2.8 fm), spectra were calculated for point geometry with one theory which were then fitted with another one, with a. as a free parameter. Using Yamaguchi form factors (which are generally considerec less realistic 12-1 e) than those of exponential shape) increases the best-fit value of aoa from -16 .9 fm to -16 .4 fm. On the other hand, calculations t by Doleschall 23) at Eo = 22 .7 MeV which include rank-one separable interactions in the 1 So(n-n), 1So(n-p), 1 P 1 , 3 Po , 3 P1, 3 P2, 1 D2' 3 D2, and 3D3 two-particle channels as well as a rank-four 3 S1 -3 D1 tensor force yield virtually the same value for am as the EBS code with exponential form factors, shifting the best-fit value from -16.9 fm to -16.7 fm. However, Doleschall's calculations which were carried up to Jx = ~+ in the three-nucleon system predict a higher cross section in the n-n FSI region thus decreasing the ratio of the peak cross sections for n-p QFS and n-n FSI by about 20 % which improves the agreement between theory and experiment considerably at this energy . In view of this it appears justified to assume a theoretical uncertainty in the extraction of a., from kinematically complete n-d break-up experiments of well below OS fm [ref. ~]. S. Summary and conclusions The neutron-neutron final-state interaction has been investigated in a kinematieally complete high-precision measurement of the 2H(n, np)n reaction in order to obtain a more accurate value for the n-n scattering length, using an experimental technique and geometry which were different from those of comparable earlier experiments 6-s). The deduced value of am virtually coincides with that obtained by Salter et al. 4) in the 2H(x- , 2n)y reaction but is slightly more negative than the results of refs. 6`8) although all of them agree within error bars . Combining the present result with those of refs. 4.6-11) leads to a weighted mean value for the n-n scattering length of am = -16.6 f0.4 fm. Assuming apcp = -17.1 fm for the Coulomb corrected, purely nuclear p-p scattering length 24) the result of this experiment is compatible with recent calculations by Coon et al. 2 °) who predicted Ia.I > Iapp I and Ian. I - 19c'15 1 fm as a consequence of charge symmetry breaking due to electromagnetic p°-co mixing . This would imply that the 'S o n-n interaction is slightly more attractive than the p-p one as required also by the binding-energy differences of minor nuclei 26.27 ). However, the weak point of such a comparison of am and ac - is the fact that, contrary to earlier belief, the Coulomb correction of the experimental p-p scattering length appears to be dubious because it depends strongly on the unknown inner part of t These calculations were performed at the Laboratory for Nuclear Physics of the ETH, ZBrich, Switzerland .

'H(n, np)n

15f

the nuclear potential 28). Consequently, one might follow the suggestion of Sauer 29) and use la.1 as an upper limit on Idpp 1 to impose an effective offshell constraint on the nucleon-nucleon potential. Thus, while until a few years ago most theorists considered the Coulomb corrected value of d-, in conjunction with charge symmetry of nuclear forces, to be the most reliable source of information on a. [ref. 30)] the situation isjustthe opposite today : there are now quite accurate and reliable experimental results on the neutron-neutron scattering length which can be used to pin down acs. Of course, still nothing can then be learned about charge symmetry until the off-shell behaviour of the nuclear potential is known better from independent sources. The authors would like to thank Dr. P. Doleschall for his calculations including higher partial waves and tensor forces. They acknowledge the great effort and cooperation of the cyclotron operations and technical staff. This work was supported in part by the Bundesministerium fur Forschung and Technologie. References 1) 2) 3) 4) 5)

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