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On the determination of the n-n scattering length by the 2H(n,2n)p reaction using thick targets
Volume 91B, number 1
PHYSICS LETTERS
24 March 1980
ON THE DETERMINATION OF THE n - n SCATTERING LENGTH
BY THE 2H(n, 2n)p REACTION USING THICK TARGETS W. von WITSCH, B. GOMEZ MORENO and W. ROSENSTOCK 1 lnstitut fiir Strahlen. und Kernphysik der UniversitiitBonn, D5300 Bonn, Germany
Received 10 December 1979
A computer experiment demonstrates that the values of lannl deduced from the kinematically complete experiments on the 2H(n, 2n)p reaction employed thick targets are probably too small by 1-2 fm because neutron scattering in the target has generally been neglected.
Two reactions have mainly been used for the determination of the n e u t r o n - n e u t r o n scattering length: the pion-induced break-up of the deuteron and the 2H(n, 2n)p reaction. Of these, especially the latter has become a very attractive experimental tool in recent years since numerical solutions to the Faddeev equations have become available [1 ] which can be used for a theoretically sound analysis of kinematically complete three-nucleon experiments. In most of these a thick C6D 6 scintillator was used as a target in which E3, the energy of the break-up proton, was measured as an additional kinematical constraint. The results of two such experiments, done at 14 MeV [2] and at 18.4 MeV [3], were ann = - 1 6 . 0 + 1.2 fm and ann = - 1 6 . 3 + 1.0 fm, respectively, while a third one, employing a different geometry, yielded ann = - 1 6 . 3 + 1.6 fm [4]. On the other hand, from a more recent experiment at bombarding energies between 17 MeV and 27 MeV [5,6] in which a thin target was used values of ann between - 1 6 . 9 +0.5 fm and - 1 7 . 4 +0.4 fm were obtained depending on the range of data used for the analysis, and the values deduced from the most careful investigations of the 2 H 0 r - , 2n)7 reaction were ann = - 1 8 . 3 + 0.5 fm [7] and ann = - 1 6 . 7 -+ 1.3 fm [8] : Regarding these results it appears that they fall into two distinct groups: while from the thick-target measurements of the ~H(n, 2n)p reaction [ 2 - 4 ] a relatively 1 Now at the INT of the FraunhofergeseUschaft, Euskirchen, Germany.
small weighted mean value of 16.2 -+0.7 fm is obtained for the absolute value of ann the experiments of refs. [ 5 - 8 ] give lannl = 17.5 + 0.3 fro. It is the aim of this letter to propose an explanation for this apparent discrepancy, viz. the scattering of the neutrons by the target nuclei which was not taken into account in the analyses of refs. [ 2 - 4 ] . Scattering in the target was first considered to some extent by Salter et al. [8] for the 2 H ( n - , 2n)~, reaction who found only a small impact on the extracted value of ann in this particular case (~:~0.2 + 0.3 fm); however, it is not obvious that this holds for the 2H(n, 2n)p reaction as well. In order to investigate the influence of scatterin~g in a typical thick-target measurement of the 2H(n, 2n)p reaction a computer experiment has been performed, taking the experimental set-up and procedure described in ref. [3] as a basis for the Monte Carlo simulations. At 18.4 MeV, there is an 8% probability for the incoming neutron to undergo elastic scattering by either deuterium or carbon in a cylindrical C6D 6 target of 4 cm diameter, in effect modifying the direction and the energy distribution of th e beam. Furthermore, each of the break-up neutrons has a probability of nearly 20% for being scattered out of its path towards the detector (outscattering), with an average deflection angle A0 of almost 60 ° . More significantly, some of these "lost" events will be replaced by neutrons originally emitted in other directions but scattered back into the detectors (inscattering). Although most of the inscattered events
Volume 91B, number 1
PHYSICS LETTERS
will be rejected by kinematic considerations, on the order o f 10% will survive all kinematic cuts and alter the measured energy distribution. In general, these effects will smear out and broaden the final-state interaction peak thus causing - if not accounted for - the extraction of too small a value for l annl. For the computer experiment, the Monte Carlo simulation was performed in basically the same way as described in ref. [3]. The probability for scattering was obtained from the energy-dependent total cross sections for elastic scattering b y deuterium and carbon and the effective target thickness; the scattering angles were chosen using representative angular distributions da/ dO at 18 MeV for the beam and near 5 MeV for the break-up neutrons. Only the elastic scattering of one of the two final-state neutrons was allowed for and the possible influence of polarization effects was not taken into account. The effect of inscattering was treated in the following way: assume that the two neutrons n 1 and n 2 are emitted at angles 01 and 02 with energies E 1 and E 2, respectively, and that n 1 is scattered through A01 = 0 1 - 0'1 so that it misses its detector (outscattering). Another event is then considered where n 1 is originally produced at the angle 0'1 (with 0~ =02) I but scattered back through --A01 = 01 -- 01 into the detector. For the sake of simplicity it is assumed here but not in the actual Monte Carlo simulations - that the whole process takes place in a plane. The relative weight for this "replacement" is then simply given by 1 the break-up cross section (Faddeev factor) o ( 0 1 , 0 2 ) multiplied by the ratio of the cross sections for elastic scattering at the two energies E l and E 1 . The inscattered event is retained only if it survives the kinematic cuts applied in ref. [3], i.e. if the final energies o f the two neutrons as well as the energy E 3 deposited in the target-scintillator fall within the kinematically allowed regions determined in a simulation without scattering. All Monte Carlo simulations were carried out using exact three-body calculations [9]. The full simulation including target scattering was done with ann = - 1 7 . 0 fm, and the events were projected onto a central kinematic curve by means of the a-parametrization described in refs. [6,10]. The one-dimensional "experimental" spectrum thus obtained was then fitted in the usual way with simulations in which scattering had not been taken into account, using ann as a free parameter. A critical quantity in the analysis is the width of the window about E 3 which is determined by the resolution
24 March 1980
of the detector and by the kinematic broadening due to the finite geometry; if scattering took place in the target E3, of course, is the sum of all pulse heights produced b y the various recoiling particles. Assuming, e.g., a 5% resolution of the target-scintillator detector at the typical proton energy E_ = 5.3 MeV, and requiring E 3 to lie within E 0 -+-A E 3 ,Vwhere E 0 is the proton recoil energy calculated for central angles and A E 3 is the full width at half maximum of the E 3-distribution without scattering, the best fit to the - 1 7 fm "experimental" spectrum was obtained with ann = - 1 5 . 5 -+0.5 fm while with an assumed resolution of 4% or 6% bestfit values o f - 1 5 . 7 5 fm and - 1 5 . 2 5 fm were found for ann , respectively. Scattering of the projectile in the target was found to have only a small influence on the extracted value of ann. The present results suggest that the n - n scattering length is probably more negative b y about 1 - 2 fm than the hitherto "accepted" value of - 1 6 . 3 fm [11 ]. For a more precise answer to this fundamental question a complete reanalysis of the respective experimental data would be necessary which is beyond the scope of this investigation. This work was supported in part by the Bundesministerium fiar Forschung und Technologie.
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10
R eferen ces [1] R.T. Cahill and I.H. Sloan, Nucl. Phys. A165 (1971) 161; W. Ebenhbh, Nucl. Phys. A191 (1972) 97. [2] W.H. Breunlich, S. Tagesen, W. Bertl and A. Chalupka, Nucl. Phys. A221 (1974) 269. [3] B. Zeitnitz et al., Nucl. Phys. A231 (1974) 13. [4] J. Kecskem6ti, T. Czib6k and B. Zeitnitz, Nucl. Phys. A254 (1975) 110. [5] W. von Witsch, B. G6mez-Moreno, W. Rosenstock, K. Ettling and J. Bruinsma, Phys. Lett. 80B (1979) 187. [6] W. yon Witsch, B. G6mez-Moreno, W. Rosenstock, • K. Ettling and J. Bruinsma, Nucl. Phys., to be published. [7] B. Gabioud et al., Phys. Rev. Lett. 42 (1979) 1508. [8] R.M. Salter Jr., R.P. Haddock, M. Zeller, D.R. Nygren and J.B. Czirr, Nucl. Phys. A254 (1975) 241. [9] J. Bruinsma, W. EbenhSh, J.H. Stuivenberg and R. van Wageningen, Nucl. Phys. A228 (1974) 52. [10] P.H. Schram, J. Doornbos, W. Krijgsman and C.C. Jonker, Nucl. Phys. A291 (1977) 413. [11] I. Slaus, Proc. Intern. Conf. on Nuclear structure (Tokyo, 1977), ed. T. Marumori, J. Phys. Soc. Japan 44 (1978) Suppl. p. 60.
PHYSICS LETTERS
24 March 1980
ON THE DETERMINATION OF THE n - n SCATTERING LENGTH
BY THE 2H(n, 2n)p REACTION USING THICK TARGETS W. von WITSCH, B. GOMEZ MORENO and W. ROSENSTOCK 1 lnstitut fiir Strahlen. und Kernphysik der UniversitiitBonn, D5300 Bonn, Germany
Received 10 December 1979
A computer experiment demonstrates that the values of lannl deduced from the kinematically complete experiments on the 2H(n, 2n)p reaction employed thick targets are probably too small by 1-2 fm because neutron scattering in the target has generally been neglected.
Two reactions have mainly been used for the determination of the n e u t r o n - n e u t r o n scattering length: the pion-induced break-up of the deuteron and the 2H(n, 2n)p reaction. Of these, especially the latter has become a very attractive experimental tool in recent years since numerical solutions to the Faddeev equations have become available [1 ] which can be used for a theoretically sound analysis of kinematically complete three-nucleon experiments. In most of these a thick C6D 6 scintillator was used as a target in which E3, the energy of the break-up proton, was measured as an additional kinematical constraint. The results of two such experiments, done at 14 MeV [2] and at 18.4 MeV [3], were ann = - 1 6 . 0 + 1.2 fm and ann = - 1 6 . 3 + 1.0 fm, respectively, while a third one, employing a different geometry, yielded ann = - 1 6 . 3 + 1.6 fm [4]. On the other hand, from a more recent experiment at bombarding energies between 17 MeV and 27 MeV [5,6] in which a thin target was used values of ann between - 1 6 . 9 +0.5 fm and - 1 7 . 4 +0.4 fm were obtained depending on the range of data used for the analysis, and the values deduced from the most careful investigations of the 2 H 0 r - , 2n)7 reaction were ann = - 1 8 . 3 + 0.5 fm [7] and ann = - 1 6 . 7 -+ 1.3 fm [8] : Regarding these results it appears that they fall into two distinct groups: while from the thick-target measurements of the ~H(n, 2n)p reaction [ 2 - 4 ] a relatively 1 Now at the INT of the FraunhofergeseUschaft, Euskirchen, Germany.
small weighted mean value of 16.2 -+0.7 fm is obtained for the absolute value of ann the experiments of refs. [ 5 - 8 ] give lannl = 17.5 + 0.3 fro. It is the aim of this letter to propose an explanation for this apparent discrepancy, viz. the scattering of the neutrons by the target nuclei which was not taken into account in the analyses of refs. [ 2 - 4 ] . Scattering in the target was first considered to some extent by Salter et al. [8] for the 2 H ( n - , 2n)~, reaction who found only a small impact on the extracted value of ann in this particular case (~:~0.2 + 0.3 fm); however, it is not obvious that this holds for the 2H(n, 2n)p reaction as well. In order to investigate the influence of scatterin~g in a typical thick-target measurement of the 2H(n, 2n)p reaction a computer experiment has been performed, taking the experimental set-up and procedure described in ref. [3] as a basis for the Monte Carlo simulations. At 18.4 MeV, there is an 8% probability for the incoming neutron to undergo elastic scattering by either deuterium or carbon in a cylindrical C6D 6 target of 4 cm diameter, in effect modifying the direction and the energy distribution of th e beam. Furthermore, each of the break-up neutrons has a probability of nearly 20% for being scattered out of its path towards the detector (outscattering), with an average deflection angle A0 of almost 60 ° . More significantly, some of these "lost" events will be replaced by neutrons originally emitted in other directions but scattered back into the detectors (inscattering). Although most of the inscattered events
Volume 91B, number 1
PHYSICS LETTERS
will be rejected by kinematic considerations, on the order o f 10% will survive all kinematic cuts and alter the measured energy distribution. In general, these effects will smear out and broaden the final-state interaction peak thus causing - if not accounted for - the extraction of too small a value for l annl. For the computer experiment, the Monte Carlo simulation was performed in basically the same way as described in ref. [3]. The probability for scattering was obtained from the energy-dependent total cross sections for elastic scattering b y deuterium and carbon and the effective target thickness; the scattering angles were chosen using representative angular distributions da/ dO at 18 MeV for the beam and near 5 MeV for the break-up neutrons. Only the elastic scattering of one of the two final-state neutrons was allowed for and the possible influence of polarization effects was not taken into account. The effect of inscattering was treated in the following way: assume that the two neutrons n 1 and n 2 are emitted at angles 01 and 02 with energies E 1 and E 2, respectively, and that n 1 is scattered through A01 = 0 1 - 0'1 so that it misses its detector (outscattering). Another event is then considered where n 1 is originally produced at the angle 0'1 (with 0~ =02) I but scattered back through --A01 = 01 -- 01 into the detector. For the sake of simplicity it is assumed here but not in the actual Monte Carlo simulations - that the whole process takes place in a plane. The relative weight for this "replacement" is then simply given by 1 the break-up cross section (Faddeev factor) o ( 0 1 , 0 2 ) multiplied by the ratio of the cross sections for elastic scattering at the two energies E l and E 1 . The inscattered event is retained only if it survives the kinematic cuts applied in ref. [3], i.e. if the final energies o f the two neutrons as well as the energy E 3 deposited in the target-scintillator fall within the kinematically allowed regions determined in a simulation without scattering. All Monte Carlo simulations were carried out using exact three-body calculations [9]. The full simulation including target scattering was done with ann = - 1 7 . 0 fm, and the events were projected onto a central kinematic curve by means of the a-parametrization described in refs. [6,10]. The one-dimensional "experimental" spectrum thus obtained was then fitted in the usual way with simulations in which scattering had not been taken into account, using ann as a free parameter. A critical quantity in the analysis is the width of the window about E 3 which is determined by the resolution
24 March 1980
of the detector and by the kinematic broadening due to the finite geometry; if scattering took place in the target E3, of course, is the sum of all pulse heights produced b y the various recoiling particles. Assuming, e.g., a 5% resolution of the target-scintillator detector at the typical proton energy E_ = 5.3 MeV, and requiring E 3 to lie within E 0 -+-A E 3 ,Vwhere E 0 is the proton recoil energy calculated for central angles and A E 3 is the full width at half maximum of the E 3-distribution without scattering, the best fit to the - 1 7 fm "experimental" spectrum was obtained with ann = - 1 5 . 5 -+0.5 fm while with an assumed resolution of 4% or 6% bestfit values o f - 1 5 . 7 5 fm and - 1 5 . 2 5 fm were found for ann , respectively. Scattering of the projectile in the target was found to have only a small influence on the extracted value of ann. The present results suggest that the n - n scattering length is probably more negative b y about 1 - 2 fm than the hitherto "accepted" value of - 1 6 . 3 fm [11 ]. For a more precise answer to this fundamental question a complete reanalysis of the respective experimental data would be necessary which is beyond the scope of this investigation. This work was supported in part by the Bundesministerium fiar Forschung und Technologie.
-
10
R eferen ces [1] R.T. Cahill and I.H. Sloan, Nucl. Phys. A165 (1971) 161; W. Ebenhbh, Nucl. Phys. A191 (1972) 97. [2] W.H. Breunlich, S. Tagesen, W. Bertl and A. Chalupka, Nucl. Phys. A221 (1974) 269. [3] B. Zeitnitz et al., Nucl. Phys. A231 (1974) 13. [4] J. Kecskem6ti, T. Czib6k and B. Zeitnitz, Nucl. Phys. A254 (1975) 110. [5] W. von Witsch, B. G6mez-Moreno, W. Rosenstock, K. Ettling and J. Bruinsma, Phys. Lett. 80B (1979) 187. [6] W. yon Witsch, B. G6mez-Moreno, W. Rosenstock, • K. Ettling and J. Bruinsma, Nucl. Phys., to be published. [7] B. Gabioud et al., Phys. Rev. Lett. 42 (1979) 1508. [8] R.M. Salter Jr., R.P. Haddock, M. Zeller, D.R. Nygren and J.B. Czirr, Nucl. Phys. A254 (1975) 241. [9] J. Bruinsma, W. EbenhSh, J.H. Stuivenberg and R. van Wageningen, Nucl. Phys. A228 (1974) 52. [10] P.H. Schram, J. Doornbos, W. Krijgsman and C.C. Jonker, Nucl. Phys. A291 (1977) 413. [11] I. Slaus, Proc. Intern. Conf. on Nuclear structure (Tokyo, 1977), ed. T. Marumori, J. Phys. Soc. Japan 44 (1978) Suppl. p. 60.