Total cross sections for the 6Li(n, α)3H reaction between 2 and 10 MeV

Nuclear Physics A330 (1979) 1- 14; (~) North-Holland Publishing Co., Amsterdam

I 2.A.I I

Not to be reproduced by photoprint or microfilmwithout written permission from the publisher

T O T A L C R O S S S E C T I O N S F O R T H E 6Li(n, g)3H R E A C T I O N B E T W E E N 2 A N D 10 MeV C. M. BARTLE

Department o/Physics, University of Wisconsin, Madison, Wisconsin 53706, USA * and Department oJ Physics, University of Cape Town, Rondebosch 7700, Cape Town, South Africa **

Received 18 June 1979 Abstract: Precise measurements of the 6Li(n, 0t)3H cross section between 2.16 and 9.66 MeV have been

made. The reactions are observed in a 6Lil(Eu) scintillator which serves simultaneously both as a target and a detector of the charged particle reaction products. Calculations show the importance of accounting for the events produced by neutrons slowed down in a 6Lil(Eu) scintillator as well as by neutrons backscattered from the light guide. Evidence is found of the formation of the jr = ~- state at an excitation energy of 10.25 MeV in 7Li.

E

NUCLEAR REACTION 6Li(n, ct),level,Eenriched= 2.16-9.66target.MeV; measured or(E), 7Li deduced

1. I n t r o d u c t i o n

In the present w o r k the 6Li(n, 003H total cross section has been measured between 2.16 and 9.66 MeV. Earlier w o r k covering part o f this range includes the w o r k o f Ribe 2) f r o m 0.88 to 6.52 MeV, G a b b a r d et al. 3) f r o m 19keV to 4.066 MeV, M u r r a y and Schmitt 4) from 1.2 to 7.96 M e V and Clements and Rickard s) from 0.156 to 3.900 MeV. There is some disagreement between the earlier results. In particular, the values o f the cross section f o u n d in the w o r k o f Clements and R i c k a r d are considerably lower than the values f o u n d by the other workers. T h e experimental m e t h o d used in the present w o r k is described in detail elsewhere 6- 9). T h e 6Li(n, 0t)aH reactions are observed in a 6LiI(Eu) scintillator *** which serves simultaneously b o t h as the target and as the detector o f the charged particle reaction products. N e u t r o n s f r o m the 2H(d, n)3He reaction are electronically collimated t h r o u g h the scintillator by c o u n t i n g the associated 3He ions emitted at the kinematically related angle. T h e m e t h o d also yields absolute n e u t r o n flux * Work supported in part by the US Department of Energy. ** Present address. *** Manufactured by the Harshaw Chemical Co., Cleveland, Ohio, USA. 1

October1979

2

c.M. BARTLE

measurements. A careful assessment has been made of the possible sources of experimental error including transmission losses from the neutron beam before reaching the scintillator, the self-shielding of the scintillator - in particular the nature of the energy-attenuated flux, and multiple scattering effects. The excitation function obtained is in good agreement with an earlier evaluation lO).

2. The experimental spectra The experiments were carried out with the University of Wisconsin EN tandem accelerator. The experimental system is shown in fig. 1. Fast coincidences detected

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Fig. 1. The experimental layout. Deuterons bombard a deuterated polyethylene target. The 3He particles are detected at angle 0~, and the associated neutron beam at angle 0, is encompassed by the 6Lil(Eu) scintillator. between the 3He recoil ions and the neutron-induced events produced in the 6LiI(Eu) scintillator identify those reactions produced principally by the electronically collimated neutron beam. The timing resolution of these coincidences is typically 3 ns ( F W H M ) [ref. 6)]. Pulse-height spectra were coincidence-gated by the events in the peak in the time spectrum, as well as by events in a background region of the spectrum. The latter coincidences were subtracted from the former to eliminate the small number of random events arising from the background count-rate in the scintillator. The pulse height spectra obtained at four energies are shown in fig. 2. There are

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CHANNEL Fig. 2. Typicalpulse-heightspectra inducedby neutrons in a 6Lil(Eu) scintillator. three distinctive features in the spectra, which are well illustrated at the lower energies. As shown in detail below the broad high pulse-height distribution is from 6Li(n, ct)aH reactions produced by neutrons of full incident energy. The peak situated at slightly lower pulse heights arises from 6Li(n, ~)3H reactions produced by neutrons slowed down in the scintillator by 6Li(n, nd)4He, 6Li(n, n)6Li and a27I(n, n~/)127I reactions, principally by the latter mechanism. Some events are also contributed to this peak by reactions produced by neutrons backscattered from the light-guide which is situated immediately behind the scintillator. At lower pulse heights a continuous distribution arises mainly from 6Li(n, nd)4He and 1 2 7 I ( n , ny) 1271 reactions. 3. Derivation o f the response curves

Fig. 3 shows a spectrum of 6Li(n, ct)aH events produced by fast and thermal neutrons superimposed. It can be seen that the distribution produced by fast

4

C . M . BARTLE I

400

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CHANNEL Fig. 3. Superimposed spectra induced by thermal and 2.71 MeV neutrons in a 6Lil(Eu) scintillator. The channel width is different than that shown in fig. 2.

neutrons is broader than the corresponding distribution produced by thermal neutrons. This is a kinematic effect related to the sharing of energy between the a-particle and triton emitted in the crystal, and the differing response of the scintillator to these particles 11). Fast neutrons lead to a wider energy range being available to the product particles and therefore a broader distribution is observed. To express this in quantitative terms for these particular spectra is difficult since response curves are poorly documented for the product particles emitted in 6LiI(Eu). The calculations of Steuer and Kelsey 13) indicate that for 5 MeV particles the ratio of the triton to the or-particle response is about 2 : 1. The actual pulse height, R x, observed from a particular 6Li(n, ~)3H event can thus be expressed as RT = gt(Et) + R~,(E~) = [kt(Et) - k~(E~)] E t + k~( E~)E x, where E t is the emitted triton energy, E~ the corresponding a-particle energy, E x the total energy available to the product particles ( E t + E a ) , R t ( E t ) the triton response at energy Et, R~(E~) the a-particle response at energy E~, kt(Et) a function relating R t and Et, and k~,(E~,)a function relating R~ and E~. Thus given the details of the response curves the width of the 6Li(n, 003H distribution can be predicted. Calculations by Steuer and Kelsey ~3) indicate kt(E) is a constant over the present energy range whereas k~(E) exhibits a non-linear energy dependence. Response curves can be obtained from the present data because the maximum

Li(n, oQ3H

5

pulse height in the 6Li(n, a)3H distribution arises primarily from the forward emission of the triton (i.e. RT ~ R,(Et)). For example, at E n = 2.71 MeV the values of E t and E, for 0° triton emission are 5.87 and 1.63 MeV respectively. The response calculations of Steuer and Kelsey suggests that about 90 % of the total response corresponding to the observed pulse height will arise from the detection of the triton alone. Thus a plot of the positions of the upper edges (defined here as the pulse height at half the height of the upper edge) of the 6Li(n, a)3H distributions against the corresponding emitted triton energies in the forward direction yields an approximate triton response curve. Channel numbers were used to represent the triton response. The resultant data, fitted by the linear-least-squares method is shown in fig. 4. As predicted by Steuer and Kelsey 13) the data conforms well to the linear fit and the extrapolated line passes through the origin. The a-particle response curve is derived from the positions of the lower edges of the 6Li(n, a)3H distributions. Events observed at these positions correspond to aparticle emission at 0°. Since the a-particle response is less than the triton response these are the events of lowest overall pulse-height since the a-particle has its maximum allowable share of the total energy. The response curve is obtained by subtracting the triton contribution determined by the kinematic details and the previously I

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Fig. 4. The initial triton response curve deduced from the 6Li(n, ct)3H spectra.

6

C . M . BARTLE

determined triton response curve (fig. 4). Corrections to the response curves are made by an iterative method. To accomplish this the predicted c~-particle responses are fitted by the least-squares method to the empirical expression R~(E~) = AE~ + B(1-e-CE~),

where A, B and C are constants. This functional form was chosen for the following reasons. Firstly, it corresponds to a linear response curve at high energies as is typical of such data. Secondly, it allows the flexibility of choosing A and B by the least-square method at energies corresponding to the experimental data, whereas C is chosen to give good agreement with the or-particle response attributed to the 6Li(n, ~)3H distribution observed for thermal neutrons. It was found that the best choice of C satisfied the condition 1 >> e -CE`. Thus the response curve is found to be linear (curve E in fig. 5) above E= = 2.06 MeV, corresponding to reactions produced by thermal neutrons, to E= = 10.63 MeV, corresponding to s-particle emission at 0° for 9.66 MeV incident neutrons. The triton response curve was then corrected in a similar manner for the c~-particle contributions to the total response at the upper end of the 6Li(n, c03H distributions. Two further iterations were made at which point the change in the standard deviation of the triton response points about the least-squares-fitted line changed by less than 2 % from the previous cycle. The response curves derived in this way are shown in

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Curves for 6Li](Eu)

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Fig. 5. The final response curves deduced from the 6Li(n, ct)3H spectra are compared with earlier results. Line A is the position of the proton response curve deduced by Ophel 12), line B is the position of the initial triton response curve (fig. 4), line C is the final triton response curve, line D is the electron response curve and line E is the final ~t-particle response curve.

Li(n, ~)3H

7

fig. 5. The standard deviation of the points about the triton response curve is 4.8 units, and of the points about the a-response curve is 4.7 units along the response axis. These curves agree well with the measurements of Ophel ~2) and the calculations of Steuer and Kelsey 13). Comparison with the points taken from the curve in ref. 12) for a-responses was accomplished by normalizing to the electron response curve shown in fig. 5. This curve was obtained in the present case by observing the position of the photo-peaks using ),-rays of known energy detected in the 6LiI(Eu) scintillator. As found previously 12) the electron response curve has a slope intermediate in value between the triton response curve and the a-particle response curve. Points for a-particle responses taken from the calculated curves given in ref. 13) are normalized to the triton response curve. Since the curve of ref. 12) is determined by only two experimental points and the calculations of ref. 13) are attributed an accuracy of ___25 ~o the results are in good agreement. The equations of the response curves given in fig. 5 are: Rt =

32.71 E t ,

R e = 25.95 E e, R, = 19.74 E~-22.62 (1 - e - 2 ~ ' ) , where Rt, R e and R, are in arbitrary units, and Et, E e and E, are in MeV. The functional form chosen for R~ is not entirely satisfactory at energies below 1 MeV since slightly negative values of R, are predicted. However, this can be ignored for the present purposes since this is an extrapolated region of the curve and is not used in the present calculations. The good agreement between the response curves derived from the 6Li(n, ~)3H distributions, and the earlier response curve data supports the assumption that the broad peaks shown in fig. 2 are from reactions of neutrons having the full incident energy. These response curves were used to investigate the spectrum from sloweddown neutrons which produce events in the lower channel numbers. 4. Analysis of the events produced by slowed-down neutrons Some incident neutrons are slowed down in the scintillator before producing 6Li(n, ~)3H reactions. As discussed in relation to fig. 2 the principle slowing down mechanisms for these neutrons are the 6Li(n, nd)4He, 6Li(n, n)6Li and I ZVl(n, nT) l zT1 reactions. These events run from under the lower end of the full energy distribution to a position, as illustrated in fig. 3, near that of 6Li(n, ~).3H events produced by thermal neutrons. A detailed computer code SK1M was developed to predict quantitatively the shape of this distribution. In addition to the slowing-down mechanisms mentioned neutrons backscattered from the lucite light guide immediately behind the scintillator were included.

8

C.M. BARTLE

Statistical models were employed in the calculation of the spectrum of the slowed-down neutrons. In the case of 1271 the inelastically scattered neutrons form a Maxwellian evaporation distribution 14) N(E) = AEexp(2 B ~ " o - E ) , where N(E) is the number of neutrons per unit energy range, A and B are constants, E is the neutron energy and E 0 is the incident neutron energy. Values for B were chosen from the experimental data for 1271(n, n?,)1271 reactions given in ref. 14). For E n in the range 2.16 to 6 MeV the value used was 18.9 MeV i and in the range 6 to 9.66 MeV the value used was 16.1 M e V The 6Li(n, nd)4He reaction occurs by two mechanisms 15). The reaction can proceed sequentially via the 6Li(n, d)SHe reaction followed by the break-up of 5He. In this case there is expected to be a preference for low energy neutron emission 15). Simultaneous three-body break-up can also occur. The neutron spectrum in the c.m. system is of the form 15)

N(E) = C~/'E(Emax-E), where E is the neutron energy and Ema x is the maximum allowed neutron energy for three-body break-up. Since the simultaneous three-body break-up has a threshold of 1.7 MeV and the sequential reaction has a threshold of 2.8 MeV only the former need to be considered at lower energies. Furthermore the three-body break-up reaction provides the higher energy neutrons which are important in accounting for the reactions of slowed-down neutrons under the full energy peak. Calculations here are based on the form expected for the simultaneous three-body break-up. The 6Li(n, n)6Li angular distribution is assumed to be isotropic in the c.m. system. Therefore the neutron energy distribution is assumed to b e flat between the minimum energy of 0.5E o and the maximum energy of E o. The neutron energy spectrum is therefore of the form

N( E) = D, where D is a constant. The values of A, C and D were chosen such that ~N(E)dE yields the correct number of scattered neutrons. Cross sections were taken from refs. 1, 10). Backscattering from the lucite light guide was also taken into account. The primary effect is that neutrons are elastically scattered from 12C back through the scintillator. Calculations are based on the kinematically available energy of about 0.71 E o and the known 12C elastic scattering cross sections. Typical neutron energy distributions arising from the slowed-down flux component are shown in fig. 6(a). For the purposes of the calculation the neutron energy range was divided into ten increments and the number of neutrons per MeV computed at each of these energies as outlined above. Energies were converted to channel

c()3H

Li(n,

9

numbers using the response curves assuming that neutrons of a particular energy produce 6Li(n, ~)3H events of maximum pulse height. The number of 6Li(n, c03H reactions actually produced at each energy was calculated from cross sections for the reaction given in ref. 10). Three further computations were involved. Firstly, at each energy the 6Li(n, ~)3H events were spread over a pulse-height range corresponding to the width of the experimental spectra, based on the response curves NEUTRON ENERGY (Met/)

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Fig. 6. (a) Calculated energy distributions for slowed-down neutrons due to various reactions in a 6Lil((Eu) scintillator. The case shown is for the experiment conducted with 4.69 MeV neutrons. (b) The 6Li(n, 0()3H pulse-height distributions corresponding to the energy distributions in (a) taking account of resolution effects in the scintillator.

10

C.M. BARTLE

and the reaction kinematics. Secondly, the experimental resolution function was folded in. Since the 6Li(n, ~)3H distribution produced by thermal neutrons is not broadened by kinematic effects the experimental resolution was based on the F W H M (7 7'o) of this distribution. An example of the components of the resulting 6Li(n, ~)3H spectra are shown in fig. 6(b). Finally, the components were added and scaled to the channel energy width in the experiment. The case of E, = 4.69 MeV is illustrated in fig. 7. l

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Fig. 7. The ~Li(n, z03H pulse-height distribution produced by slowed-down neutrons is compared with the experimental data for 4.69 M e V incident neutrons.

As shown in fig. 7, good quantitative agreement was obtained with the data. This supports the proposition that the events immediately below the full energy 6Li(n, ~)3H distributions are correctly interpreted as arising from slowed-down neutrons. Events extending below the full energy peak were thus subtracted from the summed area of this peak to yield the actual number of events produced by neutrons with the full incident energy. 5. Cross section calculations The number of 6Li(n, ~)3H events was determined from the integration of the 6Li(n, ~)3H peak after subtraction of the background produced by energy attenuated neutrons as discussed above. Typically this reduces the total number of events in the peak by 6-7 %. The number of incident neutrons was estimated by counting the 3He ions corrected for the mean attenuation of the neutron beam in the target chamber wall and in the scintillator. The concentration of target nuclei in the scintillator, and the scintillator thickness were supplied by the scintillator manufacturer.

Li(n, ~)3H

11

Calculations show that about 3 ~o of neutrons are lost as the beam passes through the target chamber wall and that attenuation of the beam in the scintillator results in a further loss of about 4 ~o. The mean attenuation of the neutron beam in the target chamber wall takes account of neutron absorption in the wall and scattering of neutrons out of the primary beam. The calculation of the mean attenuation within the scintillator takes account of those neutrons which are slowed-down by the 6Li(n, nd)4He, 6Li(n, n)6Li and ~Z7l(n, nT)t27I mechanisms, and absorption of neutrons by the 6Li(n, ~)3H reaction. A Monte Carlo multiple-scattering correction was made to account for neutrons elastically scattered by iodine in the scintillator. These neutrons retain essentially their full energy and therefore contribute 6Li(n, c~)3H events of full energy. The calculation takes account of the fact that the neutron beam does not fully illuminate the scintillator and assumes that the beam profile is gaussian in shape 6). In fig. 8 i.s shown the result of a calculation of the effective increase in the thickness of the scintillator due to multiple scattering on iodine. Typically the effective increase in length is about 1 ~o. I MultipLe Scattering

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Fig. 8. The multiple scattering correction for elastic scattering on 1271 in a 6Lil(Eu) scintillator. The scintillator used was 2.54 cm in diameter and 1.27 cm in thickness.

A small correction is also included for edge effects, i.e. particles which escape from the scintillator before they have deposited all their energy. Edge effects are minimized because the diameter of the neutron beam is smaller than the diameter of the scintillator. Typically the ranges of the product triton and a-particles are small compared with the dimensions of the 6Lil(Eu) scintillator. The 6Li(n, ~)3H distribution is broad, and events are still liable to fall within the observed pulsedistribution even following the escape of one of the particles from the crystal.

C. M. BARTLE

12

TABLE 1 Results of the OLi(n, ~)3H cross section measurements Mean neutron energy (MeV)

2.16 2.34 2.52 2.71 2.87 3.14 3.42 3.54 3.61 3.77 3.89 4.20 4.69 5.30 5.65 5.89 6.28 6.65 7.08 7.51 7.98 9.01 9.66

Energy width (FWHM) (keV)

80 100 100 120 120 120 120 140 140 140 140 160 200 240 240 240 240 240 320 400 400 500 500

Cross section (mb) 201 +8 199 +7 182 _+6 168 +6 152 +_6 140 +6 122 +-5 114 +5 113.9_+5.6 110.8+_4.8 110.7_+4.8 104.4 -+-3.7 92.9 -+ 3.4 77.4-+4.0 69.0 + 2.8 70.8 _+3.8 61.4 ± 3.5 55.9-+2.0 56.2 ± 2.3 49.8 ± 2.3 45.4 +- 2.0 38.6_+ 1.5 37.0 + 1.6

The error in events due to slowed-down neutrons under the 6Li(n, ~)3H distribution is estimated to be half the total correction, i.e. typically ___3 ~,,, of the total number of counts in the peak. Tl~e statistical error in the number of 6Li(n, ~)3H events is typically +2~o. The error in estimating the attenuation of the neutron beam is taken as +20~o of the attenuation produced. This is typically _+2~o of the integrated number of 3He events. Estimating the number of 3He particles gives typically an error of + 0.5 ~o depending on the interference of other events such as those from the 12C(d, ~)I°B reaction 6). The scintillator thickness quoted by the manufacturer is known to +0.5 ~o. Multiple scattering contributes a further ± 1 ~i to the uncertainty in the thickness. These errors were combined in quadrature. The resulting cross sections and errors are shown in fig. 9 and listed in table 1. 6. Discussion As shown in fig. 9, the excitation function is in good agreement with the evaluation of Pendlebury 10), which is largely based on the measurements of Gabbard et al. 3) in the MeV region. Good agreement is found with the result of Ribe 2) (values corrected as suggested by Murray and Schmitt 10)) and the single measurements at

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2.5 MeV by Elpidinski et al. lo) and at 2.15 MeV by Perelygin and Tolstoy 10). In the energy range 2 to 4 MeV the values obtained by Murray and Schmitt 4) are approximately 25 % higher. However there is reasonable agreement at higher energies. It may be significant that the energy range over which the results of ref. 4) are in good agreement were obtained using the 2H(d, n)3He reaction as the neutron source. However the lower energy results where the agreement is poorer were measured

12

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14

C . M . BARTLE

with the 3H(p, n)3He reaction. A systematic error may have arisen when the neutron source reaction was changed. The results of Clements and Rickard 5) are much lower than previous data and appear to be normalized incorrectly. In fig. 10 is shown a plot of the cross section difference between the values given by the Pendlebury evaluation and the present results. Whereas the evaluation is smooth near E n = 3.5 MeV the present results show an inflexion in this region. Since the excitation energy in VLi which corresponds to this inflexion is 10.25 MeV it appears likely that this feature corresponds to the formation of the ~-, T = ½ state that has been reported at that energy in VLi (ref. 16)). Further evidence is found in the angular distributions which can be derived from the present pulse-height spectra 17). Moreover, evidence for the formation of this state was found by Holt et al. 18) in studies of the scattering of polarized neutrons by 6Li. 7. Conclusion

The total cross section for the 6Li(n, ~)3H reaction has been measured between 2.16 and 9.66 MeV. A careful assessment has been made of the corrections and errors due to the transmission of the neutron beam, the self-shielding caused by the scintillator, the multiple scattering within the scintillator and of edge effects. Measurements of the neutron flux have been accurately determined using the associated particle technique. The excitation function is found to be in good agreement with the Pendlebury evaluation. The curve however shows an inflexion point near 3.5 MeV, not previously observed, which provides some evidence for the formation of the 10.25 MeV state in VLi from the total cross section curve alone. The author is indebted to Professor P. A. Quin and Dr. D. T. L. Jones for their assistance during the experimental periods and for useful discussions. Thanks are also due to R. Ten Haken, A. Stanford, G. Wong and Ms. R. Das for experimental assistance. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17)

D. 1. Garber and R. R. Kinsey, BNL 325 3rd edition, vol. 11, Jan. 1976 F. L. Ribe, Phys. Rev. 103 (1956) 741 F. Gabbard, R. H. Davis and T. W. Bonnet, Phys, Rev. 114 (1959) 201 R. B. Murray and H. W. Schmitt, Phys. Rev. 115 (1959) 1707 P. J. Clements and 1. C. Rickard, AERE - R7075, 1972 C. M. Battle and P. A. Quin, Nucl. Inst. 121 (1974) 119 C. M. Battle, Nucl. Instr. 124 (1975) 547 C. M. Battle and P. A. Quin, Nucl. Phys. A216 (1973) 90 C. M. Battle, Nucl. Instr. 117 (1974) 569 E. D. Pendlebury, AWRE 0-60/64 (1964) K. H. Purser, Austral. J. Phys. 12 (1961) 231 T. R. Ophd, Nucl. Instr. 3 (1958) 45 M. F. Steuer and C. A. Kelsey, Nucl. Phys. 83 (1966) 401 D. B. Thomson, Phys. Re,/. 129 (1963) 1649 R. Batchdor and J. H. Towle, Nucl. Phys. 47 (1963) 385 F. Ajzenberg-Selove and T. Lauritsen, Nucl. Phys. A227 (1974) 1 C. M. Bartle, Proc. Conf. on nuclear cross sections and technology, Washington DC, 1975 (NBS SP) p. 688 18) R. J. Holt, F. W. K. Firk, G. T. Hickey and R. Nath, Nucl. Phys. A237 (1975) 111