Differential cross section of the 2H(n, nnp)-reaction at En = 13MeV

Nuclear Physics AS01 (1989) 51-85 North-Holland, Amsterdam

DIFFERENTIAL

CROSS

*H(n, onp)-REACTION

SECTION

OF THE

AT E,, = 13 MeV

J. STRATE, K. GEISSDijRFER, R. LIN, W. BIELMEIER, J. CUB, A. EBNETH, E. FINCKH, H. FRIESS, G. FUCHS, K. GEBHARDT and S. SCHINDLER Physikalisches Institut der Universitiit Erlangen-Niimberg, Erwin-Rommel-Str. 1, OS520 Erlangen, Fed. Rep. Germany

Received 8 March 1989

Abstract: The differential cross section of the nD break-up reaction was investigated at E,= 13 MeV using the Erlangen multidetector neutron facility. Twenty-two different configurations including np final-state interaction, collinearity, coplanar- and space star were measured in a kinematically complete experiment. The results are compared with rigorous Faddeev calculations based on the Paris potential. The discrepancies between data and calculations indicate imperfections in the potential and may be caused by three-particle effects such as wrong off-shell behavior of the potential or an additional three-body force.

E

NUCLEAR REACTIONS ‘H(n, nnp), E = 13 MeV, measured u (E,, E,, , Enz, B,, @,, O,, @J&Kinematically complete experiment; C,D,, target. 22 angular configurations. Faddeev calculations with Paris MT-potentials.

1. Introduction

The three-nucleon system with all particles in the continuum gives new information about the quality of nucleon-nucleon (NN) potentials used in Faddeev calculations. Owing to the difficulties in including the Coulomb interaction in the computation, the data of the nD break-up reaction are of crucial importance for the comparison with theoretical predictions. Up to now the differential cross sections were very rarely investigated in kinematically complete experiments due to the experimental difficulties in detecting both neutrons. The few previous measurements ‘) concentrated on special configurations, such as the final-state interaction or the quasi-free scattering with relatively high cross sections, resulting in higher count rates. For a detailed comparison with rigorous Faddeev calculations *), however, absolute cross sections for a large part of the phase space are essential. The Erlagen multidetector neutron facility ‘) is well suited for such an investigation. It combines a dc neutron beam favorable for coincidence experiments, with the time-of-flight (t.0.f.) technique for the neutron detection. In addition, the collimated neutron beam permits to work with many detectors, thereby measuring a 0375-9474/89/$03.50 @ Elsevier Science publishers B.V. (North-Holland Physics Publishing Division)

52

J. Srrate et al. / ‘H( n, nnp)

number of diff erent configurations simultaneously and avoiding normalization problems between them. 2. Experimental

set-up

The accelerated deuteron beam (I, = 1.5 n,A) entered a deuterium gas cell (length: 5 cm, pressure: 9 bar), where monoenergetic neutrons with E,, = (13.0 * 0.38) MeV were produced via the D(d, n)3He reaction. In addition, a continuous spectrum of low-energy neutrons results from the D(d, np)D reaction. Owing to the large energy gap of about 6 MeV, break-up events induced by neutrons from the different reactions could be well discriminated. By using an iron collimator and additional shielding of water and paraffin, a definite dc neutron beam was obtained under 8 = 0”, which bombarded the completely deuterated target scintillator (NE 232, height: 8 cm, diameter: 4 cm) located at a distance of 2.4 m from the gas cell (fig. 1). This target enabled the determination of the proton energy and gave a signal for the t.o.f. measurement of the scattered neutrons, which were detected with 22 scintillators (NE 213, height: 10.1 cm, diameter: 5.3 cm), located at a distance of 70 cm. All detectors were equipped with ny pulse shape discrimination 3,4). Break-up events were defined by triple coincidence between the target and one detector on each side of the beam axis. The detector positions were symmetrically arranged to the neutron beam, so that each configuration existed once more in mirror image. Due to the rotational symmetry to the beam axis, this doubled the count rates and gave an internal control by comparison of two independent and simultaneous measurements

I RON

VACUUM-C~AMRER

I

and

CONCRETE

I

t I,,.+,,,+ z.scn

Fig. 1. Experimental

set-up.

I

J. Strate et al. / ‘H(n,

nnp)

53

50.5O

above and 50.fl” below scattering plane

17.0°

25.0°

39.0°

50.5O

62.5”

detector positions

75.5’

_I I 90.0”

97Li0

110.0 u

right side

Fig. 2. Break-up ~on~gurations measured simultaneously. For each angular combination the kinematical curve is shown in the E;eurro”E;e”‘ro” plane (10 MeVx 10 MeV). Dotted parts of the curve are below one of the software thresholds. Special kinematic situations are marked. Configurations without a curve are kinematically not allowed.

of each configuration.

The detection

angles

(see fig. 2) were chosen

to include

all

special kinematical configurations such as np final-state interaction (FSI), collinearity (COLL), coplanar- and space-star (CST- and SST). Star configurations are characterized by equal momenta of the three outgoing nucleons in the c.m. system, which build up an equilateral triangle because of momentum conservation. If the beam axis extends inside the plane of this triangle we talk about CST configuration, if orthogonal to this plane, about SST con~guration. For the measurement of the SST configuration at 13 MeV, a neutron detector had to be fixed in space under a polar angle of Olab = 50.5” to obtain the required

.I. Straie et al. / ‘H( n, nnp)

54

scattermg

plane

right

side

Fig. 3. Complete detector set-up in perspective view. The four detectors out of the scattering plane have a polar angle of 0 = 50.5”. Each of them in combination with the corresponding detector under 0 = 50.5” in plane enabled the measurement of the SST configuration; one of these detector pairs is marked.

relative azimuthal angle of @ = 120” to the corresponding neutron detector in the scattering plane as shown in fig. 3. Due to the low differential cross section, four detectors were fixed in space to quadruple the count rate of this important configuration. Besides the break-up reaction, we also measured the elastic nD scattering simultaneously

for an absolute

as well as for an on-line

normalization control

of the differential

of the experiment

count-rate. LED pulses were fed into all scintillators small drifts in the overall amplification.

break-up

cross section

due to the very-low for an off-line

break-up

correction

of

A block diagram of the electronics is given in fig. 4. Six quantities of a break-up event were stored in list mode: t.o.f.reTf, t.o.f.Ftleguh:, At.o.f. =t.~.f.,~r~-t.o.f.+~, proton energy in the target scintillator E,, and the proton recoil energies in the neutron detectors E ;,‘T;“i’ and E z$‘. For elastic scattering three quantities were stored: One t.o.f.-value, one Erecoi’ value and the deuteron recoil energy Ed in the target scintillator. In addition, a pattern word was generated for each event by the BU-LOGIC & TIMING unit. This contains the information about the detectors concerned, thereby defining the angular configuration, and about the distinction between breakup events (triple coincidence), events of the elastic scattering (coincidence) or events caused by the LED-pulses.

J.

CAMAC

-

PDP

Strate et al. /

'H(n, nnp)

AMP, Spactroscopy

11173

Fig. 4. Block diagram

PS,,,Pulse-Shape

Amplifier Discriminator

of the electronics.

3. Data evaluation Fig. 5a shows the raw data of one break-up configuration after energy calibration, together with the kinematical locus for point geometry (ideal S-curve), which was calculated

by energy and momentum

conservation.

Background

is seen from break-

up events induced by low-energy neutrons from the D(d, np)D reaction and from events by multiple scattering. As a result of the triple-coincidence requirement, the number of accidental events was very small, because no events in connection with the high count

rate of neutrons

from the elastic nD scattering

were observed;

they

should appear at E2 = Efilast (Olab = 75.5”) = 5.77 MeV in fig. 5a. The experimental data are spread around the ideal S-curve due to the finite geometry of the scintillators and the electronic resolutions, resulting in uncertainties of the t.o.f.-, angular- and energy-determination. Therefore, the data evaluation had to accomplish both the subtraction of background events and the projection of the break-up events to the S-curve. Background identification was possible through the determination of all threeparticle energies. The neutron energies were calculated from the flight time, the proton energy was taken from the calibration of the light output in the target detector (fig. 6). In addition, one more quantity is available for background discrimination.

J. Sirare et al. / ‘H( n, nnp)

56

“

5

d.11

;,z. .z a..

6

:

_

,’ ,, ,,

,::

,8,,,=15.50

E,

.:.:

,.

I =5.11

ne’ V

,:y;. i.

4-

32I I-

; I

u I

2

3

4

5

6

1

e

tlevs

El

Fig. 5. (a) Energy calibrated total raw data in the E~‘ronE~u’ron plane. (b) Data after effect of all thresholds and windows, with the border line of maximal experimental uncertainty, calculated by the MC simulation. (c) Simulated data.

All real break-up events, induced by monoenergetic 13 MeV neutrons, have to have + En2+ E,= 13 - 2.225 MeV (deuteron binding the same energy sum of Es,,=E,,, energy) = 10.775 MeV. Sorted in an energy-sum spectrum, they thus built up to a peak at this energy, broadened by the total experimental uncertainty (fig. 7a). A window around this energy, a raising of the lower software thresholds of the single-nucleon energies (E',""" = 800keV, EF""= 500 keV) and additional windows in the t.o.f. and At.o.f. spectra reduces the background almost completely (fig. 5b). A further reduction of the background and the assignment of the events to the S-curve was achieved by a Monte Carlo simulation of the experiment. The code

J. Srrate et al. / ‘H(n,

I

2

3

9

5

6

nnp)

7

8

9

10

11 E ItleVI

Fig. 6. Light output in the target scintillator (NE232) of deuterons (x) from the elastic nD scattering together with a polynom-lit (solid curve), of protons (0) from the break-up reaction and furthermore the correlation L,(E) =fI_,(2E) (dashed curve) 5).

chooses randomly a point in the gas cell where the neutrons are produced, a reaction point in the target scintillator and detection points in both neutron scintillators thereby account

specifying angles by the simulation:

the energy

losses

and

and flight paths. The following effects were taken into The broadening of the incoming neutron energy due to

energy

straggling

of the deuterons

before

the D(d, n)3He

reaction, the attenuations of the neutron fluxes, uncertainties of angle and flight path due to the size of the scintillators, the time resolution of the electronics, the energy resolution

of the target scintillator

and finally the neutron

detection

efficiency,

which was measured in a separate experiment “) with an accuracy of 3%. This simulation was performed along the S-curve (statistics about 60 000 per MeV) for each configuration. A simulated spectrum of one angular configuration is shown in fig. 5c. The intensity distribution in the E1E2 plane matches the experimental distribution (fig. 5b) quite well. Only measured events within the calculated area of fig. 5c are assigned to the S-curve. A special method was developed for the projection of the data back to the S-curve ‘). In addition to the simulation of the experiment, the Monte Carlo code also calculated a set of probability factors for each pixel of the E1E2 plane (see fig. 5c), which indicate the different origins on the S-curve. These factors are then used to assign the experimental data of each pixel (see fig. 5b) back to different parts of the S-curve. This procedure is equivalent to a two-dimensional numerical unfolding.

_I. Strate et al. / ‘H(n,

58

nnp)

events 225

(4

200

, =

39.0n

=

0.0’

75.5” ~ = leO.o" , =

175 150 125 100 75 50 25

b

7

El

3

I0

11

12

13 energy

bat

round

100

b)

contr~butlon

xm~

IMeV

1

I X I I, = 1

=

1: =

80

‘*

33.0” O.oa 75.5”

= 1e0.0”

60

90

20

6

7

8

3

10

11

12

13 energr

sum

IMeVl

Fig. 7. (a) Energy-sum spectrum of break-up events inside the calculated area shown in fig. Sb together with the window and background interpolation for the region of true events. (b) Final background contribution versus the energy sum in this region.

J. S&ate

An exception

is the angular

all configurations

uncertainty;

again.

detectors.

nnp)

59

here is the result only an average,

In most break-up

the differential cross section some special configurations we determined

all possible

/ ‘H(n,

within the solid angles of the detectors

be disentangled

therefore,

et al.

angular

however,

because

up and cannot the variation

of

within the finite angular spread is very small, but in a strong dependence is observed *). In such cases,

by Monte Carlo simulation

combinations

Subsequently

configurations,

are summed

the probability

distribution

of

due to the finite size of the target and both neutron

we scanned

this angular

distribution

and performed

the

corresponding theoretical calculations, which are thus related to slightly different S-curves (real S-curves). The ideal as well as the real S-curves were counted from their point of intersection with the E,, axis, which shifted the position of maxima considerably “). Therefore the calculated cross section of each real S-curve was projected to the ideal S-curve for point geometry by the same method as for the experimental data ‘), taking into account the calculated probability factors as mentioned above. The result of this averaging procedure showed in the worst case a deviation of less than 5% compared with the calculation for the ideal S-curve. Owing to the strong deviations that the uncertainty in angular

between theory and the experimental determination is therefore negligible.

data it seems

The density distribution along the S-curve which was used in the simulation, slightly influences the assignment. Therefore in a first step, a homogeneous distribution was taken to project the experimental data. The resulting distribution was then the basis for a second Monte Carlo simulation yielding a second set of probability factors. A few additional iterations do not significantly change the count-rate distribution along the S-curve. For this reason, we always stopped after the first iteration. In the reprojection method the total number of measured events is conserved. A small amount events

of background

(fig. 5b). Its total number

the intensities

outside

(< 10%) still remains could be estimated

hidden

in the region of true

from a linear

interpolation

the 10.775 MeV line of the energy sum spectrum

of

(fig. 7a). In

this way, events in the middle of the energy-sum line have a small background contribution and the contribution increases at the outer ends of the line. This functional dependence (fig. 7b) was then used to correct each selected listmode event by its individual energy sum before reprojection to the ideal S-curve. This ensured the final background subtraction. A certain control of this procedure was obtained by the evaluation of angular configurations, which are kinematically not allowed (upper-right corner in fig. 2). In these configurations only accidental and multiple scattered events can occur and their contribution could be compared with the subtracted background mentioned above. Fig. 8 demonstrates how the spectrum along the S-curve of fig. 5b is modified by the final background subtraction (8a) and by the corrections for the neutron attenuation (8b) as well as for the detection efficiency (8~). The structures along the S-curve remain the same, the relative intensities, however, change mainly through the energy-dependent detection efficiency.

J. Strate et al. / ‘H(n,

60

nnp)

L Fig. 8. (a) Background distribution, (b) attentuation factors and (c) efficiency factors along the S-curve (left) and their effect on the reprojected count rate distribution (right), respectively.

To determine the absolute values of the differential cross section, the incoming neutron flux and the target density had to be known. Since the exact determination of these quantities is rather difficult, we normalized the break-up data by evaluation of the elastic nD scattering, measured simultaneously. These data were analyzed in a similar way and the results are shown in fig. 9. This normalization procedure has two advantages. First, the corrections due to attenuation and detection efficiency were very similar, thereby reducing systematic errors. Second, for comparison with theoretical

predictions,

the calculated

elastic

cross section

from the same code as

J. Strate et al. / ‘H(n,

nnp)

61

mbarn/sr

20

40

60

80

100

120

140

160

theta c.m. lde$l

Fig. 9. Differential

cross section

for the break-up

reaction

of the elastic nD scattering adjusted via ,y2 minimization.

can be used

to the Paris prediction

for the normalization.

(solid curve)

This avoids

errors

arising from the uncertainties of an absolute cross-section measurement and was justified, since, at low energies, the Paris potential prediction describes the data of the elastic scattering very well ‘). The error bars in the differential cross sections (figs. lOa-31a) represent the counting statistics (2%-6%) and the uncertainty in the background determination (~2%). The systematic error is mainly an uncertainty in the scaling and results from the data corrections (5 % ) and from the normalization to the elastic of about

nD scattering

6-10%

dependent

(~2%).

Thus, the absolute

on the different

cross section

configurations

has an error

and the length

of the

S-curve.

4. Results and discussion The results of 22 different break-up configurations are shown in figs. lOa-31a. The S-curves of the other configurations are too short or too much influenced by thresholds and therefore not suited for a comparison with theoretical predictions. The full and the dashed line in the figures are taken from a rigorous Faddeev calculation of Witala et al. based on the Paris potential lo) and on a slightly modified version of a charge-dependent force acting in the ‘So state ‘), since the Paris potential

J. Sirate et al. / ‘H(n,

62

is

fitted

to

pp

data.

The

calculation

nnp)

includes

the

partial

waves

‘S,,, 3S,-

3D,, 3P0, ‘P,, 3P1, 3P2-3F2, ‘D, and 3Dz. The dotted curves result from a Faddeev calculation with the simple Malfliet-Tjon potential MT 1,111 and the new W-matrix method

‘I).

All different discussion. S-curve

configurations

had to be systemized

For this, we developed

the maximal

time

a simple

of two nucleons

into groups

but illustrative within

the range

for a meaningful

model.

Along

each

of the NN force

is

subsystems ( TYax ) by the asymtotic momenta given This yields Tyax + co for FSI configurations. Likewise we calculated the maximal time in which all three particles stayed inside the range of the NN force (Ty”“). There is always Ty”“a Tf;ax; the equal sign is valid only calculated for all two-nucleon from kinematical conditions.

for the space star configuration. The ratio Tyax/TyaX, plotted in figs. lob-31b, is independent of the assumed range of the NN force. The similarity of configurations is now given by the values of this ratio. Values near zero are dominated by two-nucleon interactions and are similar to FSI and regions near one might be more favorable for displaying three-particle effects. These kinematical criteria are further modified by the phase-space factor which is given as dotted curve in figs. lob-31b. The measured differential cross section of the np FSI (figs. 14,22 and 26) is higher than the calculation with the Paris potential for angles Olab 2 25”. The computation with the charge-dependent

‘S, state yields

larger values

indicating

the importance

of a correct isospin dependence of the potential used for calculating break-up cross sections, but it fails to reproduce the data as well. The Malfliet-Tjon potential sometimes agrees (fig. 14) but misses the data at other angles completely (figs. 22 and 26). The regions near the FSI where the T1;““/ TY ratio is small (figs. 11, 18, 19, 21, 24 and 25) show exactly the same behavior, agreement at small angles and shortcoming as the angle increases. At the collinearity point (figs. 15, 19 and 25) and in the region

nearby

(figs. 17,

18 and 24), the data are also higher than the predictions although the different charge-dependent calculations are nearly identical. The same effect is seen in the space star configuration (fig. 31) and in all measurements with high values of the Tyaxl TT=’ ratio (figs. 10 and 28-30).

It is questionable

whether

corrections

in the

NN interaction can solve the discrepancies in such cases. From these comparisons, the following conclusions can be drawn: If rigorous calculations with potentials which are better adjusted to the nnp system, also fail to reproduce all data, other effects have to be considered even at these low energies. Different off-shell behavior was investigated by Stuivenberg “) and the effect of a three-body force was studied by Meyer 13). In both cases a simple potential was used in an approximated Faddeev calculation. Nevertheless, the additional threeparticle effects changed the differential cross section at those places where large discrepancies occur and also in such a direction which would diminish the deviations. More theoretical studies are necessary to solve these problems.

J. Strate et al. / ‘H(n, nnp)

rnb/sr2.

63

MeV

2.50

2.00 E.

=

13.0

MeV

1.50

1.00

0.50

aI

\ 2

TmaxYTmax2

4

phase

b

space

a

I0

12

14 S

CMeVI

factor

1.00 0.90

-

0.90

-

0.70

-

0.60

-

2

Lt

6

a

I0

12

I4 S IMeVl

Fig. 10. (a) Differential break-up cross section in comparison with the Paris prediction (solid curve), curve) and the MT I, the Paris prediction including charge dependence in the ‘S, state (dashed III-prediction via W-matrix method (dotted curve). (b) Kinematical criterium (solid curve; explanation see text) and the phase-space factor (dashed curve) along the S-curve.

J. Strate et al. / ‘H( n, nnp)

mb/sr2.MeV a 5.00 -

0, =

50.5'

@, =

0.0"

4.00

3.00

2.00

I -00

i

Tmax3Tmax2 1.00

-

i

4

12

I0

I4

16 S IMeL')

Phase space factor

b _.--

0.90

___----___ --._

,’

-\

/’

0.80

‘\ \

,’

‘\

I’

0.70

\

0.60 0.50 0.Lt0 0.30 0.20 0.10

__2

‘--__ 4

6

8

I0

Fig. 11. Same as fig. 10.

12

I4

16 S IMeV)

J. Strate et al. / ‘H(n,

mb/sr2.

nnp)

65

MeV

a, =

2.50

17.0°

0.0'

Q, = El, =

62.5’

L, = 180.0°

2.00

,

t

E, = 13.0

*

MeV

1.50

1.00

0.50

2

phase

TmaxYTmax2

a

6

space

10

12

19

lb S IMeVl

factor

1.00 0.90

-

0.80

-

0.70

-

0.60

-

b 2

4

6

a

I0

Fig. 12. Same as fig. 10.

12

14

lb S tMeV1

.I. Strate et al. / ‘H( n, nnp)

66

mb/sr2.

Me’/

a 2.50

-

2.00

-

:

En = 13.0

MeV

1.50

1.00

-

0.50

-

2

Phase

Tmax3/Tmax2 1.00

4

8

6

space

I0

12

ILt

16 S IMeVl

factor

-b

0.90 0.50 0.70 0.60 0.50 0.40 0.30 0.20 0.10

---___ 2

4

6

B

I0

Fig. 13. Same as fig. 10.

12

19

lb S IMeVl

J. Strate et al. / ‘H(n,

nnp)

67

mb/sr2.MeV 7.0

a

FSI 1

0,

: ,I j

6.0

0,

: :

q

39.0O O.o" 62.5'

Q, = IBO.OO

f : ; 11-c ,.

5.0

q

6, =

E,

q

13.0 MeV

Lt.0

3.0

2.0

1.0

2

TrnaxWTmax2

4

6

a

I0

12

19

16 S IMeVJ

phase space factor

1.00 0.90 0.80 0.70 0.60 0.50 0.Lt0 0.30 0.20 0.10

2

r

6

Fig. 14. Same as fig. 10.

16 S IMeVJ

68

J. Strafe

mb/sr’.

et

al. / ‘H(n,

nnp)

MeV

a

LOLL

3.5

1

a,

50.c

q

a, =

3.0

a,

ai! = 2.5

++

0.0*

=

62.5”

lBO.Ofi

En = 13.0

MeV

2.0 1.5 1.0 0.5

6

2

Tmax3Tmax2

1.00 0.90

phase

space

.

-

0.70 -

12

I0

factor

b ,

0.80

B

/’

I’

1)’

+_-----__

-.

‘. ‘\

‘\

\\

\\ , \

Fig. 15. Same as fig. 10.

I6 S IMeVl

J. Strate et al. / ‘H(n,

nnp)

69

mb/sr2. MeV

3 2.50

2.00

a,

=

$,

=

62.5O

0,

=

0,

= laO.o”

0.0O 62.5’

En = 13.0 MeV 1.50

t

1.00

0.50

2

12

Tmax 3/Tmax2

phase

SPPCC

Ilt S IMeVl

factor

I.0EI-I3

,_----.

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-\

1 1:

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Fig. 16. Same as fig. 10.

10

‘.

. .

12

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J. Sfrute et al. / ‘H(n,

nnp)

mb/sr'. MeV

I 0, =

L7.0O _

@, =

0.0O

a, =

75.5"

a2 = 190.0" -

2.0

En = 13.0 MeV

0.50

al

-2

TmaxWTmax2

Lt

6

B

10

12

14 S IMeVl

phase space factor

1.00 0.90 0.80 0.70 0.60 -

.c._ 2

Lt

6

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Fig. 17. Same as fig. 10.

10

12

--_ 14 S IMeVl

b

.I. Strafe et al. / ‘If(

71

n, nnp)

mb/sr2* MeV Lt.5 -

1

a 0,

4.0

7

a, =

-

25.0" 0.0”

0, = 75.C $2 = 130*0* E" = 13.0 HeV .'--I.. +

2.5 2,0 1.51.0 0.5-

)

Tmax3/Tmax2 1,00 1 b 0‘90 0.80 0,70 -

phase space factor

J. Strate et al. / ‘H( n, nnp)

72

mb/sr2*

Me’.’

a 3.5

-

3..0

-

2.5

-

2.0

-

1.5

-

1.0

-

0.5

-

En

2

Tmax3/Tmax2 1.00

Lt

phase

6

space

8

10

a,

q

4,

=

q

13.0

39.0” O.o”

MeV

12

I4 S IMeVl

12

14 S IMeVl

factor

b

0.90 0.80 0.70 0.60 0.50 0.90 0.30 0.20 0. LB

Fig. 19. Same as fig. 10.

.I. Strate et al. / “H(n,

73

nnp)

3 0, =

2.50 I

50.5'

$, =

0.0"

0, =

75.raQ

0, = lB0.0"

2.00

1.50

1.00

0.50

12 S IMeVl

phase space factor'

Tmax3/Tmax2 1.00 -

b

0.30 -

,_---._ , _.

0.80 0.70 0.60 0.50 -

0.30 0.20 0.10 __+-

#' : : ,I I' ,' #,' 2

', '\ '. .*.. 4

6

8

Fig. 20. Same as fig. 10.

10

---.._

12 S IMeVJ

J. Strate

74

et al. / 2H(n, nnp)

mb/sr2* HeV

8, =

17.0°

a, =

0.0”

0,

=

$2 =

90.0O 180.0’

En = 13.0

Tmax3/TmaxE

phase

ware

MeV

factor

1.00 0.90 0,811) 0,70 0.&O 0,50 0.90 0.30 0,2# 0. t0

6

8

10

12 S IMeVl

Fig. 21. Same as fig. 10.

_

-

J. Strafe et al. / ‘H(n,

75

nnp)

mb/sr'* MeV

a

FSI a,

1 ,.’._

5.00

: .' ., :

:

=

25.0”

@, =

0.0”

a, =

90.0°

dJ2

q

190.0°

3.00

12 S lMeVl

TmaxSTmax2

1.00 -

phase space factor

b

0.90 0.80 0.70 -

12 S IMeVl

Fig. 22. Same as fig. 10.

J. Skate et al. / ‘H(n,

nnp)

mb/sr'.MeV

a a, =

2.50

4, = a2 =

Q,

q

39.0O

O.o" 90.0°

laO.o"

E, = 13.0 MeV 1.50

0.50

2

Tmax3/Tmax2 1.00 -

4

6

10 5 IMeVl

phase space factor

b

0.90 0.90 0.70 0.60 0.50 0.40 0.30 0.20 0.10 -

: : I' I' ,' __*'

'\ '. '*._ 2

4

6

Fig. 23. Same as fig. 10.

9

-_-__

I0 S IMeVl

J. Strate et al. /

77

‘W(n, nnp)

3.5 -j

a,

=

a1 = 3.0

a2 = i

17.0O o.oQ 97.5”

4$ = 190.8”

2.5 En = 1340 MeV 2.0 1.5 1.0 0.5 -

Phase

Tmax3/Tmax2 1-m

-

0.90

-

0.90

-

space

factor

b

2

4

6

Fig. 24, Same as fig. 10.

8

10

S IMeVI

78

_I. Strate et al. / ‘H( n, nnp)

2. Hs!,

mb/

IC.

COLL

3

3.5

:

1

a, = 4,

=

25.0O O.o”

3.0

2.5

2.0

1.5

1.0

0.5

4

2

6

El

I0 S IMeVl

phase s-ace factor

TmaxWTmax2 1.00 - b 0.90 0.80 0.70 0.60

__--------_______

.-._

I’ 2

4

6

8

-__

10 S IMeVl

Fig. 25. Same as fig. 10.

J. Strate

ef al. / ‘H(n,

79

nnp)

mb/sr'.MeV FSI

a

8, =

1 .', .'', _' :

5.00

: :

4.00

:

c, =

., ;

%

13.0" _ O.o"

= ll0.0"

@z = lBO.Oa *

,r, ;

E, = 13.0 MeV

3.00

2.00

1.00

Tmax3/Tmax2

1.00 0.90

-

0.80

-

t=hase SPECS factor

1

b

0.70 0.60 0.50 0*40 0.38 0.20 0.10

s

Fig. 26.

Same as fig. 10.

10 S IMeVl

80

J.

Strateet al. / ‘H( n,

nnp)

a

3.5

8, =

e, =

3.0

O.o”

oe = llO.OO

2.5 -

2.0

25.0”

n

Q2 = 180.QD

1 I

fn = 13.0

I

HeV

1.5

1.0

0,s

1

TmaxYTmax2

2

3

6

7

B

9 s I&V,

phase space factor i , J

0.70 0.60 0.50 0.lt0 0.30 0.20 0.10

Fig. 27. Same as fig. 10.

_i. Strafe et al. / ‘H( n, nnp)

a

0, = $, = 0, =

17.0° O.oq 50.c

@e = 120.5’ E,

Tmax3Tmax2

phase swce factor

Fig. 28. Same as fig. 10.

= 13.0 MeV

82

J. Strate et al. / ‘N( n, nnp)

mb/sr2.

MeV

a 2.50

2.00

-

-

q

0,

=

0,

=

25.0O

-

+

E,

= 13.0

50.5’

MeV

I

:

2

Lt

Tmax3lTmax2

phase

b

space

8

I0

12

1Lt S IMeVl

factor

1.00 0.90 0.80 0.70 0.b0 0.50 0.40 ‘.

0.30

_’

.-

-.

‘\

,’ ,’

0.20

I’

\ I I

\\ \

I’

-

\

I

/

,’ 0.10

\

.’

‘Y_ _ 2

Lt

b

El

Fig. 29. Same as fig. 10.

I0

12

_

O.o”

4$ = 120.0n 4 4

1.50

8,

14 5 IMeVl

-

83

J. Strate et al. / 2H(n, nnp)

lnb/SP2~ rlev

a a,

-

2.50

=

@, = 0, 2.00

=

39.0” 0.0” 50.5”

4$ = 120*o”

-

E, = 13.0

MeV

-

I.50

2

6

ct

TmaxB/Tmax2

Phase

space

8

12

10

S IMeVI

factor

iii;;

0.50

;

-

0.Lt0 0.30

-

-

0.20

-

0.10

-

I’

, ,’

c’

,.--

__--

_____--------_____

--__

*-.*

*.

‘\\

,/ f’I’ #’ 2

..

4

6

a

Fig. 30. Same as fig. 10.

I0

\

t

‘,

‘\

‘.

.._ 12

S IMeVJ

J. W-ate et al. /

‘H( n, nnp)

mb/sr'.MeV SST

a

0, =

1

2.50 -

En +

+

50.5"

q

13.0 Me'.'

+ 4

1.00 -

O.on

El, =

0, = 120.0" -

2.0P) -

1.50 -

50.5" _

0, =

I

c

+

............................~~'

0.50 -

10

TmaxWTmax2

12 5 IMeVl

phase space factor

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

S lMeV1

Fig. 31. Same as fig. 10.

J. Strate et al. / ‘H(n,

nnp)

85

Valuable discussions with Drs. W. Gliickle, W. Sandhas, W. Tornow and H. Witala and the financial support of the Deutsche Forschungsgemeinschaft are gratefully acknowledged.

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