A DISCUSSION OP THE ANGULAR DISTRBUTION OF SPECTATOR PROTONS IN DEUTERIUM EXPERIMENTS

V. Bakken and T. Jacobien Institute of Physics, University of Oslo,

Norway.

RefXisfc 80-27

A DISCUSSION OF THE ANGULAR DISTRIBUTION OP SPECTATOR PROTONS IN DEUTERIUM EXPERIMENTS

V. Bakken and T. Jacobsen Institute of Physics, University of Oslo,

Norway.

Abstract

Several experimental and physical reasons for laboratory system anisotropy of spectator protons in deuterium bubble chamber experi­ments are briefly discussed phenomenologically. The angular distri­butions of the proton spectator from a series of experiments have been examined and compared with the expected behaviour. It is pointed out that due to the presence of several important aspects one cannot from the observed distributions obtain direct evidence for ona single of these effects such as the flux effect, which has been claimed in some publica­tions .

2

1 • Introduction Data in hadron-neutron reactions are usually obtained by means of

interactions on deuterona. It is assumed that the beam particle interacts essentially with only one of the nucleons in the deuteron, while the other nucleon acts merely as a spectator, i.e. the spectator model.

To test the validity of this model and check the goodness of the experimental procedures, the momentum and angular distributions of the proton spectators are compared with the expectations from the deuteron wave function. To make this prediction the validity of the spectator model and the impuls approximation [1] is usually assumed. This approximation implies that during the collision no three-momentum is transfered to the spectator, which therefore in the final state retains the Fermi momentum it had in the deuteron at the time of the inter­action .

In many publications it has been claimed that on the basis of the impuls approximation an isotropic deuteron wave function should imply an isotropic angular distribution of the spectator. A few years ago it was, however, pointed out that the variation of the invariant flux factor with the Fermi-momentum of the target neutron should cause a non-isotropic distribution of the spectators [2,3].

To make a meaningful comparison between the prediction and the experimental observations, also technical and experimental difficulties must be seriously considered. In the literature the various effects have been taken into account only to a very limited extent. In some cases some of the relevant effects are discussed neglecting the presence of the others.

In this note we will shortly discuss the various effects which are of importance for the angular distributions of the proton spectator. We start by discussing in section 2 the most important experimental effects. In section 3 the various physical effects are treated. In section 4 we compare the observed angular spectator distributions with the expected behaviour. A short summary is given in section 5.

i

2. Experimental reasons for deviation from Uotropy We discuss shortly some of the technical difficulties which influence

the angular distribution of the spectator protons as obtained in deu­terium bubble chamber experiments.

2.1 Scanning biases According to the commonly used deuteron wave functions the Fermi

momentum of a nucleon in the deuteron is below 300-400 MeV/c. A proton makes a visible track in the deuterium bubble chamber if

it has a momentum above 80-90 MeV/c. This means that about 1/3 of all spectators are expected to leave a visible track in the bubble chamber, assuming the spectator model to be valid. In many experiments the sample is restricted to events with visible spectators, while others also include the unseen spectator events.

Very short spectator tracks are subject to heavy scanning losses, especially for strongly dipping tracks. Of particular importance for the angular distribution of the spectators are the losses close to the beam track, i.e. for cos 8 — 1 , where 8 is the angle between the momenta of the spectator and the incident beam particle in the laboratory frame. Similar losses occur also for other values of cos 8 but are then spread over a much wider angular range, however, mainly for cos 8 > 0. The loss of very steep spectator tracks will be most clearly seen in the distribution of the azimuthal angle, and is strongest for short tracks. The loss of steep tracks will also be reflected in a loss in the cos 6 -distribution, most strongly near cos 8 ~ 0. How these losses depend on the spectator momentum is illustrated in figs. 2,3 by data from our pd experiment at 19 GeV/c [17]. In fig. 1 we have illustrated how these scanlosses can be corrected for in the spectator momentum distribution.

If unseen spectators are included in the analysis, the major part of the events with an undetected spectator events would be accounted for. However, for this sample the kinematic programs have difficulties in determining the correct spectator momentum, see 2.2, and are there­fore discarded.

2.2 Kinematic fit programs For the sample of measured spectators, the kinematic programs

operate in the "standard" way, i .e. as for interactions in hydrogen. It is , however, well known that very short stopping tracks will have large uncertainties in the angular variables, and that a correct treatment of these tracks are sensitive to the errors assigned to the measured end

1

point. The program will also have difficulties with events where the spectator reacts close to the vertex; this occurs more frequently in a deuterium chamber than in hydrogen. The standard way of handling the unmeasured spectators is to generate spectator momentum components with values equal to zero and with suitable errors as a first approxi­mation in the fits. This procedure is found to work fairly well for 4C-events, but has serious limitations for IC-events, for which the spectator momentum is badly reconstructed. Also for 4C-events the fit­ted momentum values for the spectator will be somewhat distorted, especially at high beam momenta.

The kind and amount of distortion of the observed cos 6 distri­bution of the spectator, due to the effects discussed above, will tend to vary from one experiment to another, and from one channel to another.

2.3 Wrong identification of the spectator nucleon Normally, the spectator is identified as the nucleon which has the

smallest (fitted) laboratory momentum. This procedure will fail in some cases. However, for the large majority of events the identification will be correct, due to the smallness of the spectator momenta. In the sample of observed spectators the fraction of misidentified events will be typically 5% [17], depending on the specific reaction channel and the applied spectator momentum cut. It is important to notice that the mis-identification rate depends strongly on the momentum and angle cos 6 of the spectator: For backward spectators there is essentially no mis-identification since the Fermi motion of the target then causes the momentum of the produced, slow proton to be higher than it would be on a stationary target. For forward spectators the effect will be op­posite. Obviously, the rate of misidentification will increase with increa­sing spectator momentum. Since the produced protons in most cases have rather high values of cos 8, the misidentification will tend to enhance the observed cos 6 spectator distribution at high values of cos 6.

The distortion of cos 6 of forward spectators will, however, depend much on the angular distribution of the slow proton. (If the slow nucleon is a fitted neutron, the event will be assigned to a dif­ferent channel, see below.)

Below we discuss the different types of misidentification in more detail.

s

For a reaction of the type

(1) (x + n t ) • p g + (x' • N • mesons) • p $ ,

where t and s stand for target and spectator, respectively, the following possibilities for misidentification exist: a) If the produced slow nucieon N is a proton with a momentum lower than the "true" spectator, the wrong proton will be chosen as the spectator (even if the momentum of N and p is correctly recon­structed). The frequency of wrong assignments will depend on the overlap of the momentum distributions of the spectator and the slow proton. b) If N is a neutron with a lower momentum than the spectator p , reaction (1) will be classified as a neutron spectator reaction

(2) (x + p j + n •* (x' + p + mesons) + n

and vice versa will (2) sometimes be classified as (1). Reaction (2) is a 1C reaction, and in particular at high energies the fitted momentum of the slow neutron can be considerably distorted. In that case the degree of mixing between (1) and (2) will be enhanced. c) Coherent reactions of the type

(3) x + d -> (x' + mesons) + d

are relatively rare. Since the momentum of the final state deuteron is small, the proton and deuteron identities may in some cases be inter­changed and this would then influence the spectator distribution in the break-up channel, corresponding to reaction (3).

In addition to the misidentifications mentioned above, events may in the kinematic fits be assigned to a wrong reaction. This might to some extend depend on the spectator momentum and could then also influence the observed angular distribution of the spectator.

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3, Physic»! reasons for deviation from Uotropy On the baris of the deuteron wave function one expects in terms

of the spectator model the angular distribution of the specutor to be nearly isotropic in the laboratory system.

We now discuss phenomenologieally some physical reasons for the deviation from an isotropic angular distribution for spectator protons.

3.1 The validity of the spectator model The spectator model and the impulse approximation implies that no

three-momentum is given to the spectator during the collision between the beam particle and the deuteron. However, some amount of energy must obviously be transferred to the spectator during the collision, since the energy of the spectator in the final state is higher than it was in the deuteron. One is therefore lead to believe that at the same time some three-momentum is transferred to the spectator nucleon. thereby also affecting the expected angular distribution of the spec­tator.

It is reasonable to assume that when the target neutron and the spectator proton leave their region of interaction in opposite directions, the impuls approximation is better satisfied than when they leave this region in the same direction. Therefore, the impuls approximation is likely to be best satisfied when the target neutron has the direction of the incident beam particle, while the spectator proton goes in the oppo­site direction, i .e. for spectators in the backward hemisphere as seen in the laboratory system.

Below in sections 3.1.1 and 3.1.2 we discuss two specific effects which influence the validity of the spectator model and the expected angular distribution of the spectator.

3.1.1 Phase space limit Since the impuls approximation usually is taken for granted in

deuteron experiments, the spectator proton is often thought of as completely de-coupled from the rest of the colliding system. However, even if the impuls approximation should work perfectly, the constraints from energy and momentum conservation of the complete beam deuteron reaction cannot de disregarded. Particularly for low energy experi­ments, backward spectators with large Fermi-momenta will be suppres­sed. As an illustration we have in Table I given the values of the minimum beam momentum needed to obtain a backward spectator (cosf) = -1) with momentum 0.2 GeV/c in the reaction x d + p g x n for different beam particles x .

3.1.2 Double scattering and rescattcring Double scattering means that the bean particle scatters succes­

sively on the two nucleons within the deuteron. Within the Glauber theory |4] this process is known to account for coherent reactions, i.e. reactions where the deuteron is unbroken in the final state. Inelastic coherent processes is known to correspond to a few percents of the total cross section [18]. Rescattering includes other types or final-state interactions on the spectator, due to secondary particles.

From studies of multiplicity distributions in hadron-deuteron inter­actions it is found (19] that rescattering or double scattering takes place in 15-20% of the events, depending somewhat on the nature of the beam particle, but not much on the beam momentum or the multiplicity. However, very little is known about the rescattering and double scat­tering in exclusive channels. A study of rescattering effects in 3- and 4-body final states in pd interactions at 19 GeV/c indicates a total rescattering or double scattering probability of about 20% [16]. A similar study of annihilation processes in pd scattering gives a slightly higher percentage (20). In the reaction pd •» p.pwt it" a special type of final state interactions in terms of d -production, was found to involve more than 30% of the events [9].

In order to find the effect of rescattering and double scattering on the angular distribution of the spectator, some detailed model is needed. However, some common results from such rescattering can be deduced: From geometrical considerations one expects that the initial- and/or final -state interaction probability is greatest for high spectator momenta, since a high Fermi momentum corresponds to a small proton-neutron separation in the deuteron. One also expects that final state interaction, which is found to be the dominating process [16,20], will effect the backward spectators less than the forward spectators. In the overall CM system the spectator will be a fast backward-moving particle and an initial and/or final state interaction on the spectator will increase the laboratory momentum of the spectator, backward spectators will be knocked from the backward to the forward hemisphere whereas forward spectators will in general become stronger collimated along the beam direction. Provided elastic double (re)-scattering is dominating, the cose -distribution will tend to be enhanced at cosB s 0.7-0.8. Therefore, double- and re-scattering will only lead to a small deviation from the spectator model for backward spectators, since they are knocked rather uniformly out of the backward hemisphere, whereas the forward specta-

s

tors will have an excess of high-momentum spectator» and a cose-distri-bution which is enhanced at large values of cose. The angular and momentum distributions in figs. 1,2 are seen to be consistent with a picture of this type.

Available information seems to indicate that double- and re-scat­tering are in most cases the most important of the effects which influen­ces the spectator distributions.

3.2 Energy dependence of the cross section Hadron-nucleon cross sections depends on the CM energy of the

collision. For exclusive channels the cross section increases with the energy from threshold, reaches a maximum at typically 1 GeV/c beam momentum from where it decreases with increasing energy. For a given beam (x) momentum the effective CM energy of the xn collision depends on the Fermi momentum of the neutron target: it is largest when the neutron approaches the beam, i.e. for forward spectators and smallest when it goes in the beam direction, i.e. for backward spectators. The CM energy is dependent on the momentum component p cose, p being the Fermi momentum of the spectator. At low energies where o(xn) varies strongly, the effect on the cos6 distribution of the spec­tator will also be strong. At high energies where o(xn) decreases only slowly with increasing energy, the effect will be small and tend to enhance large values of cos6.

3.3 The flux effect It has been pointed out by several authors [2,3] that the effective

flux of beam particles in an xn collision, n being a bound neutron, is a function of the velocity of the neutron ta'.-get. Thereby it also effects the angular distribution cos8 of the spectator, implying that the obser­ved number of forward spectators should exceed that of backward spectators. This effect has bisen discussed [3,6,7] quantitatively in terms of the Lorentz invariant flux factor.

The concept of flux effect is in this context based on an analogy with a macroscopic kinematical model where the target particles have some periodic movements along some trajectories within a target volume. Firstly, when a beam particle x with a velocity u passes through a target volume while a target neutron n has a velocity v < u, and a target proton p has a velocity -v, x must "meet" p and "overtake" n, as seen in the laboratory system.

9

However, if the two nucleons «re coupled and bound to move alternately with the velocities +v and -v over some finite range, x has a probability

(1) P + = HO + v /u)

to "meet" n (or p) and a probability

(2) P. = « 1 - v/u)

to "overtake" n (or p ) , according to a macroscopic model. Thus, for the deuteron, where the direction of v is isotropically

distributed, i .e.

(3) N(cos 6)= constant,

where 6 is the angle between v and u in the laboratory system, the probability for xn collision can be written

(4) P(cos8) « V.1 - (v /u )cose )a x n ,

where a is the energy dependent xn cross section (n off-shell), xn ^ Assuming that the free spectator proton has a momentum -mv, i.e. the impuls approximation, (m = the rest mass of the proton)

(5) P(cos8) a: ^(1 + (v /u)cos8)o x n

would be the expected angular distribution of the spectator protons in the reaction xd •» P S D e c t a t o r

+ anything, according to this model. If the Hulthén-distribution is taken to represent the Fermi-

momentum distribution of the nucleons, and if the corresponding velo­city-distribution is found, the result found above applies for each interval of v with a weight given by the Hulthén distribution. Integrating over the v-distribution, the angular distribution found above will be slightly modified.

Since the deuteron wave function predicts an average velocity of a nucleon within a deuteron <"> ~ 0.1 c, ths expected angular distribution of the spectator can be written approximately as

(6) W(cos 6) cc (I + (0.1 c/u) cos 8)o,

I l

Since 0.1 c/u is Urge for low energy experiments, a large flux effect is expected. For high energy experiments where u * c, the effect will be smaller, and fairly energy independent about

<?) W<cose) « 1 + 0.1 cose.

The crucial assumptions for this model are of course whether the proton and the neutron have trajectories in the deuteron (32), and if it has any meaning to discuss a change of the direction of motion of the proton and the neutron in the intermediate state of the xd collision. These conditions have been ignored in all previous discussions.

3.4 Some minor effects We finally mention some effects which are .of minor importance for

the expected angular distribution of the spectator. Screening means that the total xd cross section is smaller (ca

5%) than the sum of the total cross sections on free protons and neut­rons. It might well be that this screening, for specific channels as well as inclusively, depends on the momentum and the angle of the spectator, and therefore affects the appearance of the cos6 -distribution.

In reactions where there is a slow produced proton in aadition to the proton spectator, the Pauli exclusion principle will tend to suppress reactions where the two protons have comparable momenta. Since the produced protons are essentially always emitted in the forward hemis­phere in the laboratory system, this will for such reactions suppress the number of forward spectators.

The coherent channels exercise an absorbtive effect on the corre­sponding breakup reactions in the region of phase space where the slow proton and the slow neutron are close in momentum space. One expects that this leads to a small depletion in the angular distribution of forward spectators in the breakup channels.

Finally, the small D-wave component in the deuteron and contri­butions of baryon resonances (M) the deuteron wave function could lead to a small anisotropy in the angular spectator distribution.

I I

4. A discussion of experimental angular distribution» It follows from the discussion in sections 2 and 3 that several

effects tend to distort the angular distribution of the observed proton spectators compared with the basic prediction of isotropy. Some of these effects are seen to depend strongly on the momentum of the spectator. Therefore the accepted momentum interval of the spectators will be of great importance for the observed angular distribution of the spectator We have furthermore seen that the various effects will influence the different part of the cos6 distribution to a varying degree. The stron­gest distortions will in general occur for forward spectators (cose > 0) whereas backward spectators will be less effected, except for a scan loss of spectators near cos8 = -1 for momenta just above the visability limit.

The angular distributions in fig. 2 from pd reactions at 19 CeV/c [17] represent typical examples of spectator distributions in high energy deuterium bubble chamber experiments. The backward spectators follows roughly the expected momentum distribution with a fairly flat cosB-distri-bution. For forward spectators there is a substantial excess of high-momentum tracks compared with the prediction of the commonly used deuteron wave functions. In the cos8-distribution there is an excess of events with cos8 > 0 compared with the backward spectators and the cose-distribution is much more peaked towards cos8 = 1 than predicted by the flux effect.

In order to summarize the observed angular distribution of the proton spectator as obtained in a series of deuterium-filled BC experi­ments, we have below compared their cos8—distributions with the expec­ted isotropic behaviour (modified by the flux effect of eq.(7)) in terms

o of a x -fit. Only measured spectators are considered. It is noticed that somewhat different upper spectator momentum cuts have been applied in the different experiments. Only statistical errors are considered.

4.1 Consistency test for -1 £cos8 SI We have made a fit of the distribution function

W(cos8) = A(l + -— cosB), where <v> is the mean spectator velocity as computed from the deuteron wave function and u the beam velocity, to the angular distribution of the proton spectators of the reactions given in Table II. From the x -values of Table II it is seen that the observed distributions are i.» nearly all cases inconsistent with the prediction of

1^

the luodel (isotropy modified by the flux effect) in the full angular range -1 Scos6 S 1. In some of the experiment* the Inconsistency is very strong, demonstrating clearly the presence of effects not included in the model.

4.2 Consistency test for -0.9 i cos8 i 0 It follows from the earlier discussion that in the angular region

-0.9 S cose S 0 the deviations from isotropy is expected to be moderate. We have therefore made a new set of fits to the data of the experiments in Table HI in this restricted angular region. We have made fits both with a flat angular distribution and with the distribution function pre-2 dieted from UIP flux model. The obtained values of x are given i Table III. The results show that in this restricted angular region most of the data are consistent with both predictions. The small difference between the two hypotheses could well be due to the effects of rescattering etc. and cannot be used to favour one of the hypotheses over the other.

In some of the publications the authors claim that their data pro­vide evidence for the presence of the flux effect. We think that such a statement is not well justified due to the presence of a series of other important effects which influences the spectator distributions.

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5. Discussion The aim of this note has been to give a «ho:-; account of the

various technical and physical effects which incluence the appearence of the spectator proton as observed in deuterium bubble chamber experi­ments. Particular emphasis is given to the angular cos6 distribution. We find that such a discussion is appropriate since in many experiments conclusions are drawn from the spectator distributions without giving proper attention to the various effects which influence these distribut­ions.

The deviations from an isotropic angular distribution are expected to be strongest for spectators which go forward in the laboratory system and which have high momenta. For high momentum spectators double- and re-scattering effects together with wrong selection of spectator nucleons are expected to be the dominating effects. For spectator momenta just above the visability limit scan loss is important. Both double- and re-scattering, wrong choice ot spectators and the flux effect tend to enhance the cose-distribution towards cose = 1.

We have in a series of experiments compared the observed angular distributions of the proton spectator in a series of experiments with the prediction of the spectator model including the flux effect. If the full angular range -1 £ cose £ 1 is considered, the data show strong devi­ations from the predicted behaviour. For backward spectators in the interval -0.9 < cosB S 0 the data are consistent with isotropy as well as with the prediction which follows when the flux effect is included. Finally we would like to stress that, according to our description, the presence of a flux effect depends on the consept of nucleon trajectories within the deuteron and on the possibility of a change in the direction of motion of the nucleons in the intermediate state of the xd collision. The validity of these requirements may be questioned. It is not poss­ible, however, on the basis of the available data, to acertain whether the flux effect should be included or not. This is partly due to the smallness of the flux effect at high energies, but it is also due to the presence of other more important effects such as double/re-scattering which is not easily accounted for quantitatively.

N

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1?

Table I The value of the minimum beam momentum needed to obtain a backward spectator proton (cotO * -1) with momentum 0.2 GeV/c in the reaction xd -» p g xn.

Beam particle x Beam momentum (GeV/c)

Y 0.06 n 0.2 K 0.4 p 0.6

IK

Table II Fits of Eq.(6) to the cos6 -distribution of the visible proton specutor in the momentum interval 90 ~ p(P s ) ~ 350 MeV/c, for all values of cose included.

Ref . Reaction Momentum (GeV/c)

X2/NDF Momentum cut (MeV/c)

9 - . + -p d •» P.pn i t 5.5 227/19 stopping

10 P d •» p NN + pions 19 57/24 < 350

6 P d * p spp n~ 5.5 30/19 stopping

11 + . + - o i d - " p p n n n 1.1-2.4 68/19 < 300

28 pd * P spp n" 5.9 15/9 stopping

29 dp * p sppi" 25 43/19 < 300

33 K+d •» P«.Vp 12 180/99 stopping

34 pd •» p.pnn n~ 7 52/9 stopping

35 n+d -» p +4-prongs 15 32/19 stopping

19

Table III Fits of an isotropic distribution and of Eq.(6) to the cos 6 -distribution of the visible proton spectator in the angular region -0.9 < cosS < 0.0 for slightly different intervals of the spectator •omentum. Ref Reaction Hoaentun X 2/NDF X 2/NDF

(GeV/c) Isotropy Eq. (6) 9 pd •* p pn 71 7T 5.5 15/9 18/9 12 pd * p spn n" 14.6 8/8 8/8 x

6 pd -. p pp n" +, s + - o

n d •» p pn n n

5.5 11/9 11/9 11

pd -. p pp n" +, s + - o

n d •» p pn n n 1.1-2.4 11/8 22/8 13 n <J -» 4 charged 2.7 35/23 82/23 10 pd •» p spp n" 19 17/11 19/11 14 pd •» p p n"p 7.0 9/10 11/10 " 15a + s - + K d -» p sn K 8.25 16/9 39/9 x

5 pd •» p + particles 100 2.3/4 2.0/4 21 pd < 1 1/4 1.2/4 * 22 dp •» ppn 3.3 8/9 7/9 X

23 dp * ppn 3.3 4.6/9 4.5/9 24 + o* K d -• p pK 1.9 10/9 4.5/9 x

25 + s

n d •» p p/m 1.1-2.3 85/25 70/27 X

26 K"d •» p k°n"N(toO,k=0, .1,2 3.4 22/10 27/10 x

27 8 - + -

K d ->p k n J n 5.5 22/20 30/20 " 28 pd + p spp it" 5.9 6/4 5/4 x

29 dp + P sppt" 25 12/4 19/4 x

30 n +d * p p(kji°),k<l 5.1 103/19 90/19 x

s + -•* P-P" n n " 42/20 38/20 X

+ - o * P SP n " " " 43/20 29/20 X

-» p p n n"(tot°) ir 47/18 46/18 x

31 pSle •» He snp g 5 6 5 / i 0 2 0 / 1 0 y

33 K+d + P S K V P 12 65/45 76/45 34 pd -» p s p n n V 7 5.5/4 3.4/4 35 n +d p + 4-prongs 15 9/9 5/9

Stun 614/332 687/332 x spectator nucleon momentum i 300 MeV/c.

3 y He - spectator.

20

Figure captions

Fig. 1 Momentum distributions of the observed proton spectator in the reactions pd + pgppn", pd + p pnn*n" and pd •» psppn~n° at 19 GeV/c (18). The shaded regions represent corrections for scan loss as determined from the angular distributions of the spectator (figs. 2,3). The curve represent the prediction of the Hulthén wave function normalized to the data in the momentum interval 120-200 MeV/c.

Fig. 2 The angular distribution cos6 of the spectator versus the momentum of the spectator for the same data as in fig. 1. The curves represent the prediction of the spectator model modified by the flux effect, normalized to the sample of backward spectators.

Fig. 3 a) A scatter plot of the azimuthal angle of the spectator versus the momentum of the spectator for the same data as in fig. 1.

b) The projection on the azimuthal angle of the data in a ) .

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