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p p Annihilation into two mesons using the 3P0 model
Volume 139B, number 1,2
PHYSICS LETTERS
3 May 1984
PP ANNIHILATION INTO TWO MESONS USING THE 3P 0 MODEL A.M. GREEN, J.A. NISKANEN 1 Research Institute for Theoretical Physics, University of Helsinki, Helsinki, Finland and S. WYCECH 2 Institute for Nuclear Studies, Warsaw,Poland
Received 22 December 1983
The NN optical potential due to annihilation into two mesons is derived. The model is based on quatk-antiquark rearrangement plus a single quark-antiquark annihilation into the vacuum. The imaginary part of the optical potential is dominated by the NN(13p O) component and results in a central ~p potential that is considerably weaker than that of Dover and Richard.
Broadly speaking, theories for n u c l e o n - a n t i n u c l e o n annihilation at low energies fall into two distinct categories. Firstly, there is the traditional model of fig. l a which can be viewed as the exchange o f a nucleon between the initial NN with the direct emission o f two mesons. Secondly, there are those models based on quark rearrangement that lead directly to three mesons. Both of these approaches have been reviewed recently in refs. [1,2]. The two-meson emission model of fig. la has been treated in most detail in ref. [3]. For specific channels pp -~ M1M 2 it seems to give an acceptable account o f the rather limited amount of experimental data mainly M1M 2 = mr, ,r,). But, in its most reasonable version it is able to yield less than 20% o f the total annihilation cross section. However, there are several criticisms against this calculation, the most serious being the neglect o f A-exchange, violent form factor dependence, coupling constant uncertainty and the neglect o f N A + AN, AA configurations -- see refs. [1,2] for more details. I On leave of absence from the Department of Theoretical Physics, University of Helsinki. 2 Partly supported by the Polish-US Maria Ski'odowska-Curie Fund under Grant no. P-F7F037P. 0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-HoUand Physics Publishing Division)
MI
a)
M2
M~
N
N
M
N b)
M~
M2
N
Q c)
Fig. 1. NN annihilation into two mesons via (a) N-exchange, (b) a single q~ annihilation, and (c) two q~ annihilations and a single q~ creation.
In this letter an attempt is made to overcome some o f the above objections by treating the N~I annihilation at the quark level as shown in fig. 1b. The approach employed is an extension o f the earlier quark rearrangement model [2], in which one o f the qq pairs is now in the 13p 0 state and so can annihilate directly into the vacuum. It should be added that an additional contribution to the Nhl ~ M1M 2 also comes from the mechanism shown in fig. lc. In the literature there are given reasons why fig. lb should dominate over lc and vice versa. In ref. [4] the approximate equality of the matrix elements for NN -~ p0n+lr- and N ~ / ~ con+n - suggests fig. l b is much more important 15
Volume 139B, number 1,2
PHYSICS LETTERS
than fig. lc. This conclusion depends on the result that the Nlq interaction based on meson exchanges seems to be stronger in T = 0 states than T = 1 [5], and so enhances the NN ~ con+n - cross section over that observed for the 0°rr+n - [6]. On the other hand, in ref. [7] Genz, by considering only the mechanism in fig. lc, is able to get an understanding of the reactions p~ ~ lr°rt 0, 7r°~), nOr?' and rm'. He then concludes that fig. lb must be much less important than fig. lc. This analysis would have been more convincing if both processes had been included initially and the ratio of their effects extracted - as in ref. [4]. Furthermore, the above reactions on which Genz bases his arguments contribute in all < 1.5% to the total annihilation. If, as is generally thought, the NN -+ M1M 2 contributes 1 0 - 2 0 % of the total annihilation, then he is only showing that a small fraction of the NN MIM 2 annihilation is dominated by fig. lc. Therefore, the bulk of the annihilation into two mesons could well come from fig. lb - the viewpoint adopted in this paper and opposite to that of ref. [8]. In the evaluation of fig. lb the N, N and meson (Mi) wavefunctions are taken in the form if(N) = (ct/rr) 3/2 exp[-IO~(S2
+
etc.,
(1)
where s = 2-1/2(r 1 - r2), t = 6-1/2(r 1 + r 2 - 2r3) and x = r 1 - r 1, - the primed coordinates referring to the C:l'S.The qCt annihilation vertex for the 3P 0 model is in the coordinate representation 0 = i33,%/~(3/47r) 1/2 [2VxX(qC:l, s = 1)]Y(qff)=°6(x), (2) where 7 = 3.4 the value found in ref. [9] by fitting a series of meson decays and baryon coupling constants. However, it must be admitted that these latter situations are less complicated than now. Therefore, it is an assumption that the same value of 7 is appropriate. In eq. (2) the factor of 3 is needed when colour wavefunctions are used [10] - a feature that is necessary for situations beyond those originally considered [8]. The factor o f x / 2 - ~ t a k e s into account the" SU(3) flayour structure of the vacuum, since the q~t before the annihilation have the flavour structure of the co-meson. For the transition [Ngl] S, L=I J T --. MIM2 ' in the CM system, this results in the potential
16
Vtr = K C [ N b I ( S J T ) -~ M 1 M2] r X e x p [ - i1a t -r
'2
3., *. Zt~ + 3v)r2)] [YI(t:)x(NN,S)] J , (3)
where K = - 7 -~ (~5/2/rr3/2)v3/2/(1 + v) 1/2 , v = 2/3/o~, and r, r' are the relative distances between the NN and M1M 2 respectively. The factor C[ ] is the SU(4) Clebseh-Gordan coefficient for the specific coupling. The K contains a statistical factor of 6, al/3 x/~ from colour and another 1/3 X,/-3 from the jacobian. A striking feature of the transition potential in eq. (3) is that it is separable and acts only in NN relative p-states. Therefore this model for N~I -+ M 1M 2 is presumably not the whole story since at present there is no reason to believe that such decays cannot also take place from relative s-states. However, some experiments do indeed show a need for a remarkable amount of p-wave annihilation [10]. The transition potential of eq. (3) gives rise to a pwave NN optical potential of the form ([Ngl] S,L= 1 J T I V ( r ' r", E)I [NKI] S,L= 1 JT)
t2)] ,
~(M1) = ([3/n)314 e x p [ - ~ / 3 x 2] ,
3 May 1984
(4)
= V(r)I(SJT, E)V(r"),
where V(r) = r e x p [ - -38a(1 + 3v)r 2] ,
I(SJT'E)=
~3 K2
M1M2
C2[ ] I(M1M2E )
(5) (6)
and I(M1M2E) = 1 /7
f dk k 2 E ( N ~ ) exp(-k2/o~) - E(M~) - ~(M2)
" (7)
In eq. (7) E(NN) is the NN CM energy and E(Mi) = (k 2 + M2) 1/2 - i Pi/2. In the following the width (Pi) is only retained for the 0-meson. It should be added that the relativistic treatment of the mesons and the inclusion of the width of the 0-meson both have significant effects. For the imaginary part this results in the curves shown in fig. 2 for the separate p-wave components. One of the most striking features is the dominance of the NN(13P0) potential - being an order of magnitude stronger than the others. This shows
Volume 139B, number 1,2 {SJT) (111}
//
/~--~%
'Ira MopI MeV}
7001rnI [E ( NN}] (MeVz } 6OO
xx x
//
3 May 1984
PHYSICS LETTERS
\x\
~x{lO0}
5OO
(120)
4OO
80C
~a}
600
(011} 40[ [121}
100 ~
{010}
20(
(101) -300
-200
-100
E(NN}{MeV)
100
200
Fig. 2. Im I(SJT, Ecru) of eq. (6) for the various (S/T). The
squares show the p~ spin average. ~ = 2.78 fm -2, v = 2/x/~-the values corresponding to a proton charge RMS radius of 0.6 fm and V(qq-) = 2V(qq) = rg. N.B. The 13P0 component (i00) has been reducedby a factor of 1/10 and the 13p 1 component is zero. that the underlying 13p 0 q~l annihilation mechanism persists at the N~/level. It should be added that in the phenomenological potential o f ref. [ 12] no such 13p 0 dominance is observed. Another feature is the decrease o f the potential in each partial wave as the energy increases above the NN threshold. This effect is brought about by the internal wavefunctions o f the N and N leading to the exponential factor in eq. (7). In order to compare the imaginary part o f the separable potential V(r, r") in eq. (4) with standard phenomenological potentials, it is necessary to calculate a local approximant U(r). One way o f achieving this is to demand
(8)
U(r)$(r) f dr"/'2 V(r, r")$(r"), =
with if(r) =Ar to ensure ~k(r) has the p-wave asymptotic form as r-+ 0. This results in
U(r) = 7rl/23-3/229/2
[a(1 + 3u)] - 5 / 2 r - 1
V(r).
(9)
In fig. 3 a comparison is made between the imaginary component of the potential in ref. [5] (D.R.) and Vc the gp central part o f the above local potential. It is seen that the latter is considerably smaller than D.R. at r "~ 0.8 fin for energies 50 ~< Ecru ~< 200 MeV - the range over which the D.R. potential was derived. The conclusion to be drawn from the above is that the NN ~ MIM 2 mechanism described here is, on average, not the most important source of annihila-
04
o~
o'.8
i.o
r(frn~
Fig. 3. A comparison between the imaginary part of the potential in ref. [51 and Vc the spin averaged ~p local potential in eq. (9) due to NN ~ MIM 2 ~ NN at the two Ecm energies
(a) 50 MeV, (b) 200 MeV. N.B. Vc is not strongly dependent on v - the only free parameter once 3' is taken from ref. [9].
tion, although it does give a considerable effect in the 13p 0 partial wave. This is based on the three observations that, compared with the phenomenological potentials, (a) the spin averaged potential Vc is considerably weaker (b) the spin dependence is completely different and (c) the energy dependence is opposite to that usually assumed. However, there is at present no reason for excluding the above mechanism as being the main one for annihilation into two mesons. This will only be possible when the bulk o f the NN -~ M 1M 2 reactions have been measured - in particular M1M 2 = pp, coco and cop. Also, when making theoretical predictions for these branching ratios, it is necessary to include the NN initial state interaction together with N ~ + A~I and A ~ admixtures. These could radically alter any predictions - as in ref. [8] - that only take into account the C[ ] factor o f eq. (3), and the phase-space effect - even when the latter is modified by the form factors generated by the N, N and M i internal quark wavefunctions. This is particularly important for the separable potentials o f eq. (3), since in a Schr6dinger equation approach the real part o f the optical potential can generate nodes within the range o f the transition potential. Such an occurrence leads to a saturating effect in which the annihilation passes through a maximum as the strength o f the transition potential increases - see figs. 6, 7 o f ref. [2].
17
Volume 139B, number 1,2
PHYSICS LETTERS
The authors acknowledge useful conversations w i t h Dr. M. Chaichian and Dr. P. Z e n c z y k o w s k i . One o f us (SW) thanks the Research Institute for Theoretical Physics, Helsinki, for their support during the period when this w o r k was carried out.
References [ 1 ] A.M. Green, Proc. Intern. Summer School on NN-interaction and nuclear many-body problems (Changchun, China, 1983), eds. S.S. Wu and T.T.S. Kuo (World Scientific, Singapore, 1984). [2] A.M. Green and J.A. Niskanen, Nucl, Phys. A412 (1984) 448; and a review in HU-TFT-83-54. [3] B. Moussallam, Nucl. Phys. A407 (1983) 413. [4] R.K. Logan, S. Kogitz and S. Tanaka, Can. J. Phys. 55 (1977) 2059. [5] C.B. Dover and J.M. Richard, Phys. Rev. C21 (1980) 1466.
18
3 May 1984
[6] P. Pavlopoulos et al., Proc. 2nd Intern. Conf. on NN interactions (Vancouver, 1977), AlP ConL Proc. No. 41 (ALP, New York) p. 340. [7] H. Genz, Phys. Rev. D28 (1983) 1094. [8] S. Furui, A. Faessler and S.B. Khadkikar, Tiibingen preprint (December 1983). [9] A. Le Yaouanc et al., Phys. Rev. D8 (1973) 2223; D l l (1975) 1272; M. Chaichian and R. K6gerler, Ann. Phys. 124 (1980) 61; J.P. Ader, B. Bonnier and S. Sood, Nuovo Cimento 68A (1982) 1. [10] A. Le Yaouanc et al., in: Introduction to the quark model of elementary particles, Vol. 2, ed. D. Flamm. [11] L. Tauscher et al., Proc. Vlth European Symp. on NN interactions (Santiago de Compostela, Spain, 1982), Ann. Fis. (Madrid) 79 (1983) 24. [12] J. Cot6 et al., Phys. Rev. Lett. 48 (1982) 1319.
PHYSICS LETTERS
3 May 1984
PP ANNIHILATION INTO TWO MESONS USING THE 3P 0 MODEL A.M. GREEN, J.A. NISKANEN 1 Research Institute for Theoretical Physics, University of Helsinki, Helsinki, Finland and S. WYCECH 2 Institute for Nuclear Studies, Warsaw,Poland
Received 22 December 1983
The NN optical potential due to annihilation into two mesons is derived. The model is based on quatk-antiquark rearrangement plus a single quark-antiquark annihilation into the vacuum. The imaginary part of the optical potential is dominated by the NN(13p O) component and results in a central ~p potential that is considerably weaker than that of Dover and Richard.
Broadly speaking, theories for n u c l e o n - a n t i n u c l e o n annihilation at low energies fall into two distinct categories. Firstly, there is the traditional model of fig. l a which can be viewed as the exchange o f a nucleon between the initial NN with the direct emission o f two mesons. Secondly, there are those models based on quark rearrangement that lead directly to three mesons. Both of these approaches have been reviewed recently in refs. [1,2]. The two-meson emission model of fig. la has been treated in most detail in ref. [3]. For specific channels pp -~ M1M 2 it seems to give an acceptable account o f the rather limited amount of experimental data mainly M1M 2 = mr, ,r,). But, in its most reasonable version it is able to yield less than 20% o f the total annihilation cross section. However, there are several criticisms against this calculation, the most serious being the neglect o f A-exchange, violent form factor dependence, coupling constant uncertainty and the neglect o f N A + AN, AA configurations -- see refs. [1,2] for more details. I On leave of absence from the Department of Theoretical Physics, University of Helsinki. 2 Partly supported by the Polish-US Maria Ski'odowska-Curie Fund under Grant no. P-F7F037P. 0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-HoUand Physics Publishing Division)
MI
a)
M2
M~
N
N
M
N b)
M~
M2
N
Q c)
Fig. 1. NN annihilation into two mesons via (a) N-exchange, (b) a single q~ annihilation, and (c) two q~ annihilations and a single q~ creation.
In this letter an attempt is made to overcome some o f the above objections by treating the N~I annihilation at the quark level as shown in fig. 1b. The approach employed is an extension o f the earlier quark rearrangement model [2], in which one o f the qq pairs is now in the 13p 0 state and so can annihilate directly into the vacuum. It should be added that an additional contribution to the Nhl ~ M1M 2 also comes from the mechanism shown in fig. lc. In the literature there are given reasons why fig. lb should dominate over lc and vice versa. In ref. [4] the approximate equality of the matrix elements for NN -~ p0n+lr- and N ~ / ~ con+n - suggests fig. l b is much more important 15
Volume 139B, number 1,2
PHYSICS LETTERS
than fig. lc. This conclusion depends on the result that the Nlq interaction based on meson exchanges seems to be stronger in T = 0 states than T = 1 [5], and so enhances the NN ~ con+n - cross section over that observed for the 0°rr+n - [6]. On the other hand, in ref. [7] Genz, by considering only the mechanism in fig. lc, is able to get an understanding of the reactions p~ ~ lr°rt 0, 7r°~), nOr?' and rm'. He then concludes that fig. lb must be much less important than fig. lc. This analysis would have been more convincing if both processes had been included initially and the ratio of their effects extracted - as in ref. [4]. Furthermore, the above reactions on which Genz bases his arguments contribute in all < 1.5% to the total annihilation. If, as is generally thought, the NN -+ M1M 2 contributes 1 0 - 2 0 % of the total annihilation, then he is only showing that a small fraction of the NN MIM 2 annihilation is dominated by fig. lc. Therefore, the bulk of the annihilation into two mesons could well come from fig. lb - the viewpoint adopted in this paper and opposite to that of ref. [8]. In the evaluation of fig. lb the N, N and meson (Mi) wavefunctions are taken in the form if(N) = (ct/rr) 3/2 exp[-IO~(S2
+
etc.,
(1)
where s = 2-1/2(r 1 - r2), t = 6-1/2(r 1 + r 2 - 2r3) and x = r 1 - r 1, - the primed coordinates referring to the C:l'S.The qCt annihilation vertex for the 3P 0 model is in the coordinate representation 0 = i33,%/~(3/47r) 1/2 [2VxX(qC:l, s = 1)]Y(qff)=°6(x), (2) where 7 = 3.4 the value found in ref. [9] by fitting a series of meson decays and baryon coupling constants. However, it must be admitted that these latter situations are less complicated than now. Therefore, it is an assumption that the same value of 7 is appropriate. In eq. (2) the factor of 3 is needed when colour wavefunctions are used [10] - a feature that is necessary for situations beyond those originally considered [8]. The factor o f x / 2 - ~ t a k e s into account the" SU(3) flayour structure of the vacuum, since the q~t before the annihilation have the flavour structure of the co-meson. For the transition [Ngl] S, L=I J T --. MIM2 ' in the CM system, this results in the potential
16
Vtr = K C [ N b I ( S J T ) -~ M 1 M2] r X e x p [ - i1a t -r
'2
3., *. Zt~ + 3v)r2)] [YI(t:)x(NN,S)] J , (3)
where K = - 7 -~ (~5/2/rr3/2)v3/2/(1 + v) 1/2 , v = 2/3/o~, and r, r' are the relative distances between the NN and M1M 2 respectively. The factor C[ ] is the SU(4) Clebseh-Gordan coefficient for the specific coupling. The K contains a statistical factor of 6, al/3 x/~ from colour and another 1/3 X,/-3 from the jacobian. A striking feature of the transition potential in eq. (3) is that it is separable and acts only in NN relative p-states. Therefore this model for N~I -+ M 1M 2 is presumably not the whole story since at present there is no reason to believe that such decays cannot also take place from relative s-states. However, some experiments do indeed show a need for a remarkable amount of p-wave annihilation [10]. The transition potential of eq. (3) gives rise to a pwave NN optical potential of the form ([Ngl] S,L= 1 J T I V ( r ' r", E)I [NKI] S,L= 1 JT)
t2)] ,
~(M1) = ([3/n)314 e x p [ - ~ / 3 x 2] ,
3 May 1984
(4)
= V(r)I(SJT, E)V(r"),
where V(r) = r e x p [ - -38a(1 + 3v)r 2] ,
I(SJT'E)=
~3 K2
M1M2
C2[ ] I(M1M2E )
(5) (6)
and I(M1M2E) = 1 /7
f dk k 2 E ( N ~ ) exp(-k2/o~) - E(M~) - ~(M2)
" (7)
In eq. (7) E(NN) is the NN CM energy and E(Mi) = (k 2 + M2) 1/2 - i Pi/2. In the following the width (Pi) is only retained for the 0-meson. It should be added that the relativistic treatment of the mesons and the inclusion of the width of the 0-meson both have significant effects. For the imaginary part this results in the curves shown in fig. 2 for the separate p-wave components. One of the most striking features is the dominance of the NN(13P0) potential - being an order of magnitude stronger than the others. This shows
Volume 139B, number 1,2 {SJT) (111}
//
/~--~%
'Ira MopI MeV}
7001rnI [E ( NN}] (MeVz } 6OO
xx x
//
3 May 1984
PHYSICS LETTERS
\x\
~x{lO0}
5OO
(120)
4OO
80C
~a}
600
(011} 40[ [121}
100 ~
{010}
20(
(101) -300
-200
-100
E(NN}{MeV)
100
200
Fig. 2. Im I(SJT, Ecru) of eq. (6) for the various (S/T). The
squares show the p~ spin average. ~ = 2.78 fm -2, v = 2/x/~-the values corresponding to a proton charge RMS radius of 0.6 fm and V(qq-) = 2V(qq) = rg. N.B. The 13P0 component (i00) has been reducedby a factor of 1/10 and the 13p 1 component is zero. that the underlying 13p 0 q~l annihilation mechanism persists at the N~/level. It should be added that in the phenomenological potential o f ref. [ 12] no such 13p 0 dominance is observed. Another feature is the decrease o f the potential in each partial wave as the energy increases above the NN threshold. This effect is brought about by the internal wavefunctions o f the N and N leading to the exponential factor in eq. (7). In order to compare the imaginary part o f the separable potential V(r, r") in eq. (4) with standard phenomenological potentials, it is necessary to calculate a local approximant U(r). One way o f achieving this is to demand
(8)
U(r)$(r) f dr"/'2 V(r, r")$(r"), =
with if(r) =Ar to ensure ~k(r) has the p-wave asymptotic form as r-+ 0. This results in
U(r) = 7rl/23-3/229/2
[a(1 + 3u)] - 5 / 2 r - 1
V(r).
(9)
In fig. 3 a comparison is made between the imaginary component of the potential in ref. [5] (D.R.) and Vc the gp central part o f the above local potential. It is seen that the latter is considerably smaller than D.R. at r "~ 0.8 fin for energies 50 ~< Ecru ~< 200 MeV - the range over which the D.R. potential was derived. The conclusion to be drawn from the above is that the NN ~ MIM 2 mechanism described here is, on average, not the most important source of annihila-
04
o~
o'.8
i.o
r(frn~
Fig. 3. A comparison between the imaginary part of the potential in ref. [51 and Vc the spin averaged ~p local potential in eq. (9) due to NN ~ MIM 2 ~ NN at the two Ecm energies
(a) 50 MeV, (b) 200 MeV. N.B. Vc is not strongly dependent on v - the only free parameter once 3' is taken from ref. [9].
tion, although it does give a considerable effect in the 13p 0 partial wave. This is based on the three observations that, compared with the phenomenological potentials, (a) the spin averaged potential Vc is considerably weaker (b) the spin dependence is completely different and (c) the energy dependence is opposite to that usually assumed. However, there is at present no reason for excluding the above mechanism as being the main one for annihilation into two mesons. This will only be possible when the bulk o f the NN -~ M 1M 2 reactions have been measured - in particular M1M 2 = pp, coco and cop. Also, when making theoretical predictions for these branching ratios, it is necessary to include the NN initial state interaction together with N ~ + A~I and A ~ admixtures. These could radically alter any predictions - as in ref. [8] - that only take into account the C[ ] factor o f eq. (3), and the phase-space effect - even when the latter is modified by the form factors generated by the N, N and M i internal quark wavefunctions. This is particularly important for the separable potentials o f eq. (3), since in a Schr6dinger equation approach the real part o f the optical potential can generate nodes within the range o f the transition potential. Such an occurrence leads to a saturating effect in which the annihilation passes through a maximum as the strength o f the transition potential increases - see figs. 6, 7 o f ref. [2].
17
Volume 139B, number 1,2
PHYSICS LETTERS
The authors acknowledge useful conversations w i t h Dr. M. Chaichian and Dr. P. Z e n c z y k o w s k i . One o f us (SW) thanks the Research Institute for Theoretical Physics, Helsinki, for their support during the period when this w o r k was carried out.
References [ 1 ] A.M. Green, Proc. Intern. Summer School on NN-interaction and nuclear many-body problems (Changchun, China, 1983), eds. S.S. Wu and T.T.S. Kuo (World Scientific, Singapore, 1984). [2] A.M. Green and J.A. Niskanen, Nucl, Phys. A412 (1984) 448; and a review in HU-TFT-83-54. [3] B. Moussallam, Nucl. Phys. A407 (1983) 413. [4] R.K. Logan, S. Kogitz and S. Tanaka, Can. J. Phys. 55 (1977) 2059. [5] C.B. Dover and J.M. Richard, Phys. Rev. C21 (1980) 1466.
18
3 May 1984
[6] P. Pavlopoulos et al., Proc. 2nd Intern. Conf. on NN interactions (Vancouver, 1977), AlP ConL Proc. No. 41 (ALP, New York) p. 340. [7] H. Genz, Phys. Rev. D28 (1983) 1094. [8] S. Furui, A. Faessler and S.B. Khadkikar, Tiibingen preprint (December 1983). [9] A. Le Yaouanc et al., Phys. Rev. D8 (1973) 2223; D l l (1975) 1272; M. Chaichian and R. K6gerler, Ann. Phys. 124 (1980) 61; J.P. Ader, B. Bonnier and S. Sood, Nuovo Cimento 68A (1982) 1. [10] A. Le Yaouanc et al., in: Introduction to the quark model of elementary particles, Vol. 2, ed. D. Flamm. [11] L. Tauscher et al., Proc. Vlth European Symp. on NN interactions (Santiago de Compostela, Spain, 1982), Ann. Fis. (Madrid) 79 (1983) 24. [12] J. Cot6 et al., Phys. Rev. Lett. 48 (1982) 1319.