Radiative transitions of baryons in the MIT bag

ANNALS

OF PHYSICS

117, 5-18 (1979)

Radiative

Transitions

of Baryons A. J. G.

in the MIT Bag

HEY

Physics Department, Southampton University, England BARRY R. HOLSTEIN* Department of Physics and Astronomy, University of Massachusetts, Amherst, Massachusetts AND

D. P.

SIDHU+

Brookhaven National Laboratory, Upton, New York 11973 Received December 26, 1977

Resonance photoproduction is studied via the MIT bag model and comparison is made with a single quark transition SU(6), analysis. Correspondence is found between the two pictures. The bag model predictions are shown to be in good qualitative agreement with experiment; however, specific numerical results are rather model dependent and in general less successful. 1. INTRODUCTION

The photoproduction of baryon resonanceshas been, and remains, an important testing ground for quark models [I]. Recently, stimulated by the work of Melosh [2] and others [3], it has proved useful to discussthese transitions in terms of their general SU(6),. structure rather than in terms of any specific model. Indeed, the standard oscillator quark models have difficulty describing the data in any quantitative sense whereas the less specific “single-quark transition operator” SU(6),, analysis is very successful[4]-at least for the [To, 1-l multiplet [5]. The data is analyzed in terms of three SU(6)W Y O(3) reduced matrix elements, corresponding to the electromagnetic current operator transforming as a sum of three tensor operators: symbolically, JZrn -

AL+

-+ Ba& + Co,Ljm.

The first term transforms asa (3%; W = 0; L, = + I} representation of SU(6), x O(3) and corresponds to an “orbital flip” term in quark models. Similarly, the secondpiece * Work supported, in part, by the National Science Foundation. + Work supported, in part, by the Department of Energy under Contract No. EY-76-C-02-0016. c OOO3-4916/79/OlOOO5-14$05.00/O All

Copyright 0 1979 rights of reproduction

by Academic Press, Inc. in any form reserved.

6

HEY,

HOLSTEIN,

AND

SIDHU

transforms as (25; W = 1, W, = fl; L, = 0} and is equivalent to a “spin flip” term. The third operator, transforming as (35; W = 1, W, = 0; L, = &l}, corresponds to a spin-orbit type term: This is neglected in most quark models [6] since they are motivated by the idea of nonrelativistic motion for the quarks. Phenomenologically, however, this type of term is of greater or comparable importance to the spin-flip “3” term [4]. It is therefore of interest to examine these photon transitions in a quark model with very different input assumptions; namely, a quark model in which the quarks are massless and confined. Until recently, it proved difficult - obtain “nonrelativistic looking” SU(6) multipleit structure from such relativistic quark models and consequently impossible to investgate the question of an SU(6) transition structure. However, there has been significant progress with regard to the spectrum of the MIT bag [7]. A serious problem for this model has been its apparent inability to generate only the [IX), 1-l multiplet and no other negative parity resonances, below about 1800 MeV in mass. A count of the available negative parity states for one excited quark, revealed far too many states -enough to fill a [56, I-] as well as the [IO, 1-l multiplet [8]. A recent calculation by Rebbi [9] appears to have clarified the situation. By considering small surface fluctuations of the bag about a spherical cavity configuration he has been able to identify the translational mode of the ground state [56, O+]. In fact, to a good approximation all these extra [j%, 1-l states correspond to the translated ground state 56. Thus, using this result, it is now possible to look at the problem of photoproducing the [IO, I-] in the MIT bag model, using wavefunctions corresponding to confined relativistic massless quarks. Since the photon interacts only with a single quark during the transition the form one obtains must necessarily be compatible with general Melosh structure [lo]. What is not clear, however, is the identification in terms of specific integrals of bag wavefunctions of the individual reduced matrix elements A, B, and C. In particular, since there is a rather involved relation between thejj-coupling of massless quarks to the LS-basis, the matrix elements A, B, and C, could a priori be related or one of them vanish, thus resulting in more specific predictions than those of the Melosh approach. In this paper, we show that the Bag model, has in fact, three independent reduced matrix elements for photon transitions, namely,

Here, El and M2 are the electric dipole and magnetic quadrupole operators occurring in a multipole expansion of the electromagnetic current, and S, , P+ , Pg refer to the specific Bag wavefunctions involved. (The nomenclature will be discussed in detail below.) These three matrix elements are linearly related to the A, B, C parametrization: the MIT bag model is therefore able to reproduce the full Melosh algebraic structure (Tables I and II), including the Moorhouse selection rule [ll]. The magnitudes of these parameters may be explicitly evaluated. Qualitative success is obtained in that the C term is of the same order of magnitude as A and B. The precise ratios for A:B:C depend on rather delicate cancellations and phases and these we regard as less stable to our approximations. The prediction of sizeable “spin-orbit” effects in

RADIATIVE

TRANSITIONS

TABLE

OF

I

Algebraic Structure for [F, 1-l Photoproduction

SU(6)

State

Targei

A 3,e

+ ; (:,‘:’ p + ; (y? y + !$ ,y ..-___-.-.0

0 4 --(-) 35

1 IiS y

BARYONS

in Terms of Bag Matrix Elements

8

HEY,

HOLSTEIN,

AND

TABLE

SIDHU

II

SU(6), Structure for @I, 1-l Photoproduction

in terms of Melosh Parameterisation

W6) State

Target

P

n

*8

P

-

n

-

P

+ ; (;)I”

A + ; (;)I’=

C

+ ; (i)“’

A -f(3’!‘+)lirC

0

P ‘8

0

112

0

312 n

a10l/e

P/n

210 3/z

Ph

-;(!)‘iaB+~(L)l’*c

-#)“*B+$(yc

-

+ ; (;)“’

A - ; (;)“’

+;A-&?+

C

+z

’ zic

1 0 1 l/2 5

A+g

1 01 118 j

B+z2

1 1 l/2 0

C

RADIATIVE

TRANSITIONS

OF BARYONS

9

photoproduction of the [IQ, I-] is a significant successfor the MIT bag and an indication of the relevance of relativistic quark dynamics. The plan of the paper is asfollows. Section 2 contains a resumeof the salient features of the MIT bag model and some details of the P-wave wavefunctions. The third section details the application of the model to photoproduction and the multipole expansion. Section 4 summarizes the results both with respect to algebraic structure and to actual numerical comparison. We end with some words of conclusion and comment on possible extensions of these calculations.

II. THE MIT BAG AND THE [IQ, I-] We shall consider the “zeroth-order” approximation of the MIT bag model in our calculations; we ignore gluon corrections. A fuller account of the motivation and theory of the model exists in many places in the literature [7]; here we merely sketch the basic outline. Hadrons are imagined to consist of confined masslessquarks and gluons. The “bag” is parameterized by a universal pressure term B in the Lagrangian which stabilizes a finite cavity configuration and confines the quark and gluon fields to the bag. Confinement of gluo-electric flux forces the observable states to be color singlets. Tnsidethe Bag, the quark-gluon coupling constant, 01~= g”,‘4n, is assumedto be much less than unity and gluon corrections treated perturbatively [12]. From the viewpoint of quantum chromodynamics the long range strong coupling gluon forces may perhaps be imagined as approximated by the bag pressure B: inside, one has only the residual short-distance weak gluon coupling effects to take into account. Henceforth, then, we ignore gluons. We now write down the single particle eigenfunctions for masslessquarks in a spherical cavity. Inside the bag they satisfy the free Dirac equation, iti* = 0

(1)

and on the surface they are required to satisfy -.-ii . y$

= $

(2)

for no flux of quark quantum numbers through the surface, and F - V(I,@)

= --2B

(3)

for no flow of momentum and energy through the surface. Equation (2) results in an eigenvalue condition for the energy of the allowed modes. In this paper we are interested in three modes, #nHjnr, labeled by principal quantum numbers n, parity index K, total angular momentum j, and =-component M. Namely these are the ground state “S, ‘.‘” wavefunction

IO

HEY,

HOLSTEIN,

AND

SIDHU

with n = 1,

K

= - 1, j = l/2, and the two “P-wave” wavefunctions,

with n = 1,

K

= $1, j = l/2, and

with n = 1,

K

= -2, j = 3/2. Here the normalization N(K)

=

factor

N(K)

is

WM

R3/*[2Ws(W,

+

K)]‘/’

and +3,2M is the usual j = 3/2 spherical harmonic [13]. The ground state 156, Of] baryons are obtained from configurations of (l&J3 states and have been examined extensively in the literature [7, 121. Here we are concerned with the low-lying negative parity baryons obtained from the (1SI,2)21P312 and (1S,,2)21P,,2 configurations. Only the sl12 and the PII states can satisfy the quadratic surface boundary condition locally: the requirement aE/aR = 0 for the P3,2 states is merely a statement of global pressure balance. In our work we continue to use a spherical cavity for these states aIthough this is clearly onfy an approximate procedure [8, 141. A detailed check of the number of states obtained by combining the quarks in flavor and spin-space overall-symmetric wavefunctions leads to the spins and parities hown in Fig. 1. Also shown are the available states for [IO, 1-l and [X5, I-] LScoupled multiplets which are easier to enumerate. Rebbi’s calculation [9] has shown that the [56, 1-l formed from combinations of the lP,,, and IP,,, quarks wavefunctions corresponds almost entirely to a translation mode of the ground state. We therefore project out this combination of states and are left with wavefunctions for the [TO, I-] states in terms of bag P,,, and P.7,2 wavefunctions. This procedure is an exercise in Young tableaux which is straightforward but redious: the details are contained in the appendix of Ref. [14]. (We in fact use a different set of phase conventions). We therefore obtain wavefunctions for the physical [ICI, l-1 states which are in general linear combinations of (SI12)2P,,2 and (SI,2)2P3,2 eigenstates, and the different quark kinetic energies and the gluon corrections leads to mixing of these wavefunctions [14]. At the present level of sophistication, however, the eigenstates are sufficiently close in mass that we shall ignore such effects. Taking the phenomenological pressure term B1j4 = 120 MeV leads to the following masses for the states using M = 1 q/R

+ B(4/3) rrR3

(6)

RADIATIVE

TRANSITIONS OF BARYONS

11

FK. 1. Negative parity excited states.

(ignoring gluon terms) and requiring i;M/%R = 0:

(S1LJ3: M = 1180 MeV (&,*)*p,,* : M = 1420 MeV (s,,2)2p3,2

z-z 2.04

Wl-1

:

M = 1335 MeV

R-l == 144 MeV Wlil = 3.81 R’-1

= I35 MeV

w-2 .--z3.20 R”-l = 138 MeV.

The average massof the P states is therefore around 1400 MeV, somewhat low for the average massof the [IQ, 1-l (which is nearer 1600 MeV). Most of the blame probably lies with our crude treatment of the P,!, stateswhich have a rather low eigenfrequency. In our calculations we assumean average massof 1400 MeV for the [TO, 1-I states.

III.

PHOTOPRODUCTION

IN

THE RAG

The photo-excitation of nucleon resonancesmay be parameterized in terms of the two helicity amplitudes,

12

HEY,

HOLSTEIN,

AND

SIDHU

describing the absorption of a helicity +I photon to produce a h = l/2 final state, and, for resonances with J > 312, A,=----

l (N*# 1 d+l) - J 1 N&) c&?Y2

(8)

for a helicity 3/2 final state. Here, J is the electromagnetic current, q the photon three-momentum and I the polarization vector for a helicity +I photon E(+l) = --(l/4/2)

(1, +i, 0).

(9)

In the bag model, we are unable (as yet) to treat the problem of moving bag states in a covariant manner; transition amplitudes must be evaluated in a static approximation. The electromagnetic current operator in the bag may be written E(+l)

. J

=

&3 s

e(+l)

.

$+aQ$eiaqr

(10)

Bag

where the quark fields have the usual expansion in terms of bag eigenstates

(11) are interpreted as quark annihilation operators for it > 0; The coefficients aornnjnz (y.is the internal symmetry index for flavor and color, while mcjm are the usual Dirac indices. The matrix Q is a singlet in color space and the charge matrix for flavor

In the static approximation this operator is sandwiched between the relevant bag wavefunctions and the current operator developed in a multipole expansion &a-r = jo(qr) + 3ij,(qr) P,(cos 0) - Sj,(qr) P,(cos 0) + ... .

(13)

For transitions within the [5X, Of] multiplet only the diagonal terms in the expansion (11) corresponding to (l&,,) states are retained. The relevant piece of the multipole expansion is 3ij,(qr) P,(cos 0) and the resulting current operator contains vector (J = 1) and tensor (J = 2) terms corresponding to magnetic dipole (Ml) and electric quadrupole (E2) transition moments. The Ml portion of the current is just the magnetic moment operator. p=j

Bagd3x

&x#+aQ#

(14)

to lowest order in q. The predictions for the ground state magnetic moments have been discussed by several authors [7, 12, 151. Moreover, it is easy to see that there are

RADIATIVE

TRANSITIONS

OF BARYONS

13

no E2 moments: This is because the transition operator is taken between states of a singlej = l/2 quark. Thus the bag model reproduces the successful SU(6), prediction [l] of pure Ml excitation of the A A,YNA = v’/3 AiN’.

(15)

For transitions to the [TO, 1-l states we must keep the off-diagonal terms connecting S’,,, states to P,,, and P,,, states. Since the current acts at the quark level we see immediately that there are three basic amplitudes:

s112 S 112-

-

Pl,,

:

El only allowed,

P3lZ : El and M2 allowed.

In general, some of the physical transitions would permit an E3 amplitude: This is predicted to be zero in this model, in agreement with the single-quark transition operator SU(6), framework [16, 171. We must evaluate E(il)

.J

G

Bag

d3s

$+d+l)

* ay5eiq.r

s

- El -c h12 for transitions El

to the [IO, l-1, where ~1 sBag

d3.u $+{~+l . ajo

- ZyXqr)[~(+‘)

* aP,(cos O)lJclj $

(17)

and d3x t,b+{(-5j,(qr))[E+1

* aP2(cos 19)]~,~} 1,4.

Cl 7b)

The M2 operator is defined by projecting out the J = 2 piece from the relevant product which also contains a J = 1 piece. Using the explicit [IO, 1-l wavefunctions the helicity structure of the transitions may be parameterized in terms of three reduced matrix elements, namely,

where < is the P,,, - S,,, relative phase, 5’ the P,,, - S,,, phase, the N’s are normalization factors related to N(K).

14

HEY,

N-,

AND

SIDHU

co”1

=

Nl =

HOLSTEIN,

R3 2(0.-, -

l/2

1) sin2 w-~

I

112 ml3 C R’3 2(w, + 1) sin2 w1 I 112

N-2 =

R”3 2(w_, :‘2)

j12(w-,)

I

while the R’s represent radial bag integrals R;,, =

s 0R dr r2j,(qr) jo(w-dR)

jo(wlR’)

Ry, =

s 0 R dr r2j,(qr).L@-lrIR)

j&w/R’)

Ry; = 1 R dr r2j,(qr) ,j,(w-,r/R)

jl(o-,r/R”)

0

(20) Rf; = 1 R dr r2j,(qr) j,(w-,r/R)

j,(w-,r/R”)

0

R$ = 1 R dr r2j,(qr) jl(w-dR)

jdw-/W

0

R;, =

s0

R dr Pj2(qr) j,(w-g/R)

j2(oe2r/R”).

Note that the radial integrals are taken over the smallest (ground state) bag radius. Table I gives the resulting structure. Note the familiar Moorhouse selection rule [I l] -no excitation of 4SN*‘s from proton targets-is reproduced. In terms of the usual Melosh parameterization-shown for completeness in Table II-there is an exact correspondence between the reduced matrix elements A, B and C and the Bag parameters LY,p and y A = -(2/v’5)

ci - (4 d/2/3) p

B = -(2/d7)

a + (2 x0/3)

c = +(2/dT)

a - (2 1/Z/3) p - 2 d/z y.

p - 2 d/z y

(21)

We remark that although we are performing a nonrelativistic type multipole expansion in the photon momentum, the quark motion is relativistic. Thus if we neglect all q2 corrections in the multipole expansion, the parameter y vanishes corresponding to vanishing M2 transition moments. Thus in this approximation the bag model predicts B = -C

+ O(q2).

(22)

RADIATIVE

TRANSITIONS

OF BARYONS

13

1t is therefore clear that the bag model does produce a nonzero “spin-orbit” type C term of the sameorder of magnitude as the other two terms. In this respect we regard the bag, with its relativistic internal motion of the quarks, signiJicantly superior to nonrelativistic models. In the next section we consider in more detail the phenomenological comparison of the model with experiment. IV. PHENOMENOLOGY

OF PHOTON TRANSITIONS

We have seenin the previous sectionshow the bag model with its (jj) structure can nevertheless successfully reproduce the SU(6), x O(3) algebraic structure of the Melosh approach. We first make somequalitative remarks concerning the predictions for the 283!estate, usually identified with the D13(1520), before looking at numerical predictions in more detail. The D13 is the best known resonanceof the secondresonance region and its helicity amplitudes are relatively well-determined. It is also found to be almost a pure 28,,, state [l, 41. Since there are four amplitudes expressed in terms of three reduced matrix elements there is one relation between them. It is [18] A:,,

+

$452

= (I/

v%4;,2

+

&4;,2)

(23)

which is reasonably well satisfied by the data [19]. If we attempt to ignore all 4’ corrections (set y = 0) we obtain two relations

which are evidently consistent with the general relation (23). These are not, however, well-satisfied data essentially becauseA& - 0 while A:,2 is large. Thus it is clear that we must keep q2 corrections if we wish for reasonable phenomenology. Let us therefore consider the predictions in more detail. We remark that there is an ambiguity owing to the arbitrary choice of phase [t’ between the (S,,2)2P,:2 and wavefunctions (seeEq. (18)). In principle, this ambiguity may be eliminated (&2)2p3,2 by calculating the decay amplitudes for the [x0, 1-l decay via pion emission. In the observable experimental photoproduction amplitudes there would therefore be no such ambiguities. Since we do not wish to consider the complicated problem of pion transitions-presumabIy by fissioning of bags-we express our results in terms of the phase 55’. We have performed the integrations indicated in Eq. (20) numerically. The results are shown in Table III. The parameters p. y are evidently quite sensitive to the precise value of q utilized. On the other hand, it is not clear what value of q should be used in order to compare with experiment. If we define q as the photon momentum in the N* rest frame then for

q = I q I2 (M;,

- MN2)/2MN,

rl == ’ p I = 40 and

z

.38 GeV,

MN* N 1400 MeV.

(25)

16

HEY, HOLSTEIN, AND SIDHU TABLE

III

Bag Matrix Elements: Numerical Results Photon 3-Momentum q (in GeV/C) 0.00

-0.43

-0.47

0.35

-0.45

-0.15

-0.14

0.55

-0.52

+0.06

-0.20

0.00

However, in view of our no-recoil approximation it may be prudent to use a value somewhat lower. Thus we quote the result for a range q values above. A reasonable fit to the experimental amplitudes (q2 = 0) is given by [4, 161 &iexp N -.28

~eexpII -.55

yexp E -.19

(26)

Comparison with the bag model results (cf. Eq. (25)) shows that only Z is well predicted in this model independent of assumptions about q. The P3,2 amplitudes 8, F are correct as far as their order of magnitude goes, but their specific values are quite sensitive to the precise value of q. The best overall prediction is probably obtained in the vicinity of q M .35 GeV. However, the best value for /? is when q = 0. What then should we conclude from the results ? First, we showed that the MIT bag model with light quarks does have large “spin-orbit” type terms which are in better qualitative agreement with the experimental data than nonrelativistic “heavy” quark models, wherein C < B. Thus, e.g., we find that at q = 0, B = -C in the bag model calculation (cf. Eq. (22)). Secondly we found that recoil corrections (i.e., q # 0) are quite important and are very sensitive to phase-space, mass-splitting, etc. Our crude model with no recoil and not employing mass eigenstates should probably not be expected to give trustworthy detailed numerical predictions but rather, to provide reasonable order of magnitude, qualitative results, and this is indeed what was found (cf. Table III). Overall then, we consider the MIT bag model to be reasonably successful in predictions for resonance photoproduction amplitudes. Certainly the present calculation, which includes Psj2 modes, provides a significant improvement over previous work by Donoghue, Golowich, and Holstein [15] which included only the spherical S,,, , PII cavity modes. There are of course a number of weaknesses in our calculation-neglect of gluon exchange effects inside the bag, use of a “nonrelativistic” form for the transition current, and so on. However, the most important goal for the future is to remove our no-recoil approximation. This is a glaring deficiency of our procedure and could well be the root of our problem in obtaining detailed numerical agreement. In fact the no-recoil kinematics q,, = MN* - Mj,r q = I g I = qo(Wv* + MrdPMw

RADIATIVE

TRANSITIONS

17

OF BARYONS

may be considered as corresponding not to q2 = 0 but rather to q2 rv -0.4(GeV/c)2 (for MN* = 1.6 GeV). We have taken experimental photoproduction amplitudes which are consistent with the reduced matrix elements A, B and C, roughly in the ratio A : B : C N 8 : 2 : 5. In fact the latest electroproduction data [20, 211 are consistent with this ratio changing rapidly from q2 ==0 to q2 = -0.4(GeV/c)” namely [22], to A : B : C - 3 : 4 : 2. This corresponds to a considerably smaller value of pexp , more consistent with our calculated value. However, until we really know how to deal with the problem of a nonstationary bag such detailed numerical analysis seemssomewhat inappropriate. Significant further progress will only be achieved by improving on our no-recoil approximation in a fully consistent manner.

ACKNOWLEDGMENT Two of us (A.J.G.H. Brookhaven

for their

and hospitality

B.R.H.) during

wish to thank Larry Trueman the inception of this work.

and

the Theory

group

at

REFERENCES 1. A. DONNACHIE, Review talk in the proceedings of the “1975 International Symposium on Lepton and Photon Interactions at High Energies,” Stanford, California, 1975, edited by W. T. Kirk. 2. H. J. MELOSH, Phys. Rev. D 9 (1974), 1095; Cal. Tech Ph.D. Thesis, 1973, unpublished. 3. A. LOVE AND D. V. NANOPOULOS, Phys. Lptl. 45B (1973), 507: F. J. GILMAN AND I. KAKLINER. Phys. Rev. D 10 (1974), 2194; A. J. G. HEY AND J. WEYERS, Phys. Lett. 40B (1974), 69. 4. A. J. G. HEY, P. J. LIXHFIELD AND R. J. CASHMORE, Nucl. Phys. B 95 (1975), 516; R. J. CASHMORE. P. J. LITCHFIELD, AND A. J. G. HEY, Nucl. Phys. B98 (1975), 237. 5. See, however, J. BABCOCK, J. L. ROSNER, R. J. CASHMORE AND A. J. G. HEY, Southampton preprint THEP 76/77-3: to be published in Nuclear Physics. This paper indicates the existence of a potential problem for the [5_6, 2+] transitions. 6. K. C. BOWLER, Phys. Rev. D 1 (1970). 926; includes such a term in his discussion of photoproduction in a non-relativistic quark model. See also the classic quark model photoproduction paper of L. A. Copley, G. Karl and E. Obryk, Nucl. Phys. B 13 (1969), 303, which contains some discussion of such terms. 7. A. CHODOS, R. L. JAFFE, K. JOHNSON, C. B. THORN, AND V. F. WEISSKOPF, Phys. Rev. D 9 ( 1974). 3471; A. CHODOS, R. L. JAFFE, K. JOHNSON, AND C. B. THORN, Phys. Rer. D 10 (l974), 2599. 8. T. A. DEGRAND AND R. L. JAFFE, Ann. Phys. 1N.Y.I 100 (1976). 425. 9. C. REBBI, Phys. Rev. D 14 (1976), 2362. 10. H. J. LIPKIN, Phys. Rev. D 9 (1974), 1579. 1 I. R. G. M~~RHOUSE, Phys. Rev. Lett. 16 (1966), 772. 12. T. A. DEGRAND, R. L. JAFFE, K. JOHNSON, AND J. KISKIS, Phys. Rec. D 12 (1975), 2060. 13. We use the notation of J. Bjorken and S. D. Drell, “Relativistic Quantum Mechanics,” McGrawHill, New York, 1964. 14. T. A. DEGRAND, Ann. Phys. (N.Y.) 101 (1976). 496. 15. J. F. DONOGHUE, E. GOLOWICH, AND B. R. HOLSTEIN, Phys. Rev. D 12 (I 975). 2875. 16. J. BABCOCK AND J. L. ROSNER, Ann. Phys. (N. Y.) 96 (1976), 191, 17. F. J. GILMAN AND I. KARLINER, Ref. [3]. 18. A. J. G. HEY AND J. WEYERS, Ref. [3].

18

HEY,

HOLSTEIN,

AND

SIDHU

19. Particle Data Group, Rev. Mod. Phys. 48, No. 2, Part II (1976). contribution to the Oxford Baryon Resonance Conference, published by Rutherford Laboratory (1976), edited by R. T. Ross and D. H. Saxon. 21. F. FOSTER, private communication. 22. A. J. G. HEY, contribution to the Oxford Baryon Resonance Conference, published by Rutherford Laboratory (1976), edited by R. T. Ross and D. H. Saxon. 20. J. GAYLER,