VOLUME 63, NUMBER 3 P H Y S I C A L R E V I E W L E T T E R S 17 JULY 1989

Bourdeau and Mukhopadhyay Reply: In our Letter,l we computed nonrelativistically the longitudinal and scalar quadrupole amplitudes (Lt + and S,+, respectively) in the yvN—»A transition in two different quark-shell-model (QSM) approaches. We found that the relation

/ co^ i* = & £ < i + , ( 0

obtained from gauge invariance or electromagnetic-cur­rent conservation, could be badly broken in the QSM's due to truncation of the quark-model space, and were, in our chosen examples, to varying degrees. In his Com­ment, Abbas2 criticizes our choice of the A wave func­tion in the approach of Vento, Baym, and Jackson3

(VBJ). Part of his concern arises from an unfortunate misprint4 in our paper, wherein /3—0.35 should have read 3/? = 0.35 (this is correctly used in Fig. 1 of Ref. l) . We also neglected to mention that our VBJ wave func­tions are obtained by an extension of VBJ's published work,3 in which we assumed a n r " 3 dependence in the tensor interaction between quarks arising due to one-pion exchange, following Robson.5 Treating our version of the VBJ wave functions as a model example, our con­clusions regarding them concerning violation of (l) remain unchanged.

Abbas2 is right in pointing out that the wave function for A in the original VBJ paper3 is different from the one we used. It is

I A'> = ( 1 — 2/3') , /2 | A 4SS) ~ (/?') 1/2 I A 2DM)

+ (p,){/2\A4Ds>, (2)

correcting VBJ's sign error in their Eq. (10). He then worries whether our conclusions concerning the failure of (1) are still valid for this wave function of the A and VBJ's nucleon wave function. The answer is an emphat­ic yes. To demonstrate this, we take VBJ's nucleon wave function parameter y=0.22 fitting gA, etc. We deter­mine p! in (2), as in our Letter,1 by fitting it to the E2 amplitude (or E2/M1 ratio). This gives 2/3' —27%. Current conservation is again badly violated. Thus, us­ing our1 Table I, L1 + =ss— 3.1 and 7 by current and charge approaches at the photon point (&2=0), in units of 10" 3 GeV~1/2. At A: 2 =-0 .3 GeV2, these numbers are —8.9 and 11.9, respectively, compared with —15 and 7.5 (from Fig. 1) in our version of the VBJ model. Thus, our conclusion on the failure of (1) in the VBJ ap­proach remains valid, even with (2).

Finally, let us make some remarks concerning the phe-nomenological implications of our extension of the VBJ approach and the original wave functions in this ap­proach. Following Robson, the tensor force between quarks arising from one-gluon exchange and one-pion exchange [the form motivating Eq. (4) of VBJ] has an

r dependence in each case. This makes the form (2) less compelling. We do not use the relation p,=sy/ ( H - / ) as do VBJ and Abbas, utilizing the approxima­tion that the quantity p/AE defined in VBJ is the same for TV and A. We determine p' from a fit to the E2 tran­sition amplitude. Our wave functions fit gA and repro­duce other nucleon properties, and we get for /VJVA» as defined by Abbas, a value of 3.34, using Abbas's Eq. (4) for our extension of the VBJ approach; this is somewhat lower than experiment and the estimate in the original VBJ model. However, given the uncertainty of our p' due to the imprecision of the E 2 amplitude (or E 2/M1 ratio), this discrepancy is not serious. Again we stress that all these remain to us merely toy models to demon­strate the failure of (1).

We conclude that Abbas's suggestion, that our "con­clusions regarding the (original) VBJ model will have to be modified, perhaps quite significantly," is unfounded, as is his contention that our modified VBJ wave function is phenomenologically worse than the original one for the A.

We thank A. Abbas for his correspondence and L. Zhang for discussions. One of us (N.C.M.) thanks the U.S. Department of Energy for support (Contract No. DE-FG02-88ER40448).

Michele Bourdeau High Energy Physics Group Syracuse University Syracuse, New York 13210

Nimai C. Mukhopadhyay Department of Physics Rensselaer Polytechnic Institute Troy, New York 12180-3590 and Institute of Nuclear and Particle Physics University of Virginia Charlottesville, Virginia 22901

Received 8 June 1988 PACS numbers: 13.60.Rj, 12.40.Aa, 13.75.Cs, 14.20.-c

l M. Bourdeau and N. C. Mukhopadhyay, Phys. Rev. Lett. 58 ,976 (1987).

2A. Abbas, preceding Comment, Phys. Rev. Lett. 63, 334 (1989).

3V. Vento, G. Baym, and A. D. Jackson, Phys. Lett. 102B, 97 (1981).

4 We detected another misprint: Table I, third column, fifth row, y/5 should be VJ.

5D. Robson, in "Research Program at CEBAF," Continuous Electron Beam Accelerator Facility report, 1986 (unpub­lished), p. 5-87.

© 1989 T h e A m e r i c a n Physica l Society 335