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Calculation of the 3He charge form factor with the Reid potential
Volume 40B, number 4
CALCULATION
PHYSICS LETTERS
OF THE 3 He CHARGE
24 July 1972
FORM FACTOR
WITH THE REID POTENTIAL*
M. McMILLAN Department of Physics, University of British Columbia, Vancouver 8, British Columbia, Canada
Received 30 May 1972 The 3He charge form factor has been calculated with the Reid soft-core potential using an altered Feshbach-Rubinow equivalent two-body method. A minimum near the experimental one is found, supporting the conclusion of Yang and Jackson. Several papers reporting calculations o f the 3He charge form factor have now appeared in the literature since the results of the Stanford electron scattering experiment were published [ 1 ] nearly two years ago. The charge form factor data, which extend to 20 fm - 2 m o m e n t u m transfer and feature a minimum at q2 = 11.6 fm - 2 , have attracted considerable interest because the form factor at these large m o m e n t u m transfers is sensitive to the existence of short-range repulsion in the nucleon-nucleon interaction. While calculations based on a number of the phenomenological descriptions of the short-range interaction have given a minimum near the experimental one, there is apparently still considered to be some uncertainty in the case of the Reid [2] soft-core potential (see ref. [3] for a brief review of work to date). Other calculations are in progress [3], but in view o f the apparent uncertainty at the present time, we report the results of a simple calculation done some time ago with this potential. In ref. [4] we used an altered Feshbach-Rubinow [5] equivalent two-body m e t h o d to obtain an approximate triton symmetric S-state wave function component corresponding to the Bressel-Kerman-Rouben [6] potential. The b o d y form factor calculated with this component had a zero for q2 = 13.8 fm - 2 . We have repeated that calculation using the Reid potential; fig. 1 shows our 3He charge form factor results for both the Reid and the Bressel-Kerman-Rouben potentials. (We have used the Janssens et al. [7] analytic expressions for the nucleon form factors.) We have not included any contributions to the form factor from the
References
* This work has been supported in part by a grant from the National Research Council of Canada.
[1] J.S. McCarthy, I. Sick, R.R. Whitney and M.R. Yearian, Phys. Rev. Lett. 25 (1970) 884.
1o-J
i0-~
IO-2
v
IO-4.
10-.5
10-6
1
0
4
-
7 ~ 8 12 q2 (fm-2)
16
20
Fig. 1. The square of the 3He charge form factor. The experimental points are from ref. [ 1]. S' and D wave function components, although their inclusion, at least phenomenologically [8], will improve the agreement with the experimental data. Our calculation, admittedly crude, supports the conclusion of Yang and Jackson [9] that the Reid potential does yield a minimum near the experimental one.
437
Volume 40B, number 4
PHYSICS LETTERS
[2] R.V. Reid, Ann. of Phys. 50 (1968) 411. [3] Y.E. Kim and A. Tubis, Phys. Lett. 38B (1972) 354. [4] M. McMillan and D. Maroun, Nucl. Phys. A159 (1970) 661. [5] H. Feshbach and S.I. Rubinow, Phys. Rev. 98 (1955) 188. [6] C.N. Bressel, A.K. Kerman and B. Rouben, Nucl. Phys. A124 (1969) 624.
438
24 July 1972
[7] T. Janssens, R. Hofstadter, E.B. Hughes and M.R. Yearian, Phys. Rev. 142 (1966) 922. [8] M. McMillan, Phys. Rev. C3 (1971) 1702. [9] S.N. Yang and A.D. Jackson, Phys. Lett. 36B (1971) 1.
CALCULATION
PHYSICS LETTERS
OF THE 3 He CHARGE
24 July 1972
FORM FACTOR
WITH THE REID POTENTIAL*
M. McMILLAN Department of Physics, University of British Columbia, Vancouver 8, British Columbia, Canada
Received 30 May 1972 The 3He charge form factor has been calculated with the Reid soft-core potential using an altered Feshbach-Rubinow equivalent two-body method. A minimum near the experimental one is found, supporting the conclusion of Yang and Jackson. Several papers reporting calculations o f the 3He charge form factor have now appeared in the literature since the results of the Stanford electron scattering experiment were published [ 1 ] nearly two years ago. The charge form factor data, which extend to 20 fm - 2 m o m e n t u m transfer and feature a minimum at q2 = 11.6 fm - 2 , have attracted considerable interest because the form factor at these large m o m e n t u m transfers is sensitive to the existence of short-range repulsion in the nucleon-nucleon interaction. While calculations based on a number of the phenomenological descriptions of the short-range interaction have given a minimum near the experimental one, there is apparently still considered to be some uncertainty in the case of the Reid [2] soft-core potential (see ref. [3] for a brief review of work to date). Other calculations are in progress [3], but in view o f the apparent uncertainty at the present time, we report the results of a simple calculation done some time ago with this potential. In ref. [4] we used an altered Feshbach-Rubinow [5] equivalent two-body m e t h o d to obtain an approximate triton symmetric S-state wave function component corresponding to the Bressel-Kerman-Rouben [6] potential. The b o d y form factor calculated with this component had a zero for q2 = 13.8 fm - 2 . We have repeated that calculation using the Reid potential; fig. 1 shows our 3He charge form factor results for both the Reid and the Bressel-Kerman-Rouben potentials. (We have used the Janssens et al. [7] analytic expressions for the nucleon form factors.) We have not included any contributions to the form factor from the
References
* This work has been supported in part by a grant from the National Research Council of Canada.
[1] J.S. McCarthy, I. Sick, R.R. Whitney and M.R. Yearian, Phys. Rev. Lett. 25 (1970) 884.
1o-J
i0-~
IO-2
v
IO-4.
10-.5
10-6
1
0
4
-
7 ~ 8 12 q2 (fm-2)
16
20
Fig. 1. The square of the 3He charge form factor. The experimental points are from ref. [ 1]. S' and D wave function components, although their inclusion, at least phenomenologically [8], will improve the agreement with the experimental data. Our calculation, admittedly crude, supports the conclusion of Yang and Jackson [9] that the Reid potential does yield a minimum near the experimental one.
437
Volume 40B, number 4
PHYSICS LETTERS
[2] R.V. Reid, Ann. of Phys. 50 (1968) 411. [3] Y.E. Kim and A. Tubis, Phys. Lett. 38B (1972) 354. [4] M. McMillan and D. Maroun, Nucl. Phys. A159 (1970) 661. [5] H. Feshbach and S.I. Rubinow, Phys. Rev. 98 (1955) 188. [6] C.N. Bressel, A.K. Kerman and B. Rouben, Nucl. Phys. A124 (1969) 624.
438
24 July 1972
[7] T. Janssens, R. Hofstadter, E.B. Hughes and M.R. Yearian, Phys. Rev. 142 (1966) 922. [8] M. McMillan, Phys. Rev. C3 (1971) 1702. [9] S.N. Yang and A.D. Jackson, Phys. Lett. 36B (1971) 1.