Kar, K C

Mitra, S N

English

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88 PROTON-PROTON SCATTERING AT LOW VELOCiTY By K. C. KAR AND S. N. MITRA ABSTRACT. It is shown that Kar's formula for proton-prolon scattering explains the angular variation 6f 'departure frol11 Mott's formula' as observed by Ragan and others for 10\\1 velocities, if it is assllmed that the short range yulta\\'a force is due to the formation of mesons having mass 152 e.u. and short TOnge charge } or othl'r submultiple of its mass. The mass thus determined is different from the 1IIass I~o e.\1. obtained previously by applyillg Kar's formula to high velocity proton-proton sC'atterinq Recently one of us O';:ar, r942) derived a formula for proton-pr~ton scatter-ing assuming the short range interaction l>otential to be of ,,\i"ukawa type V = - (A i r)e- a r. The formula was found to be in very good agreement with the observations of Heydenburg, Hafstad and Tuve (r939) at high velocity of incidence. The values of a and A in Yukawa potcntial for which there is agreement with the above experiment givc for the mass of meson m = lIO e.u. (approx.) and for the short rajlge meson charge V A = 6c (approx.). These identi-cal values of mass and clrarge of lIIesotron have more recently been obtained by Kar and Roy (r94.)) by applying the above Kar's formula (modified for the absence of Coulomb repUlsive force) to neutron-proton scattering at high velocity of incidence. Again, Kar and Roy h943) have shown that the binding energy of deuteron may be correctly determined by their self-consistent method, if it is assumed that the energy is due to a meson field of mass IIO e.u. Thus, it follows from Kar's theory of scattering that whenever a proton, due to its high velocity, comes very near a neutron or a second proton, a short range field is developed due to the temporary creation of mesons, of mass IIO e.u., within neutron and proton. It has been pointed out before on several occasions that the mesons arc only temporarily created; for otherwise there would have been some cases for which the short range meson field is found to be repulsive. Actually, however, we find the meson field to be always attrac-tive, although positive and negative mesons are found in nature. Now, in the different experiments referred to above, on neutron-proton and proton-proton scattering, the absolute values of the intensity of scattering are never given. Only the ratio of the observed intensity to the Mott's value for Coulomb interaction is given for different scattering angles. This ratio is evidently considered as a measure of the departure from Coulomb scattering given by Mott's formula. It is found experimentally that the observed value of the departure as defined above becomes maximum at 45° for proton-proton scattering at incident velocities 867 k.e.v., .776 k.e.v. and 670 k.e.v. The departure decreases with the angle of scattering and attains a value nearly ·s for very small angle. These characteristic changes with the angle for different incident velocities are completely explained by Kal·S theory of scatteringci'ted above. 304 K. C. Kar and S. N. Mitra Recently, however, Ragan, Kanne and Taschek (1941) have studied proton-prolon scattering at low velocity of incidence. They find that, for inc!dent velocities between 200 k.e.v. and 300 k.e.v., the departure attains a minimum . .. A , ~ ) Ls ., , \ \ , If ... value at 45°, instead of a maxi· mum as before. It is' evident from Fig. 1 that the departure rises symmetrically on either side of 45'~. For smaller angles the rise continues up to very small angle, whereas for larger angles the rise is followed by a decrease in the departure (D) at about 57", which appears to continue up to 90°. Thus the experi· mental D - () curve, which is drawn dotted in Fig. I, is not symmetrical about 45°. This asymmetry, it appears, is due to multiple scattering at small (J .... -~.,:----.. *D-----:::6<~D-----.,..,!40 angles. And, at low velocity of , - incidence, the Wenzel angle, FIG. 1 Curve A-Incident Velocity 249.5 k.e.v. Curve D-- " " 2g8.3 k.e.v. giving the limit of multiple scattering, may be as large as 35° as in Fig.!. At first sight the observations of Ragan and others (1941) appear to be anomalous and to go against the theory of scatteriug given by Kar (1942). However, on close examination we find that Kar's. theory, which is perfectly rigorous, is also applicable to low velocity proton·proton scattering. The fitting values of the parameters A and a in Yuka\va potential are, however, different in this case. It is found that for meson mass 111 = 152 e.u. and short range meson charge ;,/ A = i X 152 e, there is very good agreement for the angular range between 35° and 55°~ for incident velocity 249.5 k.e.v., while for incident velocity 298.3 k.e.v., there is very good agreement for the above angular range for meson mass m= 152 e.u. and short range meson charge ;,/ A = i x 152 e. It is significant that the short range meson charges are submultiples of the same meson mass in both the cases. Further, for higher incident velocity the fraction rapidly decreases. This suggests that there must be some interesting relation between the meson mass and its short range charge. Ragan and others (toe. cit.) have not studied the .angular variations for other incident velocities . . Consequently it is not possible for us to find out if the meson of mass me; 153 e.u; have other submultiple values for its short range charge. Fortu. nately, however, Ragan, .Kanne and Taschek have given the values of the departure at 45° for a number of incident velocities. We find that for incident Proton-Proton Scattering at Low Velocity 305 velocities 275.3 k.e.v. and 321.4 k.e.v. the values of the departure at 45" are correctly given by Kar's formula if we take the meson mass m=Y52 e.u. but short range charges i x 152 e.u. and t- x 152 e.u. respectively. In the following table, the theoretical values thus obtained are compared with the experimental values given by Ragan and others. Incident Proton energy 176.5 k.e.v, 200.2 225·9 " 2.0.9.5 275·3 .. 298 3 321·4 Angle of Scatterill g .. " TARLE I 1/1 (Mottl (Expt. ) 0·544 0.448 0353 0.256 0.177 o.uS o.r>703 Ell (Mott.) ('1:hcoretical) 0.2565 0.178 o.II54 0.0819 vA Ie ~ x 152 ~ X 152 1 X 15'1. ·Ax 152 It follows from the above table that up to proton energy 321.4 k.e.v., the mass of meson formed due to the virtnal fission of proton is 152 e.u., while its short range charge is as low as 30 e.u. So it is quite likely that at higher incident energy, the charge may be still lower qnd may be so low as 6 e.u. obtained theoretically for incident energies between 670 k.e.v. and 867 k.e.v. It is, however, significant that for snch high incident energies, the mass of meson Jbtained theoretically is IIO e.u. while for lower energies the mass is greater, b;ing 152 e.u. Without commenting on the law of fission of proton, it may be said that the mesons formed within a neutron or a proton have variable mass and charge And it is highly probable that this formation of bound meSons of variable mass is intimately connected with the widely varying masses of free lllesons yet determined by different experimenters. In conclusion, we may remark that the down ward bend in the D - (1 curve at 57° degrees may be explained if it is assumed that, within the protons, mesons of different mass and charge are formed at this distance. The mass and charge are such that D-8 curve has a maximum at 45°. Thus the curve between 57° and goO may be considered as a portion of the above curve having maximum at 45°. Investigations in this direction are still in progress. PHYSICAL LAIlORAl'ORY, PHIlSI/JE!IIO' COI.l,I\(;11 A~D PHYSICAL L,,1l0RAl'ORY, Vr!)YASA(iAR COl.l.EnE, CAlCUTl'A. RI·;FERENCES Heydenbnrg. N. p" Hafstad, L. R. and 'ruve, M. A., 1939, J>hys. Rev., 66,1078. Kar, K. C., 1942, Ind. Jour. l'hys., 16,187. Kar, K. C. and Roy, R. R., 1943, llld. Jour. l'hy-", 17, 316 and 321. Ragan, G. I •. , Kanne, W. R. and Taschek, R. F" 1941, Phys. I~ev., 60. 6l8. 

Proton-Proton Scattering at Low Velocity

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Proton-Proton Scattering at Low Velocity

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