RELATION BETWEEN PROTON-NUCLEUS AND PROTON-NUCLEON INTERACTION AT 20 GeV

Transcription

1 IC/66/120 ATIONAL ATOMIC ENERGY AGENCY INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS RELATION BETWEEN PROTON-NUCLEUS AND PROTON-NUCLEON INTERACTION AT 20 GeV W. E. FRAHN 1966 PIAZZA OBERDAN TRIESTE

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3 IC/66/120 INTERNATIONAL ATOMIC ENERGY AGENCY INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS RELATION BETWEEN PROTON-NUCLEUS AND PROTON-NUCLEON INTERACTION AT 20 GeV* W.E. FRAHN** TRIESTE December 1966 * To be submitted to Physics Letters. ** Permanent address: Physics Department, University of Cape Town, S. Africa.

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5 ABSTRACT It is shown that the parameters for proton-nucleus scattering at 19.3 GeV/c are closely related to those for proton-nucleon scattering at the same energy. -1-

6 RELATION BETWEEN PROTON-NUCLEUS AND PROTON-NUCLEON INTERACTION AT 20 GeV Recent partial-wave analyses [l,2^] of the differential and total cross sections of 19.3-GeV protons scattered by complex nuclei [3^\ have revealed that the sign of the real part of the coherent nuclear scattering amplitude at this energy is negative, corresponding to a predominantly repulsive nucleon-nucleus interaction. One expects that this property is closely connected with the fact that the elastic proton-nuc_leon_ amplitude has an appreciable negative real part in the multi-gev region QO I n the present note we show, by means of a simple impulse approximation, that the parameters of the coherent proton-nucleus scattering are in fact quantitatively related to those of protonnucleon elastic scattering. The proton-nucleus scattering data at 19.3 GeV/c have been described in terms of a parameterized scattering function n^ = S(X) = exp i26(x)j of the form [V] S(X) - 1 [ 3 ] p C\. A, where g(x) = [l+exp(a-x)/a] and x= +5. The parameters A and A are semiclassically related to the radius R and the diffuseness d of the interaction region by the relations A=kR, A=kd, where k is the cm. momentum, E is the transparency, and y measures the strength of the real part of the proton-nucleus interaction

7 For the following calculations we may neglect Coulomb and spin-dependent terms. In this case the coherent proton-nucleus scattering amplitude resulting from eq.(l) is given by f (t) - ± (2) where F(x) = irx/sinh (irx) is the Fourier transform of dg/dx and t the squared four-momentum transfer. In impulse approximation QQ the amplitude f(t) is related to the proton-nucleon scattering amplitude f n (t) by - Af n (t) <S,(t) f (3) where A is the target mass number and G(t) the nuclear form factor» Since at 19,3 GeV/c the p-p and p-n amplitudes are very nearly equal we may write f.(t) - The p-p scattering data at 19.3 GeV/c are best fitted with Cj - C R = C = 10.0 (GeV/c)- 2 and yct) = Y = [i»] Assuming a GauBsian form factor G(t) = exp(^bt) with B = 4R 2 we obtain f (t) - A ^t p ( y [ i ] -3-

8 Because of our approximations, the validity of eq. (5) is restricted to light nuclei and small momentum transfers. On the other hand, eq. (2) gives the forward scattering amplitude as.f(o) -^.1,^(1-.) [: + (6) Comparison of eqs. (5) and (6) yields two relations between the proton-nucleon and proton-nucleus parameters (7) The right-hand side of eq. (7) is essentially the total proton-nucleus cross section a t, thus we have approximately Of. = A G^ot (pp). This result follows of course directly from the impulse approximation (3) by means of the optical theorem. With a tqt (pp) = mb at 19.3 GeV/c [f*]» eq. (7) is in reasonable agreement with the o^ data for the lightest nuclei, while for heavier targets c t increases less than linearly with A because of screening J/7J. According to eq. (8), the ratio y between the real and imaginary parts of the p-p forward scattering amplitude should be given by the quantity 2p/kR Cl-e). Values of the latter, calculated from the parameters obtained in ref.l, are shown in table 1. For the light nuclei 2y/kR (1-e) varies between and -0.45, which is consistent with the value Y - -0,33 * 0,03 determined from the p-p data at 19.3 GeV/c V]. -4-

9 Another comparison of p-nucleus and p-nucleon interaction parameters can be made by means of the relation [_8 j (9) between the p-nucleon forward scattering amplitude and the volume integral of the proton-nucleus potential U(r) = V(r) + iw(r). If we define the volume integrals of the real and imaginary potentials by I(V) = jv(r)dr and I(W) = {W(r)dr, respectively, eqs. (9) and (8) yield the relations I*. f n (o) I(W) UR (i-c-) In ref. 1, proton-nucleus potentials U(r) have been calculated from the parameterized phase shifts in high energy approximation kr Numerical integration of these potentials yields values of I(V) and I(W) whose ratios are also listed in table 1. It is seen that for most target nuclei the ratio I(V)/I(W) agrees surprisingly well with the value of 2y/kR (1-e), in accordance with eq. (10) 0-5-

10 Finally, we show that the diffuseness parameter d determines the range of the proton-nucleus potential U(r). Although for S(A) in the form (1) the integral in eq. <n) cannot be evaluated in closed form, it is possible to derive an asymptotic expression for r>>p, uco * -u* A/4 K ( ) - - u (f ±f «P (JLL # U2) where K Q (x) is the modified Hankel function and U = (TTA)- 1 [p/a + i(l- )] k 2 /(m 2 + k 2 )*. The values d = fm obtained in ref. 1 correspond to field masses in the region MeV. We have found that the parameters which describe the coherent interaction of high-energy protons with complex nuclei are consistent with those of the two-nucleon interaction. This conclusion is corroborated by a recent investigation by Benestad and Olsen [9j ^n the one hand this confirms the expectation that in the multi-gev region the impulse approximation is sufficiently reliable for calculating the nucleon-nucleus interaction for light nuclei from two-body scattering data. Conversely, it suggests that the study of hadron collisions with light complex nuclei is a useful additional means of investigating hadron-nucleon interactions. I would like to thank Professor A. de-shalit for useful discussions and Professor Abdus Salam for his hospitality at the International Centre for Theoretical Physics. -6-

11 References 1. W.E. Frahn and G. Wiechers, Phys. Rev, Letters 16 (1966) 810; Ann. Phys., in press. 2. A. Dar and S. Varma, Phys. Rev. Letters 16 (1966) G. Bellettini, G. Cocconi, A.N. Diddens, E. Lilletnun, G. Matthiae, J.P. Scanlon and A.M. Wet here 11, Nuclear Phys. 79 (1966) G. Bellettini, G. Cocconi, A.N. Diddens, E. Lillethun, J. Pahl, J.P. Scanlon, J. Walters, A.M. Wetherell and P. Zanella, Physics Letters 14 (1965) 164, 5. W.E. Frahn and R..H. Venter, Ann. Phys, 24 (1963) H. Bethe, Ann. Phys. 3 (1958) 190; A.K. Kerman, H. McManus and R.M. Thaler, Ann. Phys. 8 (19 59) N.R. Steenberg, Nuclear Phys. 3 2 (196 2) R. Lipperheide and D.S. Saxon, Phys. Rev. 120 (1960) Benestad and H. Olsen, Phys. Rev. Letters 17 (1966)

12 Table 1 Ratios of real to imaginary parts of proton-nucleus interaction at 19.3 GeV/c Target 6 Li 7 Li 9 Be l2 C kr(l-e) I(V)/I(W) Target 27 A1 *3.6 Cu pb 238u 2tl kr(l-e) I(V)/I(W)

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14 Available from the Office of the Scientific Informotion and Documentation Officer, International Centre for Theoretical Physics, Piazza Oberdan 6, TRIESTE, Italy 7000