Phenomenological study of proton compton scattering and pion-nucleon reactions at resonance energy

Volum~ I$, m~mber 4

PHYSICS L E T T E R S

15 April 1965

COMPTON RESONANCE

PHENOMENOLOGICAL STUDY OF PROTON AND PION-NUCLEON REACTIONS AT

SCATTERING ENERGY

S. MINAMI

Department of Physics, Osaka City Universily, Su~iyoshi-ku, Osaka, Japan Received 8 March 1965

With an i s o b a r model, it is shown that the p h u e shift (#?d) of proton Compton scatterir~g due to a r e . m a s t state N* is equal to zero at the e x citation energy of the N*. An example is given by performing a phenomenological a n a l y s i s of pionnucleon and photon-proton collisions at the 2nd resonance, On the b a s i s of the analysis, both q(),*p - . 2~+N) and o ( ~ + p ~ ~+p) at the r e s o nance a r e estimated. Moreover it is pointed out that tim phase shift (012) of p-p s c a t t e r i n g may be nearly equal to z e r o at the excitation energy of the D12 resonance. F i r s t , let u s consider the following r e a c t i o n s : a + B ~ B* ~

a+B,

4H)

where a (or b) is a boson, B is a baryon, and B* is a resecamt stale in the h-B system with isotopic sp!- ? ~ ~ i n J , b ~ the B* is not necessarily a r e . m a n 1 state in the a - B system. As is well kr~ow~ elastic s c a t t e r i n g a + B - . a + B due to ~ e B ~ can be d e s c r i b e d in t e r m s of the R m a t r i x (~ . ~ exp (216U) - 1). qrj(a + B -- a + B) =

.-- ~" ~ 1¾ 1~, q~

•

•

•

•

.

.

•

i#a

~Mb

•

•

,

•

•

45)

°

P a r t i a l widths of the B* into the c h a n n e l s a+B, b+B, . . . a r e denoted~ respect|vely~ by r a , r b , . . . ~ and

r ~ r a + rb+ . . . .

r.r~.

(6)

In what follows we c o n s i d e r r e a c t i o n s (I), ~ll), . . . at r e s o n a n c e (w = ~r)" Then, f r o m eqs. (3) and 45),

IMil 2 = 4 r a r ~ / r 2

(I)

~b+B,

~- IM~ f~- l~e

~u(a+B -- b+B) : 4J÷½) ~ (~'~r) 2 + r~/4 ,

fori~a.

47)

Putting t h e s e e x p r e s s i o n s into eq. (2), we get 2

.[j

= 1 - 4 ra(r

-

ra)/r2 = 41 - 2 ra/r~2. 48)

T h a t is, 2 ra/r = 1 • nij.

49)

H.ere tt should be noted that when YlJ is given, t h e r e a r e two kinds of values of Fa. We shall call c a s e (i) the adoption of the upper sign of the double sign in eq. (9), and c a s e 4ii) the adoption of the lower sign. F r o m eqs. 44) and (9) it follows that

42)

, i j ( a + B - . a+B) at ~or = (J+~) ~-~ a~(1 ~:Ti[j)2.

(3)

Comparing eq. (10) with eq. (1) we c a n say the following: A s the p h a s e shift (Sf~ at t h e r e s o nance, only the following values a r e allowed.

.

a is a factor which depends on the spln of the O m o n a. The cross sections for reactions (1), (10, . . . can also be e x p r e s s e d by the Breit-Wigner refinance formula.

~90°

for c a s e (i)

'

(10)

(11)

5IJ ~ ~ 0 ° (in g e n e r a l n~r) for c a s e 4ii) * If r a > ( r / z ) , otj m u s t be n e a r l y equal to 90°, becfiuse 1 >~ Till >~O. If r a < ( r / 2 ) , 51,1 m u s t be

nearly equal to 0 °. In this c a s e the B* cannot be a~

a

,

(4) * At f i r ~ sight it seems that the solution in v a s e (it)

should be disregarded. However, this is not correct as will be seen from the following example. 342

Volume 15, number4

PHYSICS L E T T E R S

regarded as a resonant state in the a-B system. If r a = r/2, we cannot say anything about the value of 6 fj, and this corresponds to scattering due to a 'q~lack" nucleus. For case (i) there is no need to add any more explanation because of the well known result. As an example of case (ii), w e can consider proton Compton scattering at the excitation energy of a nucleon isobar, since the experimental cross section [I] of the scattering has pronounced peaks at the energies corresponding to the Ist and 2nd resonant states in the pionnucleon system, and a(~,+p-~ 7+P) in case (i) becomes to be about 104 times as much as the experimental value [1]. Next let us show from a phenomenologlcal analysis that the value of 5fj for proton Compton scattering at the 2nd resonance is nearly equal to zero. In this case, B, B*, a, b,... in reactions (1), (II), ... correspond, respectively, to nucleon, the 2nd resonant state in the ~-N system, 7, ~, ... Recently Roper [2] has given both pion-nucleon phase shifts and absorption parameters as functions of energy from 0 to 700 MeV. According to his result, 513(~) = 90 °

and

~113(~)~ 0.33

(13)

at pion energy 676 M e V corresponding to the D13 resonance. Employing these values we perform a phenomenological analysis. Hereafter subscripts I and J are rewritten by 21 and Z], respectively. 513(~) and z/13(Ir)(or 513(7) and ~/13(7))indicate the phase shEt and absorption parameter for ~-N (or 7-P) scattering due to the D13 resonance. F r o m eq. (13) we can estimate the partial width (r~.)of the D13 resonance into the channel ~ + N. 2r~/r = 1 + ~13(~) = 1.33.

(14)

Partial width r T for the channel 7+N is estimated by employing experimental data for 7-Y 0 process. Note that the factor a in eqs. (1)-(5) has the followh'~g values: I for ~-N collision, ot = ½ for 7-P collision. Effects of the w+N channel are not taken into account *, since the experimental angular distribution of ~+N ~ ~I+N reaction at the DI3 resonance is not of a form (I + 3 cos 2 ~), but isotropic [3]. Partial width r2~ can be estimated b y e 2 . = ~ r - r~ - r~. The cross section of 7-7rv due to the DI3 resonance is tentatively estimated as follows: a130, +p ~ nU+p) = ~a13(~ + p ~ ~+N) 35/~b at 826 M e V corresponding to the D13 res* But it m a y be necessary to examine this assumption.

15 April 1965

onance **. Then we get the following res~flts for partial widths. r~/r=0.665,

r2Vr=0.327 ,

rT/r=0.008.

(15)

The absorption p a r a m e t e r for proton Compton scattering at the D13 resonance can be calculated

by

~13(~) = 1 - ~--FZ F

+

= 0.964.

(16)

Since 2 F ~ / F = 1 - ~/13(T), the phase shift 5 13(Y) at the D13 resonance is nearly vqual to zero (cf. eq. (11)). We can now estimate the c r o s s sections of 7-2~ and proton Compton scattering due to the 2rid resonance by using the values in eq. (15). The r e s u l t s a r e the following: values in eq. (15). The r e s u l t s are the foHowiag: a13(7+ p ~ 2~+N) at DI3 resonance ~ 52 l,b,

(t7)

a13(7+P ~ 7+p) ~ 1.26 /~b, and / at DI3 r e d a l 3 / d 9 at 90°~ 8.8x 10-32cm2/s r / sonance.

(18),

It may be said that these values are consistent with experiments [1, 5]. Previously we t r i e d to d e s c r i b e proton Comp~ ton scattering at 250-800 MeV in t e r m s of shadow scattering due to photoproduction of pions [6]. At that time we assumed that rx,th 533(~) and 613(7) are equal to zero. Such a t r e a t merit can be supported by the conclusion given in this paper, so far as the phenomena in the neighborhood of the P33 o r D13 resonan(:e zre concerned. Finally we d i s c u s s the phase shift of p-p scattering at resonance. Dyson and Xuong [7] predicted a resonance D12 with a m a s s qf 2160 MeV in the p-p system and r e f e r r e d to the following facts ***. The angular distribution of the reaction 7~+ ÷ d -- p + p is observed to (0.31 ± 0,03) + cos 2 0 at resonance, in agreement with the assignment J = 2. However, there is a discrepancy between the SU6 prediction and a phase shift analysis of p-p scattering at 660 MeV which shows a small D2 phase shift. Paying attention to these facts we have suggested in a previous note [8] that the D12 should not be r e garded as a resonance in the p-p system, but a s a resonance in the ~-d system. If this is the case, we may have another example of case (f0. That is, the phase shift (~12) of p-p scattering at the D12 resonance is nearly equal to zero. ** This value is not lnco~lstent with experimvnts. For the egperimental results, see ref. 4 for example. *** For the detailed references, see ref. 6. 343

Volume 15, zmmher 4

PHYSICS L E T T E R S

15 April 1965

5. J.M.Sellen, G.Cocconi, V.T.Cocconi and E. L. Hart, Phys.Rev. 113 (1959) 1323. 6. S.Minami, Nuovo Ctmento 21 (1961) 401. 7. Freeman J.Dyson and Nguyen-Huu Xuong, Phys.Rev. Letters 13 (1964) 815. 8. S.Minamt, to be published.

Ref_erences 1. R.F.Stlening, E. Lob mad Martin Deutseh, Phys. Rev. Letters 1O (1963) 536. 2o L.Dav/d Roper, Phys.Rev.Letters 12 {1964) 340. 3. F. Bulos et ai., Phys. Rev. Letters 13 (1964) 486. 4. Ph.Sslin, Nuovo Ctrnento 28 (1963) 1294.

* * * * *

EXCHANGE

MECHANISM

FOR co-PRODUCTION

IN r , + - n I N T E R A C T I O N S *

H. O. COHN Oak Ridge National Laboratory, Oak RtdKe, Tennessee and W. M. B U G G and G. T. C O N D O University of Tennessee, Knoxville, Tennessee and Oak Ridge National Laboratory, Oak Ridge, Tennessee Received 15 March 1965

Recently, considerable attention has been focused on decay correlations and exchange mechanisms in the production ofp mesons in -nuclenn interactions. The one meson exchange mcfJel with absorptive corrections as developed be/several authors [1] has exhibited considerable success in describing the salient features ofp and N* production from ~-nucleon encounters as well as K* and N* production in K-nucleon collisions. The purpose of this note is to present the corresporting data for w production in the reaction ~+ • n -- p + co. The production of co mesons in ~.*-p collisions has been reported by the A B C co|laboration [2}, by Shen et al. [3], and by Alff ~t aL [4]. However, the reactions a r e not directly comparable since in the l a t t e r c a s e the co is p r o d~ce~ either in conjunction with an N* o r an unc o r r e l a t e d n~', p pair. We have ana|yze.d ~ 2800 ~)vents of the type •+*d ~ (p)+p÷~'÷~'+~ from3.25GeV/c~ ~e~)ns incident on the B N L 20 inch deuterium b~bble chamber. These events arise from two topologies, 4 prong events and 3 prong events ~ibere the spectator proton does not leave a visible recoil in the chamber. The latter events w e r e kinematically fitted by setting the spectator m o m e n t u m eqtml to zero. All events were required to have at least one proton identifiable by Research spo~ored by the U.S.Atomic Energy Commissio~ under contract with the Union Carbide Corporatkm.

ionization which delimits our discussion to m o mentum transfers ~< 50 m2~. No corrections have been incorporated in the m o m e n t u m transfer distributions for those events where the spectator proton was not visible. Figs. l(a) and l(b) show the C h e w - L o w plots for the 3~ events as well as for 2800 2~ events from the reaction ,~+ + d2--(p) + p + ,7+ + ~-o The narrow co band at m 3~ -- 0.6 G e V is clearly resolved and shows that co production is present at m u c h higher m o m e n t u m transfer (A2) than is pproduction which has practically vanished at A 2 = 15 m2~. The~e plots also indicate the presence of the ~ and f" mesons in our experiment as well as a 3~ resonance in the mass region of the A 2 (1310). As in the recent ~'d experiment of Saclay-Orsay-Bari-Bologna Collaboration [5], we have been unable to demonstrate that this is a p~ resonance as might be expected from its close equality with the A 2 (1310) mass. A n important test of the validity of any model for resonance production is the variation of the production cross section with m o m e n t u m transfer. It is the narrowness of this distribution in p production that requires modification of the one pion exchange model either via the application of form factors or through the introduction of absorptive effects. In fig. 2(a) we2Present a histogram of co production versus A . N o background subtraction was deemed necessary due to the narrow width of the co and the similarity of the distribution for adjacent m a s s regions. The