Photoproduction of π

Zeitschrift for P h y s i k A

Z. Physik A 294, 253-256 (19801

{;, by Springer-Verlag 1980

Photoproduction of

§ from 9Be

M. Nilsson, B. Schr6der, B. Billow, J. Grintals, G.G. Jonsson and B. Lindner Department of Physics, University of Lund, Lund, Sweden K. Srinivasa Rao and S. Susila* Matscience, The Institute of Mathematical Sciences, Madras, India Received November 8, 1979 The reaction 9Be(7, rc+)9Li has been studied with bremsstrahlung in the energy range 100-800MeV employing the radioactivity method. The cross section curve deduced is compared with an impulse approximation calculation including a volume and a surface production model. In the energy region 200-300MeV the experimental cross section, approximately 7 ~tb, is best reproduced by the surface production model with a cut-off parameter r0 equal to 2.8 fm, i.e. somewhat larger than the r.m.s, radius of 9Be.

Introduction During the last few years there has been an increased interest in photopion nuclear physics. The field is of theoretical interest due to its close connection with pion nuclear physics and the possibility to obtain nuclear structure information as well as information concerning the pion-nuclear optical potential. Recently Booth [I] reviewed the field of charged pion photoproduction from threshold to 350 MeV. One of the more favourable reactions, 9Be(~,rc+)9Li, has so far not been reported above the threshold region. This reaction is well suited for the radioactivity method due to its decay by neutron emission permitting experimental equipment with a large detection effiency leading to good statistics in the yield curve of the bremsstrahlung experiment. Also from a theoretical point of view the reaction is favourable as there are only two bound states in 9Li.

Experiment The bremsstrahlung induced yield of the reaction 9Be(~),r~+)9Li has been measured with the radioactivity method. Irradiations were performed in a collimated bremsstrahlung beam from the Lund 1,2 GeV Electron Synchrotron at endpoint energies from 100* University Grants Commission of India, Teacher Fellow

800MeV. A calibrated Wilson-type quantameter measured the intensity of the beam. The target material was metallic beryllium of high purity. Since 9Li is a delayed neutron emitter the activity was measured by counting the neutrons. Decay data for 9Li was taken from [23 and are given in Table 1. BF3-tubes were used to detect the neutrons after thermalization. The moderator consisted of a 50cm paraffin cube having a 5cm diameter plexiglas tube through the center. Six 3 cm diameter 20 cm long BF3-tubes were inserted into the moderator close to and parallel with the plexiglas tube in an axial geometry. The bremsstrahlung beam passed through the target situated in the center of the plexiglas tube. To reduce the neutron background the cube was covered with borated paraffin. The plexiglas tube had thin windows for beam entrance and exit and vacuum was achieved in order to minimize the contributions from other processes. The six BF3-tubes were parallelled and after suitable pulseshaping and discrimination the pulses were fed into a multichannel analyser. Multiscaling was performed to check the half-life and in order to make a proper background subtraction. Since the efficiency of the detector is energy-dependent, Monte Carlo calculations were performed to calculate the relative efficiency as a function of neu-

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254

M. Nilsson et al.: Photoproduction of ~+ from 9Be 1

I

I

This procedure was repeated for a large number of times at each energy. Irradiations were also performed with different target thicknesses in order to determine the background due to neutrons produced within the target causing the reaction 9Be(n,p)9Li. The yield of the reaction 9Be(7,rc+)9Li is given in Fig. 2. The errors shown are the statistical ones including background subtraction. From this yield curve cross sections were evaluated using the Tesch smoothing method [3]. The result obtained is given by the solid line in Fig. 4. The errors in the cross sections are estimated to be about 15 ~o in the resonance region and about 25 ~o at higher energies.

I

z

~10

Qr I

103

I

10~.

1 10~

[

10S

106

NEUTRON ENERGY [eV)

Fig. 1, Relative detector efficiency as a function of neutron energy

Theory I

1

I

,0+,,00,++~'0

10

I

-

The reaction 9Be(7,rt+)9Li is investigated within the impulse approximation. The nuclear transition operator is given in this approximation by: A

A

T= ~ ti= ~ (gj.K+L)exp(ik.rj)z;

o-

j=l

i11

g

01 200

I I 1 t,00 600 800 F, [HEY) Fig. 2. Total bremsstrahlung yield for the reaction 9Be(~2,rc+)9Lias a function of electron energy

where k = v - / , is the momentum transfer to the nucleon, v and p being the momenta of the incident photon and the outgoing pion, v0 and #0 their energies and z - the isobaric spin operator for rt + production and K and L are the spin-dependent and spin-independent parts of the free nucleon photoproduction amplitude for which we choose the forms given by the dispersion theoretic approach of Chew et al. [4]9 If we denote by 1i) and If) the initial and final nuclear states, then the differential cross section is given by: dG

Table 1. Properties of the delayed neutrons from the decay of 9Li

(1)

j=l

d-O = (2~)- 2 ~ t~o ~,

My

I(fl Tli)l 2

(2)

[2] Neutron energy (MeV)

Intensity(~o)

0.3 0.66

29.8• 2.2• .^+2.7 3.0_0.3

1.15•

tron energy (see Fig. 1). Measurements with a calibrated 252Cf source gave an efficiency of 4 . 0 ~ from which the efficiency curve was normalized. Knowing the major neutron peaks and their relative intensities (see Table 1) the absolute efficiency (including solid angle) is found to be 5.8 ~o. The irradiations lasted about 2s after which the beam was cut off and the target analysed during 2 s.

where the bar over the sum denotes the average over photon polarization 9 The details of the calculation can be found in earlier papers [5]. Positive pion photoproduction from 9Be5 giving rise to the 93Li6 daughter nucleus, induces essentially a single-particle transition, viz. the 1 P3/2-proton state in 9Be becomes a 1 p3/2-neutron state in 9Li. Hence, the contribution to the cross section is solely due to this single particle transition9 We have found [5] that a reasonable agreement between shell model calculations and experiments can be obtained, even when a simple description is made for the nuclear states, provided we invoke the surface production model. Though it is a purely phenomenological model, it has turned out to be a useful one, as it is to be gauged by its successful

M. Nilsson et al.: Photoproduction of n ~ from 9Be 100

I

I

I

I

255

I

I

I

I 30

l 60

I

I

I--

1

I 150

[ 180

80

60 c

.D ::L

i0-~

"o

b

"o

t,O r0=Ofm

20 10-z . ~ .....................

0

I

150

1

250

I

~"-" ......

I

I

350 Ey (MeV)

r0= 2./+6 fm 'l "~ fm

/+50

Fig. 3. Calculated total cross section for the reaction ~Be(y,~)9Li using volume (ro= 0) and surface (ro> 0) production models for the pions

I /,_,X [

-

FI!

150

I

I

\

250

I

r

',',

350 Ey tHeVl

t,50

Fig.4. Solid curve: Total experimental cross section for the reaction 9Be(7, n+)gLi as a function of photon energy. Dashed curves: Theoretical cross sections for the same reaction assuming a surface production model for the pions with different values of r0

0

l I 90 120 @ (deg)

Fig.5. Differential cross section for n* photoproduction from 9Be at E~.= 200 MeV assuming a surface production model for the pions. The experimental data are from Ref. 8 multiplied by a factor of 2.5

application [5, 6] to charged pion photoproduction from complex nuclei. For the radial wave functions, we take the harmonic oscillator forms with the oscillator strength parameter b = 1.6fm, which is in agreement with electron scattering data [7]. The surface production cut-off parameter ro (defined in Ref.5), if chosen to correspond to the r.m.s, radius of 9Be, should be r0 = ( r Z ) l / 2 = 2 . 4 6 f m , consistent with electron scattering data [7]. In Fig. 3 the theoretical cross sections, as a function of incident photon energy, are given in the volume production model (r0=0) and in the surface production model for r0=2.46fm and 2.8fro. The theoretical curve in the volume production model is not only an order of magnitude higher than the experimental data (see Figs. 3 and 4) but also exhibits a peak in the first pion-nucleon resonance region. The result in the surface production model exhibits a smooth variation of the cross section as a function of incident photon energy similar to the cases [5] of charged pion photoproduction from I2C and 160. In Fig.4 we show the curves obtained in the surface production model with cut-off parameters corresponding to 2.7, 2.8 and 2.92 fm. The results with r0 =2.8fro seem to be in reasonably good agreement with the experimental data in the resonance region.

256

In Fig. 5 we show the angular distribution for 9Be(y, 7t+)gLi where the states in 9Li are those which arise due to the single 1 p3/z-proton transition in 9Be. The theoretical curves in the surface production model correspond to cut-off parameter values of 2.7, 2.8 and 2.92 fm. The experimental values are those of Ohashi et al. [-8] multiplied by a factor of 2.5 as per Furui's estimation [9] of the photoproduction cross section from the electroproduction cross section of Ref. 8. The qualitative agreement of the angular distribution alone is to be noted, since we have not separated in our analysis the contribution to the cross section for the ground-to-ground state transition in 9Be(7, rc+)9Li process. We have presented here preliminary results of our theoretical study of 9Be(7, rt+)9Li , and a detailed analysis taking into account explicitly nuclear structure effects and FSI through an optical potential will be reported elsewhere. We are indebted to Hans-Olof Zetterstr6m and G~Ssta Engstr6m at FOA for assistance with the Monte Carlo calculations. This work has been supported by the Swedish Natural Science Research Counsil. One of us (KSR) wishes to thank N O R D | T A for a fellowship, which enabled the author to get acquainted with the experimental group at the beginning of this experiment.

References 1. Booth, E.C.: Photopion nuclear physics, pp. 129-154. New YorkLondon: Plenum Press 1979 2. Tomlinson, L.: Atomic Data and Nuclear Data Tables 12, 190 (1973)

M. Nilsson et al.: Photoproduction of 7t+ from 9Be 3. Tesch, K.: Nucl. Instr. Meth. 95, 245 (1971) 4. Chew, G.F., Goldberger, M.L., Low, F.E., Nambu, Y.: Phys. Rev. 106, 1345 (1957) 5. Srinivasa Rao, K.: Proc. Tamil Nadu Acad. Sci 1, 127 (1978) and references therein; Devanathan, V., Rho, M., Srinivasa Rao, K., Nair, S.C.K.: Nucl. Phys. B2, 327 (1967) 6. Freed, N., Ostrander, P.: Phys. Rev. CII, 805 (1975); Phys. Lett. B61,449 (1976) Kelly, F.J., McDonald, L.J., fJberall, H.: Nucl. Phys. A139, 329 (1969) 7. Elton, L.R.B.: Nuclear Sizes. Oxford University Press 1961 Bentz, H.A., Engfer, R., Buhring, W.: Nucl. Phys. A101, 527 (1967) 8. Ohashi, H., Nagahava, K., Yamazaki, M., Shoda, K., Sung, B.N.: Photopion nuclear physics, pp. 193-198. New York-London: Plenum Press 1979 9. Furui, S.: Photopion nuclear physics, pp. 199-204. New YorkLondon: Plenum Press 1979

M. Nilsson B. Schr6der B. Billow J. Grintals G.G. Jonsson B. Lindner Department of Physics Lurid Institute of Technology University of Lund S~ilvegatan 14 S-22362 Lund Sweden K. Srinivasa Rao S. Susila Matscience The Institute of Mathematical Sciences Madras-600020 India