The Ep = 2.66 MeV resonance in O16(p, p)O16

Nuclear Physics 68 (1965) 417--425; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or m i c r o f i l m without written permission from the publisher

T H E Ep = 2,66 M e V R E S O N A N C E I N O16(p, p ) O .6 V. GOMES, R. A. DOUGLAS, T. POLGA and O. SALA Laboratdrio 'do Acelerador Eletrostdtico, F.F.C.L., Universidade de S~o Paulo, Sc7oPaulo, Brasilt Received 26 October 1964 Abstract: The absolute differential cross section has been measured over the Ep = 2.66 MeV resonance [Ex(Fiv) = 3.10 MeV] in OlS(p, p)O 1' at the following angles in the centre-of-mass system: 54.5°, 70.5°, 90.0°, 107.0°, 125.5°, 140.5° and 151.3°. Also angular distributions (15 angles from 0c.m. = 30-5° to 155.6°) were measured at the following energies: 1.473, 1.931, 2.481, 2.652, 2.660, 2.668 and 2.978 MeV. A partial wave analysis of the results was performed. The first analysis used only cross section data as the input to the computer programme. The results fail to predict the observed off'resonance polarizations. A second analysis using both cross section and polarization data for the input gives a satisfactory fit to all experimental data. The parameters which give the best fit to the data are _P = 20-4-1 keV (lab), Er = 2.6634-0.007 MeV, J~ = ½-. E[

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NUCLEAR REACI'IONS. O*6(p, p), Ep = 1.473 to 2.978 MeV; measured t;(Ep; 0). [ F 17 deduced level, J, zr, /". I 1. Introduction

T h e elastic scattering of p r o t o n s f r o m O t6 was first studied by L a u b e n s t e i n a n d L a u b e n s t e i n 1). T h e cross sections at 0lab = 164 ° was m e a s u r e d as a f u n c t i o n o f energy using a solid target a n d a magnetic analyser. A partial wave analysis o f these d a t a yielded the following parameters for the resonance at 2.66 MeV: F = 19.9 keV, J~ = ½+. E p p l i n g 2) a n d H e n r y et al. 3) m e a s u r e d absolute differential cross sections using a gas target. O n the basis of the f o r m o f the yield curve at 90 ° E p p l i n g c h a n g e d the a s s i g n m e n t to J~ = ½- for this resonance a n d H e n r y confirmed the result. Early i n 1962 Salisbury a n d Richards 4) published a complete phase shift analysis of the u n p u b l i s h e d data of E p p l i n g a n d Henry. More recently, m e a s u r e m e n t s o f the p o l a r i z a t i o n o f the scattered p r o t o n s were m a d e b y Blue a n d Haeberli s). T h e phase shifts o b t a i n e d b y Salisbury a n d Richards were n o t i n complete agreem e n t with these data. Blue a n d Haeberli also m a d e a phase shift analysis which gave agreement with b o t h the scattering a n d p o l a r i z a t i o n data. I n the present experiment the elastic scattering o f p r o t o n s f r o m O 16 was m e a s u r e d using a gas scattering c h a m b e r a n d a surface barrier detector. ? This work was partially supported by the AFOSR (Grant No. 310-63) and the WisconsinS~o Paulo cooperative programme through the National Science Foundation and the Fundaq~o para o Amparo de Pesquisa do Estado de Sao Paulo (FAPESP). 417

418

v. COMESet aL 2. E x ~ r i m e n t a l Arrangement

Fig. 1 shows the general experimental arrangement and electronics. Fig. 2 shows a m o r e detailed view o f the scattering chamber.

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Fig. 1. General experimentalarrangement. 1 electrostatic accelerator, 2 steering magnet, 3 electrostatic analyser, 4 gas scattering chamber, 5 surface barrier detector, 6 electronic equipment Ortec (low noise charge sensitive pre-amplifier and amplifier and Nuclear Data 256 channel analyser), 7 quadrupole lenses.

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Fig. 2. Gas scattering chamber. 1 defining slits, 2 anti-scattering slits, 3 entrance foil It~0 A Ni, 4 exit foil 5000 .~. Ni, 5 magnetic and electrostatic electron suppressor, 6 collector cup, 7 defining slits of detector collimator, 8 anti-scattering slits, 9 surface barrier detector. The b e a m f r o m the Universidade de Sgo Paulo electrostatic accelerator 6) was analysed magnetically and electrostatieally. It entered the gas scattering c h a m b e r t h r o u g h a 1000/~ nickel foil and left t h r o u g h a 5000/~ nickel foil. The entrance collimator defined the angular spread o f the b e a m to __+0.5 °. The evacuated collector cup employed both magnetic and electrostatic electron suppression.

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420

v.

GOMES

et aL

The scattered particles, after passing through a collimator which accepted particles with a maximum angular spread of _ 0.75 °, were detected by a surface barrier detector. The solid angle of the detector for a scattering event occurring at the centre of the chamber was 2.55 x 10 -4 sr. The pressure of the gas was measured with a manometer using octoil of specific gravity equal 0.98. The pressures used varied from 5 to 8 cm of oil giving a maximum target thickness (0~ab = 155.6 °) of 0.3 keV for 2 MeV protons. The temperature of the scattering chamber was measured with a mercury thermometer and the gas was assumed to have the same temperature as that of the chamber. The effect of local heating of the gas by the beam was not appreciable since the yield per unit charge collected did not depend on the beam intensity. The value of the yield divided by the pressure was measured for pressures ranging from 1 to 20 cm of oil. This ratio was found to be independent of pressure indicating that scattering in the gas did not affect the collection of the beam. The electronics for the detector consisted of a low noise charge sensitive preamplifier (Ortec system) and a 256-channel analyser (Nuclear Data). The resolution obtained was 30 keV. The electrostatic analyser was calibrated using the T(p, n)He s, Beg(p, n)B 9, O16(d, n)F 17 and C13(p, n)N x3 reactions, all with solid targets. The thickness of entrance foils were determined by measuring the Be9(p, n)B 9 threshold with and without the foil in the beam path. The energy is believed to be known to an accuracy of 7 keV, the largest uncertainty arises from uncertainties in the entrance foil thickness. However, all data reported were taken with the same entrance foil. Fig. 3 shows the measured angular distributions and fig. 4 shows the excitation functions. 3. Calculation of Cross Sections

The cross section in the laboratory system is given by the following relation 7): Y O'(01ab) :

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NnG sin 0lab'

where Y is the yield per 1 #C of beam collected, N is the number of protons in 1 ?tC, n is the number of atoms per cm 3 in the target chamber, G is the geometrical factor (in sr. cm) and calculated according to the method used by Silverstein 7), 0lab is the laboratory angle. 4. Calculation of Errors

Table 1 gives the estimated errors in the absolute cross sections. At small angles the rapid variation of the cross section with angle produces a larger uncertainty in the cross section. At 30 ° this uncertainty is 5 ~o. At the smaller angles the higher counting rates resulted in appreciable counting losses due to the dead time of the

THE O16(p, p)O TM REACTION

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multi-channel analyser. A measurement based on a life-time oscillator gave losses up to 6 ~o for the 30 ° point at the lowest energy. This 6 ~o would represent the true correction if the beam were constant, but for a beam which varies in intensity it represents only a minimum correction. Because of this uncertainty the 30 ° point was given less weight in the analysis. The statistical error was less than 2 ~o for all angles except the very back angles where it was less than 3 ~o. The total uncertainty in the cross section is about 4 ~ for all angles. TABLE 1 Estimated errors

Source of error

Percentage error in cross section

angle measurement a) pressure of gas temperature of gas beam collection multiple scattering gas purity geometrical factor dead time of analyser

1 ~o b) 1 0.5 1 2 1 ~o 2 negligible b)

a) The uncertainty in the angular measurement is estimated to be 0.3°. b) At small angles these errors are larger. See text for estimates.

5. Theoretical Analysis The differential cross section in the centre-of-mass system may be expanded in terms of partial waves. The following simplifying assumptions are valid in this analysis. a) Elastic scattering is the most important process involving the compound nucleus level. b) Only one level with angular momentum and parity well defined is involved. With these assumptions the differential cross section in the centre-of-mass system can be represented by the following equation:

1

tr(0) = ~5 [IAI2+[BI2]' where the explicit expansion of A and B in terms of partial waves is given in ref. 1). We henceforth shall follow the notation of ref. 1). The polarization of the scattered protons in terms of the above notation is given by the following equation s): P(O)

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422

v. COMES et aL

The phase shift analysis of the experimental data was first carried out graphically 9). This analysis established the p~ nature of the resonance. However, a more accurate analysis was desired as the fit obtained was only approximate. This analysis was carried out on a CDC 1604 computer * A search programme was employed in which a given set of initial phase angles was used to calculate the differential cross section and polarization for predetermined angles at a given energy. The programme compares these results with the experimental values in terms of the following error function:

where e~ is the estimated experimental error in the cross section measurement at 0i, and e[ is the estimated experimental error in the polarization measurement at 0~. The computer calculates the values of the partial derivatives ax2/dSz and selects a new set of phase angles changing the initial phase angles by an increment proportional to the appropriate partial derivative such that the quantity a = ,/E

2 1

is equal to a given value. This procedure is repeated until a minimum in the function Z2(rz) is obtained. The quantity A is then reduced successively until the minimum X2(3t) is located with the desired precision. The first analysis was made using our absolute differential cross section data. Angular distributions at the off resonance energies 1.473, 1.931, 2.481 and 2.978 MeV were analysed using up to d wave phase angles. The non-resonant phase angles in the region of the resonance were then determined by interpolation. Nineteen angular distributions were analysed allowing only the p½ phase angles to vary. Figs. 5 and 6 show the calculated phase angles as a function of energy. Figs. 3 and 4 show the calculated differential cross sections (smooth curves) and the experimental points. Fig. 7 shows the function (x2/N) ~ for each angular distribution. This function has the value unity when the discrepancy between the calculated and experimental cross sections is equal to the estimated experimental error. The calculated polarizations at 3 MeV using these phase shifts are shown in fig. 8 (solid line). Also shown are the measurements of R. Blue and W. Haeberli ,t. It is apparent that these phase angles do not predict the correct polarization. A second phase shift analysis was made using as input data not only the present cross section measurements but also Blue and Haeberli's polarization angular distribution at 3 MeV and their measurement at 115 ° and 2.5 MeV. The analysis was carried out in the same way as described above. Figs. 5 and 6 show the new set of t The authors wish to thank Prof. W. Haeberli for t h e u s e o f his programme and the Numerical Analysis Laboratory of the University of Wisconsin for the use of their facilities. tt The authors wish to thank Prof. W. Haeberli for communicating these results before publication.

423

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424

phase angles obtained. Figs. 3 (dashed curve) and 9 (smooth curve) show the calculated cross sections and also the experimental points. Fig. 7 also shows the contributions to ( x 2 / N ) ~ from the discrepancies between calculated and experimental cross sections. It is noted that the value of this quantity is generally smaller for the set of phase angles obtained by the use of cross section and polarization input data (open circles). Thus the inclusion of the polarization data enabled the computer to find a better fit to the cross section data. (Compare figs. 4 and 9). That is, with only cross section data input the computer found a minimum in the X2(rz) function which was not the deepest. With the addition of the polarization input data this minimum was rejected and a lower minimum found. Z +LO

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Fig. 10. Excitation function of the polarization at 115°. The results of the first analysis are represented by the triangles, the second analysis by the crosses and Blue and Haeberli's results by the circles. (The polarization data required thick enough targets that the predicted sharp maximum and minimum would not be seen experimentally.)

Fig. 8. also shows (dashed curve) the calculated polarizations at 3 MeV obtained f r o m the phase angles of the second analysis. Fig. 10 shows Blue and Haeberli's polarization excitation function at 115 ° and the results predicted from our two analyses. It is seen that the second analysis gives a satisfactory fit to all of the data if it is recalled that the polarization measurements required targets thicker than the width of this sharp resonance.

6. Conclusion Absolute cross sections have been measured for the elastic scattering of protons f r o m 016 in the region in which the 3.10 MeV level in the compound nucleus F 17

THE O18(p, p)Ols REACTION

425

is excited. A n analysis o f these cross section data has been c a r d e d out which gives a satisfactory representation o f this data, but fails to fit Blue and H a e b e d i ' s polarization data. A second analysis, using b o t h cross section and polarization data as the input, has resulted in a slightly better fit to the cross section data and a sarisfactory representation o f the observed polarization. The a n o m a l y at 2.663_+0.007 M e V in the elastic scattering o f protons f r o m oxygen is adequately explained by the assumption o f a single level with F = 20 +__I keV and J~ = ½-. We wish to acknowledge the assistance of Sr. Yoshiyiri H u k a i in designing and m o u n t i n g the scattering c h a m b e r and Sr. M~trio Capello in its construction. We wish to t h a n k Professors H. T. Richards and W. Haeberli for valuable discussions.

References 1) 2) 3) 4) 5) 6) 7) 8) 9)

R. A. Laubenstein and M. J. W. Laubenstein, Phys. Rev. 84 (1951) 18 F. Eppling, Ph.D. Thesis, University of Wisconsin, (1952) unpublished R. R. Henry, G. C. Phillips, C. W. Reich and J. L. Russell, Bull. Am. Phys. Soc. 1 (1956) 96 S. R. Salisbury and H. T. Richards, Phys. Rev. 126 (1962) 2147 R. A. Blue and W. Haeberli, Phys. Rev., in the press O. Sala and R. G. Herb, Phys. Rev. 74 (1948) 1260 E. A. Silverstein, Nucl. Instr. 4 (1959) 53 J. V. Lepore, Phys. Rev. 79 (1950) 137 V. Gomes, R. A. Douglas, T. Polga and O. Sala, Ci~ncia Cultura, 14 (1962) 146