Elastic scattering and reactions of protons on argon-40

2.C: 2.L ]

Nuclear Physics 28 (1961 ) 428--437; (~) North-Holland Publishing Co., Amsterdam l~ot to be reproduced by photoprint or microfilm without written permission from the publisher

ELASTIC

SCATTERING

AND REACTIONS ARGON-40

OF P R O T O N S

ON

A. C. L. BAR_,NARD * and C. C. K I M **

Department of Physics and Astronomy, State University of Iowa, Iowa City, Iowa **t Received 3 J u n e 1961 Thin targets of n a t u r a l argon gas were b o m b a r d e d with p r o t o n s with energies b e t w e e n 0.8 and 3.5 MeV. Differential cross sections were measured a t t h r e e angles for elastic scattering a n d for t h e reactions A40(p, p ' 7)A 4° and A4°(p, c¢)ClaL M a n y anomalies were observed in t h e elastic scattering cross section, t h e strongest being a t 1.88, 2.45 and 3.4 MeV. Spin a n d p a r i t y ]'~ = { - and ½+ were assigned to t h e levels corresponding to t h e first two of these. The a n o m alies corresponding to t h e previously reported A4°(p, 7 ) K 4t resonances were too small to be d e t e c t e d in this e x p e r i m e n t . I n t h e range of incident p r o t o n energy b e t w e e n 2.4 a n d 3.4 MeV, t h e r e were a b o u t 40 resolved or p a r t l y resolved resonances in t h e yield of cc particles.

Abstract:

1. Introduction The observation of y-rays from proton capture in A 4° was reported in 1948, b y Bostr0m, Huus and Koch 1), who found five separated resonances in the incident proton energy range from 900 to 1235 keV. Freier et al 2) studied the elastic scattering b y natural argon of protons with energies between 1.7 and 2.8 MeV. Strong anomalies were observed in the differential cross section at 155 ° (laboratory) at proton energies near 1.90 and 2.48 MeV. In contrast to the y-ray work, the elastic scattering showed evidence of overlapping of compound-nucleus states. Since the K 41 compound nucleus is formed excited to 7.84 MeV plus the kinetic energy of the system, it is unlikely that the levels corresponding to incident energies of a few MeV will be well separated from their neighbours. In the present experiment, protons elastically scattered b y natural argon (99.60 ~/o A4°) were observed at centre-of-mass angles 90.0 °, 123.5 ° and 160.0 °. for incident proton energies from 0.9 to 3.5 MeV. The reactions A 4° (p, p'y)A 4° and A 4° (p, ~) C13v were observed through the charged reaction products. Some unpublished data taken at Duke University b y Vorona, Olness and Lewis 8) are also included here in the interests of completeness. Lewis observed protons elastically scattered from natural argon at 0cM = 167.5 °. t P r e s e n t address: t h e Physics D e p a r t m e n t , Rice University, H o u s t o n , Texas *t P r e s e n t address: t h e Physics D e p a r t m e n t , U n i v e r s i t y of S o u t h e r n California, Los Angeles, California *it W o r k s u p p o r t e d in p a r t b y the U.S. Atomic E n e r g y Commission. 428

ELASTIC

SCATTERING

429

Since this report was drafted, a translation of some Russian work on A ~o (p, p)A 4° has become available 4). The cross section was measured at three angles in the incident energy range 1.7 to 2.7 MeV. Anomalies at 1.86 and 2.45 MeV were assigned l = I and l = 0, respectively, in agreement with the present work.

2. Apparatus The gas scattering chamber used in conjunction with the State University of Iowa electrostatic generator has been described in detail b y Bashkin, Carlson and Douglas 5). It consists of a gas-filled chamber into which the proton beam passes through a 0.1/~m thick nickel foil. Charged reaction products and scattered particles originating in a well-defined reaction volume m a y pass through a defining system into a charged-particle detector, which is a 0.010 cm thick CsI(T1) wafer. The reaction volume, and hence the target thickness, depends on the angle of the detector relative to the incident beam. This angle m a y be varied between 20 ° and 160 °. The output from the detector goes to a 256-channel pulse-height analyzer, and to scaling channels consisting of an amplifier, pulse-height discriminator and scaler. These form two independent ways of examining the detector output. In this experiment a complete pulseheight spectrum was printed out from the analyzer at each angle and each proton energy, so that the cross sections for scattering and reactions producing charged particles were measured simultaneously. Cross sections obtained in this w a y were checked against those obtained from scaler readings. A y-ray detector (5.1 cm diameter b y 4.4 cm deep NaI (T1) crystal) is also mounted on the chamber to measure gamma yields at approximately 90 ° .

3. Results Fig. 1 shows the charged-particle spectrum at 0c~ = 160 ° for an incident proton energy of 3.376 MeV. Three groups are observed. B y considering the w a y in which the pulse-height of these groups changed with incident proton energy (fig. 2), the groups were identified as elastically scattered protons, inelastically scattered protons and alpha particles from the reaction to the C13~ ground state. These are denoted as p, p', and ~¢o, respectively, on fig. 1. The observation of A 4° (p, p'?)A 4° and A 4°(p, 0¢)C13~has not previously been reported. In general, the yields of particles from these two reactions were small compared with the yields of elastically scattered protons. The spectrum shown in fig. 1 was one of the highest yields of reaction products. Fig. 3 shows the elastic scattering differential cross section at 0cm ----- 125.3 ° for low incident proton energies. It is clear that since the cross section shows no significant departures from the general Rutherford form, the anomalies

430

A.

C. L .

BARNARD

AND

C.

C. K I M

corresponding to the 7-ray resonances in the region (fig. 4 and ref. z)) are small. The target thickness for this part of the experiment was about 7 keV, so that very narrow anomalies might be hidden b y target thickness smearing effects. Yields of 7-rays from the reaction A*°(p, 7)K 41 were obtained b y measuring yields with argon in the target chamber and subtracting the yields measured with helium in the chamber. A bias level of Ev ~ 5 MeV was used. The elastic scattering differential cross sections at 0cM = 160 ° for higher energies, together with the cross sections for the two reactions, are shown in fig. 5. In contrast to the previous figure, substantial departures from the 30(

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Fig. 1. Spectrum from charged-particle detector a t a

"high" incident proton energy.

Rutherford form are seen. The largest anomalies are at about Ep = 1.88, 2.45 and 3.4 MeV. Statistical errors on the elastic scattering cross section are small and the target thickness was about 10 keV here. The scattering cross sections are in general agreement with those of Freier et al 3). The reaction cross sections have rather poor statistical accuracy, as only about 300 counts were taken at the peak of the largest resonance in the alpha yield. However, the reaction data were taken at three different angles of observation, and there was good agreement between the positions of the resonances at different angles. This curve suggests that in K 41 at about 11 MeV excitation, about 40 levels per MeV have reasonable alpha partial widths. In fig. 6 the complete elastic scattering data are shown, the cross sections

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SCATTERING

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316

PULSE HEIGHT versus

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1©1 INELASTICALLY SCATTERED PROTONS FROM A40(p,p')A 40e

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PROTON ENERGY- LAB (MeV)

Fig. 2. Variation of pulse-height of charged-particle groups with incident proton energy• 12C

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I.I PROTON

12 13 ENERGY--M*V

Fig. 4. Yield of ~,-rays with E 7 ~ 5 MeV from the reaction A 4°(P,7)K4x. Arrows indicate rcsonances corresponding to those in ref. 1).

A. C. L. BARNARD AND C. C. KIM

432

now being'in units of the R u t h e r f o r d cross section. T h e d a t a at 0cM = 167.5 ° were m e a s u r e d at D u k e U n i v e r s i t y 3), a n d the e n e r g y calibration was t a k e n f r o m this curve. F r o m the a p p e a r a n c e of the curves it seems t h a t the 167.5 ° d a t a were t a k e n with a t h i n n e r t a r g e t t h a n the o t h e r data. i

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4.

Discussion

and

Conclusions

T h e excitation nergies of levels in K 41 located b y resonances in the A 4° (p, ~)CP 7 a n d A4°(p, p'~)A 4° reactions are listed in the first p a r t of table 1, whilst the second a n d t h i r d parts list some levels located t h r o u g h elastic scattering a n d A~°(p, ~)K 41 data. To the present a u t h o r s at least, the gross b e h a v i o u r of the elastic scattering cross section is surprising. Inspection of the 0cM = 160 ° curve shows a sudden onset of anomalous b e h a v i o u r at a b o u t Ep = 1.8 MeV. Since it is highly likely t h a t there are levels in the lower e n e r g y region, it is concluded t h a t their p r o t o n widths m u s t be small. T h e p r o t o n p e n e t r a b i l i t y is not changing rapidly with energy here; therefore the onset m u s t correspond to a r a t h e r sudden increase in the r e d u c e d widths for p r o t o n emission. Such b e h a v i o u r could

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ELASTIC SCATTERING

435

possibly be related to the "giant resonances" of Lane, Thomas and Wigner s) From the complex shapes of the elastic scattering curves in the higher energy region, it is clear that there is considerable overlap of neighbouring levels, so that a single level approximation of dispersion theory ~) is not expected to be applicable. However, some information can be gleaned from fig. 6 using this approximation. The anomaly at Ep = 1.88 MeV laas a small but definite peak ar #cM -~ 90° with no sign of a dip. It therefore probably AA°{p,p) A A°

ANOMALY

CURVES -

FOR

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Fig. 7. E l a s t i c - s c a t t e r i n g a n o m a l y a t Ep = 1.88 MeV. P o i n t s a r e e x p e r i m e n t a l d a t a . C u r v e s a r e c o m p u t e d for p - w a v e p r o t o n s a n d a r e s o n a n c e w i d t h /~ = 1 keV. T a r g e t t h i c k n e s s is angled e p e n d e n t a n d is i n d i c a t e d o n t h e figure.

corresponds to an odd value of l, the orbital angular momentum quantum number of the incoming proton. At Ep = 2.45 MeV there is a dip at 90 °, corresponding to an even /-value. Some brief calculations were therefore made with incident p-waves at the lower anomaly and s-wave at the upper. The single level approximation was used to give curves for zero target thickness. Several identical curves were then displaced in energy and added to take into account the "smearing" effect of finite target thickness in a rough way. At the Ep ----- 1.88 MeV anomaly, such calculations gave the curves shown in

436

A.C.L.

BARNARD

AND

c.

c.

~-IM

fig. 7, the'values of the parameters of the calculation being given in the caption• (The target thicknesses shown on the figure are a consistent set for the different angles). Since this incident proton energy is below the A4°(p, n) K 4° threshold 8) and since the observed reaction width is very small, the proton fractional partial width ~ = Fp/Fwas taken to be unity• It can be seen that the experimental data are well fitted with ~'== ~-, except at 0CM = 167.5 ° where there is qualitative agreement. The fit here could be somewhat improved A"m(p,p)A4° ANOMALY AT 2.46 MeV P-4keV CURVES FOR S-WAVE ¢'°r 0¢= ;"67.5" A

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by taking a smaller target thickness. Since there are other nearby levels, the fit deteriorates away from the resonance energy. The alternative value of /'" for I = 1, i.e. /'" 1- gives a calculated anomaly which, even with zero target thickness, has a peak value below the experimental points at the peak. as target thickness smearing will accentuate the disagreement, this value of/'" was rejected. The shapes of the anomalies are qualitatively similar for f-waves. However, both for ~'~ = ~-- and ] - with zero target thickness the minimum

ELASTIC

SCATTERING

4~7

would be higher and the disagreement stronger. Further, the maximum values of the calculated anomalies are extremely high at 0cM = 160 °, nearly four times the Rutherford value for i n ----~-- and seven times it for ~'~ ----~-. The smearing effect of the target thickness (roughly 10 keV at this angle) is insufficient to reduce these calculated values to the experimental maximum value of about 1.3 times the Rutherford cross section. It is concluded that the spin.and parity of the level corresponding to the Ep -----1.88 MeV anomaly are ~-. Since there obviously are interference effects from nearby levels, this assignment is not so certain as would be possible with isolated states, but the above arguments make the assignment plausible. The results of the s-wave calculations for the upper anomaly appear in fig. 8. This anomaly is above the neutron threshold and some a¢ particles and inelastically scattered protons are observed, so that ~ need no longer be unity. Since neutrons from a ½+ state to the ground state of K 4° require l = 3, the neutron penetrability and hence the neutron width might be expected to be rather small near threshold. For this reason and because the observed alpha partial width was small, ap = 1 was used in the calculations. It can be seen that this leads to a calculated anomaly much stronger than that observed, so that ap must be appreciably less than unity. This suggests that at this energy, just above the reported neutron threshold s) (Ep ---- 2.4 MeV) the neutron width is quite large. For d-waves at 0CM ---- 125.5 °, the calculated anomalyis qualitatively different from that observed. The calculated g-wave anomalies are about six times the Rutherford value at 0CM ---- 160° and target thickness smearing seems inadequate to reduce this to the experimental value. It is therefore likely that the level corresponding to the Ep = 2.45 MeV anomaly has/'~ = ½% The authors thank Professor H. W. Lewis of Duke University for making available his unpublished data and permitting its inclusion here. Professor James A. Jacobs is thanked for m a n y valuable discussions.

References 1) 2} 3) 4) 5) 6) 7) 7)

K. J. Brostrom ,T. Huus and J. Koch, Nature 162 (1948) 695 G. D. Freier, K. F. Famularo, D. M. Zipoy and J. Leigh, Phys. Rev. 110 (1958) 446 H. W. Lewis, private communcation A. K. Val'ter, I. Ya. Malakhov, P. V. Sorokin and A. Ya. Taranov, Bull. Acad. Sci. USSR (Columbia Technical Translations) 23 839 S. Bashkin, R. R. Carlson and R. A. Douglas, Phys. Rev. 114 (1959) 1543 A.M. Lane, R. G. Thomas and E. P. Wigner, Phys. Rev. 98 (1955~ 693 See, for example, J. W. Olness, W. Haeberli and H. W. Lewis, Phys. Rev. 112 (1958) 1702 H. T. Richards and R. V. Smith, Phys. Rev. 74 (1948) 1870