Aluminium (p, γ) resonances with H1+, H2+ and H3+ ions

Nuclear Physics 21 (1960) 108--115; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permi~on from the publisher

A L U M I N I U M (p, 7) R E S O N A N C E S WITH H~+, H2+ AND Ha+ IONS P. F. D A H L , D. G. C O S T E L L O A N D W. L. W A L T E R S

University ot Wisconsin, Madison, Wisconsin R e c e i v e d 27 J u n e 1960 A l u m i n i u m (p, 7') r e s o n a n c e s were s t u d i e d w i t h H1 +, H2+ a n d Ha + ions, u n d e r a v a r i e t y of conditions, to clarify discrepancies b e t w e e n m o l e c u l a r ion r e s u l t s a n d r e s u l t s w i t h Hx+ ions. T h i c k t a r g e t g a m m a - r a y yield c u r v e s f r o m I-t, + ions a r e v e r y a s y m m e t r i c . T h e y are a c c u r a t e l y f i t t e d b y a s s u m i n g t h e electron in t h e ion is t o r n a w a y t h e m o m e n t t h e t a r g e t is s t r u c k . T h e e n s u i n g C o u l o m b force p u s h e s t h e t w o p r o t o n s a p a r t . P r o t o n energies in t h e l a b o r a t o r y s y s t e m are s u b s t a n t i a l l y c h a n g e d , a n d s o m e p r o t o n s p a s s t h r o u g h t h e r e s o n a n c e twice. Six r e s o n a n c e energies were m e a s u r e d w i t h p r o t o n s in t e r m s of t h e Li(p, n) t h r e s h o l d a t 1881.1 keV. Values o b t a i n e d a r e (in keV) 632.8-4-0.2, 9 2 3 . 4 ± 0 . 3 , 937.7-4-0.3, 992.4-4-0.3, 1001.7=[=1.0 a n d 1213.6d:0.5.

Abstract:

1. Introduction It is customary to extend the proton energy range of electrostatic accelerators by making use of H2+ and Ha+ ions which are available from hydrogen ion sources. Molecular ion beams are also convenient for calibrating the energy scale of the energy selector used in conjunction with the accelerator; thus a (P, 7) resonance or (p, n) threshold reaction furnishes three calibration points when H1+, H2+ and H3+ ions are used. Recent careful measurements of the resonance energies and widths of narrow (p, ~) resonance reactions have revealed discrepancies in results when thick target gamma-ray yield curves obtained with H , + ions are compared with corresponding curves from protons. The former yield curves are quite asymmetric, which throws doubt on their use in precise reaction studies and calibrations. It has not been entirely clear whether these discrepancies are of instrumental origin, or whether they reflect the anomalous behavior of molecular ions in the target. The present work was undertaken to throw further light on these effects.

2. Experimental Equipment The ion beam from the electrostatic accelerator 1) is first deflected in a magnetic field where the desired mass component is sorted out, then traverses a one-meter cylindrical 90 ° electrostatic energy analyzer before entering the target chamber. For the present work the analyzer was adjusted for an energy resolution of 0.1%, giving a total theoretical energy spread of 2 keV at 1 MeV 106

ALUMINIUM (p, 7) RESONANCES

107

proton energy. The voltage scale of the analyzer is calibrated in" terms of the Li (p, n) threshold a t 1.881 MeV, and the linearity of the scale over the region of interest has been checked by measurements of several resonances and thresholds with protons. No detectable long-time drift of the voltage scale was encountered over the period of about six months during which the experimental data were taken; reproducibility of extrapolated threshold energies and resonance energies was generally considerably better than 0.05 %. Gamma rays are detected with a 5 cm × 5 cm NaI (T1) crystal in conjunction with a photomultiplier tube and standard amplifying and counting circuits.

KNIFE-EDGE HEATING PROTO APERTUR~TELECTRON S E A L TARGET-- COIL-~ NA [ DETECTOR

!

-!

....

•o

I

\

l

FOREPUMP ALU~IA5 OVENFOR HEATINGTARGET INSULATOR Fig. I. Target chamber. The circuitry includes a current integrator for measuring the incident beam current. The target chamber is illustrated in fig. 1. Part of the work was done with aluminium foil targets approximately 50 keV thick to a 1-MeV proton beam. Thin targets of aluminium and thick targets of lithium were prepared by evaporation of aluminium or lithium fluoride, respectively, in a seprate evaporation chamber. Some thick targets of aluminium were also made in this way. The lithium targets were covered with a fine copper mesh to prevent error in the current measurements due to charge accumulation on the non-conductive targets. For all evaporated targets thin disks of copper were used for target backing. Considerable trouble was experienced at first with carbon deposits on the targets, which were probably due to vapors originating from a vacuum valve

108

P. F. DAHL, D. G. COSTELLO AND W. L. WALTERS

near the target chamber. This problem was solved b y recessing the targets in an " o v e n " as illustrated. The target chamber was kept at 150 ° C, and the proton current at the target was restricted to about 0.2/~A. These were found to be optimum conditions for preventing build-up, while at the same time avoiding melting the foil targets by the beam. Under these conditions reproducibility of yield curves was quite good even after prolonged running on the same spot on the target.

3. E x p e r i m e n t a l

Results

3.1. Y I E L D C U R V E S F R O M Hx+ A N D H=+ I O N S

Most of the work was concerned with the Al~(p, y)Si ~8 resonance which according to Bondelid's and Kennedy's measurements 2) is at 992.4 keV.

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Fig. 2. Yield curves for t h e resonance a t 992.4 keV o b t a i n e d w i t h HI+ a n d H=+ ions, and a t a r g e t 50 keV thick. S t a n d a r d deviations in t h e values of d a t a p o i n t s are less t h a n t h e d i a m e t e r of the circles. Here, Eb denotes the m e a n incident p r o t o n energy, a n d E= t h e resonance energy. I n t e g r a t ed charge per d a t a p o i n t was 41/~C. B a c k g r o u n d m e a s u r e d b y intercepting the b e a m near the t a r g e t c h a m b e r entrance was s u b t r a c t e d f r o m t a r g e t yields. No corrections could be m a d e for b a c k g r o u n d originating in t h e t a r g e t b a c k i n g a n d t w o beam-defining apertures.

In fig. 2 is shown a set of typical thick target gamma-ray yield curves, obtained with the proton beam and the H~.+ beam. The energy corresponding to one-half maximum yield on the curve from protons is taken as the resonance energy, and the interquartile range * on the curve agrees well with t h a t predicted on the basis of the electrostatic analyzer geometry and a theoretical triangular proton energy distribution. Additional sources of broadening, including the natural width of the resonance, are small in comparison to the energy spread in the proton beam. The leading edge of the resonance step in the curve from H,.+ ions is very asymmetric, with the yield starting about 3 keV below the resonance. Near the * W i d t h between ¼ and ~ m a x i m u m yield.

(p, y) RESONASCES

ALUMImUM

109

resonance e n e r g y t h e c u r v e flattens out v e r y quickly, a n d r e m a i n s r e l a t i v e l y flat for several keV before it rises g r a d u a l l y to a m a x i m u m yield which agrees a p p r o x i m a t e l y w i t h t h a t of the H1 + yield. T h e t w o curves n e v e r fully m e e t , owing to t h e presence of an a d d i t i o n a l w e a k r e s o n a n c e a b o u t 10 keV a b o v e the m a i n resonance. I t should be n o t e d t h a t t a r g e t s 5 to 10 keV thick, generally considered t h i c k for resonance i n v e s t i g a t i o n s in this region, are n o t sufficiently t h i c k to bring out t h e full s h a p e of the c u r v e f r o m H2+ ions. 3,2. O T H E R

TARGETS AND INVESTIGATIONS

An a t t e m p t w a s m a d e to establish t h e s h a p e of t h e c u r v e f r o m H2+ ions w h e n the metallic t a r g e t was replaced b y a l u m i n i u m oxide. A l t h o u g h results were not v e r y satisfactory, owing to t a r g e t difficulties, a c u r v e of the s a m e general s h a p e was indicated.

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PROTON ENERGY (keV) Fig. 3. Y i e l d c u r v e s f r o m four a d j o i n i n g r e s o n a n c e s w i t h H i + a n d H ,+ ions, a n d t a r g e t s 50 keV t h i c k . T h e i n s e r t sh ows c u r v e B a n d p a r t s of c u r v e A a n d C on a l a r g e r scale. A s l i g h t l y h i g h e r y i e l d w a s o b t a i n e d d u r i n g r u n s B a n d C t h a n d u r i n g r u n A w h i c h w a s m a d e a m o n t h e a r l i e r w i t h a di ffe re nt t a r g e t a n d s l i g h t l y d i f f e r e n t c o u n t e r c o n d i t i o n s . Y i e l d v a l u e s in t h e d a s h e d e nc l os ure of c u r v e A were m u l t i p l i e d b y a f a c t o r of 1.15 to g i v e t h e p o i n t s of c u r v e A'.

R e s o n a n c e s at 633, 923 a n d 938 keV g a v e yield curves in q u a n t i t a t i v e a~reem e n t with the c u r v e at 992 keV. I n fig. 3 are shown results f r o m a pair of runs across four adjoining resonances w i t h the two beams, a n d with t a r g e t s 50 keV thick. A yield c u r v e o b t a i n e d w i t h the d e t e c t o r set at 90 ° to the b e a m axis agrees with the yield c u r v e o b t a i n e d w i t h the d e t e c t o r in its usual position at 0 °. To check f u r t h e r on possible q u a n t u m effects a run was m a d e w i t h ions from h y d r o g e n gas whose n o r m a l p a r a - h y d r o g e n c o n t e n t h a d been enriched. No

110

P.

F.

DA.HL,

D.

G.

COSTELLO

AND

W.

L. WALTERS

difference in yield was seen, although this result is inconclusive, since the abnormal para-hydrogen content m a y have been destroyed in the ion source discharge. 3.3.

THIN

TARGET

RESULTS

Owing to the reduced counting rate and problems encountered in preparing satisfactory targets thin target data were less reproducible than thick target data. Peaks of the yield curves obtained from the two different beams appeared to agree, after correcting for target thickness, and correcting for the fact that the H2 + ion includes an electron which shares energy with the two protons. The apparent agreement in resonance energy from thin target data has been noted previously b y Bondelid and Kennedy, from whicht hey conclude that the observed thick target anomalies are not due to "non-linearity" effects a). 8.4. Y I E L D

CURVE

FROM

Hi+ I O N S

A single run was made with the Ha+ beam across a resonance at 633 keY. A yield curve was obtained of similar shape to that obtained with the H=+ beam. Quantitative information could not be extracted from the curve, however, because of a relatively high background yield, probably due in part to a neutron background from small amounts of deuterium; a small carbon deposit m a y also have been present during this run. 3.5. I N E R T

SURFACE

LAYERS

In fig. 4 are shown a series of yield curves obtained from evaporated targets on top of which thin layers of copper were evaporated, varying from about

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Fig. 4. Yield curves for the resonance a t 992 keV f r o m Hi+ ions a n d e v a p o r a t e d AI t a r g e t s covered w i t h e v a p o r a t e d copper layers of different thickness. Thickness values given in A n g s t r o m s are only a p p r o x i m a t e . S t a n d a r d deviations in t h e values of d a t a p o i n t s are less t h a n t h e size of the symbols. Here, E b denotes the m e a n incident p r o t o n energy and ER the resonance energy. Integrated charge per d a t a p o i n t was 41 /~C.

~ummuM (p, y) wso,^,cRs

111

25 A to 200 A in thickness. The result is a gradual broadening and.washing out of the features of the curve, proportional to the amount of copper. Similar progressive changes in shape of the yield curve were encountered before the carbon buildup problem was solved, and served as a convenient and sensitive indicator of the cleanliness of the target surface. 3.6. RESONANCE E N E R G Y DETERMINATIONS

Results from measurements of six resonance energies with protons, in terms of the 1881.1 keV Li(p, n) threshold standard, are given in table 1. All resonance energy measlirements were based on thick target yield curves using Hi+ ions, TABLE 1 Resonance energy values Resonance Energy (keV) 632.8-4-0.2 923.4±0.3

937.7-4-0.3 992.4-4-0.3

] [

1001.7-4-1.0 1213.6-4-0.5

and the average of six measurements of the Li(p, n) threshold. The R.M.S. uncertainties quoted include + 0 . 0 2 % uncertainty in the location of the extrapolated Li(p, n) threshold value on our energy scale, +0.02 % uncertainty in the linearity of the electrostatic analyzer, and an uncertainty in locating the midpoints on resonance yield curve steps varying from 0.005 % for the resonance yield curve steps varying from 0.005 ~/o for the resonance at 992 keV to 0.10 °/o for the resonance at 1002 keV. Further details, including a fuller presentation of data referred to, b u t not included here, are given in a Ph. D thesis b y one of the authors 4). 4. D i s c u s s i o n

Anomalous yield curves from H2 + ions have been observed previously, both at this laboratory ~) and elsewhere, although in most earlier examinations the experimental accuracy was not sufficiently good to reveal the finer details of the curves. An examination of the problem was undertaken b y Anderson eta/. 6). They concluded that the discrepancy in resonance energies as deduced from the midpoint of the thick target step was probably due to a non-linearity in the energy scale. The excess broadening of the curves from H2+ ions was attributed to internal motion of the protons in the ion. The problem has also been investigated b y Bondelid and Kennedy 3), who pointed out that the asymmetry of the yield curve below the resonance might be explained b y assuming that the H + ion survives as an ion for a penetration depth in the-target of ~ to 1 keV before breaking up. They obtained apparent

112

P. F. DAHL, D. G. COSTELLO AND W. L. WALTERS

confirmation of this explanation b y passing the ion beam through a stripping gas of appropriate thickness before it struck the target; in this case a broad b u t symmetric curve was obtained, with a midpoint in good agreement with the midpoint of the rise of the curve from protons. The detailed yield curves obtained at this laboratory would seem to exclude any possibility of an explanation from non-linearity of the electrostatic analyzer.

5. Interpretation of Results 5.1. M O D E L U S E D

Computations have been carried out for the following model. The attached electron is torn from the molecular ion the moment the ion strikes the target. The ensuing Coulomb force between the two protons pushes them apart. A proton oriented forward in the ion will receive an impulse in the forward direction, and the trailing proton will feel a retarding impulse. Forward protons from ions with axes (internuclear axes) oriented at small angles with respect to the beam axis at the time of breakup will gain energy more rapidly than they lose energy from ionization, and m a y pass through the resonance twice. A Coulomb energy of about 6 eV per proton in the centre-of-mass system results in a maximum of about ± 5 keV in the laboratory system. The forward proton from an ion with its axis oriented at 0 ° to the beam axis at the moment of break-up will receive a net gain in energy of about 1.5 keV above incident energy, and penetrates to a depth of about 1000 A in the target before the rate of energy loss becomes normal. If the ion axis is at 70 ° with respect to the beam, dE/dx for the forward proton is zero at the moment of breakup, and for larger angles dE/dx is always negative.

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INCIDENT PROTON SPECTRUMI

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Fig. 5. A n a l y t i c a l fit to t h e y i e l d f r o m Hs+ ions a t t h e 992-keV r e s o n a n c e . T h e i n s e r t s how s t h e i n c i d e n t p r o t o n e n e r g y d i s t r i b u t i o n used in t h e c a l c u l a t i o n . H e r e E i d e n o t e s t h e i n c i d e n t e n e r g y of a p r o t o n in a b e a m of m e a n e n e r g y Eb. T h e r e s o n a n c e e n e r g y is d e n o t e d b y ER. I n t e g r a t e d c h a r g e per d a t a p o i n t w a s 41 ~C.

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(p. ~) a m o a A N c ~ s

113

A calculated yield curve, fitted to the experimental data, is shown in fig. 5. The fit was made by normalizing the m a x i m u m yield of the calculated curve to the observed maximum yield of the curve obtained with protons, and b y allowing for the 250-eV shift due to the mass of the extra electron. The dielectric constant of the target material was assumed to be unity. For the curve shown the Coulomb effect was cut off rather arbitrarily at a proton separation of about 5 A, at which point the two protons have penetrated to a depth of 1200 A in the target. At this separation the Coulomb energy acquired in vacuum would be 90 ~/o of the maximum Coulomb energy. 5.2. I N T E R N A L

ENERGY

EFFECTS

A yield curve for a monoenergetic incident beam of Hs+ ions was first calculated. Internal motion was assumed to be zero in this step. Final curves were obtained using as proton energies at the instant of breakup distributions of various plausible shapes, including a Ganssian and triangular shape. In all cases effects of internal motion were lumped together with the beam energy spread from the electrostatic analyzer. The best over-all fit to the data was provided b y a distribution of the Serber 7) form

N(E)

=

Eoa [(E-- Eo)Z+Eoa]!

(1)

where E 0 represents the mean incident ion energy, a is a constant, and the half-width is given b y E i = 1.533 (Eoa)½. Most of the observed thin target yield curves are similar to the Serber form, with a narrow width at hMfmaximum yield and a long tail at the base. The energy spread from the internal vibrational motion of the two protons in the molecular ion depends on how the ions are distributed in the various excited vibrational states. The zero-point vibrational energy of the H , + ion is known to be 0.14 eV, and its dissociation energy is 2.6 eV 6). An internal energy of 1 eV corresponds to a maximum classical energy spread of 2L2 keV in the laboratory systena, if the energy of the centre-of-mass is 1 MeV. The energy spread resulting from internal motion m a y therefore be approximately the same as the energy spread passed b y the electrostatic analyzer. A halfwidth of 1.6 keV was used in eq. (1), and the tail was cut off at -[-4 keV. A summary of the calculation is given in the appendix. 5.3. E F F E C T S

OF ABNORMAL IONIZATION

The theoretical fit was found to be insensitive to the inclusion of small contributions from two other possible effects: the effective stopping power of the target medium m a y be above normal or below normal for a short distance into the target. Increased stopping power might be expected from the collective behavior of the two protons immediately after the electron is torn away.

114

P. 1r. DAHL~ D. G. COSTELLO A N D W. L. W A I T E R S

Decreased stopping power would result if ions survive as such for a short distance into the target. If these effects do exist they m a y effectively cancel each other. 5.4.

INERT

SURFACE

LAYERS

The calculation was modified to include various thicknesses of copper layers on the target, and the resulting yield curves are in qualitative agreement with what is observed under these conditions: the sharp bend in the curve near the resonance energy is gradually washed out. Quantitative fits to the experimental data were not attempted in this case, however, since the actual thicknesses of the copper, or carbon layers were only poorly known. 5.5. YIELD CURVES WITH HIGHER RESOLUTION All of the present data were taken with the electrostatic analyzer set for a fixed resolution of 0 . 1 % , in order to pass a proton beam of reasonable current through the slit system. Our calculations indicate that with higher resolution a broad peak should appear in the yield curves immediately above the resonance energy, rather than the flat plateau observed. Thinner targets m a y also produce a peak; a slight peak was observed a,t times, when semi-thick targets of 5 to 10-keV thickness were used. Such a peak m a y be detected in fig. 4. No a t t e m p t was made to treat the yield from H3 + ions analytically. The authors wish to express their appreciation to Professor R. G. Herb for his continued guidance and encouragement during the present experiment. They are also grateful for helpful discussions with Professor R. G. Sachs, Professor H. W. Lewis and E. A. Silverstein. This work was supported by the U. S. Atomic Energy Commission and by the Graduate School from funds supplied by the Wisconsin Alumni Research Foundation.

Appendix A short summary of the computation is given here. The yield m a y be represented by

ff

I

Y(Eb) = N ~=0°° ~=-~ E,f_oog(Eb, Et)W(Et, E, x)a(E)dEdElda~,

(2)

where N represents the number of atoms per gram in the target, a(E) represents the cross section in cm ~ per atom, W(Et, E, x)dE is the probability that a particle incident on the target with energy E 1 has an energy between E and E+dE at a depth x grams/cm 2 in the target, g(Eb, El)dE1 is the probability that a particle in the incident beam of mean energy Eb has an energy between

ALUMINIUM (p, 7) RESONANCSS

110

E, and E t + d E , s). We assume t h a t g(Eb, E,) = g(Eb--El) and ~(E) is taken to be a 0-function, so t h a t the yield becomes

Y(Eb) = N f Ei~--oo °° g(Eb--E,)dEt f~ ~0 ° W(Et, ER, z)d.~.

(3)

Here E R is the resonance energy. The function W(Et, ER, x) was taken as

W(Et, E R, z) = f:-o 6 {ER--[6~(x) cos 0 - - / ~ + E t ] } sin 0 dO,

(4)

where 6' (z) cos 0 represents the laboratory energy due to the Coulomb repulsion, 0 is the angle the molecular ion axis makes with respect to the beam axis at the time of break-up, and kz is the energy loss in the target at a depth x. Integration of W(Et, ER, Z) over x resulted in a yield curve for a monoenergetic beam of incident protons which is discontinuous at E t = E R. To overcome this difficulty at the resonance energy, g(Eb--Et) was assumed to have a narrow rectangular shape of a width negligible compared to that of the energy distribution defined by the electrostatic analyzer, and an approximate value for the monoenergetic yield at the point of singularity was calculated accordingly. Numerical integrations were then performed over various assumed incident proton energy distributions. Details of the calculation are given in ref. 4).

References I) Michael, Berners, Eppling, Knecht, Northcliffe and Herb, Rev. Sci. Instr. 30 (1959) 855 2) R. O. Bondelid and C. A. Kennedy, Phys. Rev. I15 (1959) 1601 3) R. O. Bondelid and C. A. Kennedy, N R L Report 5083 (Naval Research Laboratory, Washington, D.C., 1958) 4) P. F. Dahl, P h . D . Thesis, University of Wisconsin, 1960 (unpublished) 5) Herring, Douglas, Sflverstein and Chiba, Phys. Rev. 100 (1955) 1239 (A) 6) Andersen, Gj6tterud, I-loltebekk and L~nsj6, Nuclear Physics 7 (1958) 384 7) R. Serber, Phys. Rev. 72 (1947) 1008 8) Nuclear Reactions I, editedbyP. M. E n d t a n d M . Demeur (North-Holland Publishing Company, Amsterdam, 1959) p. 293