High energy (p, 2p) reactions and proton binding energies

I.E.1

2.L !} Nuclear Physics 7 (1958) 1 0 - - 2 3 ; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

H I G H E N E R G Y (p, 2p) R E A C T I O N S AND PROTON BINDING ENERGIES H. TYRIAN, P E T E R

H I L L M A N * a n d T H . A. J. M A R I S **

The Gusta] Werner Institute [or Nuclear Chemistry, University o[ Uppsala R e c e i v e d 9 April 1958 A b s t r a c t : T h e e n e r g y carried a w a y b y each of t h e t w o c o i n c i d e n t p r o t o n s f r o m (p, 2p) r e a c t i o n s in e l e m e n t s b o m b a r d e d b y 185 M e V p r o t o n s h a s been m e a s u r e d b y r a n g e a n a l ysis. To t h e e x t e n t t h a t t h e collision is quasi-elastic, t h e difference b e t w e e n t h e s u m of t h e s e energies a n d t h e i n c i d e n t energy, corrected for t h e recoil e n e r g y of t h e residual n u c l e u s , gives t h e b i n d i n g e n e r g y of t h e s t r u c k p r o t o n in t h e nucleus. S h a r p g r o u p s w h i c h c a n be a s s o c i a t e d w i t h t h e n u c l e a r shell s t r u c t u r e h a v e been o b s e r v e d in t h e l i g h t e l e m e n t s . T h e r e s u l t s d e t e r m i n e directly t h e spin-orbit s p l i t t i n g in t h e lp-shell a n d t h e b i n d i n g e n e r g y of t h e ls-shell for t h e l i g h t e s t nuclei. O n l y t h e s p e c t r u m of Be 9 m i g h t give s o m e i n d i c a t i o n of a n a-particle s t r u c t u r e .

1. Introduction As discussed in the preceding paper 1), it is of interest for the theory of nuclear structure to study the (p, ip) reaction initiated in nuclei by high energy protons. At proton energies (above 50 MeV or so) for which at least the light nuclei become appreciably transparent, such experiments have not been previously performed, and those at lower energies ~) are complicated by the preponderance of multiple collisions. The experiments of Selove 3) on the energy spectra of deuterons from high-energy (p, d) reactions give information somewhat similar to that obtained in the present work, but emphasizing surface interactions almost exclusively 1). Earlier experiments have studied the energy distributions of protons scattered in the nearelastic 4) and quasi-elastic 5) regions, the energy distributions of one of two coincident protons *), and the angular correlations between proton pairs ~). The significance of the results of most of these experiments, which established the existence of quasi-elastic scattering, is limited by the generally poor resolutions, and they yield mainly estimates of the average momentum distributions inside the nucleus. For discussions see refs. e, ~). The initial object of our experiment is the measurement of the energy required to remove a proton from a nucleus. For this purpose, it is necessary to measure simultaneously the energy carried away by the bombarding and t C E R N ( E u r o p e a n O r g a n i z a t i o n for N u c l e a r R e s e a r c h , theoretical s t u d y division); now a t SC Division, C E R N , G e n e v a . ** N o w a t t h e I n s t i t u t e for Theoretical P h y s i c s , C o p e n h a g e n . 10

HIGH ENERGY (p, 2p) REACTIONS

ll

recoil protons. A study of the correlations in angle and energy between the two protons, which we hope to pursue experimentally at a later stage, may yield information on the momentum distributions of the protons in each nuclear shell; for the moment we have measured only the spectra of the total energy carried away b y two protons in coincidence and approximately 90 ° apart (45 ° on each side) in a plane with the incident momentum, when lithium, beryllium, boron, carbon, nitrogen, oxygen, and calcium are bombarded with 185 MeV protons. A preliminary report of this work has already appeared s).

2. Method and Apparatus We use the range method to measure separately the energies of the two coincident protons, which we sum afterwards. Each proton is detected in a double- plus anti-coincidence channel. The geometry and electronic connections are shown schematically in fig. 1. There are on each side of the target four scintillators (L1, L2, L3, L4 and R1, R2, R3, R4 respectively), making up two channels; input channel I being L1L2L3 (L1 in coincidence with L2, and L3 in anticoincidence), II = R1R3R4, I I I -- L1L3L4, and IV = R1R2R3. There are then four output channels, channel A consisting of coincidences between the outputs of channels I and IV, B = I + I I , C = I I I + I V , and D = I I + I I I . This arrangement minimizes the amount of electronic equipment required, as well as allowing a simultaneous measurement of input and output channel counting rates. The channel positions are moved through the energy spectra b y insertion of remotely variable aluminium absorbers between scintillators L1 and L2, and R1 and R2. A few millimeters of absorber are usually kept in front of L1 and R1 to prevent possible large numbers of evaporation protons from entering those scintillators. The energy resolution is determined largely b y the range straggling at the highest energies, but increasingly b y the thicknesses of the crystals and associated aluminium covers, and to lesser extent of the target, at lower energies. The energy spread of the incident beam is negligible (m 1 MeV). Although available beam intensity is not a limiting factor, the targets are shaped to give the maximum mass in the beam for optimum energy resolution, in order to minimize beam intensity (and therefore room background) required for a given counting rate. The targets have isosceles triangular cross sections, with bases towards the incident beam and vertex angles 30 ° . This shape ideally gives near-zero energy spread, where however the ideal vertex angle depends slowly on emergent proton angles and energies. The sizes are chosen to give a maximum of 2 MeV energy spread over the experimental range of energies. There are additional small contributions to the resolution from the fact that the absorbers are not shaped but flat, and from the fact

12

It. TYRIAN,PETER HILLMANAND TH. A. J. MARIS

t h a t a v a r i a t i o n in the nuclear recoil energy is allowed by the large t e l e s c o p e geometries. (In the case of d e u t e r i u m only, this latter effect is large, as m a y be seen from fig. 3 below.) T h e final total e n e r g y resolution is a b o u t 4.4 MeV

PROTON BEAM

',,TARGET /I .

//

/

//

%

"x x.

/

,%RI ~ .,/ "~'A B S. ,,'~

R3 R4

A BS.'%~r',

L3"~"'., i, I L4

1 I I

Fig. I. Schematic diagram of counting geometry and electronic connections. Dashed lines indicate anticoincidence inputs. I, II, III, and I V are input mixers, and A. ]3. C, and D are final mixers.

full w i d t h at half height over the w h o l e energy range, rising slightly at t h e highest binding energies. The scintillators are all 3 m m t h i c k N E 1 0 2 plastic. L1 and R1 are 14 m m wide b y 28 m m high, L2 and R2 26 × 52 m m , L3 and R3 34 × 68 ram, and L4 and R 4 42.5 × 85 m m , spaced r e s p e c t i v e l y 90, 165, 180, and 195 m m from the target centre. E a c h is w r a p p e d in t w o layers of 0.02 m m a l u m i n i u m foil.

HIGH ENERGY" (p, 2p) REACTIONS

13

The total angular width in each telescope is about 10° horizontally and 20 ° vertically. The pulses from the RCA 6810A photomultipliers are clipped to 8musec length, shaped by series and parallel diodes, and fed through short 100 .Q cables into the coincidence circuits, those from the L scintillators via relay switches allowing remote insertion of delays. Each input mixer is a Garwin type double -plus anti-coincidence circuit modified to give, in addition to the normal slow output, a fast output of a size sufficient to feed directly two final mixers, which are of the same design but without the fast output and the anti-coincidence input. The eight mixers are mounted in a compact array to minimize the lengths of all internal leads. Resolving times are usually about 8 m/,sec in the input mixers, and slightly longer in the final mixers. Conventional amplifiers and scalers complete each final channel. High voltage for the photomultipliers (about 2 mA at 2000 V for each) is provided by a 25 mA Oltronix Type LSH 12R unit, quoted stable to 0.4 V for 10 °/o line voltage variations. The monitor is a two-scintillator telescope looking at the target, so that slight variations in the beam position (causing counting rate variations, since the target is not flat) are automatically taken into account. To normalize to the same incident beam intensity for the various targets, for purposes of absolute measurements, another two-scintillator telescope looks at a thin aluminium window at the exit of the proton beam tube in front of the target. 3. C h e c k s and P r o c e d u r e

Of the protons recorded in each channel (a few percent of those entering each telescope) only a fraction of a percent are in coincidence with protons recorded in the opposite channel. Most of the remainder are not in coincidence because of the poor angular and energy correlations between the two protons emerging from a quasi-elastic collision (spread out over more than a steradian and m a n y MeV due to the nuclear momentum distribution), or because they are due to other nuclear processes. Accidental coincidences are therefore the main limiting factor on the counting rates and therefore on the statistical and total errors. There are several pulse combinations possibly responsible for accidental coincidences, but by far the bulk come from non-accidental counts ill the input channels, in accidental coincidence with each other. This is checked by observing the linear relationship between channel width and accidental rate, by putting absorbers in front of the appropriate anticoineidence counter. Accidentals can therefore be measured by remote insertion of equal &'lay cables into all L inputs. These delays nmst be longer than the coincidence resolution time ( ~ 8 m#sec) but, since the proton beam has a time-structure corresponding to the cyclotron radiofrequency, nmst be an integral number

14

H. TYR]~N, PETER HILLMAN AND TH. A. J. MARIS

(ill' our case one is sufficient) of r.f. cycles. We have determined the correct length ( ~ 40 m/~sec) empirically b y maximizing accidental rate versus cable length. The accidental rate should not follow the spectrum, but should be a smooth function of absorber thickness. (For targets other than hydrogen the momentum distribution in the nucleus completely smoothes out all peaks in the sel~arate telescopes.) This is illustrated in fig. 9. for carbon. Normally acci-

tO

CI2(p'2P)Bit

l "

,t 0

I Energy(MeV) I Binding

4=0

I ~

30

20

Xl 10

I

0

Fig. 2. The spectrum of summed proton energies for carbon, showing the accidental counting rates (crosses) and the correction for nuclear absorption in the scintillators (lowest curve).

dentals are only measured once every few absorber steps, except when unstable beam conditions are suspected. While it is not possible to improve appreciably the radiofrequency dutycycle (fractional on-time) of the external proton beam, it was found possible to increase the frequency modulation pulse length from a normal 12/~sec to about 40-- 60 #sec b y lowering the cyclotron magnetic field, giving smaller energy gain per turn near the extraction radius, and thus a larger time spread. No other cyclotron controls had any noticeable effect. The effective total d u t y cycle was about 1/400. We usually use only about l0 T protons per second in the incident beam, much less than the full regenerated beam. The beam intensity is however reasonably steady only at full internal intensity. Therefore we use an aluminium diffusing screen in the regenerated beam before it enters the extraction channel, to reduce the external intensity while operating with full internal beam.

HIGH E N E R G Y

(p, 2p) REACTIONS

15

The most critical requirement of the experiment is on the efficiency of the anti-coincidence counters, because there are up to fifty times more protons passing through each channel-scintillator than stopping in it. An unavoidable source of inefficiency is the nuclear absorption of protons in that scintillator or the following aluminium foils, which will cause of the order of a percent of the transmitted protons to be lost to the respective anticoincidence counter, and therefore to be recorded in each channel -- amounting, in the lower energy regions, to a large fraction of the spectrum height. The number of transmitted protons in coincidence with normally recorded protons in the opposite channel is approximately given just by the integral of the observed real spectrum above that point. The fraction incorrectly counted due to the geometrical, optical, or electronic anti-coincidence inefficiencies is believed to be small, due to the good agreement among different channels at different times and under variable conditions, particularly at near-zero points on the spectra. These same points give upper limits to the nuclear absorption inefficiency, only a little higher than the values of this correction calculated from known carbon inelastic and hydrogen cross sections, corrected roughly for forward emission of secondary charged particles from carbon inelastic collisions, as estimated from the Monte-Carlo calculations of Rudstam 9) and Metropolis et al. 10). This calculated correction has been applied to all final spectra. Its magnitude is illustrated by the lowest curve in fig. 2. The coincidence counter optical and electronic efficiencies are ensured by obtaining high-voltage and scaler-discriminator plateaus. This is done with anti-coincidences turned off, for greater speed and because a more critical test is obtained with protons not stopping in the scintillators, and therefore giving much smaller light pulses. The relative channel sizes, which depend on crystal thicknesses and sizes (no one crystal is defining) are calibrated by observing the relative heights of some prominent peak in the four channels. For reasons of counting rate this is conveniently that from deuterium in heavy water, the angular correlation between the two protons from deuterium being much better than that from other elements. (Ordinary hydrogen would give exact angular correlations, and if the two telescopes are not perfectly positioned, would give a distorted picture of the channel sizes.) The result is shown in fig. 3, indicating practically equal channel sizes. (The great width of the peak is due, as mentioned above, to the variation in "nuclear" recoil energies allowed by the finite telescope geometries.) The same test checks the calculated energy separations of the channels. The observed spectra from any three channels are thereafter simply normalized in energy to that of the fourth. The energy variation of the channel efficiencies is due mainly to nuclear absorption in the absorbers, which reduces these a calculated maximum

16

H.

TyRIaN,

PETER

HILLMAN

AND

TH.

A. J .

MARLS

o f -9 2 o/ /o at the highest proton energies (lowest binding energies). This calculated correction has been applied to all spectra, assuming all protons inelastically scattered in the aluminium absorbers to be lost completely. The "anti-correction" due to those which are merely degraded in energy or create secondary charged particles, is calculated to be negligible. For the present, we have always kept the left and right absorber thicknesses about equal. Channels B and C are then essentially similar. We change the sum of the absorber thicknesses in steps usually equal to one third of the

Coinc bannel A B C

20C

""

a

IOC

42

44

45

48

50

52

54

55

mmAI-obsorber

l:ig. 3. The s p e c t r u m of s u m m e d p r o t o n energies as seen in t h e four s e p a r a t e c h a n n e l s for h e a v v w a t e r . The o x y g e n c o n t r i b u t i o n is small. N u m b e r s of c o i n c i d e n c e s a re p l o t t e d ve rs us total Al-absorber thickness.

A--I) energy separation. Nearly every final point thus consists of at least two measurements, and alternating points belong respectively to channels A@I) and B@C. Ill converting the spectra to an energy scale, published range-energy tables are used u), and in addition a zero-point (free proton) check is obtained either from the natural water content of the targets, or from thin polythene foils attached to their front faces. The cross sections are corrected for the increase in energy width of each channel with decreasing proton energy, as calculated from the range energy tables. A correction is also made to the

HIGH ENERGY IP, 2p) REACTIONS

17

energy scale for the recoil energy of the nucleus, which is kinematically determined except for the finite telescope resolutions. This correction is generally very small in the present cases, because of the angles chosen. The beam is approximately 10 mm in diameter at the target position. The D 2O, Be, B, N z, 0 2, and Ca targets have base widths, facing the beam, of 10 mm, and the Li and C targets 15 and 7.5 mm respectively. The heavy water and powdered boron containers are of 0.1 mm aluminium. The cryostatic target container for oxygen and nitrogen is a 0.023 mm soldered nickel foil triangle, surrounded b y a 40 mm diameter aluminium c 5 linder machined to 0.2 mm thickness. Helium gas is maintained at atmospheric pressure between the nickel and the aluminium to prevent distortion of the nickel by a pressure differential. The helium is supplied through a tube pleading up through the cryostat reservoir. The remainder of the cryostat is conventional. The background caused b y the cryostatic, boron, and heavy water containers is separately measured and found to be small. For all other targets "targetout" counting rates are negligible. The liquid nitrogen is condensed under pressure b y liquid air, from pure nitrogen gas, and should be sufficiently free of oxygen, though there was a trace of water present. In order to obtain absolute values of the cross sections, activation of aluminium b y AlZ7(p, 3pn)Na 24 is used to determine the incide-,t proton intensity. (Na 24 is practically the only activity present after a few hours of "cooling".) To make possible a direct transformation to the e//ective beam intensity over our non-flat (triangular) targets, a stack of thin aluminium foils arranged to have the same shape of mass distribution across the beam (though of course much thinner along the beam) is used. This is exposed for a known number of counts on the "target-independent" monitor mentioned above, which in turn is normalized to the target-dependent monitor counts for each target. Corrections then have to be made for the numbe:~ of nuclei in the various targets, the telescope geometries and channel energy-widths, and for the absorption of protons in the aluminium absorbers and in the crystals as described above. 4. R e s u l t s

The results are shown in figs. 4 and 5, plotted as d a / d ~ 1d.(22d E 1 dE 2 in units of/~b • ster-" MeV -2. Smoothed values of the backgrounds of random coincidences have been subtracted from all experimental points. Only statistical errors are shown. Other errors should be small, except for those arising from the corrections for nuclear absorption in the crystals, which should however, as m a y be seen from fig. 2, be a smooth function of energy, and large only in the region of high binding energies. Because of some uncertainties in the determination of the zero point of the energy scale, the abso-

18

H. TYR~N, PETER HILLMAN AND TH. A. J. MARLS

93%LiT(p'2p)He61

tO

(p.pd )

I II I I I

I,

I I

BE.(HeV)

Itl

I 501

i

~

IIt,I

40

30

20

10

i

Be9(p.2p) Li 8 (~pd)

I

i

50

BE(MeV) (D

,,.

i

!

l

I

i

40

30

20

10

i

Exc.E.(MeV)40

I

30

I

20

m

10

o

(p, pd )

' I

i ~

,

I

II

B.E.(MeV)

50

I

Exc.E(MeV)

l,llI ~

I

I

I

I

40

30

20

10

I

I

I

I

40

30

20

10

[

~'-.

•

0

,c

v~~o

BE('~*' ~ Exc.E. (Met/)

I

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30

210

, I

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,

~'~'o I

0

Fig. 4 a n d Fig. 5. A b s o l u t e cross s e c t i o n s for t h e (p, 2p) r e a c t i o n a t 185 MeV v e r s u s b i n d i n g e n e r g y of t h e r e m o v e d p r o t o n . S e p a r a t e e n e r g y scales for e a c h t a r g e t a l s o s h o w t h e c o r r e s p o n d i n g e x c i t a t i o n e n e r g y of t h e r e s i d u a l nuclei. R e l a t i v e e rrors s h o u l d n o t be m u c h l a r g e r t h a n t h e s t a t i s t i c a l errors s h o w n on each p o i n t ; a b s o l u t e errors s h o ' l l d be less t h a n 40 %, a n d t h e e rror in c o m p a r i n g t w o s p e c t r a s o m e w h a t less.

HIGH E N E R G Y

(p, 2p) REACTIONS

19

10 N14(p,2p)C13

I

(p,pd)

I

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B.E.(MeV)

50 I

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(p,pd)

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Exc.E (MeV)

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H. TYRIAN, P E T E R HILLMAN AND TH. A. J.

MARIS

lute energies may have an error of 4-1.5 MeV. Contributions from (p, np) reactions should be negligible because of the low detection efficiency for neutrons. Arrows on the figures indicate the points in the spectra above which protons and deuterons from the (p, pd) reaction could not have sufficient range to be recorded in coincidence. 5.

Discussion

The present measurements select proton pairs in which the protons are scattered 90 ° apart and symmetric in both angle and energy. This situation is similar to that for free proton scattering and it follows from momentum conservation that, neglecting the scattering in the nucleus and the large solid angles of the detectors, the measured ewmts correspond to a knocking out of a proton which is almost at rest in the nucleus. From this point of view, we appear to favour the interactions in the lower shells which have a small mean ~-inetic energy, and especially those in the lowest s-shell. However, the strong scattering in the nuclear field and the large solid angles of the detectors will make this effect u n i n , ortant in comparison with the influence of the variation of the absorption in the nucleus for the various shells (fig. 1 of the preceding paper). The lithium spectrum shows two peaks. The protons of the peak of lowest binding energy leave the residual nucleus with a small excitation energy and are evidently knocked out of the p-shell. The second maximum is made up of protons with binding energies of about 26 MeV. This is some MeV more than the binding energy of a proton in the a-particle, and therefore we suppose that the second maximum corresponds to a knocking out of an s-state proton. Its height might be expected to be at least twice that of the first one, because the s-shell contains two and the p-shell one proton, but the absorption in the nucleus evidently depresses the s-peak considerably more than the p-peak. This is in qualitative agreement with fig. 1 of the preceding paper. Using the reduction coefficient of this figure and formula (2) of the preceding paper one m a y make the following estimate of the order of magnitude of the cross section for the s-peak in lithium. For our case k 3 ~ 0 and therefore the conventional proton-proton cross section may be used. B y integrating over the momentum one finds for this cross section

dO'plo

~dcrppk 2

~ 1 m

dk, = /~ v0 h 2k°c°sOx" ~m IR[2"

Solving this equation for ~m ]R[ 2 and inserting the result in (2) gives da21,o __ ~ dR2 ,~

dk x

[gtm(k3)l~ ~ k 0 c ° s O l f

• Old 1

The value of the function ~'m~t [grin(k)[ 2 for the ls-state in a parabolic

HIOH ENERGY

(p, 2p) REACTIONS

2|

potential with classical frequency ~o at the point k = 0 is 2(h2/m~o~)3/2. With this value, taking (~2/2m)kl 2 = (~2/2m)k~2 = E and ~ = 45 °, we have ~%.o

d~21,o (m) 2

dOldE1d/22dE ~ = dkld----~

~

Iklllk21 .I

= 4~-Z/~EEo -I/~ (?~oJ)-31z ~_Q6 (E 1+ E z + E n + E b - E0). For ?~o = 41 A-XlzMeV 12), E = 75 MeV, E 0 = 180 MeV and da/dO ---11 mb/sterad, d~21,0 = 0.446(EI+Ez+Ea+Eb_Eo). dO1 d E l don d E 2 Using the reduction factor 0.08 of fig. 1 of the preceding paper the cross section finally becomes 0.0356 ( E l + E z + E n + Eb-- Eo)mb • ster -2 MeV -z. Because of the level width and our finite energy resolution the 6-function is replaced by a Gaussian in the measurements. The area of this Gaussian in a plot of cross section versus (Ex+E2) has to be compared with the value 0.035rob • ster -2 MeV -1. Experimentally it is 0.04rob • ster -2 MeV -1. As has been remarked in the preceding paper, strong deformations of the initial or final nuclei cause deviations of the spectrum from the expectations on the basis of the simple shell model. This is probably the case for beryllium and to a lesser extend also for boron. The spectrum of beryllium shows two maxima. The structure of Be 9 may be similar to that of Be 8, except for an additional neutron which we do not see. Therefore there could be some tendency to an ~-particle structure. In case of a pure ~-particle structure there would be one maximum of the same energy as the s-peak in lithium. If, on the other hand, the simple shell model were valid a spectrum like that of lithium but with a higher first peak would be expected. The measurements indicate an intermediate situation in which the first peak is moved considerably upwards, showing t h a t the knocked out particles are strongly bound, though not so strongly as those in the ~-core of lithium. This is the only indication of a possible x-particle structure in any of the light nuclei investigated. A difficulty for the interpretation of the results for boron is caused by the fact t h a t the target consisted of natural boron (81 ~ B 11 and 19 ~ BI°). The proton group originating from the p-shell is clearly recognizable but the peak is deformed. The maximum at 36 MeV seems to originate from the s-shell collisions. Carbon shows a high peak probably leading mainly to the ground state of B n. Clearly the peak corresponds to p-shell particles being knocked out. In pure/'-?" coupling only the 3/2-- ground state, would be excited. In L - S

22

H. TyRI ~N, P E T E R HILLMAN AND T H . A. J .

MARIS

coupling 1/2-- and 3/2-- states would be present in the ratios of their statistical weights, one to two. Mainly the ground state and the 2.14 MeV state would be expected to be involved. At higher binding energies there'exists a clear residue of the s-peak, whose height is somewhat more depressed than one would calculate from the reduction factor, probably because of its large width. Here and in all other spectra it is interesting to see how small and smooth the background from the multiple collisions indeed turns out to be. The small peak near 50 MeV is probably due to secondary deuteron pick-up. The spectrum of N 14 is like what one would expect for j-,/coupling, which should be rather good for nuclei nearing a closed shell. Over the peak caused by P3/2 particles the Pl/z peak appears. In oxygen the P~/2 peak has increased in height to considerably more than half t h a t of the P3/2 maximum. This is probably caused by the difference in absorption originating from the fact t h a t the Px/2 wave function has a longer tail at the nuclear surface, because of its smaller binding energy. This explains also the relatively large size of the Pa/2 peak in the nitrogen spectrum. The separation of the two peaks in the oxygen spectrum agrees well with the interpretation of the 6.3 MeV state in N ~5 as a state with a hole in the P3/2 shell. In these last two nuclei the s-shell is no longer clearly visible. The spectrum of calcium shows one peak about as sharp as our energy resolution allows, leading to about 6 MeV excitation in K 39. This result is not yet fully understood. Two maxima of the d3/2 and ds/2 particles, perhaps smeared out by multiple collisions, were expected. Also the height of the observed maximum is surprisingly large (see fig. 1 of preceding paper). A tentative explanation might be given by the assumption that the ground state of Ca4° contains a strong admixture of a state in which a nucleon pair is excited into the fT/z state of the next shell. This is in agreement with the existence of a 0+ excited state in Ca 4° as low as 3.3 MeV excitation energy. The mean radius of an f-state for harmonic oscillator wave functions is 13 ~o larger than t h a t of a d-state. Because in a nucleus like Ca clean knock out processes strongly favour the surface the peak in the spectrum might be caused by f-state protons and the contribution of the d-state could be hidden under it. If a proton of an f-state pair is knocked out, the nucleus is left with an excited particle in the f7/2 state and has ]' ---- 7/2-. Fig. 6 shows the binding energies of the different proton types we believe we have observed in the light nuclei, as a function of atomic number. The energy of 19 MeV required to eject a proton from He 4 leaving H a in its ground state falls well on the extrapolated s-curve. Of course further measurements are required. Energy and angular correlations, especially for the lightest elements, might give information on the nuclear wavefunctions and, by comparison with a detailed calculation, on

HIGH E N E R G Y

(p, 2p) REACTIONS

23

the distortion of the incoming and outgoing waves. The building up of the s- and d-shells in the elements between oxygen and calcium should be studied.

!( /

/

/

/

,e

/,( I / e ~u

20

m

10

P

.4.1"? I

0

He 4

I

1

Z/ I

I

I

I

Li 7 Be 9 B llC 72 N 14 016

A

Fig. 6. The binding energies of the protons in various shells versus atomic number, as taken from the positions of the peaks in figs. 4 and 5.

By using higher bombarding energies one should be able to follow the inner shells further and to extend and improve fig. 6. Prof. The Svedberg's support was as always very welcome. Per Isacsson was responsible for most of the electronic design, construction, and maintenance, and was at all times cheerfully helpful. We thank A. Svanheden for making the aluminium foil activation measurements and together with the cyclotron crew for providing the proton beam. Two of us (P. H. and T. M.) express their gratefulness to Prof. Svedberg and all the members of the Institute for their great kindness and hospitality during their stay. The work was supported by the Swedish Atomic Energy Commission. References 1) 2) 3) 4) 5) 6) 7) S) 9) 10) 11) 12)

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