Energy measurements of proton resonances in light nuclei

Kuperus, J. Smulders, P. J.M. Endt, P. M. 1959

Physica 25 600-609

ENERGY MEASUREMENTS OF PROTON RESONANCES IN L I G H T NUCLEI by J. K U P E R U S , P. J. M. SMULDERS and P. M. E N D T Fysisch Laboratorium der Rijksuniversiteit, Utrecht, Nederland

Synopsis A search has been m a d e for (p, 1,) resonances in all stable nuclides f r o m 19F t h r o u g h 38S for p r o t o n energies in t h e 0 . 2 0 - 0.85 MeV range. T h e energies of eighty-one resonances were m e a s u r e d w i t h an a v e r a g e precision of 0.24 percent. F o u r n e w resonances, at 4 3 1 . 0 4 - 1 . 3 , 4 3 6 . 9 4 - 1.3, 480.1 + 1.0, and 7 2 5 . 5 4 - 1.2keV, were observed in the 2~Ne(p, ~)~3Na reaction, and one n e w resonance, at 501.4 4- 1.4keV, was found in the ~SMg(p, ~)26A1 reaction.

1. Introduction. The first relatively extensive experimental survey of (p, y) resonances below E~ = 500 keV in hght nuclides has been performed by T a n g e n Sl). Since then separated isotopes have become available and the measurements have been extended to higher proton energies z)18). In several of these later investigations the proton energy resolution and, consequently, the precision in the resonance energies reported, has been low. In some reactions the experimental error was only slightly smaller than the average distance of resonances, which makes the proper classification and tabulation of these resonances difficult. In the present investigation the resonance energies have been measured of 81 resonances for target nuclides in the 1OF through 83S region and for proton energies up to 850 keV. The average experimental error amounts to 0.24 percent. The work was started mainly to obtain a good calibration for the analysing magnet. However, it appeared that without very much more work the whole A -- 19-33 region could be covered.

Protons were accelerated with the Utrecht 850 kV Cockroft-Walton generator and analysed with a 90 degree magnet of 20 cm orbit radius. The magnetic field was measured with a nuclear resonance gaussmeter. The gamma-ray yield was determined with a scintillation counter. If a resonance at proton energy E is observed at a gaussmeter frequency v one has the relation v ~ - : K E , in which K is the calibration constant of the magnet. This constant was determined by observation of a number of resonances with energies accurately determined by others (see § 3). 2. E x p e r i m e n t a l procedure.

-

-

600

-

-

ENERGY MEASUREMENTS OF PROTON RESONANCES IN LIGHT NUCLEI 601

Of course, the relation v2 = K E is not relativistically correct. If, however, it is assumed that the calibration energies used were corrected for r~lativistic effects, the errors made in applying the non-relativistic relation both in the calibration and in the measurement of a resonance energy, not used in the calibration, cancel to some extent. The remaining error, being several times smaller than the experimental error in the whole region of proton energies considered here, can then be neglected. All measurements were performed with targets which were several times thicker than both the beam energy spread and the natural width of the resonance. Actually, the natural width is negligible for all resonances but for those in the F19(p, ar) reaction. For thick targets the resonance shows a fairly steep low-energy edge, a more or less flat top and a gently .sloping high-energy edge. The difference in steepness of the front and the back slopes is caused by the energy straggle introduced by the fact that not all protons having penetrated in the target to a certain depth have lost the same energy. It can easily be proved that the resonance energy is given by the point on the low-energy slope where the yield has risen to half the maxim u m value, if it is assumed that the beam energy spread at the surface of the target is a symmetric function, and that the target is infinitely thick. The errors introduced b y incomplete fulfilment of any of these two conditions are several times smaller than the error (see below) assigned to the measured resonance energies. Most targets were prepared b y evaporation in vacuo of the element or of a suitable compound onto 112 m m copper backings. In this way targets of CaF2, NaBr, Mg, MgO, A1, SiO2, ZnsP~, and ZnS were obtained. Also enriched SiNe, 2~Ne, 25Mg, 26Mg, 29Si, 80Si' and Cd38S targets have been used, obtained from the Atomic Energy Research Establishment, Harwell, England. The neon targets were of the absorption type, made by bombarding a nickel backing with the mass separator beam. Targets of the latter type were also kindly supplied by the Laboratorium voor Massaspectrografie in Amsterdam. Carbon build-up on the target presents a special problem in precision measurements of resonance energies. This effect was very much reduced by the use of a suitably designed cold trap in front of the target, and b y making exclusive use of freshly prepared targets. By remeasuring the first resonance after a run consisting of measurements on several resonances possible carbon build-up can be detected through a shift of the resonance energy. All shifts observed were several times smaller than the error finally assigned to the measured resonance energies. The steepness of the low-energy slope of a resonance is a good measure of the quality of a target. For a perfectly homogeneous thick target and for an infinitely narrow resonance the steepness is determined only by the beam energy spread. With narrow energy defining slits of equal width s

602

J.

KUPERUS,

P. J. M. S M U L D E R S

TABLE

AND

P. M. E N D T

I

Measurements of the magnet calibration constant (in MHzS/MeV). See T a b l e II for the n u m b e r i n g of resonances. Resonance

Group a Ref. 31

2SNa 2 5 24Mg 2 2SMg 7 2eMg 3 27AI 4 aosi I alp I 2 3

951.I 948.6 949.7 959.1 951.0 949.0 944.5 945.4 943,0 947.5

Resonance

4- I0 4- I0 4- I0 4- 12 4- 5 4- 8 4- 10 4- II -_5. 1 l 4- 11

2~AI

6 7 8 9 I0 II 12 13 14 15 16 17

Group b Ref. 3 945.0 945.2 943.7 944.7 945.3 946.9 946.0 945.3 947.6 946.5 946.4 946.1

444444444444-

Resonance

I.I I.I 2.4 1.0 1.0 2.2 0.9 1.9 1.5 1.2 1.2 0.8

Group c Ref. 17-21

23Na 2 5 24Mg 2 ~'SMg 7 2eMg 3 97A1 4

947.8 946.9 946.5 949.4 944.3 947.3

444444-

2.0 1.5 1.5 1.5 1.0 1.8

Resonance

Group d Ref. 1

24Mg 3

9 4 4 . 3 4- 1.5

group

average

internal error

external error

final error

a b c d

949.3 945.7 946.4 944.3

2.8 0.3 0.6 1.5

1.2 0.24 0.8 --

2.8 0.5 0.8 1.5

Final average : 945.9

0.4

0.4

0,4

(in mm), placed at the entrance and exit of the analysing magnet (r = 20 cm), the beam energy distribution at the target can be regarded as triangular with a base width equal to sE/200. For this ideal case the steepness of the low-energy slope of a resonance, expressed e.g. as the interquartile range, i.e. the energy interval between the points of 25% and 7 5 ~ of the maximum yield, is given by AE = sE(! --½%/9.)/200. For all resonances the interquartile range as actually observed, AEobs, was compared to AEtheor. For calibration purposes only those resonances were accepted for which the ratio/IEobs/AEtheor came out smaller than 2. The error finally assigned to a measured resonance energy, apart from the error in the calibration constant, was taken equal to AEobs. This must be considered as a quite conservative limit, amply taking care of all sources of error mentioned above. Measurements performed at different times and with different targets on the same resonance never differed by more than this error. Only for the 18F resonances numbered 2, 3, 5, and 6 (see Table II) which have a large natural width a smaller error has been taken, corresponding to a frequency error of 20 kHz. In Fig. 1 the 453 keV 26Mg(p, 7)27A1 resonance is shown as measured with slits of 0.75, 1.5, and 3.0 mm, respectively. It is seen that the halfmaximum yield points coincide within 0.1 keV. The values of AEobs/AEtheor

ENERGY MEASUREMENTS OF PROTON RESONANCES IN LIGHT NUCLEI 603

are 1.0, 0.8, and 0.65, respectively. That for the wider slits these values come out smaller than unity, indicates t h a t the wide slits are not completely filled b y the beam. In all measurements reported below slits of 0.75 mm width have been used.

f

/~._~.

"Mg(p,.y)'kl

. U 2 " . " ~ "x.

gamma-ra~ ~/ / y , ld " Iii f (counts) Vl.~,;

L~

~

,,s3 , , , ESoNmcE

"x~

at variable slltwldth ¢ ~.

.~..,.x x~,,~

.--

-.....

.%.

/'

t

/i,

A 1~

mm

--.~--....

I#

. x

500

o f

~ PROTONENERGY(keV)'

'

'

'

I

455

,

,

,

,

I

460

,

,

i

,

I

465

Fig. 1. G a m m a - r a y yield curves m e a s u r e d at the 453 keV 26Mg(p, y)27A1 resonance w i t h e n t r a n c e and exit slits of the analysing m a g n e t b o t h equal to 0.75, 1.5, and 3.0 m m , respectively. The h a l f - m a x i m u m p o i n t on t h e low-energy slope indicated b y an arrow is seen to be almost i n d e p e n d e n t of slitwidth.

All resonances below E~ ---- 350 keV and some resonances in the 350-425 keV interval were measured with the H2 + beam. It has been remarked by several authors 3)6) t h a t this introduces an additional broadening of the front slope of the resonance, while also the resonance m a y be shifted to slightly lower energy. The second effect has also been observed in the present work but is certainly smaller than 0.1%. The first effect is taken into account automatically by the procedure of error assignments indicated above. Of course, the mass of the electron in the H2 + ion has to be considered in the comparison of H2 + and H I + resonance energies. 3. Calibration and results. All measured resonance energies are given in Table II, second column. The resonances marked with an asterisk were used for the determination of the magnet calibration constant K. From each measured resonance frequency and the corresponding reference energy given in column 4 a K value was computed with an error compounded from the observed inter-

604

J. K U P E R U S ,

P. J. M. S M U L D E R S

TABLE

AND

P. M. E N D T

II

Measured proton resonance energies. The resonances marked with an asterisk have been used for calibration purposes. The letters A through G in column 3 give a rough indication of the relative resonance strength. Resonances in.class A are on the average 10 times s t r o n g e r t h a n those in class B etc. Initial nucleus

Present experiment (in keV)

Relative resonance strength

I 2 3 4 5 6

226.9 -I- 3.4 340.6 -4- 0.9 484.2 -4- 1.0

E B B

667.6 -4- I.I 838.9 -4- 1.3

A B

21Ne I

766.1 4- 1.8

E

~Ne 1 2 3 4 5 6 22Na I 2* 3 4 5* 6 7 8 9 24Mg I 2" 3*

431.0 436.9 480.1 639.8 662.3 725.5

1.3 1.3 1.0 1.6 1.7 1.2

F E D D E E

308.4 4- 0.5 375.2 4- 0.9

D F

511.4 591.1 675.6 737.9 743.0

-4- 0.6 -4- 0.6 4. 0.9 4- 0.7 -4- 0.7

D D D E R

222.9 4- 0.5

418.7 -4- 0.5 823.5 -4- 1.4

F E E

222 -4- 1 2i) 417 4- 4 s*)

225.5 -4- 0.2 so) 418.4 -4- 0.5 20) 824.9 -4- 0.4 *)

I 2 3 4 5 6 7* 8 9 I0 II 12 13 14

316.4 389.3 435.2 495.6 501.4 513.4 532.4 564.6 592.3 655.5 684.7 722.9 774.7 811.2

-4- 1.8 -4- 1.7 -4- 1.3 -4- 1.4 4- 1.4 -4- 1.5 -4- 0.6 4- 1.5 -4- 1.6 -4- 0.9 -4- 0.9 4- 1.8 4- 1.8 -4- 1.3

E D D E D E F D D E D D D D

310 392 430 492

315.7 391.5 436.5 495.6

-4-44444-4-

15 82) 15 22) 1522) 1522) 15 sz) 15 22) 15 22)

l 2 3* 4 5 6 7

294.1 338.7 453.4 661.8 718.5 809.4 840.7

4- 2.8 -4- 0.9 4- 0.6 -4- 0.7 -4- 1.2 -4- 0.9 4- 1.9

E E D D D D C

290 4- 3 si) 300 -4- 15 ss) 336 -4- 15 21) 338.5 -4- 0.5 2o) 340 4- 1523) 343 4451 4- 2 ai) 454.2 ± . 0 . 3 20) 458 -4- 1523) 450 4662 -4720 4813 4840 ±

10sa) 1032) 10 22) I0 32) I0 22) 10 22)

*2F

~2Mg

2eMg

-44. -444. -4-

M e a s u r e m e n t s (in keV) b y others 222 -4- 2 s*) 339 -4- 2 21) 479 4- 4 al)

224.4 340.4 483.1 596.8 671.6 834.8

.4- 0.4 4- 0.4 -4- 0.5 -4- 1.0 4- 0.7 + 0.9

i9) is) is) 21) 9,) z*)

250.8 307.8 373.5 443.8 510.9

4- 0.2 4- 0.3 4- 0.4 -4- 0.6 -4- 0.6

17) i7) 17) 17) 17)

340.5 -4- 0.3 7) *2) so) 483.5 _ 0.3 7)

765 9)

636 2a) 660 aa) 255 310 375 445 510 594 675 740 744

-4- 3 2i) -4- 3 s*) + 4 s*) -4- 5 21) -4- 5 s,) 5) 22) 5) 5) s)

-4- 3 -4- 4 -4- 4 4- 5

21) 21) 2*) 2,)

508 4- 7 s*) 525 -4- 6 a*)

675 12) 720 16) 777 16) 820 l,)

-4- 0.7 + 0.7 4. 0.7 4- 0.7

2o) 20) 2o) 22)

321 395 441 501

513.4 4- 0.7 ao) 518 530.4 4- 0.7 2o) 580 607 667 688

-4-44-4-

15 22) 15 22) 388 -4- 15 22) 15ss) 1522) 494 4- 152~)

+ 1522)

510 -4- 1522)

-4-444-

563 588 650 683 722 777 812

15 22) 15 22) 1522) 152a)

ENERGY

MEASUREMENTS

OF

RESONANCES IN LIGHT NUCLEI

PROTON

605

T A B L E IT (Continued) Present

Relative

experiment

resonance

(in keV)

strength

2 3 4* 5

224.1 ~ 0.7 294.8 4- 4.0 327.5 4- 0.8 405.3 4- 0.7 446.2 -4- 0.5

G G F F

6*

504.0 4- 0.5

F E

506.1 4- 0.5

E

611.0 631.5 653.9 678.3 730.7 735.1 742.4

F D D E D D E E

Initial nucleus .'VAl

1

7* 8* 9* 10" 11" 12" 13" 14' 15" 16" 17"

4444444-

0.6 0.6 1.2 1.2 0.7 1.5 1.0 759.9 4- 1.0 766.7 4- 1.0 773.0 + 1.0

D D

M e a s u r e m e n t s (in keV) b y others 225 295 325 404 443 504.5 506.5 612.4 632.3 654.3 677.6 730.6 735.6 741.1 759.4 766.3 772.8

4- 3 st) 4- 3 81) 4- 3 81) 4- 3 81) 4- 5 .'1) 4- 0.3 s) 4- 0.3 .') -4- 1.0 s) 4- 0.3 s) 4- 0.3 s) 4- l.OS) -4- 0.3 .') 4- 0.3 5) 4- 0.7s) 4- 0.3 s) 4- 0.3 s) 4- 0.3 s)

226.3 294.1 325.6 404.7 438.5

44444-

1.5 0.5 0.4 0.4 0.5

504.0 4- 0.~ xg) 609 630 652 677 728 733 738 757 764 771

444-4± 4± 444-

1.2 xo) 1.3 xo) 1.3 lo) 1.41°) 1.5 xo) 1.5 lo) 1.510) 1.5 lo) 1.5 xo) 1.5 lo)

asSi

I

368.9 4- 0.7

D

367 4. 4 sl)

367 4- 2 se)

.'gSi

1 2 3 4

326.4 415.3 697.5 730.1

4-+ 44-

1.2 1.3 0.7 1.2

E D D E

326 4- 3 .'l) 414 4- 4 sJ.)

326 .'4) *5)

50Si

1* 2 3 4 5 6

498.3 619.6 669.8 759.3 776.4 834.2

+ 444. 44-

1.0 1.2 1.0 0.9 1.0 1.3

E D F E D E

499 4- 5 sl)

.'lp

I* 2* 3* 4 5 6

354.8 438.7 540.9 641.3 811.2 820.0

444444-

0.7 0.9 1.1 0.8 1.0 1.0

F F • D E D E

355 + 4 sl) 440 4. 5 sx) 540 ~ 6 .'1)

I 2

579.8 4- I.I 587.3 4- l.l

D D

579.8 4- 1.5 34) 587.4 4- 1.5 84)

1

446.5 4- 315

E

2

507.1 4- 1.0

D

449 4- I0 38) 513 ± 10 ss)

.'8S .'.'S

is) 18) is) 18) is)

414 s4) .'5) 11) 693 s4) *~5)xl)

729 .'4) ss) 11) 500 625 678 760 775 840

11) 11) 11) 11) 11) 11)

440 540 648 816 825

15) lS) 15) lS) s7)

*'.') .'S) .'.') i4) ss) "7)

quartile range and the error given in the reference energy. Altogether twenty-nine reference energies were used for the calibration, of which ten are given by T a n g e n 81), twelve by A n d e r s e n e.a.8), six by H u n t , H a n c o c k and co-workerslT-~l), and one by A g e r - H a n s s e n e.a. 1). Weighted averages of the K values were then computed in groups (see Table I) according to the authors from which the reference energies were taken, and an internal and external error was determined for each group average. It is seen that only for the reference energies given by H u n t e.a. the

~06

J. KUPERUS, P. J. M. SMULDERS AND P. M. ENDT

external error comes out slightly larger than the internal error. In all cases the~largest of the two errors was taken as the final error in the corresponding group average. The error in the A n d e r s e n group average has been taken somewhat larger than both the internal and the external error to account for a 0.02% error in the 990.8 keV ZTAl(p, 7) resonance used by them for calibration, and for a 0.02% error resulting from possible non-linearity. Finally, a weighted average was computed of the group averages yielding: K ---- 945.9 4- 0.4 MHz2]MeV. The external and internal error of this final average value were found to be equal. This calibration constant was used for the computation of all resonance energies given in Table II, column 2. To the errors assigned to the resonance energies contribute the experimental error (interquartile range) and the error in the calibration constant. The ZlNe and 2~'Ne measurements contain an additional uncertainty (not included), because it was not known how far the neon ions had penetrated into the nickel backing in the mass separator bombardment. From the calibration constant the orbit radius in the magnet can be found yielding r = 20.004 + 0.004 cm, in excellent agreement with the design value: r = 20 cm. In principle saturation of the magnet might cause a deviation from the proportionality between the average magnetic field on the orbit and the field at the position of the gaussmeter probe. No systematic difference, however, has been found for K values from high-energy and from lowenergy resonances. Actually the magnetic field for 850 keV HI + and Ha + ions is 6700 and 9400 oersted, respectively, which is still far from saturation. Some indication has been added in Table II column 3 as to the intensity of the resonances. Classes A through G roughly decrease in intensity by consecutive factors of 10. In all measurements the same counter was used at the same distance from the target, at an angle of 55 ° to the proton beam direction, the latter chosen to average out cos20 terms in angular distributions. All measured intensities were corrected for differences in chemical and isotopic composition of the targets used, and can thus (if differences in dE/dx are neglected) be interpreted as the relative resonance strengths. However, discriminator settings have varied widely and furthermore the composition of the 21Ne and 22Ne targets was badly known, which made us decide to present only order of magnitude intensities. The ~SNa resonances (1) and (4) were not observed in the present experiment. These resonances are indicated by T a n g e n as weaker than resonance (3) which just barely could be detected. The 19F resonance (4) is very broad; no a t t e m p t has been made to determine its energy. The Z2Ne(p, 7)28Na reaction shows t h r e e . s t r o n g and three weak resonances (see Fig. 2). Two of the stronger ones were found by B r o s t r 6 m , H u us and K o c h 9), and were later investigated in some detail by T h o r n t o n, M e a d s and Collie3a). The other four resonances, at 431.0-¢-. 1.3,

ENERGY MEASUREMENTS OF PROTON RESONANCES IN LIGHT NUCLEI 6 0 7

436.9 4- 1.3, 480.1 4- 1.0, and 725.5 4- 1.2 keV, were first observed in the present investigation with separated targets obtained both from Harwell 2500

i

i

I

I

I

(3) 22L

•

t

,23L ,

~e~, p , y )

(4)

r~o

,(5)

2000

x~

¢J

A

1500

D .J hi 1000


i ,°

0

200

11

300

,o,

400

500 600 700 BOO PROTON ENERGY ( IN keV)

Fig. 2. G a m m a - r a y yield c u r v e of t h e 2~Ne(p, 7)~SNa r e a c t i o n . T h e b r o a d p e a k a t a b o u t 320 k e V r e s u l t s f r o m 19F c o n t a m i n a t i o n . T h e r e s o n a n c e s aaumbered 1, 2, 3, a n d 6 h a v e n o t b e e n o b s e r v e d before.

25Mg(p,y)2~AI 5 0 1 . 4 keV

200

I

GAMMA-RAY YIELD

(counts)

( E y =4-BMeV)

4 9 , 5 . 6 keY 5 1 3 . 4 keV

100

o

I 490

J

I 500

,

I 510

- PROTONEI~ERGY(keV) i

520

Fig. 3. G a m m a - r a y yield c u r v e of t h e 25Mg(p, 7)26A1 r e a c t i o n in t h e E ~ = 4 9 0 - 5 2 5 k e V region. T h e n e w r e s o n a n c e a t 501.4 k e V is well r e s o l v e d f r o m t h a t a t 495.6 keV.

and from Amsterdam. The resonances numbered I through 4 (see Table II) have also been seen, with the same relative intensities, in bombardments

608

J. K U P E R U S , P. J. M. S M U L D E R S

A N D P. M. E N D T

of natural neon gas. In this case the m a x i m u m voltage of the generator was not high enough to observe resonance 6, while the resonances 4 and 5 could not be resolved. The 25Mg resonances at 495.6 and 501.4 keV have not been separated before. The assignment given here can b e regarded as unique, however, because these resonances have been observed from several targets with constant relative intensities. In fig. 3 a 25Mg(p, 7)26A1 yield curve is shown for the E~ = 490--525 keV region. The 8~S measurements have not been extended above 550 keV. At least ten resonances have been observed in the 550-850 keV region but the target was not quite thin enough to resolve these fully, while also part of them m a y have to be attributed to 34S.

Acknowledgements. This

investigation is part of the research program of the "Stichting voor Fundamenteel Onderzoek der "Materie", and was made possible b y financial support from the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek". Several of our colleagues have given active help during the measurements. Especially we want to thank Dr. C. v a n d e r L e u n , who first surveyed the Z2Ne(p, 7) yield curve. Received 5-3-59

REFERENCES 1) 2) 3) 4) 5) 6) 7) 8) 9) I0) ll) 12) 13) 14) 15) 16 17 18 19 20 21 22 22

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E N E R G Y MEASUREMENTS OF PROTON RESONANCES IN LIGHT NUCLEI 6 0 9

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