P H YSICAI REVIEW VOLUM E 133, NUMB ER 3B 10 FEBRUARY 1964

0"(p,~)N" and 0"(p p') 0"*Differential Cross Sections*

R. L. DANGLE, ) L. D. OPPLIGERpf AND 6 HARDIE)

Utsisersity of Wiscolsil, Madisol, Wisconsirs

(Received 5 September 1963)

The differential cross sections for the inelastic scattering of protons by 0"and for the 0"(P,n)N" reactionwere measured for E~ from 7.18 to 12.90 MeV. A differentially-pumped gas scattering chamber with a solid-state detector was used. Data at 8&,b =166' 00' were taken in energy steps ~& 5 keV and with a target thickness~& 3 keV. Seven other excitation curves were taken for 7.18« E~~& 10.5 MeV at Hl,b=133'48', 116'34',100' 19', 86' 24', 61' 36', 51' 25', and 33' 47'. These curves were taken with energy steps « 23 keV depend-ing upon the width of the resonance structure. The target thickness was ~& 3 keV. Data were obtained onthe alphas leaving N" in its ground state and on the inelastic protons leaving 0'6 in its 6rst, second, third,and fourth excited states. Evidence was found for the existence of 36 levels in F'~, the compound nucleus.Below E„=10.5 MeV, center-of-mass angular distributions were picked from the eight excitation curves and6tted with Legendre polynomials. Levels in F'7 at the following excitation energies were assigned totalwidths, spins, and parities as indicated: E,=7.73 MeV, I; =0.178 MeV, J~=&+; 8.07, 0.104, -', +; 8.2,0.706, —,

') 8.381 0.011, —', ; 8.42, 0.0421 s+; 8.72, 0.188, -',+; 8.95, 0.122) g, 9.16) 0.188, —,'+; 10.05, 0.2821 —,'.

All parity assignments except those for the levels at E,=8.95 and 9.16 MeV are based on the assumptionthat the F'7 level at E,=8.2 MeV is the mirror of the q level in 0'7 at E,=7.72 MeV.

1000-

OI6{ ) N13

0 (p, p') 0*

800-7.12 I

"6.92 2+

-6.14 3"6.06 0+

8 400- ptos

200-

12 22 32 42 52 62 72 82 92CHANNEL NUMBER

102

FIG. 1. Pulse-height spectrum obtained with solid-state de-tector at E„=8.87 MeV, gl,b=166'. The groups labeled P; referto inelastic protons leaving 0'6 in its ith excited state. The grouplabeled 0. corresponds to alphas leaving N" in its ground state. Theelastic proton group is not shown.

~Work supported by the U. S. Atomic Energy Commission.f Present address: University of Sao Paulo, Sao Paulo, Brazil.f Present address: Western Michigan University, Kalamazoo,

Michigan.f Present address: Armour Research Foundation, Chicago 16,

Illinois.' R. A. Laubenstein, M. J. W. Laubenstein, L J. Koester, and

R. C. Mobley, Phys. Rev. 84, 12 (1951).2 R. A. Laubenstein and M. J. W. Laubenstein, Phys. Rev. 84,

18 (1951).F. Eppling, Ph.D. thesis, University of Wisconsin, 1953

(unpublished).4 S. R. Salisbury, G. Hardie, L. Oppliger, and R. Dangle, Phys.

Rev. 126, 2143 (1962).' S. R. Salisbury and H. T. Richards, Phys. Rev. 126, 2147(1962).' G. Hardie, R. L. Dangle, and L. D. Oppliger, Phys. Rev. 129,353 (1963).

INTRODUCTION

S EVERAL investigations of the level structure ofF'~ have been made at Wisconsin using protons

elastically scattered by 0".' ' The data obtained pro-vided approximate resonant energies and widths for

levels in the energy region E~=0.28—13.6 MeV. Aphase-shift analysis of the data from E„=2.0 to 7.6MeV yielded additional level parameters in this energyregion. ' Since other particle channels are open aboveE„=5.5 MeU, the phase-shift analysis became un-certain and was discontinued at E„=7.6 MeV. Pre-liminary data were taken on these other open channelsbut the data were not extensive enough to allow a con-tinuation of the phase-shift analysis. However, theo8-resonant elastic data were reasonably well 6tted byan optical-model analysis. '

This paper reports a detailed investigation of theOts(p, n)Nts reaction and the inelastic scattering ofprotons by 0".Differential cross sections were meas-ured at el,b=166' for E~=7.18—12.90 MeU and atseven other laboratory angles for energies up toE~=10.5 MeV. Angular distributions obtained fromthese excitation curves were 6tted with Legendrepolynomials. Level parameters obtained from theLegendre polynomial analysis in the energy regionE„=7.5—10.5 MeV are reported.

EXPERIMENTAL

Apparatus

A tandem Van de GraaG accelerator was used inconjunction with the small-volume diGerentially-pumped gas scattering chamber described in Refs. 4 and8. Only modi6cations to the chamber made for thisexperiment will be described here.

During preliminary work a leakage current of5)&10 "A was noted in the charge collecting system.It was found that this current was caused by positiveions striking the back of the collector cup. The positiveions came from the VacIon pump" which was used toevacuate the collector cup region. A baQie placed in thethroat of the pump eliminated the current. Cross

' Varion VacIon pump, Model No. 911-0000.

B647

D A N G I.F. , 0 P P L I G E R, A N D H A R D I E

sections measurements" which were made with thischamber before insertion of the baffle may be syste-matically low by as much as 0.5 jo due to the leakagecurrent.

n order to obtain the energy resolution necessary toseparate closely spaced inelastic proton groups, the de-tecting system previously used" ' was replaced by onehaving a smaller angular acceptance ((3.6') and em-

p oying a solid-state detector. With this arrangementit was possible to resolve almost completely the in-elastic proton groups corresponding to 0"being left inits 6rst and second excited states. These two states areseparated by only 80 kev. Other inelastic proton groups

P~ 9)

10

0Ol

r M~e4rW rm ~

O

I

ty2O

8La IOO l9

l

—.20

:—IO

8 - Ii6 34.I

0E

8~ l33 43'(

) I :—--IOI

PN{o')— "20

~ tg V

'N

.,r. r ~ 0

20"

IO-.

8 4334 47'

8~-5I.25'

10

0

IO-

070

8~ l66 00'

75 &0 8,5 9.0 9.5 IO.O I0.5

E&LAB) MOV

rr0

vii EO. -

0'o ~

~ ~'4 r~ ~

~ ~

8~-6I 36'

f~r r

8 86 24'~ ~ ~ I

~ *40

I I

8~ IOO' l9'

r .rr row~ ' AI I

8 . II6' 34'

ir t c r

8~4I33 48'

.IO

0

lO

41-0

"IO

FIG. 3. Excitation curves for protons leaving 0'6in its second excited state.

the pulse-height spectrum. This difhculty was overcomeby exploiting the difference in dE/Ch for equal energyprotons and alphas. In these regions the proton andalpha groups were separated in the pulse-height spec-

"30

IO"——i

0 ,tg

70 7+ QO

rr r 0

8~*I66 OO'

9D Q,5 10.0 Iog

Ep LAB) MeV

FIG. 2. Excitation curves for protons leaving 0" inits first excited state.

and the alphas from the 0"(p,n)N" reaction were com-pletely resolved. Pulses from the solid-state detectorwere analyzed using a multichannel pulse-hei ht- eiganalyzer. A pulse-height spectrum is shown in Fig. 1.

20-—

IO

~I

~4334 47

—8~ 5l'25'

7yJ

8~*6I 36'

—"20

IO

0E

—-"20f

I

.—' —:—"IO

Procedure

The relative energy of the alpha particles and the in-elastic protons varies strongly as a function of angleand bombarding energy. Because of this, there wereenergy regions in each excitation curve where the alphagroup overlapped one of the inelastic proton groups in

«L~30"

20"

10- ——- -:

~ ~ ~

0

Ep (LAB)

8 86'24'

~ ' ~

RO R5

MeV

IGO IO.5

E.A. Silverstein, S.R. Salisbury, G. Hardie, and L.D.OppligerPhys. Rev. 124, 868 (1961).

FIG. 4. Excitation curves for protons leaving O"in its second excited state.

Uncertainties

The center-of-mass differential cross section is givenby

ooo

oo

8~I&(00 9'do. I' sine(sin8) s—(c,m. )=

~ ~cos(P—iI),

dfI StsG (sing)20„~'Jep'oo

whereN~~ 06' 3h'to" ~ ~

~ ~ ~,+~s g ~-1-»ssin(P —ti) =sin&

I1+

m,es, k t1s, Z,J

~ o~ e ~ ot

"20 gc$

„-'I-\

ooolet ~' lss'ss'Y is the number of particles detected, E is the numberof incident protons, e is the number of target nucleiper cm', G is the geometric factor of the counter aper-ture system, ' 8 is the laboratory angle of observation,

~ o~o "L;

~eN"

0

I

&v

thv

0 ~ /75 QO 85 90 95 KN Q5

20- ———

P~ {I }~~ l55'00'IO.

— "IQ

oat ~ ~~tt ~ y ~ o tgotoeoo~ tteooo f

~ ot ~~ \ o e q~tooeotet oooeo

0lo"

8~ 15I4 25'FIG. 5. Excitation curves for protons leaving 0'6in its third excited state.

~ t tt ~ ~ ~ ~

~ ' t ~ ta~

o toot ~ o octet, ~ t ~ ~eo ~ ' to ~

"IQ

8~m 6I'M t~ toot

~ t t Ot a~at ty ~ t tat t~ot ~

~t oo ~ eeet tt ~ tl toooo eat«'o ™e o+ttoeo t 8 e oo

grum by varying the target gas pressure or by placinga thin nickel foil (0.0005 mm) directly in front of thedetector. As can be seen in Fig. 1, pt and ps were notcompletely resolved. The groups were decomposedgraphically by plot ting each pulse-height spectrum overPt and P&, and drawing a symmetric curve for the morewell-dehned group. The yield for each group was thenread from the plots. This decomposition introduces anuncertainty of approximately 0.2 mb/sr in the crossSeCt1011S f01 Pt a11d Ppr

IO"s4

8~1~864 RA'~ ~

oe 'o'oetetttt ~ ~~eeet tto eoStStt tt \tt ~0— o oe ~

-totN toot~ I et+ ~ eo ~

8L AI "IQO I9'' "10

cS

~t ' tootst ~ ~ tttttattoo tt

oo o ooo ' oooo~ Ceooooto ~ototeop

~ oot oe~ ~ oe» oet

Q

8LAI ' II64 M'~ ~ ot

~ to eot ~ ~ ee tattoo t otooteeet

tpo oooooto tot

'IQ4IQ 48' ~oo

~ tete'e~ cF t» o~,o eo

~ i er~ ' ' oat

too to ettagto oo ett

~ tt~ ~IQ"«I66 00'

4%~

80 R5 IOO

Ei1Lsa MeV

0Lo

FIG. 7. Excitation curves for protons leaving 0'6in its fourth excited state.

~ t

and g is the corresponding center-of-mass angle.Q= (s1st+ms)c' (ms+ad—4)c', and tet, ms, tns, and r1sq arethe masses of the incident projectile, target nucleus,reaction particle, and residual nucleus, respectively.

The uncertainty in S is &0.3%, the uncertainty ine is &0.14%, and the uncertainty in G is +0.9%. Theuncertainty in the laboratory scattering angle is +6'.The statistical uncertainty in the yield varies from~1.2% at the largest cross sections to ~25% at thesmallest cross sections. The background subtractionintroduces an uncertainty in the cross sections of up to5% in the lowest 100 keV of each excitation curve.Other@rise the uncertainty due to the background sub-traction is less than 1%.

In addition, because of a 0.26% Hs impurity and

~o'o ~ t~ «tt \~"tt ~

~ ~

0

I0 .—

I'5I 25' P+ o~ 0

~ ~ te\et ~ I ~ ~ ~ ~' ~

~ ~ o ~

~ ~ ~

CS

"io bot ~,

*we~ ~ ~o

~ ~ to t ~4+ ~~6P56' ~ o ~

~ ~

Oe 0

to~e hj1

taboo ~

lo"t~~ 864 2h'

t opt

t o

~t

Fzo. 6. Excitation curves for protons leaving 0'6in its third excited state. ' E. A. Siiverstein, Nncl. Instr. Methods, 4, 53 (1959),

0''(p a)N" AND 0's(P P')0 "s CROSS SECTIONS

8650 DANGLE, OP PL ?GER, AN D HARD I E

Ilo

1 ~

~ ~ ~

~ ~~»1111~ ~ ~

oo«»oooo 1

8L~=33 47~ O ~ Oo»a 11

~1111

1 o~ ~ ~ ~ o~ ~ ~ I

~ ~ oo ~1«~1 111111111Oa 1~ '~111111I ~ 11OOOO 11

-- IO

~1!Ii

t~1 ~ Ooo I~oo, go oo ~

~~~ ~

I ~ ~ ~ '~~oooa ~ 11 ~

~ ~

~ oo ~~ ~ ~ ~

8LAB= 5l' 25'~ ~11~ 11 11 ~ ~ ~ ~ ~

~ ~~1 ~ ~ ~ ~~ a aaa ~ 1 ~ ~

8„,= el'36'

"lo

lO-

ooo 1~ ~

I

oo1~

~4

J ~ oo~ ~j o

~OO ~ ~ ~ ~~oo «1 ~1 ~ oo1 ~ ~««»» l«««o ~1 ~ Oaa a OOOO pOO ~ ~ 1 ~ ~ ~ ooooo~ ~ Oo g «ao O ~ ~ I ~

8 =86 24oo~1

~ ~o

~~o ~~ 1 ~11 ~ oaI 11~ ~ ~

~ao ~

~ I + ~ OO ~ ~ ~ 1 ~ ~~1~ ~1 a ~ aa a 1 a a 1 ~ ~

8~~= loo l9-- lo

C3

«ooa+ooo J~ 11aV& ~

~1 aOJI~ ~

~1 ~ ~ ~ 1 11 11~ ~ I ~ ~ ~ 1 ~ ~ ~ ~ 11oa ~~o ~ ~ ~ 11~11,~ ~

~1 ~ 1~ ~ 11 « ~ 11 ~ II

~ ~ «111aa adaoa

b CI— 0

b ~ lo"8A =ll6 34

~1 taa ~ ~ 1oo«J~ a ~ ooo» o«1 Choo ~'~ ~

oo ao ~ .1~o 1I I

~ oo 'oo ~ too ~ ~o 1~ ~ o oooo 1~~ + Oooo ~ OOdo ~ .ooo« ~ ~ 11 ~

-- lo

8LAsP ~

1 q ~ oo+o ~ ~ ~ ~ ~1~o ~ ~ ~ ~ oo1 ~ 1 11 ~ 111 11 ~ ~ ~ ~ ~ 11~ ~1 1« ~~ 11 ~ ~ ~ ~ ~~ 1 a 0

lo-.—

07.0 7.5 8,0

8„„=lee. OO'

l0.08.5

E (LAe) MeV

I~

9.0 9.5

a

I0.5

FIG. 8. Excitation curves for alphas leaving N" in its ground state.

a 0.26% N2 impurity found after the e&,b——166'

excitation curve was completed, these cross sectionsare low by 0.52%. Since the H& impurity was then.removed all other cross sections are low by 0.26%(the N2 impurity). The electrolytic oxygen used as thetarget gas in this experiment was purchased from thesame source" as that used in previously reported ex-periments. "Since no attempt was made to remove a

' General Dynamics Corporation, Liquid Carbonic Division,San Carlos, California.

N2 or H2 impurity, cross sections measured in theseexperiments may be low by 0.52%.

The analyzing magnet used to determine the incidentproton energy has been calibrated by Dagley et al."The calibration constant is believed to be known to&0.1%.However, sharp levels near E~=8 MeV havebeen observed to shift as much as &6 keV (&0.08%)from week to week. Therefore the incident protonenergy is assigned an uncertainty of +0.13%.

"P. Dagley, W. Haeberli, and J. X. Saladin, Nucl. Phys. 24,353 (196i).

0'e(p, 4)N'' AND 0''(p p')O''' CROSS SECTIONS

BLAS. I664 00' ~e 86424'

20"

IOrI p1

Jo»' r'

r

Ine e

IO"r *

~CC

~ ~ O'e»O~ C

~ ocro»OeW

o%

CP

Io

"IL

'l»a

C »co».

r

o

P4

I.—!»,

0

LCO ~,

0

4 ~ e

8~ l00'l9'

P

.' eo 'o

~6 ~ ll6 54'

8~e *33

E0

($6»SI»55'

bio 5"——2-

4I 0E

5".!Co

04!Q

l5"

IO ..rr

P2

2 '—

7I5 720

o

8LAe l33 48'

l

725 Z30 735

E& LAB) INOV

I ~—0 o er

~' Pl

I IY~ oo ~ ~ ~ ~ ~

»

~6 ~ 6I 56'

0735 &20 725 730 'E35

0

5e ~

Fro. 11.Details of sharp structure from 7.15-7.35 MeV in exci-tation curves of protons leaving 0"in its second excited state.

0 ore»r .'ve«e - - - - - - ~e«~eoc««e«o«oeoovoeeoreooe«

Q5 I IA) I L5 ISO IK5

Ep (LAS) MOV

8LAe 86 24'

~ o» AP ~

0~ ~ ~ ~ «o

~ o» Fo ~~ o

8LAe l004IQ'

2"8 ~ 55 4r'

FIG. 9. Higher energy excitation curves at Slab= 166'. E; refersto inelastic protons leaving 0'6 in its ith excited state and n refersto alphas leaving N" in its ground state.

Results

The excitation curves for E„&10.5 MeU are shownin Figs. 2—8. Figure 9 shows for all reaction groups thecontinuation of the 8q,b= 166' excitation curve. For allof the data, the target thickness was ~& 3 keV. The dataat 8&,b=166' were taken with energy steps ~&5 keV,while at other angles the energy steps varied up to 23keV depending upon the width of the resonant struc-ture. Figures 10-12 display in greater detail the low»o

energy region where the earlier elastic scattering data4show four sharp resonances at E„=7.180, 7.280, 7.287,and /. 305 MeV. Figures 13—18 show angular distribu-tions taken every 8 keV near E„=8.3 MeV where the

Xl ~ ~

0 o«A,

~ ~ ~~ 4»o«go

~ ~~ oo

LCO

o.~ ~ I phoo»

o»o ~

44,I"

eo 41 ~I

0

80le & ll6434'.

»Ce +~ ~ ~

~ ~

8LAe ~ I33 48'

~ e ~

o eogr +0

8' &5I 25'

VI o re Iooo »ceo~ eo

2

I

E

O

Qge»

~ ~~ ~ ~

8LA5 486'24'

6~ 'o ee ~~ ~

8~ 4 6I436'

2-L~EO

'"~ ~

OIe!a

433 47'

C+o ~

8„~4 Sl'25'

~ »C

~ 'I

0QI5 740 725 Z50

Ep (LA8) hNeV

I"~ oer ~ «e» ~

0 «oee Voo ~ ~»

~ ree

720 745 7M 745

E&(Lag MeV

L——~ v er»» 'e ~r-

'ZIS 720 725 'L50 755

Fro. 10. Details of sharp structure from 7.15—7.35 MeV in exci-tation curves of protons leaving 0'5 in its &st excited state.

Fn. 12. Details of sharp structure from 7.15—7.35 MeV in exci-tation curves of alphas leaving N" in its ground state.

DAN GLE, OI'I'L I GER, AN 0 HAk D I E

25-Pl —-fa„p„(cose)

L

25-. P2

35

fOL pL (c08 e)

20-Ep* 8.265 MeV

20-Ep=8g74 MeV Ep~8,265 MeV 30- 8+74 MeV

I5" IS "

Io-,/

n=4 /

IO-

f~~|g~yh ~ 4

25 l

20h*5

X 0 ~ I I I

30 60 90 l20I I

l50 I80 30 60 90 IRO ISO I60

40

E

OSO 6O

I I

90 l20I I

I50 l80

l5-

lo I I I I I I

30 60 90 120 ISO I80

20-Ep*8.282 MeV

Ss „Ep& &.282 MeV 25- Ep~&.29l MeV

IS I5- 20-

Io- 10-a5

IS

20-

0 I I I I I I 030 60 90 l20 I50 I80 30

(I)EOREES)

I I I I

80 90 l20 150 l80

Fzo. 13. Angular distributions over the doublet near E~=8.3MeV for protons leaving 0"in its 6rst excited state.

15 I I I I I I 5 I I I

30 60 90 IRO I50 l80 30 60 90l I I

l20 ISO 180

ee&(OE&REE&)

FxG. 15. Angular distributions over the doublet near E„=8.3MeV for protons leaving 0" in its second excited state. .

data of Figs. 2—8 (but especially Fig. 8) incticate several

closely spaced and interfering levels. All error barsrepresent statistical uncertainties only.

Pl

ANALYSIS

Theory

It is useful for purposes of analysis to express thecenter-of-mass differential cross section for a reaction

Ep~ 8,299 MeV

o„P„(COS

E ~ L307 MeVp

25-

20-Ep ~ 8.299 MeV

P225-

20-

.f.„,( e)I

Ep ~8.307 MeV

IS" IS- l5-

Io-h~3

IO- lo- yh*3 10 "

E

X0

bO 30 60 So l20 .I50 I80

5"

0 I

30I I I I I

60 90 l20 ISO 180

~so0E

OI I I I

V 50 60 90 IRO ISO

I 0 I I I I I

I80 30 60 90 l20 I50 l80

Ep= 8,3I5 MeV. Ep M24 MeV RO - Ep. &.315 MeV RO -Ep ~8,324 MeV

l5- I5-15 " l5-

IO- IO- IO-

5- hi3

I I I

30 80 90t I I

120 ISO l80 30

eelh(oEOREEs)

60 90 IS) I50 I80

5-

0 I I I I I I 0 I i I I t I

30 60 90 IRO ISO 180 30 60 90 IRO ISO I80

e~(oEeREEs)

Fxo. 14. Angular distributions over the doublet near E~=8,3MeV for protons leaving 0'5 in its irst excited state.

FIG. 16. Angular distributions over the doublet near E„=8.3MeV for protons leaving 0'6 in its second excited state.

QII(p, n)N» AND QIs(p p')QII* CRQSS SECTIQNS

TABLE I. Nonvanisbing products of Z coefficients of Legendre polynomials for 0"(p,a)N" and 0"(p,pI)0"*angular distributions.

L=O L=2 L=3 L=4

Isolated levels2

8

Interfering levels; same parity

k5I 5n

1 7

443 7

48/7200/2|

&2/7

72/78/7

36/7648/77

872/740/7

360/77

200/33

200/11

~6+8&36/5+24/5&8/3~16/5+8a24/11

+18/35+72/7+8/21

Interfering levels; opposite parity (+) for 0'6(p, pl)0"* and+2+4

1

1 7

+4/5+36/5

3

5 5

5 73 27 7

+40/3+100/7+40/7&600/9j. &9800/429

in terms of the I,egendre polynomials:

do(nS;—n'S') = (2S+i)-Ik -'

dQ

P BL(ns; ns')P L(c so )f1.

This expression describes the differential cross sectionfor a reaction proceeding from channel o. with channel I cl'c

BL=Z(lJlJ, rsL)Z(l'Jl'J, srL) sin'5p2

(2)

spin s to channel 0.' with channel spin s', k is theentrance-channel wave number, and 8 is the center-of-mass angle.

For inelastic proton scattering leaving 0"in its 6rstexcited state (0+), and for the (p,n) reaction leavingN" in its ground state (s ), the expression for BL overan isolated level can be shown" "to be simply

Ole( ) N13

8-'E&

~ &265 MeV

I3

E0

48 e-Epa &282 MeV

30 60 SO 120' 100' ISO

—&e f (COSe), g LL

S-E&a &274 MeV

ffn~6

.J~ ~

I I I I I I

30 . . SO SO 120 150 180

S ~ E ~ &291 MeV

where b is the resonant phase shift. At every energy theratio of the B~'s is equal to the ratio of the product ofthe 2 coefficients.

In a region where two levels interfere, each BI, is thesum of the terms for isolated levels LEq. (2)j and aterm resulting from interference between the levels.The interference term for two levels denoted by P and

]s12,13

I 'AOI hc'I l4cI f40'

+22(l)JI l„J„,—',L)Z(lg'JI l„'J„,srL)r,r„

I I I I

30 60 $0 120'

ISO ISO 30 SO SO

e«gxeaeEs)

FIG. i7. Angular distributions over the doublet near E„=8.3MeV for alphas leaving N" in its ground state.

&& sinbA sinl„cosC,„.(3)

'4I = 5I &I +IPI.a+I'&, ' IP„,—IP„,', where —the —Ip are

potential phase shifts. Nonvanishing products of the Z

"J.M. Slatt and L. C. Biedenharn, Rev. Mod. Phys. 24, 258(1952).

"A. M. Lane and R. G. Thomas, Rev. Mod. Phys. 30, 257(1958).

DANGLE, OP PL I GER, AN D HARD I E

5

016( ) gl3 .

8a& PiICOS 8)

ON(p, p,)0* :I-fa„s,(cas s)

8-

4-

2

E

0Q

4)4 ,

@s8299 MeV

')n s

t

I I I i I I

50 80 90 120 150 150

Els s 8,315 MeV

E&s 8307 MeV

050

I i

80 90 120

2-

E& s 8.324 MeV

I

150 150

ISO

10-L

E 5-cS

4140

I I I I30 80 90 IRO 150 ISO

Ep~ 8+I MeV

4-

2" hs5

I

0 30 60 QO IRO l50

p&@SMSV

~+

0 30

Ash Ie

s ~st& i J60 90r IRO 150 ISO

4-Ep ~ 9+9 MeV

0 30 60 90 IRO 150 $0

0 I I I I I I I I I I I I

50 80 90 120 150 180 50 80 90 120 150 150

e {DESIIEES)

Ep *IQP5 MeV

-A~6

~/

Ep & 10.41 MeV

FIQ. 18, Angular distributions over the doublet near E„=8.3MeV for alphas leaving N" in its ground state.

coeKcients for both isolated and interfering levels areshown in Table I '4"

For F", the sum over I. in Eq. (1) is limited by thefollowing conditions" "".

I I s 1 1

0 30 60 90 IRO I50 ISO

2-A16

r// ™0 36 60 90 120 150 180III

I

8~(DEGREES)

FH". 20. Sample Gts to angular distributions of inelastic protonsleaving 0" in its first excited state.

Procedure

20-

I5-

10-

, 016( )016+

rEp = 7.60 MeV

n =I~@,pn=2

20

I5-

IO-

LPL (GOS e)L

EP=7.72 MeV

ns2

15MeV

0 (p )N

15-:I- f.a„s(cas 8)

Ep *g,62MeV

Angular distributions were chose@ from the excitationcurves and fitted with a sum of Legendre polynomialsusing an IBM-704 computer. The program minimized

slO

0E

Q

I~/ 1 I

39/ 60 90

Ep = 7.91 MeV

0120 l50 30 / 60 90

/r

Ep* 8.15 M8V

I I I

l20 150 180

10- IO-"~). A-3

~0 30 60 90 120 150 180 0

~A3/r

30 60 90 120 150 180

10-

6-

4"

n=S\

n= 2~1E

4

%ID

00

Ep =881 MeV

A.4

30 60 90 l20 150I 0

180 0

Ep"-+25 MeV

~~A 2 A ~ i~~- e&e~ewe s I

30 60 90 IRO l50 ISO

I I I I I I 0 I

30 60 90 I20 150 180 30

e~(DEGREES)

I I 1

6& 90 l20 150 180

FIG. 19. Sample 6ts to angular distributions of inelastic protonsleaving 0'5 in its Grst excited state.

'4 L. C. Biedenharn, Oak Ridge National Laboratory Report,ORNL-1501 (unpubhshed).

'5 The Z coeKcients used here are related to the Z coeKcientsin Ref. 12 by Z(l),J),/„J„)SI)=2) '&+~Z(l),J),l„J~)SQ

'8 J. M. Blatt and V. F. Weisskopf, Theoretical 1Vucleur I'hysics(John Wiley Bz Sons, Inc. , New York, 1962), p. 540.

4 ~

Ep = 994 MeV

As4

IO-Ep = IO+3 MeV

swhs4

2-

/—As30 I I I

0 30 60

A*S

I I I I

120 l50 180

e~OKGREES)

Fzo. 21. Sample its to angular distributions of alphasleaving N" in its ground state.

O''(p a)N'' AND O''(P, P')O''* CROSS SECTIONS B655

Q~ 0

«5

~ eet«o~ ~ tt 0 0~ ~ ~ ~ ~ ~ ~

~ ~~ l ~ ~ tt ~ ~ th ~

0 Q5~0

~t~ t

~~ ~ e, ~ ~ ~ .1«5~ ~

~ I

~ i~ ~~ ~

~ ~

n ~ ~ «ett t«that ~ ~ ~ eot ~ ~ ~o' ~ ~~ eo, er ~ ~ ~ ~

~ t ~

l ~

IO

COEFFICIENTS OF LEGENDRE POLYNOMIALS 0 (p,a)N where S is the number of experimental points to befitted, and e is the highest degree Lengend&e polynomialused. Sample 6ts to the experimental data are shown inFigs. 19-2I. The required a&'s are shown as a functionof energy in Figs. 22-25. CoefBcients obtained by 6ttingthe angular distributions taken over the sharp structurenear E~=8.3 MeV are shown in Figs. 26 and 27.

5

«5

~«eeet ~t

t

~ n tt ~ tt ~hl l ~ ««l ~ lth tet

~ ~~« ~ ~ ~litt ~

eall ~ ~~ n ~ ~ ~~ ~ ~

~ 0 t ~~ ~

~t i «'oet

I,".hr,li~ ~ t ~ ete«e«oto

qt ~ ~ h«e «ro'e «e ~ .~,Oi ~~laoil ~e ea~ ~ ~ ~« ~ ~~ ~

ltt

a,0

~ ~ 5

Spin Assignments

As can be seen in Figs. 22 and 23, coeKcients arenonzero through a4 for both p~ and the alphas over thelevel at E~= 7.94 MeV. If we treat the level as isolated,then Table I requires J=~. However, the nonhero a&

10 "~ \

0 Q,~ ~4 ~ ~ ~ ~ ~t ~ ~ ~~~

~tt ~. A" ~ «tg ~ lteettt«l ~ It ttt«'«t le n ~~tt ~ ~ ~ ~I h ~«te ~ ~ I ~

~ ~~t

I ~ 5lo"

5"

a„o

COEFFIQENTS OF LEGENDRE POLYNOMIALS

Ole (p p )OIMr(P-)

~n «, I ~

;,n„a, I lire ttl~ ~

~a ~

75~ ~ !

et (Q ~ e«e

~ tteeath~ h on ~tootle h ~I ~ ettoeeottnon ~ oh ««lotto\el« ~ e I

80 84 9.0 9P 1010 l0.5

Ep(LAe) MeV

«5.

"10

I'rG. 22. Extracted coefficients of Legendre polynomials for angulardistributions of alphas leaving N" in its ground state.

the quantityN da)

g ur, Pz, (cosa~)i=1 LM dn),

l0"

ap 0

«5 ~ ~

-IOO 0

\

~ ~

~ ~

~ ~~ ~ ~ ~ete« I

~ \1 ~I ~e n' ~

~ ~h ~

""5

"-lo

"lo

o (p, p, )O' (0')

COEFFICIENTS OF LEGENDRE POLYNOM)ALS

~\

~o

~ ~h ~ ' n

o.;... On»"~~h~Ih ~

~ ~

0 a,

a6 o~ ~'~ ea ~ ~ ~ ta

~~ ~ at ~ ~

l ~ ~

~ ~ ~

~t ~ ~ ~ ~,-.-. "0 a5

20*

l5-

ao lo-~ ~

~I

0 ~t~ eat eea

"-5

-lO

Qg 0tth ~ ~ ~

~ ~~ ~ ~o ~ ~

e ~ te ~ ~ ~ t«ao' ~ tte ~~t I thol ~ ~ ~ ~eeet hh 10

,'~

~ ~ I 07g 8,0 loll I0.5

-5"

jo'

0~ t

/tte

~ ~ ~t» ~ 0th l «ett~ ~ ~

~~ tt~e \ ~

«'t

I

~ ~

~ at '0~ ea+ ~ ~~ ~

~ ~ ~ ~

( the«oha ''~1 le

tt~ ~ ~ ~ lt

~t ~ ~ ~ ~~ teethe ~ eeo

~he hat ~ ~ lo 0

"5~ I ~

~ ~

~eat 0~

~ ~ tl ~~ nt««teeeet

~ ~~ h ieoe1 ~

Ep (LAB) MeV

Pro. 24. Extracted coefBcients of Legendre polynomials forangular distributions of inelastic protons leaving 0" in its secondexcited state.

~,

~ \

ee

10

C 5~t

~ ~ ~ tet ~petite ~ h e ~ n I ~ t\ ~ 00 n ~ ~ t ~

~~ 0«e ~ ~ ~ ~ «ee ~

~ ~iten it ee ~ ~ te Oheo al

loat

QO5-a

oeh+

~Pore ~

~ ~ "-IO

0 ~ «th' lli ehht I ote r' ~aotoet

I I ho oo«no«It«no a+ eeoeprb«t

70 7,5 QO 8,5 9,0 905 IO.O IOQ

Ep(LAB) MeV

Fro. 23. Extracted coefBcients of Iegendre polynomials forangular distributions of inelastic protons leaving Oi' in its 6rstexcited state,

and u& over the resonance imply interference betweenthe level at 7.94 MeV and a level of opposite parity,and J= ~~ (again see Table I). There is evidence in theao curves for Pq and the alphas (see Figs. 22 and 23) fora broad level (I" 250 keV) near E„=8.1 MeV. Thisbroad level is assumed to be the interfering oppositeparity J= 2 level required to give the a~ and u3 coefFi-cients at 7.94 MeV. Such a level would also contributedirectly to the nonzero e2 coefBcient seen near E„=7.7and 8.2 MeV in the p~ angular distributions (seeFig. 23). The large aq and a8 present in pq angular dis-tributions over the level at E~= 2.58-MeV (see Fig. 23)can be explained by assigning the 2.58-MeV level a

B656 DANGLE, OPPLIGER, AND HARDIE

J= -,' with parity opposite that of the postulated broad/= as level at 8.1 MeV (see Table I). The maximum ina2 near E„=7.7 MeV is not from the level at 7.58 MeVsince it is shifted to a higher energy. This a2 is from thebroad J=~3 level as previously mentioned and theminimum in a2 near E„=7.9 MeV is probably causedby interference between the J=

~ level at 7.58 MeV andthe J=—,'level at 7.94 MeV which have the same parity.

Angular distributions over the level seen in the alphadata at E~=8.63 MeV require coefficients through u4

(see Fig. 22). This level is therefore assigned J=-', . Thenonzero aj and a3 are again explained by assuming thelevel has parity opposite that of the broad interferingJ=-,' level at 8.1 MeV. The observed ratios a~/ao ——5/4and a4/ao= 3/4 are in good agreement with the theoreti-

3Q~

Ole(p p )Ole

!i~I~0-2 Q4

I ~ +

eg ~ i

toe, a,~/ "'j"-2

202

"9"

COEFFICIENTS OF LEGENDRE POLYNOMIALS8.3 MeV DOUBI.ET,

Ole {pp )OIB*

COEFFICIENTS OF LEGENDRE POLYNOMIALS

0 (p,p3)o t2') 0 (p.p, )o 5I)~O "3 O

Q I

Q0

20"

"-5 Qo10 ~

Q2 0 -'."-5"

08,24

E& (LAB) MeV

08.24

I5"

10"Qp 5"

0 01

-:"10

9P 9S IOA) 10580 9.5 IOP' 108

Ep(LAB) MeV

FIG. 26. Extracted coefBcients of Legendre polynomials forangular distributions shown in Figs. 13-16. Solid dots are co-efEcients obtained when all polynomials through m=6 are used.(However, u4 is small and not plotted. ) Open circles are coeK-cients when only polynomials up to that required to fit the dataare used.

o (p,&)N"

COEFFICIENTS OF LEGENDRE POLYNOMIALS

S.3 Mev DOUBLET

O6

FIG. 25. Extracted coeScients of Legendre polynomials forangular distributions of inelastic protons leaving 0" in its thirdand fourth excited state.

cal ratios of the products of the Z coefficients for anisolated J= ~~ level, a2/ao ——8/7 and a4/uo ——6/7.

Baldinger et al."have reported a broad level (I' 750keV) at E,= 7.72 MeV in 0'7 with a spin and parity of

2 . The broad level at E,=8.2 MeV (E„=8.1 MeV) inF' is assumed to be the mirror of the level in 0" re-

ported by Saldinger et a/. This assumption permits the

assignment of absolute parities to levels which interfere

with the broad level at 8.1 MeV. The spin and parityassignments are then: 7.58, —,'+; 7.94, —,'+; 8.1,8.63) ~+.

The angular distributions shown in Figs. 13-18 were

"E. Baldinger, P. Huber, and W. G. Proctor, Helv. Phys.Acta 25, 142 (1952).

05

"5~ ~

I"

2" ~

O+

"3~-

3'"

03-I"2"

O2~ I

IrO)

5"

0 ~

~ ~~ ~ ~ I ~ ~

~ ~ ~ ~

Qp ~

0&R5 8.30 8.35

Ep(LAB) MeV

FIG. 27. Extractedcoefficients of Leg-end re polynomialsfor angular distribu-tions shown inFigs. 17 and 18.

0''(P, e)N'' AND 0''(P P')O''* CROSS SECTIONS

TmLE II. Reduced widths for F'7 levels. '

(MeV)

7.58

7.94

8.1

8.27

8.31

8.63

9.10

10,04

yygX10~(keV-cm)

14.24.37

17,05.20

13.64.12

28.88.66

10512.375.28.81.120.6652.241.33

43.25.48

12.11.53

26.82.10

52.04.099.678.38

18.516.0Z6.1

1.1019.20.81

1732.54

61.30.90

vuo'/~P

0.0110.00330.0130.00400.0100.00320.0220.00660.0800.00940.058'0.00670.000860.000510.00170.00100.0330.00420.00930.00120.0210.00160.0400.00310.00740.00640.0140.012O.OZO

0.000840.0150.000620.130.00190.0470.00069

&X1012

(keV-cm)

41.6136113372111368

21206940336

287057.7

4943.305.60

45.377.1

3172460

13.7107

5.886.76

55.564.012.2

2923.38

80.7189

1270016.7

1130

vuP/~P

0.0320.100.0860.280.0850.28

(1.6)(5.3)0.26

(2.2)0.0440.380.00250.00430.0350.059O.Z4(I 9)0.0100.082

0.00450,00520.0420.0490.00930.220.00260.0620.14

(9.7)0.0130.86

2X 10(keV-cm}

31.2102.2

18.861.2

14$49742.1

14622.2

19054.9

4681.843.110,580.985.72

43.928.5

21513.4

1654.89

60.63.754.361.511.76

y '/b, n

0.0870.280.0520.170.41(1.4)0.120.410.0620.530.15

(1 3)0.00510.00860.00160.00270.0160.120.0790.600.0370.460.0140.$70.0100.0120.00420.0049

a Two solutions are given for each assumed parity. Less likely values are in parenthesis and preferred solutions in italics.

hP =$(A~/pa) =i307)&10»keV-cm(a =S.iif).Lka = )I (5'/pa) =360 XiO» keV-cm (a =5.72f).

taken over the sharp structure near E„=8.3 MeVbecause it was felt that small energy shifts of the accel-erator could distort angular distributions chosen fromthe excitation curves. The analysis of the two levels(E„=8.27 and 8.31 MeV) seen in this region is based onthese angular distributions. The presence of the nonzeroa& required to fit the alpha data in this region (Fig. 27)requires that at least one of the two sharp levels hasJ=—,.On the basis of the p~ data in this region (Fig. 26),the level at 8.27 MeV is assigned J= ~~. This assignmentthen requires that the level at 8.31 MeV has J=& inorder to account for the nonzero a6 needed to fit thealpha data. The level at E~=8.3j. MeV must have avery small particle width for decay via pz, as it isscarcely detectable in the Pz data (Fig. 2). Conse-quently, it is not surprising that no a6 is needed for thep& data. The nonzero as required to fit one of the p&

angular distributions (Fig. 26) may be caused by inter-ference between the J=—,

' level at 8.27 MeV and anotherJ= ~ level of opposite parity. If the interfering level isthe J = ~5+ level at 7.94 MeV, the level at 8.27 MeV isthen J"=—,

' . The fact that the u6 needed to ht the

alpha data in this region are negative can only beaccounted for. by interference between the J=—,

' levelat 8.31 MeV and another level of the same parity havingJ=-,'. If the two members of the doublet have the sameparity this might explain the negative a6. However,since the leve1 at 8.27 MeV is quite narrow, it appearsunlikely that the interference would be strong enoughat the higher energies to produce a negative a6. It ismore likely that the negative u6 is caused by interferencewith the ~~+ level at 8.63 MeV. This interference wouldassign a positive parity to the ~~ level at 8.31 MeV.

Since coefficients through u4 are required over thelevel at E„=8.88 MeV for both the pq and alpha data(Figs. 22 and 23), the level is assigned 1=2. Angulardistributions for p2 over this level are nearly isotropic(see Fig. 24). Since neither / or 2J—1 can be zero, thisimplies that l'= 0 and hence the proton decay to the 3level of 0' is largely via s waves. Therefore the level at8.88 MeV is assigned a negative parity.

The level seen in the p~ data at E~=9.10 MeU hasnonzero coefFicients only through a& and hence isassigned J=-,'. The nonzero ai and u3 coefficients over

DANGLE, OPPLIGER, AND HARD IE

Tax,E III. Energy levels in F'7. It should be noted that forlevels at E„&10.5 MeV the approximate resonant energies andlab widths were obtained only from the 81,b=166' excitationcurves and are considered to be quite uncertain.

Since coefBcients through a6 are required to 6t the

P~ angular distributions over the level at'10.04 Mev(Fig. 23), the level is assigned J=-,'.

Resonatinggroups

Reduced WidthsZ. (MeV)

7.3597.4487.4537.4707.4797.557.737.958.028.078.28.388.428.728.788.959.169.269.409.629.899.93

10.0510.2210.4010.5010.7010.7910.9511.4411.5511.6411.7911.8712.0012.1912.2612.3512.52213.034

Z„(MeV)

7.1867.2807.2867.3047.3137.397.587.817.897.948.18.278.31

{8.708.889.109.209.359.599.879.92

10.0410.2310.4210.5210.7410.8311.0011.5211.6411.7311.8911.9812.1212.3212.3912.4912.67113.215

I'i,b (kev)

10~2(5

7&25~2

84540+5

190+3010&350+20

110m20750+25012+545%10

200~30160+20130+20200&50220&40250~100330m 75140m 20450a100300ai00270&85170a40150+30150~30130&40200&50260+60170+30160a40200&10040+20

130+40170+60200+50280m 50~&5«5

For protons on 0"at the resonant energy of an iso-lated level of spin J the total cross section for a givenreaction channel (v) can be written as

Pop2&PoPOPlP2+P0P2PoPOP2POPl&P2PodPOPl(Po)Plo,Poplp2P3o. '

POP1P2P30.'

Pd'}POPlp2P3P4+P0P1P2P4CE

P3P0PIP4P0P2&P3POP1

PIP3POP 2o|

PIO,'

P0P2(P3) (~)(P2)pa(a)P2&)'P2O(

(p )POP2

PlP4Poplp2P40. '

Po

3+827 Q,2&+b2

(4)o„=4m.hae„——2~k '(2J+ 1)F~,F„F',where F„ois the partial width for the elastic channel,I"„is the partial width for the reaction channel, anddao„ is the contribution to ao„from the level. SinceF=F„,+P„F„,the total reaction cross section can bewritten

6+b23-b6-b27+b6+b2

o,.„,~=4++„hae„——2mk '(25+1)F„,(F—F„,)F '. (5)

If it is assumed that the present measurements coverall important open channels, then Eq. (5) can be solvedfor two values of I'» and each of these can be used inEq. (4) to calculate the other partial widths. When Jis known, reduced widths can then be calculated for p~and the alphas using y„'=~F, k '2

~ ', where A g' is the

penetrability factor. The reduced widths for both solu-tions to Eqs. (4) and (5) are shown in Table II. Sincethe parity assignments are somewhat doubtful, valuescorresponding to both parities are shown. In cases whereone of the solutions is clearly preferred it is italicized.Unlikely values are in parentheses.

CONCLUSIONS

Table III shows a complete list of the levels found inF"in the energy range E,= 7.0-13.0 MeV. Informationabout levels found in elastic scattering data is takenfrom Refs. 5 and 6. The resonant energies, widths, anduncertainty in widths shown in the table are the bestvalues that can be assigned on the basis of all availableinformation. %hen possible, the energies and widthswere taken from the ao curves. Because only levels of thesame spin and parity interfere in uo, interference effectsshould be a minimum here.

Figure 28 shows energy level diagrams for F'~ and0".F"levels are those listed in Table III.Mirror levels

a J»from Ref. 5.b Parity from interference with broad level at By =8.1 which is assumed

to be 3/2 .Bracketed energy levels: In several cases, different reaction channels

show broad resonances at slightly diferent energies. It is not always clearwhether these resonances correspond to different F» states or whether theenergy for peak cross sections has been shifted (by penetration factors orinterference e8ects) and the resonances in all channels arise from the sameF'7 state, In such eases the neighboring resonances have been bracketed.

the 8.88- and 9.10-MeV levels can be explained if thelevels have opposite parity. Therefore, the 9.10-MeVlevel is assigned positive parity.

TmLE IV. Comparison of 0'7 and F'7 level parameters.

E,(MeV)

7.567.728.39

8.468.88

3 026~Y 0.0036

7+c23

9110

0.0490.016

0.00390.033

8.429.16

017

J r, (keV) ~,'/(3A'/2@a)' ~,'/(3A'/2@a)' E,(MeV)

&4 7.55750 8,2

11 8.38

7—23—26—

7+3+2

0.150.00270.00160.016

&0.010

F17

r, (keV) y„'/(3A'/2pa) y '/(3A'/2@a)

38 0.00882b

706 0.05811 0.0010

0.001742 0.033

188 0.020

a R. B.Walton, J. D. Clement, and F. Boreli, Phys. Rev. 107, 1065 (1957).b See Ref. 5.o Parity assignment from C»(a,a) C'3. See reference in caption of Fig, 28.

0's(P n)N'' AND 0's(P P')0's* CROSS SECTIONS

12.5— - 12.5

I2.0 "

FIG. 28. Comparison of energy levelsof 0'7 and F'7 from 7-13 MeV. Infor-mation about 0" levels are from acompilation by F, Ajzenberg-Seloveand T. Lauritsen, Nucl. Phys. 11, 1(1.959), except (a) levels under n' arefrom inelastic scattering work by H. K.Hall and T. W. Bonner, i''. 14, 295(1959) and C»(e,ny)Q~6 work by R. H.Spear, J.D. Larson, and J.D. Pearson,ibid. 41, 353 (1963); (b) levels under(n,o.) include work by D. M. Worley,Jr., R. Bass, T. W. Bonner, E. A.Davis, and F. Gabbard, Bull. Am.Phys. Soc. 5, 109 (1960); (c) levelsunder O.z include work by D. B.Fossan, R. L. Walter, W. E. Wilson,and H. H. Barschall, Phys. Rev. 123,209 (1961); and (d) parity assign-ments to levels from 7.94—8.49 MeVare from C»(a,o)C» work of B. K.Barnes, R. L. Steele, T. A. Belote, andJ. R. Risser, Bull. Am. Phys. Soc. 8,125 (1963). The F'7 levels connectedby a dotted line (?) are inferred frombroad resonances seen in diferent re-action groups. Interference and pene-trability effects may possibly accountfor the differences in resonant energyand hence these groups may arise fromthe same F"state.

Ex(M V}

ll.5-

I I.O—

10.5—

9.5-

9.0—

8.5-

---2—32

--"22

2

72

72

- .7-- 3

- 11.5

—I I.O

- 10.5

—IO.O

- 9.5

—9.0

—8,5

8.0-+ r ~

-- J. - 8.0

75—

r52 2 T-

2 fg+2 w 2

2

— 7,5

7.00'7

2

FI77.0

jn 0'~ and F ~ are connected with dashed lines in Fig. 28.The correspondence between the ~3+ levels near E = 7.4MeV was made by Salisbury and Richards. ' The ~levels at 7.55 MeV are considered to be mirror levelssolely on the basis of the spins and similarity in excita-tion energies since the 0"reduced width is unknown. Itwas assumed in this analysis that the ~3 level at7.72MeV in 0'~ and the ~ level at 8.2 MeV in F'~ are mirrorlevels. This assumption was based on the similarity intotal widths for the levels. It must be emphasized thatall parity assignments made in this paper except thoseto the levels at E =8.95 and 9.16 MeV are based on

this assumption. Table IV shows parameters on whichthe other correspondences in Fig. 28 are based.

ACKNOWLEDGMENTS

%e wish to express our thanks to Professor Hugh T.Richards for his continued encouragement and advicethroughout this experiment. Illuminating discussionswith Professor C. H. Blanchard concerning the theoryused in the analysis are gratefully acknowledged. Theaid of R. E.Rothe, J. Jobst, and D. R. Croley in collect-ing the data and maintaining the equipment isappreciated.