Energy levels of 38Ar from the 37Cl(p, α0)34S reaction

1.E.I:

[

Nuclear Physics A94 (1967) 625--652; (~) North-HollandPublishing Co., Amsterdam

2.C

I

Not to be reproduced by photoprint or microfilm without written permission from the publisher

E N E R G Y L E V E L S O F SSAr F R O M T H E STCi(p, ~o)S4S R E A C T I O N B. BO~NJAKOVI(~, J. A, VAN BEST and J. B O U W M E E S T E R Fysisch Laboratorium der Rijl~'sunicersiteit te Utrecht, Nederland Received 16 November 1966

Abstract: The 37Cl(p, :%)34S reaction was investigated in the energy region Ev ~ 850--2000 keV; 130 resonances were observed. Resonance strengths and energies are reported. Angular distributions of :~, particles were measured at 77 resonances. The analysis allowed unique spin and parity assignments for 28 cases. In 32 cases, two different spin assignments were possible. Formation and population parameters were determined. Formation of the 1- resonance at 1591.8 keV and the 2 ~ resonance at 1860.6 keV proceeds purely through channel spin 1. The measured level density shows a good agreement with theoretical predictions. The isobaric analogues of the lowest two excited states of 3sCl were observed although the c%decay is T-forbidden. The strength of the d n ~ 3- analogue state, split in several components, is in excellent agreement with the corresponding (d, p) strength, measured by Rapaport and Buechner. [ NUCLEAR REACTION 37Cl(p, ~a), E = 0.85-1.95 MeV; measured o(Ev; 0). I E I aSArdeduced levels, strengths, J, ~, formation and population parameters. Enriched target. I

1. Introduction Particle reactions, leading to c o m p o u n d states o f nuclei in the sd shell, have p r o v e n to be a useful to01 for o b t a i n i n g i n f o r m a t i o n on f o r m a t i o n , spins and parities o f these resonance states. In this l a b o r a t o r y , (p, c~) reactions o n light nuclei have been studied by K u p e r u s , G l a u d e m a n s and E n d t 1), who used the U t r e c h t CockroftW a l t o n g e n e r a t o r for p r o t o n acceleration. I n the region o f p r o t o n energies f r o m Ep = 200 keV to a b o u t 850 keV, no a-particles resulting f r o m the 37C1(p, ~)34S r e a c t i o n were observed. The 37C1(p, ~)34S r e a c t i o n leads to c o m p o u n d states o f 3SAr. The interest, focussed on this nucleus by w o r k o f Ern6 2), became the m a i n r e a s o n to extend the investigation o f the r e a c t i o n to higher p r o t o n energies. The w o r k b y Clarke, A l m q v i s t and Paul 3) h a d s h o w n that m a n y resonances exist in the 37C1(p, ~)34S r e a c t i o n a b o v e Ep = 1 MeV. The r e a c t i o n was also studied by Karad~ev, M a n ' k o a n d Cukreev 4) between Ep = 1.3 M e V a n d Ep = 3.0 MeV. One o f the aims o f the present investigation was to study the r e a c t i o n with higher energy resoluti on.

2. Experimental technique P r o t o n s are accelerated u p to 2 M e V with the U t r e c h t 3 M V V a n de G r a a f f generator. The p r o t o n b e a m reaches the target after 45 ° m a g n e t i c deflection. The m a g netic field is m e a s u r e d with the p r o t o n spirt resonance technique. T h e target m a t e r i a l 625

626

B. BO~NJAKOVl6 et al.

enriched t in 37C1 to 99 %. Initially, CoCI 2 and SrClz targets were also used but they seemed to deteriorate faster. Targets used in measurements of the excitation curve and of the angular distributions were thin ( ~ l0 pg/cm2). Absolute yield measurements were performed with thicker targets ( ~ 40 pg/cm2). Targets were prepared by evaporation in vacuo of the target material onto carbon foils, 10pg/cm ~ thick tt. The evaporation technique is described by Ern6 5). The targets are mounted in a vacuum chamber designed by Kuperus 6). A thin BaClz target on carbon can withstand a 1 pA beam (with a cross section of about 3 m m 2) of 1 MeV protons for many hours without noticeable deterioration. The reaction products are detected with O R T E C surface barrier silicon counters. For angular distribution measurements, seven detectors, of 50 m m 2 active area each, are located at laboratory angles of 72 °, 87 °, 105 °, 120 °, 135 °, 150 ° and 172 ° with was BaCI2,

proton beam

I

pulse shaper pulse g e n e r a t o r

diff.

t t

discriminator

I--

scaler

target detector preamp mainamplifier with clipping line st retch

multi channel analyser

Fig. 1. Block s c h e m e o f the electronics for one detector.

respect to the beam axis. The solid angles are determined by circular aluminium slits of 6.0 m m diameter at a distance of 6.8 cm from the target. The solid angles are equal within a few percent. They were determined by measuring the angular distribution of protons elastically scattered from a thin gold foil, assuming Rutherford scattering. For the measurement of the excitation curve, one detector with a 300 m m 2 active area is positioned at 135 °, at a distance of 6 cm from the target. The block scheme of the electronics is given in fig. 1. The output of the charge sensitive tube pre-amplifier is fed to the main amplifier with 80 ns delay clipping. The short clipping time effectively cuts down the proton pile-up without seriously influencing the energy resolution. The output of the main amplifier can be analysed with a differential t W e express o u r gratitude towards Dr. H. A. C y s o u w for converting the enriched NaC1, obtained f r o m O a k Ridge N a t i o n a l Laboratory, into BaCI 2. *t T h e carbon foils (type SS) were obtained f r o m the Y i s s u m Research D e v e l o p m e n t C o m p a n y , Jerusalem.

U

I,.z :3

U3

1.O

li

1],

c{P't4

2.O

xl

3o

I

CHARGED PARTICLE ENERGY SPECTRUM Ep=1346 6 I~V ®L,~ =,135 ° Ba 37CI2 TARGET ON CARBON BACKING

1PROTON P I L E - U P

x l O3

I

Fig. 2 Particle energy s p e c t r u m at the 1347 keV resonance.

5a(p,p)

[

ENERGY(MeV)

~C I(p,~)3"S

r

",,4

< t"a

628

B. BOSNJAKOVI6et

al.

discriminator and/or with a multi-channel anatyser. The channel of the discriminator is set by self-gating the pulses from a pulse generator. The purpose of the pulse shaper in fig. 1 is to equalize the shapes of the pulse generator pulses and detector pulses. This is necessary because the clipped pulses have to pass an integrating type pulse lengthener to be accepted by the analyser. A typical charged-particle spectrum, taken with a L A B E N 4096-channel analyser, is shown in fig. 2. The or-particle peak at higher energy is the % group emitted from the compound state of 3BAr to the ground state of 34S. The a-particles, emitted to the higher states of 34S, are thoroughly obscured by elastically scattered protons. The groups of elastically scattered protons, seen at lower energies, can be assigned to scattering on barium, chlorine, carbon and contaminant oxygen. The proton groups, several orders of magnitude stronger than the % group, cause an appreciable higherorder pile-up background, which is also partly shown.

3. The yield curve

The yield of the 7o particles from the 37Cl(p, ~)34S reaction was measured as a function of the proton energy with a detector at 135 °. The yield curve for proton energies between Ep = 870 keV and 1975 keV is given in fig. 3. The investigation was not extended to higher proton energies, because the mean resonance width increases strongly above the threshold of the 37C1(p, n)37Ar reaction at Ep = 1640 keV. The target thickness corresponds to an energy loss varying from 1.8 to 1.2 keV. The yield curve was measured in steps of 2.5 kHz, which corresponds to steps in the proton energy of 0.6-0.9 keV, depending on Ep. Simultaneously, the yield of the reaction 37C1(p, 7)38Ar was measured with one 10 crux 10 cm NaI(TI) scintillation crystal, positioned also at 135 ° to the beam. This 7-ray yield curve was also known from measurements by Simons e t a l . 7) and Ernd e t a L 2) and is not shown here. The purpose of the simultaneous measurement of the % and 7 yields was to decide which compound states emit both ?.-rays and ~o particles. The numerical results on resonance energies, the corresponding 3SAr excitation energies, resonance strengths and widths are given in the first six columns of table I. The numbers in the first column correspond to the resonances in fig. 3. In later runs, with still thinner targets, some of the peaks could be resolved into doublets. In such cases, a new resonance is supplied with the suffix A. Column 2 lists the resonance energies, relativistically corrected s). As calibration energies were used the eYAl(p,~,)28Si resonance at E v = 991.82__.0.10 keV 9) and the 2VAl(p,~o)24Mg resonances at E v = 1183.3_+0.3, 1364.8_+0.5 and 1381.3+0.3 keV to). In general, the resonance energies given by Ern6 z) are a little lower than those in table 1. E.g., for the 1088 keV and 1092 keV resonances of Erne 2), we find energies Ep = 1089.0+1.3 and 1094.2_+1.3 keV. We believe that our energy calibration is more precise because Ern6 bases his calibration ~ ) on low-energy 35C1(p, 7)SaAr res-

aSAr LEVELS

629

onances, of which the energies were measured 12) in 1961. The resonance energies, measured by a Finnish group, are also 1-4 keV lower than our values, depending on proton energy. Excitation energies E~ of the corresponding levels in 3SAt, listed in column 3, are calculated using the Q value Q --- 10242.4-t-2.3 keV 13). The error in Ex, amounting to about 3 keV, is determined both by the error in Q and the error in Q and the error in Ep. Column 4 lists the resonance strengths, ( 2 J + 1)FpF,o/F, which are calculated using the formulae as given e.g. by Gove 14). The absolute strengths of three isolated resonances at Ep = 955.6, 1440.4 and 1830.4 keV were determined from the steps in the thick-target yield. The strengths of other resonances are found by comparison of the areas under the thin-target resonance peaks with that of the nearest of the three standard resonances. The solid angle was taken into account. The error in the resonance strengths is estimated to be of the order of 30 %. The fifth column contains the level widths of some resonances. A plot of the measured resonance widths vs. the proton energy shows that most widths lie on a smooth curve which corresponds to the instrumental width Fi. For resonances of which the measured width /'m exceeds the instrumental width F~, the natural width F was estimated by using the linear relation F = Fro- F~. It was shown by Van Rinsvelt 15) that for F values up to about five times Fi, the linear approximation is better than a quadratic one. A 7 or n in the sixth column indicates that the resonance also emits 7-rays or neutrons, respectively. The symbol 7 is used only if during the same run the (p, 7) and (p, 7o) resonance energies were found to be identical within the experimental error. Otherwise, brackets are used to indicate that the assignment is uncertain. For a detailed discussion, see subsect. 5.1.

4. Analysis and results of angular distribution measurements The observed numbers of counts at seven (in some cases: six) laboratory angles were converted into the angular distribution W(01)oxp in the centre-of-mass system. The analysis then proceeded in different ways. 4.1. CHANNEL SPIN FORMALISM In the 37C1(p, ~o)34S reaction, only resonances of natural parity can be excited since the spin and parity of the ground state of 34S are J" = 0 +. There is no orbital momentum or channel spin mixing in the c% channel. In the incoming proton channel, on the contrary, channel spins s = 1 and s = 2 are possible since the spin and parity of the 37C1 ground state are J~ -- 3+. In the s = 1 channel, no orbital momentum mixing can occur, but in the s = 2 channel, up to three different orbital momenta are allowed. For all resonances that were analysed, however, contributions of orbital momenta higher than the lowest two could be excluded on considerations of the Wigner limit. This reduces to two the number of continuous parameters that describe the resonance formation process in the channel spin formalism. These are the channel

630

B. BOSNJAKOVId et al.

l m

,j

0

o

~

r~

_

Y: ~6

m

G r~ o ol c~

o

~.

II

< o7 I

8

8

1

8 q¢

. . . .

o

~

8 ~

o ~.-

:gd Z 8 ~13d S.I.NnOD ~

0

o 0

¢¢)

~1381~nN

r 0 0 0

__1 0 0 0

aSAr LEVELS

631

> tD IE v

i--

>.

0nbJ Z hi

Z 0

I--

0 nD_

o ~L aO

I

n~

f,.

o

0 g)

0 0 ,~.

o

0 0 ol

I

I

o

8

0 0 0

0

0

0

o 0

o 0

0

~

I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 16A 17 18 19 20 21 21A 22 23 24 24A 25 26 27 28 29

Resonance number

876.0i hl 8 7 7 . 5 1 I.l 893.8 ! I.I 897.4R I. 1 904.0j: 1.1 926.2A 1.1 927.7~1.1 939.8~1.2 955.6 ~1.2 965.0 ~_l.2 9 6 8 . 0 i 1.2 971.5~1.2 985.5 ~1.2 987.9-2_1.2 998.4 ~1.2 1000.3+1.2 1018,1 i 2 . 0 1044.6-~ 1.2 1 0 5 5 . 0 i 1.2 1060.8±1.2 1069.5--1.2 1077.2il.3 I 0 8 9 . 0 1 1.3 1092.6~1.3 1103.3 kl.3 1114.3±1.3 1118.2£1.3 1138.3 ~ 1.3 1142.3±1.3 1155.6±1.3 1164.5~1.3 1168.1 ~ 1 . 3

Ep(keV)

11095.3 11096.8 I I 112.7 1 l 116.2 11122.6 11144.2 11145.7 11157.5 11172.8 11182.0 11184.9 11188.3 11202.0 11204.3 11214.5 11216.4 11236.1 11259.5 11269.7 11275.3 11283.8 11291.3 11302.7 11306.3 11316.7 11327.4 11331.2 11350.8 11354.7 11367.6 11376.3 11379.8

Ex(keV )

0.8 1.1 1.5 4.6 0.40 2.6 4.4 0.6 7 0.8 0.25 0.25 1.6 4.8 37 2.2 0.3 1.9 1.9 12 0.9 10 0.4~0.2 50 12 2.3 0.6 160 80 60 2.9 6

(eV)

PpI~o/P

(2J-c 1)

<0.6 <0.6 <0.6 <0.6 <0.6

<0.6

<0.6

(7) ~)

<0.6 <0.6 <0.6

7 ~',b) ;~, b) ~,a, b) (y)a, bj (~)a, b)

Va,~) (7) a,b)

7 h)

~,~')

(7)a,b) (7) a,b)

Va,b)

7 a,l~)

7'a,b )

7a, h)

~a ,,)

7~t, ")

other decays

<0.6

<0.6

<0.6 <0.6 <0.6 <0.6

<0.6 <0.6

P(keV)

3334+ 1-,2 +

1 ,2 + (1-),3 1 , 2~

1-, 2 ~

(1-), 3 1 ,2 ~

1 ,2 +

3-

3

j n e)

0.809 ~z0.005

0.820!0.008

0.805±0.003 0.804±0.005 0.805±0.006 1.008±0.016 0.45 i 0 . 0 3

--0.19 ± 0 . 0 2 0.808i0.007 0.37 k0.05

0.17 ~ 0 . 0 3

0.8085_0.006 --0.56 ± 0 . 0 4

0.52 i 0 . 0 5

A n g u l a r distribution coefficients d) . . . . A2 A~ A6

--0,35 i 0 . 0 3

.

remarks

Resonances in the reaction 37C1(p, ~0)alS; energies, strengths at 135 °, widths, c o m p e t i n g decays, spins and a n g u l a r distribution coefficients

TABLE l

:-,,.

<.

©

3.

9, z

8

II I A.~3 ?JE.I . 3

1174.0~1.3 1182.54-1.3 1214.3±1.3 1235.5±1.4 1244.9 ± 1.4 1247.8±1.4 1258.44-1.4 1263.54-1.4 1271.34-1.4 1274.7:k 1.4 1279.6± 1.4 1286.0±1.4 1293.84-1.4 1300.8 -4-1.4 1307.5 ~ 1.4 1311.6~1.4 1323.6±1.4 1325.44-1.4 1327.7±1.4 1334.24-1.4 1338.4-k 1.4 1346.64-1.4 1352.6~ 1.4 1373.14-1.5 1374.3 4-1.5 1388.44-1.5 1393.64-1.5 1403.54-1.5 1409.0± 1.5 1411.74-1.5 1421.4-- 1.5 1440.411.5 1448.3 3- 1.5 1451.04-1.5 1453.6±1.5 1457.44-1.5 1468.44-1.5 1481.1±1.5 1483.94- 1.5

Ok)

31 32 33 34 35 36 37 38 39 4O 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 64A 65 66 68 69

11385.5 11393.8 11424.8 11445.4 11454.6 11457.4 11467.7 11472.7 11480.3 11483.6 11488.3 11494.6 11502.2 11509.0 11515.5 11519.5 11531.2 11532.9 11535.2 11541.5 11545.6 11553.6 11559.4 11579.4 11580.6 11594.3 11599.3 11609.0 11614.3 11617.0 11626.4 11644.9 11652.6 11655.2 11657.8 11661.5 11672.2 11684.5 11687.3

11354,A 1!

5O 18 4.4 0.40 3.8 2.3 6 19 33 14 12 12 48 15 32 4.5 2O 60 24 230 24 180 19 6 14 11 5 6 50 150 15 60 3.3 26 11 29 60 2.1 20 <0.6

<0.6 <0.6

0.74-0.6 <0.6 <0.6

<0.6

<0.6

<0.6 <0.6 <0.6 <0.6 <0.6

<0.6 <0.6 <0.6

<0.6 <0.6

[-~ z]#-

(TP') (7?)

(7)~, ~,) (~)b) 7~, b) (7)D (7)~, u) (7) b) 7a, b) (7) b)

7 ~, b)

(7) b) (7)a, ~,) (7) b)

(y)~, b) 7~, b) 7., u) 7a, b)

(7) ~)

4%52+

0% 1 -, 2 ~

11-, 2 + 1-, 2 +

1-, 2 +

4+

1-, 2+ 1-, 2 +

0 +, 1 2 +

1-

(7)'9 7 a, ~)

1-

(TP' b)

(1-), 3-

(1 -)3-

1-~ 2 +

33-

2+ 1-, 2 + 1-, 2 +

7~, b)

7., ~)

(TP)

7 ~' D (7) ~)

(7)~, b) 7~, b)

(7) ~, ~)

(7P' ")

0.47 4-0.03 1.038 4-0.016 0.05 4-0.04

--0.8874-0.010 --0.29~0.04 0.13 4-0.03

--0.46 -4-0.07 0.418+_0.013 0.92 4-0.03 1.032 jz0.009 --0.33 L 0 . 0 5

--0.7324-0.009

0.798 j:O.O14 --0.18 4-0.04 --0.3364-0.015 0.18 4-0.04 --0.6324-0.012

--0.39 :kO.06 0.8004-0.003

--0.20 4-0.03 0 . 8 0 4 ~ 0.011 0.8224-0.007

0.61 ; 0 . 0 4 --0.57 ± 0 . 0 4

0.23 -I-0.04 0.59 -I-0.02

--0.35 4-0.06

0.027 ~ 0 . 0 1 2

O. lO:kO.05

0 . 0 6 [ 0.03

--0.28 kO.05

odd terms

no odd t e r m s

k~

r~

g

70 71 72 73 74 75 76 77 78 79 80 81 82 82A 83 84 85 85A 86 87 88 89 91 92 93 93A 94 95 9~ 97 98 99

1500.1tl.6 1510.8±1.6 1515.5tl.6 1527.3 :k 1.6 1530.6~1.6 1537.5tl.6 1538.8:k 1.6 1543.3~1.6 1555.6il.6 1558.7tl.6 1566.8tl.6 1570.3tl.7 1573.2tl.7 1575.8~1.7 1584.8tl.7 1589.6tl.7 1591.8tl.7 1595.0!1.7 1607.3 ± 1.7 1611.9tl.7 1616.2±1.7 1620.6:/_1.7 1634.0tl.7 1642.5t 1.8 1648.0t 1.8 1663.4tl.8 1667.4t 1.8 1684.9~ 1.8 1693.9tl.8 1698.2 t 1.8 1705.6tl.8 1708.7 t 1.8

Resonance E~(keV) number

11703.0 11713.5 11718.0 11729.5 11732.7 11739.5 11740.7 11745.1 11757.1 11760.1 11768.0 11771.4 11774.2 11776.8 11785.5 11790.2 11792.3 11795.5 11807.4 11811.9 11816.1 11820.4 11833.4 11841.7 11847.1 11862.1 11865.9 11883.0 11891.8 11895.9 11903,1 11906.2

Ex(keV)

( 2 J + 1)

3.9£c0.6

(7)~)

I-, 2+ (n) e) (1),3(Tp, b), (n) ~) ( 1 ) , 3(rip) (),)b), (n)e)

1.0!0.6 1.1±0.6

(n) c)

32+

4.6 130 70 15 13 I00 1100

(7) a,b) (7)a, b)

(1)

1 , 3-

1 ,3 2+ 1-

1-, 2 +

0 ' , 1% 2 ~ 4+ 0% 1 , 2 + 2+

jR ~)

lOO

(7) b)

(7)a, t~) (TP' u)

(7)a, b)

(TP'~') },a,b)

7 ~') (7)D 7 a, b) 7a, b) (TP' b) (7) b) (7'P' 1~) (7) t')

(7) b) (7)a, b) (7) a'b)

other decays

60 500

<0.6

<0.6

0.7 ! 0 . 6

<0.6 < 0.6 <0.6 <0.6

F(keV)

120

220

18 15 9 50 8 28 160 370 160 340 18 12 28 13 4.4 3.3 20 1.6 3l 140

(eV)

Fp£~o/I"

TABLE 1

(continued)

0.354±0.020 0.78410.010 0.8205_0.007

0.82510.05 --0.6 t 0 . 4 0.88510.011 -- 1.09 10.05 0.73910.018 0.083 t0.020

0.806~0.015 --0.619-k0.016 --0.969±0.011

0.17±0.02

--0.16 10.04 --0.378 ~0.014

--0.37 10.16

--0.25 ~0.05

0.414t0.011 1.01 £_0.03

0.64 t 0 . 0 3

A4

1.051 t0.008

A~

0.13~-0.04

An

Angular distribution coefficients a)

odd terms

odd terms

no odd terms

remarks

© <

7'

&

4~

11929.1 11935.4 11950.0 11967.3 11973.9 11982.6 11999.2 12006.5 12017.6 12024.7 12039.2 12042.6 12054.1 12063.9 12068.0 12071.6 12082.0 12086.1 12098.1 12111.1 12117.8 12123.2 12128.1 12136.6 12143.6 12153.7

I ID'I 8 . U

4.9 310 70 410 90 50 80 200 17 42 160 80 160 140 260 160 460 90

80

140 19 240 20 100 80 34

I /U

~P'~)

7 a,b)

1.4::k0.6 2.34-0.6 1.1 4-0.6

2.14-0.6 3.0±0.6 2.62_0.6 1.1±0.6

1.54-0.6 <0.6

1.24-0.6

(7) a)

(7) a)

(TP)

(7) b) (7) b) (7) a)

1.3 _~:0.6 7a, b) 7 a,b ) <0.6 (Tp, b) <0.6 (7)a, b) <0.6 (TP) 1.04-0.6 7 b)

<0.6

11-, 31-, 2 + 1

12+

2+ 11 , 2+ 2+

1-, 3-

(1-), 3-

1-,2 + 4+

4-0.03 4-0.03 zkO.03 4-0.01

0.9544-0.015 --0.0024-0.029 --1.24 4-0.11 1.00 4-0.05 0.81 4-0.03 --0.32 4-0.05 --0.64 4-0.02

0.06 --0.53 0.14 0.70

0.8114-0.012 1.36 4-0.20 0.74 A_O.04 0.807±0.014

0.30 ±0.03 1.0024-0.014

--0.22 4-0.04

-- 1.64 4-0.04

--0.11 4-0.03

0.31 ±0.09 0.53 -k 0.06

0.50 4-0.04

--0.08±0.06

odd terms

odd terms

odd terms no odd terms

odd terms

e) Brackets indicate that the spin assignment is improbable, because a reduced width exceeds 5 ~ o f the Wigner limit.

a) In some cases, a spin assignment was not possible on the basis o f the single-level analysis. In such cases, main even terms are listed; a remark indicates whether odd terms are found too.

e) Ref. ~1); 37C1(p' n)37Ar reaction.

b) Ref. ~); 37Cl(p, y)38Ar reaction.

a) Ref. 7); 37C1(p' 7)38Ar reaction.

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126

105

I I=V.:~ ZE 1 . 0

1732.3±1.8 1738.74-1.8 1753.74-1.8 1771.5± 1.8 1778.34-1.8 1787.2±1.9 1804.3+1.9 1811.7-2 1.9 1823.24-1.9 1830.4±1.9 1845.34-1.9 1848.84-1.9 1860.64-1.9 1870.7±1.9 1874.9±1.9 1878.64-1.9 1889.3-4-1.9 1893.5±1.9 1905.82_1.9 1919.2-2_1.9 1926.14-1.9 1931.62_2.0 1936.6±2.0 1945.44-2.0 1952.64-2.0 1962.94-2.0

luv

101 102 103 104

L~

B. BO~NJAKOVI6et al.

636

spin m i x i n g f r a c t i o n r, defined as the i n t e n s i t y in the l o w e s t spin c h a n n e l o v e r t h e t o t a l i n t e n s i t y in b o t h c h a n n e l s , a n d t h e o r b i t a l m o m e n t u m

m i x i n g r a t i o e, defined

as t h e r a t i o o f t h e h i g h e r to t h e l o w e r o r b i t a l m o m e n t u m a m p l i t u d e . T h e t h e o r e t i c a l L e g e n d r e p o l y n o m i a l coefficients o f t h e a n g u l a r d i s t r i b u t i o n p o s s i b l e c h a n n e l spins s, p r o t o n o r b i t a l a n g u l a r m o m e n t a

W(J ~, s, lp, l[, O)

for

u p to lp o r l~ = 4 and

r e s o n a n c e spins u p to J~ = 6 + were c a l c u l a t e d f r o m the f o r m u l a o f Blatt a n d B i e d e n h a r n 16) a n d are p r e s e n t e d in t a b l e 2. (In the c o r r e s p o n d i n g t a b l e 1 o f ref. ~) t w o a n g u l a r d i s t r i b u t i o n coefficients f o r t h e case o f J ~ = 4 + h a v e the i n c o r r e c t sign.) D u e to the c o n t r i b u t i o n s o f different c h a n n e l spins a n d o r b i t a l m o m e n t a , t h e total TABLE 2 Legendre polynomial coefficients Ai in angular distributions for different angular m o m e n t u m combinations. Target spin Jt n ~ .~+, resonance spin j~r, proton orbital m o m e n t u m lp or l'p, channel spin s

J~

s

lp

l'p

A0

0+

2

2

2

1

1-

1

1

1

1

2

1 3 1 2 0 2 0 3 1 3 1 4 2 4 2 3 4

1 3 3 2 0 2 2 3 1 3 3 4 2 4 4 3 4

1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1

2+

3-

4+

56~

1 2

1 2

1 2

2 2

angular distribution reads

W(O)

A2

A4

As

As

1.000

+0.200 +0.800 - 1.469 +0.714 -0.306 -1.195 + 1.000 +0.800 +0.422 -0.524 + 1.104 + 1.020 +0.745 -0.292 +1.111 +1.157

-1.714 +0.735 + 0.273

-2.273

-0.818 - 1.309 +0.728 +0.551 -0.218 -0.859 +0.818 +0.961

+1.263 -0.09l

-2.741'

-0.934 1.300 + 0.404 +0.661

+ 1.744

+0.312

o f c% p a r t i c l e s e m i t t e d f r o m a r e s o n a n c e state o f s p i n J

W(O)=zW(J, 1, J,J,O)+ 1 - ~ {W(j,Z, lp lp,O) 1+~2

+ 2 e cos

t

(~,,~, W(J, 2, Ip, l'p, O)+eZW(J, 2, 1'v , lp,

0)}.

In this f o r m u l a , cos ~b~p~, is the p h a s e d i f f e r e n c e o f the C o u l o m b w a v e f u n c t i o n s f o r t

o r b i t a l m o m e n t a lp a n d lp, e v a l u a t e d at t h e r e a c t i o n r a d i u s ; b o t h r a n d e are r e a l , r h a v i n g p o s s i b l e v a l u e s in the r e g i o n 0 -< r _< 1.

3SAr LEVELS

637

In many cases, resonance spin assumptions could be excluded on considerations o f the Wigner limit. The general policy was to exclude a resonance spin if a reduced partial width exceeded 50 ~ o f the Wigner limit. If a reduced width was between 5 O//oand 50 % of the Wigner limit, the spin assignment was considered to be improbable, in this way, resonance spins exceeding 6 were excluded in all analysed cases. For J~ assumptions o f 5 - and 6 +, always only the lowest lp value was to be taken into account. C o u l o m b penetrations and C o u l o m b phases cos q ~ v , were c o m p u t e d from the power series expansion as described by Fr6berg tv) and the Feshbach-Shapiro-Weisskopf method ~8). In calculations, a nuclear interaction radius r = ro(A+l) + was used, where A is the mass number and r o -- 1.2 fro. -9G

-60 °

-30 °

3-

9£/(N-M)

0°

~ * - -

t b oo F

~ -

t

L .

::

~

:

90 ~

:

-::~

0÷

"\1

lJ

4

o

"

t-

.......... "\

~o °

F i g . 4. V a l u e s o f z 2 / ( N - - M )

60 °

........

I

~

30 °

-,~

-60* -30°

Ql°/°lirnit Ep= 1589

c/'

30"

orctg

-

6 keY

E

60*

I

>

90*

f r o m t h e a n g u l a r d i s t r i b u t i o n m e a s u r e m e n t a t t h e 1589.6 k e V r e s o n a n c e ,

plotted against the orbital momentum mixing ratio with the resonance spin and parity J~ as parameter. The minimalization of 7.2 with respect to the channel spin mixing ratio z has already been performed. The search for the best values o f the parameters r and ~ was performed by calculating the function

Z 2 = Z { W(O,)oxp- W(O,)}2g~, i

where gi are statistical weights of the observations W(0i)ex p. F r o m a contour plot of Z2/(N - M ) in the (z, s) plane, where N is the number of observational angles and M the number o f continuously variable parameters, the value o f Z~i,,/(N-M) could be found for a certain assumption of the resonance spin. A n example is given in fig. 4. Here, Z2/(N- M) is plotted as a function o f the parameter s for different J~ assumptions o f the resonance at Ep -- 1589.6 keV. This figure is a simplification insofar the minimalization with respect to the linear parameter r has already been done. The assumption J~ -- 2 + yields a m i n i m u m value of z Z / ( N - M ) = 2.1, which is in the neighbourhood o f 1, as we expect for a solution. The corresponding values o f the formation parameters are z = 0.00+_0.01 and arctg s = - 5 1 ° + 4 °. A spin assump" N - - M ) exceeds the 0.1 ~o probability limit. tion is excluded if the value of gm~n/(

B. BOSNJAKOVICet aL

638

TABLE 3 Values o f ZmIa~/(N--M) for m e a s u r e d a n g u l a r distributions at different r e s o n a n c e energies Ep a n d for different j n a s s u m p t i o n s , N being the n u m b e r o f observational angles a n d M the n u m b e r o f parameters. Values n o t exceeding the 0.1 ~o probability limit are underlined. T h e following scheme gives the 0.1 ~ probability limit values for different N a n d Y~: ~ N ~

0+' 5 - ' 6+

1-' 2+' 3 - ' 4+

6

4.10

5.42

7

3.74

4.62

A l m o s t all a n g u l a r distributions are m e a s u r e d at seven different angles. T h e three a n g u l a r distributions which were m e a s u r e d at six angles, are indicated in the c o l u m n " r e m a r k s " .

~ E p. ( k e V )j ~n. ~ 0 + 897 956 998 1055 1061 1070 1077 1093 1103 1114 1138 1142 1156 1165 1168 1173 1174 1183 1264 1271 1280 1286 1294 1301 1308 1334 1347 1373 1374 1388 1394 1404

85 135 38 65 85 4.8 13 60 72 14 75 133 374 63 20 14 119 121 26 220 57 30 125 9.3 390 900 1.8 17 28 200 118 10

1-

2+

3-

4+

5-

3.0 a) 1.2 a) 1.7 1.1 b) 1. l 5.0 2.1 4._55 1.2b) 2.0 1.7 a) 1.2a ) ~ 1 a) 19 2.8 2.2 2.7 a) 11 2.7 0.7 b) 0.8 b) 19 1.2 1.8 1.4 1.3 1.1 2.1 0.6 15 33 3.3

12 27 1.5 17 4.5 1.0 2.4 3,2 17 1.8 70 29 143 29 1.5 2.1 28 36 1.4 68 •9.5 3.7 0.9 2.2 58 530 2.7 2.0 0.8 94 70 0.7

2.3 1.3 290 1.1 310 1.6 130 1000 0.7 19 1.3 1.2 3.5 19 15.5 269 1.22 0.9 220 0.77 0.7 165 1000 90 1300 2700 298 92 16 15 32 105

12 19 425 7.3 410 5.2 245 1700 13 30 41 26 66 0.7 31 403 21 12 310 38 9.5 257 1700 189 1600 3300 560 129 41 9.9 0.9 140

51 68 510 37 410 13 400 2300 59 70 190 105 268 8.7 55 500 100 118 320 125 31 33 1650 308 1700 3300 780 137 90 65 8.5 155

6+

87 122 590 64 450 16 520 -95 97 320 175 444 22 82 585 159 187 370 220 53 37 1800 393 1850 3500 950 153 130 129 27 180

Remarks

N = 6

N=6 N=6

no solution

SSAr LEVELS

639

TABLE 3 (continued)

J~

1412 1421 1440 1457 1468 1481 1484 1500 1511 1516 1527 1538 1543 1585 1590 1592 1607 1612 1616 1621 1634 1643 1663 1667 1685 1709 1732 1739 1754 1778 1787 1804 1812 1830 1845 1849 1861 1894 1906 1919 1926 1932 1937 1945 1953 a) limit b) limit

0+

1-

2+

3-

4+

5-

6+

670 15 5,2 1,77 298 55 53 0.5 125 1.2 55 200 15 21 44 750 145 56 1030 1800 130 65 13 102 224 450 62 65 29 135 340 73 100 6.8 75 6.2 260 620 7.5 177 100 19 35 147 495

1.5 1.1 1.1 0.6 29 19 65 0.44 44 1.8 18 8.6 1.3 1.5 21.5 3.0 2.2 40 3.6b) 18 5.9 7.4 0.6 1.9b) 4.6b) 5.7 2.6 13 12 0.9 b) 21 23 1.5 9.4 4.6 0.8 360 4.4 10 7.5 2.3 0.7 1.0 1.6 20

430 0.7 0.8 2.4 101 36 2.9 0.3 87 1.8 2.5 114 1.6 9.9 2.1 590 72 12 529 340 41 3.2 0.6 47 99 135 1.4 48 11 85 257 40 50 2.7 23 0.7 1.9 408 2.5 130 72 10 1.9 90 308

1100 155 10.5 13 27 18 145 70 42 37 25 13 175 0.9 200 1500 1.0 321 18 1800 0.6 728 15 1.9 4.55 1500 163 12 180 1.2 34 17 2.1 255 324 110 210 29 110 421 6.0 1.1 275 483 11

1500 230 23 23 110 0.7 240 130 1.3 58 110 31 350 4.8 235 1600 18 768 184 2000 44 1128 29 30 50 2000 332 1.1 357 31 45 10 22.5 550 435 225 270 103 210 500 14 5.0 400 570 67

1200 275 35 31 350 2.7 420 190 5.4 78 310 80 550 12 210 1400 95 1350 585 2160 170 1290 47 79 164 2180 560 10 645 80 79 22 85 850 490 360 380 280 330 490 44 17 450 550 343

1300 320 44 38 530 8.5 480 240 23 95 420 140 700 21 225 1450 165 1690 990 2300 255 1490 65 128 278 2380 760 24 835 130 141 45 135 1100 540 450 410 480 390 515 72 28 510 590 580

Remarks

no solution

n o solution

no solution no solution

no solution

no solution no solution no solution

no solution

no solution

Spin a s s u m p t i o n can be excluded because the reduced p r o t o n width exceeds 50 ~ o f the Wigner value. Spin a s s u m p t i o n is i m p r o b a b l e because the reduced p r o t o n width exceeds 5 ~o of the W i g n e r value.

640

B. BOSNJAKOVI(~e t al.

In the case of the 1589.6 keV resonance, the values of ZZmln/(N-M) for J" assumptions other than 2 + lie well above the 0.1 ~ probability limit. The assignment J= = 2 + is therefore conclusive and unique. The values of Zmi,,/(N-M) 2 for different resonances and different spin assumptions are listed in table 3. Underlined numbers indicate a possible solution. To compute the errors in the final values of ~ and z, the assumption is made that Z 2 is a quadratic function of the variables e and ~ in the neighbourhood of the minimum. The errors are then found from the intersection of the unnormalized Z 2 function with the plane X2 = X m2 i n - / - 1 . The case J~ = 1- is an exception and will be discussed later. The values and errors of the formation parameters ~ and ~ were used to determine the Legendre polynomial coeffÉcients A i of the best fit angular distribution, and of the population parameters p(m). The latter were calculated from the appropriate formula given by Heyligers x9). The results are summarized in table 4. in some cases, one spin assumption allows two different possibilities for the formation of the resonance state. In such cases, the two different sets of possible formation parameters of course correspond to the one common, uniquely determined set of the population parameters. The Legendre polynomial coefficients are listed in table 1. For quite a number of resonances, different spin assignments are possible. These are listed together with the unique ones in table 1, column 7. Formation parameters, however, corresponding to a possible spin assignment, are not included in this publication if the assignment is not unique. Among the resonances with non-unique spin assignments, the 11 cases with possible spins 1- or 3- form a remarkable subgroup. Here, formation can be described without exception by pure channel spin s = 2 and by orbital momentum lp = 3 (for the J~ = 1- assumption) or lp = 1 (for J~ = 3-), respectively. Wigner limit considerations then exclude a J~ = 1assignment in many cases. 4.2. POPULATION PARAMETER ANALYSIS It is also possible to describe the angular distribution of the So particles in terms of the population probabilities p(m) of the resonance magnetic substates. In our notation, p(m) is the sum of the two equal population probabilities for the m and - m substates. Due to the conservation of the z-component of the angular momentum, p(m) = 0 for m > Jr+½ where Jt is the spin of the target nucleus. This means in our case that p(m) = 0 for m > 2. The angular distribution contains a number of (physical) parameters which is equal to the magnetic quantum number of the highest substate which still can be populated. Thus the number of physical parameters of the angular distribution and the number of the formation parameters of the resonance state are the same only for spins J > 1. The analysis in terms of population parameters has the advantage that the Legendre polynomial expansion of the angular distribution is linear in the population probabilities. It can be written as

W(O) = Z P(m)bi,,Pi(c°s 0). im

641

~SAr LEVELS

TABLE 4 Spins, formation and population parameters o f the single-level resonances in the Ep(keV)

J~

Formation parameters r

zTCl(p, ~0)z4S reaction

Population probabilities

arctg e

p(O)

p(l)

p(2)

897

3-

0.09 zoO.04

14 ° + 7 °

0,2642-0,012

0.468= 0.023

0.268 j-O.OI 2

956

3-

0.01 ±0.02

11 ° ±5='

0.2655_0.007

0.456 zLO.O14

0.279+0.007 0.278 ±0.004

1138

3-

0.025 =LO.OI5

2°

±8"

0.251 +0.004

0.471 +0.009

1142

3-

0.02 ±0.02

0° ± 9 °

0.252 ~0.005

0,468+0.011

0.280~0.006

1156

3

0.030±0.015

4° ±8 °

0.2505_0.004

0.472+0.011

0.278 +0.007

1165

4+

0.000±0.040 (0.240±0,025)

+ 3.5~4.0 ° (--44 ° ~ 3 °)

0,275_+0.016

0.4729-0.024

0.254+0.024

1174

3-

0.060+0.025 0.060~0.025

-- 8 ° ± 5 ° + 8,j ~ 5 o

0.2425-0,006

0.483 ~0.016

0.275 ~0.011

1183

3-

0.13 ~0.02 0.13 _-c0.02

-- 6 ° ± 4 '~ + 6° + 5 °

0.2245_0.005

0.524+0.013

0.252 ~0,008

1286

2+

0.370±0.025 0.270~0.025

--56 ° ~ 6 ° __28 ° ± 4 °

0.097 zLO.O1 l

0.452+0.025

0.451 +0.025

1308

1

0.123±0.004

0.877±0.004

1334

1-

0.089+0.003

0.911 +0,003

1394

4+

0.298~-0.014

0.4795-0.020

0.038 ~0.003

0.962 ±0.003

1

0.096~0.006

0.560~0.016

0.344 ~.0.017

(--36 ° ~ 4 °) } _ 8° ~ 3 o

0.309±0.013

0.502+0.028

0.189~ 0.020

0.232~0.009

0.551+0.014

0.217+0,010 0.677+0.009

1412

/ 0.000±0.020 [(0.215 ±0.020)

10.501 ___0.014

1511

-- 3.0°~3.5° / (--42.0°~2.5°)J

4+

/(0.20 J=O.03) ~0.03 ~-0.02

--63.0 ± 3 . 5 °

0.2234::0.017

f

1527

2+

[ 0.230±0.020 0.320:t_0.015

30 ° ~ 3 ° 50 ° j=3 o

} /

1590

2+

0.00 zkO.O1

--51 ° ~ 4

0.165~0.009

0.158+0.017

1592

1-

0.985±0.012

--~

0.010~0.004

0,990+0.004

16343-

~< e <2 co

{0.270±0.015 0.075 j=O.020

--51.0°~2.5 ° } +18°5-3 °

0.219 =kO.O05

0,4505-0.018

0,332+0.017

--18"5°+1'5°} --65.0°-k 1.5 °

0.157+0.003

0.322±0.010

0.521 +0.011

0.270+0.015

0.467:k0.019

0.264+0,022

0.189 :LO.O06

0.441 +0.011

0.3703 0.011

0.157+0.008

0.843+0.008

0.011 ~0.006

0.978+0.013

0.651:5 0.005

0.349 ~0.005

0.1564-0.008

0.4555-0.019

1643

2+

{ 0"00 ~0"01 0.225 ~0.008

1739

4+

0.00 ~0.03

1830

2+{

0"3455-0"012 0.065zk0.015

+89"0°+2"5°} + 1° =[:2°

0.965 =kO.020

40 ° ~ 2 5 °

1845

1-

1861 1894

2+ 1-"

1906

2+

1926 1945

11-

( 0.380-~:0.015 t 0.130+0.025 0.00 _~0.01

3.5°4-2.5 °

--78 ° ~_4 ° -- 9 ° Jz3 ° --66 °

~8 °

0.649-t-0.007

0.351 ~0.007

0.121 ~0.007

0.879!0.007

0.011 +0.007

0.388+0.019

I f possible formation is improbable on the ground of Wigner limit considerations, the corresponding formation parameters are p u t into brackets.

642

B. BOSNJAKOVIC e t a L

The coefficients blm have been given e.g. by Nordhagen 20). However attractive the population parameter analysis may seem, it should be kept in mind that the solutions for the population probabilities are frequently outside the physically admissible region, defined by the allowed formation parameters. In our case, the rejection or admission of a solution was decided on the basis of the channel spin formalism. The case of resonance spin and parity l - forms an exception. It is clear that the two-parameter formation cannot be expected, in general, to be determined uniquely from the one-parameter angular distribution. Therefore, the least-squares analysis of the angular distribution in terms of the population parameters was necessary for the case of J~ = 1- to determine the p(m) values. The results of the analysis are included in table 4. 4.3. L E G E N D R E

POLYNOMIAL

ANALYSIS

For a number of resonances, one-level analysis did not yield satisfactory results. Multi-level analysis was not tried, because the number of contributing levels in most cases can be easily estimated. In such cases, a simple analysis in terms of Legendre polynomials Pi(cos 0) was performed. In the least-squares fit to the theoretical distribution

W(O) = • AiPi(cos 0),

A o = 1,

i

also odd terms were taken in account. The coefficients Ai for these cases are also included in table 1. The existence, in some cases, o f odd terms does support the assumption of overlapping levels. It should be kept in mind, however, that 90 ° symmetry of the angular distribution does not exclude the possibility of a multi-level case. On the basis of a one-level resonance analysis, the resonance spin was uniquely determined for 28 resonances. In 32 cases, two possible spins and parities emerge from the analysis. In these cases, a unique answer would require additional (p, 7) or (p, p) work. The isotropic angular distributions at four resonances allow spin assignments of 0 +, 1 - and 2 +. Best fits of some of the angular distributions are given, together with the measured points, in figs. 5 and 6.

5. Discussion of the results 5.1. Y I E L D C U R V E

Information on the 38Ar compound nucleus energy levels, gathered before 1962, was summarized by Endt and Van der Leun 2). We shall restrict our discussion to a comparison of our results with more recent data. Resonances in the 37C1(p ~)38Ar reaction are reported in refs. 2,7). In column six of table 1, resonances are listed which decay by both ~o and ~ emission. We see that out of 130 resonances, found in (p, ~0) work between Ep = 850 and 1950 keV, about eighty are also 7-ray emitters. On the other hand, there are about one hundred

1/2

I

• cos~O

}

~

k

1000

_

/

J~//

1/2

, c o s~ e

./..U f

Ep = 1 6 3 4 . 0 keV

-

_

cos~e

./~

_1 __[ 1/2

.f/"Y

_2000 3n=3 -

0

0

i .

500

1000

E•=

1164 5 keV 3 = 4"

o

000

Ep=1293 8 keV 3TM = 1-,2"

500

1

/

1/2

I

/

3 n = 4*

I

;, cos2e

/J

0

Isoo

1/2

I

~ = 2"

1

I

I

, cos'e

1/2

__-,,. COS2(~ >.

/

I

0

I

~ --

r~

I

. C0S20

~00 +----~. - - -

<

1/2

I

- - ~

_

1000

Ep = 15001 keV J~ = 0",1-,2"

Ep= 1 7 3 8 7 keV

lOOO

000

2000

_3oob>~ . . . . . ~

0

0

f O00

Fig. 5. Typical angular distributions o f the % particles at eight different resonances. The solid lines give the best fits on the basis o f the channel spin formalism.

0

l

Ep = 1 5 8 9 . 6 keV

[

/

_

COSZO

1/2

--.,

0

~ooo

//

Ep= 1142 3 keV

3"~=3

il o o o /

o!

644

B. BO~NJAKOVI(~et al.

(P, 7) resonances in the same energy region which are not found in the (p, ~o) reaction. This could be attributed to the fact that many (p, y) strengths do not exceed the detection threshold. The only recent publication on the 37C1(p, ~o)34S reaction is ref. 4). The resonance energies ~eported there seem to be systematically almost 10 keV higher than ours. A thorough comparison was difficult because the measurements reported in ref. 4) have been done with much lower energy resolution. E.g., their resonance at Ep = 1624 keV was resolved in our measurements into a quadruplet of resonances at Ep = 1607.3, 1611.9, 1616.2 and 1620.6 keV. The 3VCl(p, p)3VC1 resonances, mentioned in ref. 4), have not been listed. A recent high-resolution investigation of the 37Cl(p, n)3VAr reaction by Parks et al. 22) allows a comparison with our work only in the narrow energy region Ep = 1640-1710 keV. By comparing the (p, ~), (p, n) and (p, Cto) data, we conclude that the resonance energies reported in ref. 22) are about 2 keV higher than in our (P, ~o) work.

D 0k) 2000

Ep = 1 8 6 0 . 6 3"= 2*

keY

I

I

ooo

/

cOS2 -0 '~

1/2

1

i

tr

X,

N

000'"

0

kev [

,Q

• " ~ ' ~ x

/

--I

E0=

i

----e cos @",.[ 0

I

I

1/2

J

1

Fig. 6. Two examples of extremely anisotropic angular distributions. For discussion, see subsect. 6.3. Our determinations of the resonance widths F, listed in column five, are not very accurate. As could be expected, practically all cases with a measurable width were found above the (p, n) reaction threshold a t Ep = 1640 keV. 5.2. LEVEL DENSITY Between Ep = 850 keV and Ep = 1950 keV, 130 resonances have been found. This corresponds to a mean level spacing of D = 8.5 keV at the mean excitation energy E X = 11.6 MeV in the compound nucleus. The distribution of the nearestneighbour resonance spacings S, expressed in units of the mean spacing D, is given in fig. 7 as a histogram. As at least five different J~ combinations contribute to the observed yield curve, we do not expect a Wigner-type level spacing distribution, but rather a Poisson distribution 23) e x p ( - S / D ) . The Poisson curve fits well the measured distribution down to S / D = 0.25. The dip between S / D = 0 and 0.25 is due to the

aSAr LEVELS

645

limited resolution of our experiment and indicates that in the investigated energy region about thirty unresolved doublets should exist. If we take these missing levels into account, we find an "experimental" level spacing Dexp = 6.9 keV, equivalent to an "experimental" level density Pexp = 145 M e V - ' . This result will be compared with the semi-empirical predictions of Newton 2,), and of Gilbert, Chen and Cameron (ref. 25)). The J~ dependence of the "partial" mean level spacings D(J ~) is, according to Ericson 26) D(J =) = D o ( 2 J + 1) -1 exp [ 3 ( J + 1)/2a2]. Here, D O is a level spacing not dependent on J, to be calculated from the formula given by Newton. The parameter a, discussed by Gilbert and Cameron 27), should have a value between tr = 2.0 and 3.5. We assume that resonances up to J~ = 4 + are detectable. This means that the experimental mean level spacing should be

F z D

DISTRIBUTION OF LEVEL SPACINGS 129 spacings

I

[

' m4O~ CI:I ~ ; 'X: W 3oP

J/ / Poisson distribution- e -s/e

2oL

2

0

3 -

S]D

4

5

Fig. 7. Histogram of the distribution of the nearest neighbour resonance spacing S. This spacing is given in units of the mean level spacing D. The smooth curve is the Poisson distribution e-S/O. compared with the predicted value of 4

Dpro. = {

E

J=0 natural parity

-'

Applying a correction for Do, given by Preston 2a), w e find Do = 60 keV, so that with a = 2.5 we obtain Opred

=

5.4 keV.

Another semi-empirical prediction can be deduced from the arguments given by Gilbert, Chen and Cameron 25). They showed that the total level density can be written as p = T -1 exp {(E,,-Eo)/T}, where E, is again the compound excitatioo energy, Eo is an arbitrary ground-state energy and T is the nuclear temperature. From the plot in ref. 25), we estimated the value of E 0 to be 1.2 MeV for 3BAr. The inverse nuclear temperature was computed f r o m T - 1 = 0.0165 A MeV -1 to be T - t = 0.63 MeV - t . The fraction of levels

646

B. BO~NJAKOVId et al.

observed in our experiment is f =

4 ~2 s o =

(2J+l) - 4a ~

exp {(d + ½)2/2a2}.

natural parity

With a = 2.5 we o b t a i n f = 0.436. Thus, for an excitation energy Ex = 11.6 MeV, the predicted density is Pprea = f T - I exp {(E x - Eo)/T} = 174 M e V - ~. We conclude, that there is a reasonable agreement o f the measured level density both with N e w t o n ' s formula and with the predictions o f Gilbert, Chen and Cameron. Both predicted values are somewhat higher than the measured one. This can be explained when we recognize that even some o f the low-spin resonances may be suppressed in the experiment if they are formed preferentially with a high p r o t o n orbital m o m e n t u m , it should be pointed out, however, that none o f the theoretical consideration on level densities take in account possible enhancement o f resonance strengths by analogue states. The discussion in sect. 6 shows that analogue state enhancement may play an important role. 5.3. SPINS A N D F O R M A T I O N S

Most o f the spin assignments to 38At states have not been reported before. The spin assignments o f the Russian group 4) seem to be inconclusive in m a n y cases because o f the lower energy resolution. Still, in some cases, they analysed resonances which are isolated enough to allow conclusive results. In such cases fair agreement exists with our results. Two interesting examples o f unexpected formation are the resonances at E v = 1591.8 keV (J~ = 1 - ) and E v = 1860.6 keV (J~ = 2+). The pronounced anisotropies o f the angular distributions are shown in fig. 6. Both resonances are formed almost 100 °/~othrough the s = 1 channel. Theoretically, the formation o f the two resonances is not well understood. It was tried to analyse the two cases in terms of L-S and j-j coupling schemes. Assuming a (ld~)~_ configuration for the 37C1 g r o u n d state, we couple the target p r o t o n spin st = ~ with the bombarding p r o t o n spin s o = ½ to a total spin S = 0 or 1. Similally, we couple the target nucleus orbital m o m e n t u m It = 2 with the orbital m o m e n t u m lp o f the b o m b a r d i n g p r o t o n to a total orbital m o m e n t u m L. For a given total spin S, we obtain the intensity ratio for channel spins s 1 = 1 and s, = 2 from the formula 29) z-

1-'c

_ (2s1+ 1)W2(lpltJS, LSl)WZ(spstsl It, Sjt)

(2sz+l)WZ(lpZtJS, Lsz)WZ(spStszlt, Sj,)"

Here, J is the resonance spin, Jt the target nucleus spin and the W are R a c a h coefficients. The predicted values o f r for different values o f the total spin S in L-S coupling

647

aSAr LEVELS

are compared with the measured ones:

Ep : 1591.8 keV Eo = 1860.6 keV

T(S = 0)

r(S = 1)

T(measured)

0 0

6/14 7/1o

0.985~:0.012 0.965j-0.020

The measured values apparently disagree with both values predicted by the L-S coupling scheme. We performed a similar analysis under the assumptions ofj-j coupling. The s = 1 proton capture could not be assigned to a limiting case of the j-j coupling scheme either. 6. The isobaric analogues of the lowest two excited states in asCl The ground state and lowest three excited states of the nucleus 38C1 have spin and parity J= = 2 - , 5-, ( 3 - ) and (4-), respectively 30), and isospin T = 2. The analogue states in 3BAr are expected at excitation energies between 10.6 MeV and 12.0 MeV. These levels should appear as compound states in the 37C1+p reactions at proton bombarding energies between 0.4 and 1.8 MeV. The J~ = 5- doublet, found in the 37C1(p, 2)38Ar reaction at Ep = 1088 keV and 1092 keV 2), could accordingly be interpreted by Ern6 et al. as the split analogue of the first excited state in 38C1. As the ground state of 34S has T = 1, the emission of ~o particles from T = 2 resonance states in 3SAr is T-forbidden. The generalization of this statement is: if the isospin of the compound nucleus ground state is T = T <, then (p, 7 o) excitation of T > = T + 1 compound states is T-forbidden. This may be the reason that searches for analogue states through the (p, 7o) reaction have not been reported before. On the other hand, enhancement of T < resonance strengths by T > analogue states has been predicted theoretically. According to the arguments by Wigner 3l), the strength of the analogue T > state is distributed over T < compound states. This effect should be measureable in the 37C1(p, %)34S reaction. The measured resonance strengths are proportional to Tp F~o/F. Due to the positive Q-value of the reaction Fp will be small compared to F~o for Ep ~ 1.5 MeV. Since also F~ << F~o, one finds F~o ~ F, and thus the (p, ~o) resonance strengths are essentially determined by Fp. The simple configurations of the analogue resonances in 38At, which correspond to low excited states of 38C1, imply large proton widths relative to those of neighbouring resonances, Therefore the analogue resonances are expected to stand out as relatively strong resonances in the yield curve. Due to m o m e n t u m and parity conservation, only the natural parity analogue states (J~ = 3- and 5 - ) can be excited in the 37Cl(p, go)34S reaction. 6.1. THE

Jn

~

3- ANALOGUE STATE

The strengths of 3- resonances, reduced to Fp F=o/F2P~,, where Ptp is the proton

648

B. BOSNJAKOVIC et al.

penetrability for orbital momentum lp, are plotted in the upper part of fig. 8 as a function of Ep. For some weaker resonances, included in the plot, the J~ = 3 assignment is not unique but very probable (see subsect. 4.1 ). A micro-giant resonance structure emerges distinctly. In the lower part of fig. 8 the drawn line represents the integrated reduced strengths of the 3- resonances. The dotted line is a similar plot for the J~ = 2 + reduced resonance strengths. In the latter, resonances with nonunique j n = 2 + assignments are also included. Whereas the integrated 3 - resonance strengths show a jump at about 1.14 MeV, there is no comparable j u m p for 2 + I8.10 F~

s

3

7

!

INTEGRATED REDUCE[:) STENGTHS IN WIGNER LIMIT UNITS

1 0

........

2*

' , ~ 0.8

P

lL

2

)

I

R E D U C E D STRENGT OF 3- R E S O N A N C E S ;rq W!GNER LH,4rT UNITS

± ~ 1.0

~ _ _ ~ _ ~ _ 1.2 1.4 -

,. . . . . .

; ..... : ....

-

,

~ 1.6 -

-

-

,

I~.~ 1.8

2.O

Er,( M eV )

Fig. 8. U p p e r p a r t : D i s t r i b u t i o n o f t h e r e d u c e d s t r e n g t h s o f 3 - r e s o n a n c e s in t h e 37C1(p, :c0)34S r e a c t i o n . L o w e r p a r t : I n t e g r a t e d r e d u c e d s t r e n g t h s o f 3 - ( d r a w n line) a n d 2 + ( d a s h e d line) r e s o n a n c e s . T h e t h i c k a r r o w i n d i c a t e s t h e e x p e c t e d p o s i t i o n o f t h e J = = 3 - a n a l o g u e state.

resonances. Comparison of the integrated strengths of J~ = 2 + and 3 - resonances is meaningful since the ratios of the proton and ~o penetrabilities are nearly identical for these two J~ values if the proton capture is assumed to occur with the lowest possible lp value. It should be noted that the curves of fig. 8 may be distorted for Ep > 1.5 MeV, since the assumption Fp << F~o may be invalid at the higher proton energies. Other possible distortions could stem from the fact that J~ values were not

~SArLrWLS

649

measured for all resonances, either due to the weak strengths or because doublets could not be resolved. The position of the jump has to be compared with the expected excitation energy of the J~ = 3- analogue state. According to Rapaport and Buechner 3o), the energy difference between the first and second excited state in 3SC1 amounts to 85 keV. According to Ern6 et al. 2), the analogue of the first excited state is centered around Ep = 1090 keV, so the analogue of the second excited state in 38C1 should be expected at Ep -- 1175 keV. This energy, indicated by an arrow in the lower part of fig. 8, is in fair agreement with the position of the jump in the integrated strength curve. One has to take into account the fact that the centroid of the enhanced T < resonances need not necessarily coincide with the energy of the analogue T > state. The shape of the micro-giant resonance gives some evidence for possible asymmetry, predicted by Robson's theory 32). In this respect, the gap between Ep = 1280 and 1585 keV is remarkable. Still, a fit to the cross-section formula of Robson would require an unacceptably large giant resonance width. An explanation may be sought in the fact that Robson's theory is formulated for Fp ~ F which is certainly not true in this case. The reduced strengths of the micro-giant resonance can be compared with the spectroscopic factor of the second excited state in 38C1, as measured in the 37C1(d, p)38C1 reaction by Rapaport and Buechner 30). These authors find for the 3 - state Sa = 0.59, S 1 = 0.09, where S~ is the spectroscopic factor for orbital m o m e n t u m l. In the (p, c%) reaction, the penetrability for p-capture is 180 times higher than for f-capture. Therefore the f-capture contribution to the (p, So) reaction is expected to be less than 4 %. This is confirmed in our experiment. The reduced proton width in the (p, % ) reaction will be approximately 02p = 0.25 S 1. The factor 0.25 arises from isospin vector coupling. Thus the calculated value is 02 = 0.023. The experimental value is the step in the integrated reduced strengths curve of the 3- resonances in fig. 8; it amounts to 0.019 (if we take the resonances in the Ep = 1.0-1.3 MeV region), in excellent agreement with the value calculated from the (d, p) work. 6.2. THE jR = 5- ANALOGUE STATE The detection of the J~ = 5- analogue state in the (p, % ) reaction leads to some experimental difficulties. First of all, a simultaneous measurement of the (p, 7) and (P, ~o) yields was performed, as described in sect. 3. The result is partly shown in fig. 9. Between the two J~ = 5 - ( p , 7) resonances a strong J~ = 1- or 2 + resonance was found in the (p, % ) reaction. Using our energy calibration, we label the (p, 7) resonances as Ep = 1089.0 and 1094.2 keV, whereas the (p, % ) resonance has E o = 1092.6 keV (see also table 1). In a second step, the neighbourhood of the E~ = 1092.6 keV resonance was investigated with much better statistics. The result, after background subtraction, is shown in fig. 10, on a logarithmic scale. There is a very distinct structure at the foot of the strong (p, So) resonance. The shape of a single resonance was measured with

650

~. BOSNJAKOVIC et al.

500 3 7 C I , ~p, lf)ArJ 38

d)

r-- 4 0 0

1OO

1 0 8 9 kmV 1 0 9 4 k e V

l'

[ -

!093k¢

2000

Cl(p,O
!

Zooo

i

'r

i

I I

---~,,--

'

1090 PROTON

i

!!O.0 ENERGY,[ke.')

Fig. 9. The yields o f the 37C1(p, 7)3SAr and 37C1(p, ~)3~S reactions between Ev = 1082 a nd 1102 keV. The 3.7-10.0 MeV g a m m a rays are detected with a N a l crystal, the % particles are c ount e d ~ i t h a s e m i - c o n d u c t o r detector. Both counters are fixed at 135h The m e a s u r e m e n t s are p e r f o r m e d s i m u l t a n e o u s l y with the same target.

'7

-

[

-

T

Ep = 1 0 8 9 0 1092 6 keV Z

Ep ~ 11383

11423 keV

I

Z

O©

"

-

© 1ooo, ~

il il'

I,

,' 1

¢

lOO

4

[ I

l

[

i__ l o

i L:L- 1 1085

L

+ ;il t " } A. 1090

1095

J_ [~L#, r ' 1100

1~35

1140

1145

PROTON ENERGY (keV) Fig. 10. Parts o f the 3vCl(p, ~0)~S yield curve, m e a s u r e d with i m p r o v e d statistics a nd pl ot t e d on an e x p a n d e d energy scale. The 1138 keV resonance was m e a s u r e d to de t e rmi ne the s t a n d a r d re s ona nc e f r o n t sh ape at this energy. The left-hand section reveals the existence of a resonance at Ep = 1089 keV.

aSAr LEVELS

651

the same target at Ep = 1138.3 keV. The drawn line in the left-hand section of fig. 10 is a fit to the measured points under the assumptions that a) there are two resonances at Ep = 1089.0 and 1092.6 keV, and b) both have the shape of the resonance at Ep = 1138.3 keV. As a result of the fitting procedure, the yield of the Ep = 1089.0 keV resonance is found as (2J+I)FpF,o/F = 0.4+_0.2 eV. The higher resonance of the doublet, at Ep = 1094 keV, is obscured by the tail of the strong 1092.6 keV resonance. A discussion of the J~ = 5- analogue state similar to that given for J~ = 3- is impossible, because the strength of only one 5- resonance exceeds the detection threshold. Moreover the resonance strength is limited by F,o and not by Fp; this follows from a comparison of the (p, 7) and (p, % ) strengths at this resonance. In the literature the excitation of a resonance in a (p, :~) reaction was often used as a criterion in assigning a T-value to the resonance. The present investigation shows that under certain circumstances the T-selection rule can be strongly violated in a (p, :~) reaction. In some cases, the (p, :0 reaction can even be used as a competing tool for the study of analogue states. The authors thank Professor P. M. Endt for his stimulating guidance in all stages of the investigation. Advice from Drs. J. Kuperus and F. C. Ern6 was gratefully accepted. Drs. P. J. Brussaard and C. van der Leun kindly criticized the manuscript. The authors are much indebted to W. A. M. Veltman and H. S. Pruys for their help during long runs. This investigation was partly supported by the joint research program of the "Stichting voor Fundamenteel Onderzoek der Materie" and the "Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek".

References 1) J. Kuperus, P. W. M. Glaudemans and P. M. Endt, Physica 29 (1963) 1281 2) F. C. Ern6, W. A. M. Veltman and J. A. J. M. Wintermans, Nuclear Physics 88 (1966) l; F. C. Ern6 and W. A. M. Veltman, University of Utrecht, private communication 3) R. L. Clarke, E. Almqvist and E. B. Paul, Nuclear Physics 14 (1959/60) 472 4) K. V. Karad~ev, V. I. Man'ko and F. E. Cukreev, J. of Nucl. Phys. (USSR) 4 (1966) 909 5) F. C. Ern6, in: Proceedings of the seminar on the preparation and standardisation of isotopic targets and foils, Harwell, October 20 and 21, 1965 6) J. Kuperus, Thesis, Utrecht University, 1965 7) E. Simons et al., Soc. Sci. Fennica, Comm. Phys.-Math. 30 (1965) 6 8) J. B. Marion, U.S.A.E.C. Nuclear Data TaMes 1960, Part 3 (U.S. Gov. Printing Office, Washington 25, D.C.) 9) J. B. Marion, Proc. 2nd Int. Conf. on Nuclidic Masses, Vienna 1963 (Springer-Verlag, Berlin, 1964) 10) A. W. Borgi and O. L(Snsj(J, Corrected values for some proton capture reactions (Fysisk lnstitutt, Oslo Universitet, Oslo, Jan. 1964) 11) F. C. Ern6 and P. M. Endt, Nuclear Physics 71 (1965) 593 12) M. Heitzmann and S. Wagner, Z. Naturf. 16a (1961) 1136 13) J. H. E. Mattauch, W. Thiele and A. H, Wapstra, Nuclear Physics 67 (1965) 32

652

B. BO~,NJAKOV~6et aL

14) H. E. Gove, in: Nuclear Reactions I, ed. by P. M. Endt and M. Demeur (North-Holland Publishing Company, Amsterdam, 1959) 15) H. A. Van Rinsvelt, Thesis, Utrecht University, 1965 16) J. M. Blatt and L. C. Biedenharn, Rev. Mod. Phys. 24 (1952) 258 17) C. E. FrOberg, Rev. Mod. Phys. 27 (1955) 399 18) H. Feshbach, M. M. Shapiro and V. F. Weisskopf, Nuclear Development Associates Inc. Report NYO - 3077 (1953) 19) A. Heyligers, Thesis, Utrecht University, 1964 20) R. Nordhagen, Physica Norvegica 1 (1963) 193 21) P. M. Endt and C. van der Leun, Nuclear Physics 34 (1962) I 22) P. B. Parks, E. M. Beard, E. G. Bilpuch and H. W. Newson, Nuclear Physics 85 (1966) 504 23) N. Rosenzweig and C. E. Porter, Phys. Rev. 120 (1960) 1698 24) T. D. Newton, Can. J. Phys. 34 (1956) 804 25) A. Gilbert, F. S. Chen and A. G. W. Cameron, Can. J. Phys. 43 (1965) 1248 26) T. Ericson, Nuclear Physics 11 (1959) 481 27) A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43 (1965) 1446 28) M. A. Preston, Physics of the nucleus (Addison-Wesley Publishing Company, Reading, 1962), p. 527 29) W. T. Sharp, J. M. Kennedy, B. J. Sears and M. G. Hoyle, Atomic Energy of Canada Ltd. Report AECL - 97, Chalk River, 1953 30) J. Rapaport and W. W. Buechner, Nuclear Physics 83 (1966) 80 31) E. P. Wigner, in: Isobaric spin in nuclear physics, ed. by J. D. Fox and D. Robson (Academic Press, New York, 1966) 32) D. Robson, Phys. Rev. 137 (1965) B535