High resolution proton inelastic scattering from 50Cr

F&B. 2XI

Nuckar Physics A279 (1977) 430 -4" ; @ Nor&Hoakad PubUdkhW Co., Amsta-dan Not to be rqwoducod by photoprint or micwffim widiout written perededon hom the publisher

HIGH RLSOLLMON PR(ffON DCELAMC SCAMM[NG FROM Bo Cr T. R. DITTRICH, C- R. GOULD and 0. E. MITCHELL North Carolina State UnkwWW RakI#k North Carolina and Trianok Universilks Nuclear Laboratory Dirhant, North CaroUnat

and

E. G. BLLPUCH and IL STELZER tt

Duke UnIvwWV and TUNV, Diwham, North Caroftna

Received 13 September 1976 Abstract : Resonances In the "Cr(p, P'Y) reaction were investigated with the TUNL high resolution system All prmouslY observed P-wavo resonances between E, - 2.00 and 3 .03 MoV were

studied. Measurement of the p' and the y-ray angular distributions provides sufficient infor mation to determine unambiguously theJ-valuo oftheresonance and ther-mitude and relative phase of the ineingti docay amplitu&L Expressions are given for the appropriate angular distributions andfor the transformation between the channelspin and the total angulu momentum irepresentation. Experimental results am presented for 24 p-wave resonances in "Ma including docay amplitudes and relative phases for 16 f- resonances . Six resonances formerly assigned *are reassigned J- . Inele tic spectroscopic factors were determined for two analoguo statm Pro. ton sbvngth functions wore evaluated from both the elastic and inclastic data.

E

NUCLEAR REAMONS 5 OCr(p, p), (p, p'), E - 100-3.03 MoV ; measured a(O) at 24 p-wave resonances. -"Mn deducedf, Mr, magnitudo and relative phase of inelastic decay amplitudes, spectroscopic factors, proton strength functions.

rp,,

1. Utroducdm The measurement of multipole mixing ratios of electromagnetic transitions has long been ofvalue in nuclear spectroscopy. An analogous quantity, the channel spin (s-spin) mixing ratio, is convenient in the description of nuclear reactions proceeding through compound nuclear states . In practice the s-spin mixing ratio was regarded as at most a formally useful quantity. The s-spin mixing ratio (or the related quantity, the total angular momentum or J-spin mixing ratio) Is interesting, however, because it provides both phase and amplitude information. Earlier investigations of the magnitudes of s-spin mixing ratios include that of De Meijer et af. 1), who investigated resonances in 41 Ca with the 41 K(p, cc)"Ar reaction, and of Chrien et al. '), who studied p-wave resonances in neutron capture t Supported in part by the United Sta ERDA~ tt On leave from University of Frankfurt, Germany. 430

5 OCr+P

431

on 93Nb. In neither experiment was information about relative phases obtained. Angular correlation measurements on isolated resonances provide detailed phase and amplitude information; a number of such experiments have been performed on analogue States 3). Such information may also be obtained by polarization measurements 4 )_ Our group pointed out that under restricted conditions two singles measurements are sufacient to determine both the magnitude and sign of the mixing ratio. The key point is that these simple, fast experiments mal~e feasible the study of large numbers of resonances . The following discussion is limited to inelastic scattering from p-wave resonances . At TUNL we have performed an extensive series of high resolution proton resonance measurements [see the comprehensive review by Bilpuch et a[. 6)]. We are frequently unable to distinguish between p* and p* resonances on the basis of elastic scattering alone. The measurement of the angular distribution of the inelastically scattered protons and of the subsequent de-excitation y-rays is sufficient to distinguish unambiguously between the two J-values and to determine the magnitude and sign of the mildn ratio. The spin assignments are particularly useful in the determination of proton strength functions and for examination of detailed statistical properties of single Level populations. The amplitude information is . important to establish the analogue inelastic spectroscopic factors. In addition to thew spectroscopic applications, the capability of rapidly obtaining phase and amplitude information leads to several new possibilities. One possibility is direct " more test of the random phase approximation than previously obtained. For " suitable sample of compound nuclear resonances the signs of the mixing ratios can be determined. Since the amplitudes of the two channel spin (or total angular momentum) components should separately follow normal distributions, the relative phase between the two components should be random. Conversely~ under certain conditions non-statistical behavior may be expected in the relative phases for frag. mented analogue states. nus the measurement of mixing ratios has a variety of potentially interesting applications. In the present paper we report on the first of a series of measurements of mixing ratios in the inelastic decay of isolated compound nuclear resonances . For this first experiment a target nucleus ('*Cr) was chosen with a relatively low density of compound nuclear resonances . In sect. 2 the theoretical expressions for the particle and r-ray angular distributions are presented and the analysis procedure discussed. Expressions are given for transformation between the channel spin representation and the equivalent total angular momentum representation. The experimental arrangement and procedure is briefly described in sect. 3. The data are presented in sect . 4. In the final section the general results for the spins, decay amplitudes and Inelastic relative phases are discussed. spectroscopic factors are determined for the analogue states. With the corrected spin assignments the p-wave strength functions are re-evaluated .

432

T. R. DnrMCK et al.

2. 11mmy angular The general treatment of correlations is discussed by a number of authors 8 13). Here we are concerned with the (13~ p?) reaction ; Krau et al. 14) provide expressions for the angular distributions, resulting from reactions of this type. 17he notation adopted is shown in fig. 1. Only p-wave resonances are considere& Under the conditions assumed here (A - 0', C - 2* and D - 011) 1- resonances have a unique exit channel spin, while I- resonances can decay by s' - I and 1. /j*

B .3

ENTRANCE CHANNEL CHANNEL SPIN REPRESENIATION TOTAL ANsuLAR MOMENTUM KEPRESENTAnON

I

EXIT HANNEL

T-!+TP S-Z+T

Fig. 1. Schwnadc of the hmhode roactkm and the engula momentum

COUPlint

equati=&

We assume that only one exit 1 1 value contributa in the decay of the p-wave resonances . For *- resonances both the p' and the ?-ray angular distributions are isotropic; for J - resonances one or the other of the distributions may be isotropic, but not both simul my:ously. Thus the two angular distributions are sufficient to uniquely determine the spin of the p-wave resonances. For I- resonances the two angular distributions also provide a determination of the magnitude and sign of the ratio robdin (see expressions below) . Fbxther, for unresolved doublets the two measurements lead to inconsistencies in the value of the Tni3rin ratio. For the situation assumed hem (see fig. 1), the angular distributions in the s-spin representation are jjI2_ 4rl< SL>12 (2.1) w(op') oc 1+ P2(ele)p 1

I12 + II2

1 F'II2 -2[*+<4>*] +41<4>1 21 W2(0'1~ >12+ 1<4>12 i io L

W(0") cc I + -

I
(2.2)

where Q is an attenuation coefficient, P a Legendre polynomial and <,%> and a corresponds to JIB> and corresponds to . 71m eqWvalent expressions for the angular distributions in the total angular momentum or J-spin representation are

easily derived since the transformation from the s-spin to the J-spin representation is simply (2.3) - VIE+2], - /-Tf[-2+].

It is convenient to define both a S-spin mixing ratio and the analogous quantity

(2.4)

se - V - DKS, - D,

(2.5)

01 = 0/01 = 0.

(2.6)

in thej-spin representation j,F -

From the expressions for the angular distributions [eqs. (2-1) and (2.2)] one obtains +5a2 1/-4r i--5a2

2±542--aj-4a22 4-10a2

(2.7)

9

(2 .8)

when a2 is the normalized coefficient of the appropriate P2 between Se and Jr is simply Jj, = (2+6,e)1(1-26,e) .

term. The connection

It is also convenient (as in the study of inultipole mixing in sitions) to define

tran-

(2.9)

(2.10)

The connection between Oj, and O e is (for I- resonances)

0j, - 46,e-tan -1 (-2).

(2.11)

The a2 coefficient is plotted versus # (in the s-spin representation) in 11g. 2. Then are several points of interest in this plot. First, as mentioned above, either the particle or the 7-ray distribution may be isotropic, bat not both simultaneously. Second, the s-spin mixing is incoherent in the particle distribution and coherent in the ?-ray distribution ", "). In the j-spin representation the converse holds: thejspin irnbriln is coherent in the particle distribution and incoherent in the 1-ray distribution. This may be interpreted with the aid of fig. 2. In thepspin representation the car,ves of a2 versus q5 are found by translating the curves of fig. 2 to the right by 63.43" (tan-'(-2)). The 7-ray curve then becomes symmetric about q6 - 0* and the proton curve becomes asymmetric. Third, whenever the slope of one a2 versus 45 curve is small (e.g., near q5 - -60* and +30* for 7-rays and 0 - 0* for protons), the slope ofthe other cam is large. Thus # can be rather well determined throughout its range.

434

T. IL DrrTRICH et al.

(h

Fig.2.Thaa2 coefflcimtvmusTnbdn ratio for proton andrray angular dWribntions in the dien spin representation .

I

3. FxperhnenW procedure This experiment was performed with the high resolution proton beam of the TUNL 3 MV Van de Graaff laboratory' 5). The reaction studied was 5OC4, p') 50cr* (0.782 MeV). Since previous elastic scattering measurements 7) indicated a rather low density of observed resonances, problems caused by overlapping resonances were minimized in this initial experiment. (Most of the present data were obtained with an overall resolution of 600 eV, rather than the 300-400 eV resolution we normally achieve. This resolution was sufficient for the present experiment .) Targets were prepared by evaporation of chromium (enriched to 95.9 % 5 OCr) onto carbon foils. Typical target thichmesses were 1 .0-1 .5 pg(cm' ; the carbon foils were nominally 5 pg /=~. Particles were detected with silicon surface barrier detectors located at lab angles of 90*, 105"', 135* and 160* . Relative solid angles for the detectors were determined with Rutherford scattering. The scattering chamber used was that employed in our previous elastic scattering measurements. Resonances were selected for study based onthe results ofMoses et at. '). Spectra were collected with an on-line computer, then recorded on magnetic tape for later processing and analysis. Excitation functions for elastic and inelastic scattering were first measured for each resonance studied. For all resonances with sufficient inelastic yield, spectra were then accumulated (for a much longer tune) at the resonance energy. For measurements of the 7-ray angular distributions a small, thin-walled scattering chamber' 'I ) was used. The y-rays were detected with 7.6 cm x 7.6 cm, Nal(TI) crystals located at lab angles of 30% 45% 60* and 90*. One particle detector was

located at 135* ; measurement of the elastic scattering excitation function ensured that the same resonance was studied in the different experiments. After the resonance was located, a 7-ray spectrum was accumulated at the resonance energy. Relative normalization for the NaI(M) detectors was determined with ?-rays from the 0.842 MeV state of "Al. This level is populated with the I'Mg(p, 7) reaction at the E,0 - 2.182 MeV capture resonance. The resulting 0.842 MeV I-ray has an isotropic angular distribution and is close in energy to the 0.782 MeV 7-ray of interest . An 80 cml Ge(Li) detector also monitored the I-ray to ensure that unwanted 7-rays were not included in the poorer resolution Nal(11) spectra. The 7-ray spectra were quite simple and free of significant background lines in the energy region of interest. 4. Data al. 7) Moses et observed a total of 34 P-wave resonances in the 5 OCr(p, p) reaction in the energy range of this experiment, Ep = 2.00 to 3.03 MeV. We measured exocitation functions for all of these resonances, with a typical range of 3 keV on either side of at 160* is shown in E& 3, allthe resonance energy. ne elastic excitation function with of the p-wave resonances numbered for later reference. The elastic and inin elastic widths and reduced widths for these 34 resonances are listed table 1. In addition to the total inelastic width, the reduced widths for inelastic decay withj' andf - are also listed. For ten of these resonances the inelastic scattering was too weak to study; these resonances have r,,, < I eV and are labelled "weak" in table 1. Angular distributions were measured for both the inelastically scattered protons and the de-excitation 7-rays . Yields were normalized as described in sect. 3. The resulting angalar distributions were fit to an expansion of the form ao(I +a2P2(0)). TheP = 3 term was neglected sincethe ratio of the penetrabilities P(P -- I)IP(P = 3) is 100 at E. = 2 MeV and 50 at Ep = 3 MeV. The resulting al values for the l- resonances are listed in table 2 for both the p' and the V-ray experiments, along with the value of 6,,, which results fromeach experiment. Six resonances (numbers 8, 14, 22, 24, 27 and 34) have isotropic angular distributions and are assigned P - -, in agreement withMoses et al. For two resonances (numbers 3 and 17) the mixing ratios All determined in the two eaperiments, are inconsistent Oust outside the errors). of the remaining resonances appear to have - and yield internally consistent values for the mixing ratio. Six of these resonances (numbers 2, 7, 16, 17, 32 and 33) were assigned P - - by Moses et al. The first four of these resonances have rather small elastic widths and spin misassigament on the basis of elastic scattering alone is not surprising. Resonances 32 and 33 are fairly strong in elastic scattering; the reason for the disagreement in spin assignments for these resonances is not clear. The only other available data is that ofKyker et al. 17), who measured the (p, p',j) angular distributions (but not the pI angular distributions) in the energy range Ep = 2.15 to 2.85 MeV. The energy resolution in their experiment was much worse

I

I

I

J' = I

I

436

T. R. DnTRICH et al. 50C r p .

is 12

p)

511Vr

160"

... . . . . . . . . . . .

6-

IÀ5 ' "

12-

4

.3

Lk '

Là5 '

é~ ',

4.6

d

C)

6X -

(f)

i-

0

Z) 0 . (_) 6

a

~

10

2.à5 '

2Là5 H'

'* '

13

12

' 2*0 .

2À5 '

,

'

24

25%

225

2-k 14 15

' 2SO '

'

' - ' 9.65 1

21

17

6-

0~

215 ,

P_ l'O

.

.29

30 3r4

2SIIV -- ----m-o

Ep (MeV)

Fig. 3. The IOCr(p . p) owitation.function at 160*. All p-wave resonances in bered for later reference.

this

W5

energy range are num-

than that in the present experiment or in the elastic scattering experiment. Kykw et al. studied resonances 7-9, 12,13, 16, 17, 19, and 21-24, Forresonances 7, 16 and 17, they assign J' - I - in agreement with the present results and in disagreement with the assignments of Moses ef at. For resonances 22 and 24 Kyber et at claim I - and J*, respectively . Both the present results and those of Moses et at. give I- assignments for both resonanceL The overall agreement among the three expemnents is satisfactory.

437

80 0r+p TAXE 1

The p-wave resonances in "Mn ReLl) 1 2 3 4 5 6 7 8 9 10 ll 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 29 29 30 31 32 33 34

4

iff

. r,

V,2b)

OOM

F9, (OV)

V,,I(r _ J)b)

(OV)

2.0388 2.0615 2.1077 2.1330 2.1574 2.2335 2.2972 2.3194 2.3293 2.3554 2.4136 Z4539 2A920 2.5191 2.5206 2.5495 2.6283 2.6747 2.6946 2.7242 2.7490 2.7812 2.Ml 2.9229 2.8470 2.9549 2.8553 2.9224 2.9325 2-9599 2.9854 3.0021 3.0226 3.0292

1-

15± 5 20± 5 0 77±10 340±50 15± 5 380±50 30±10* 350±300 550±55 50±10 30±20 45±15 130d :25 100d:20* 100±20 2D±10 30±10 40±15 375±50* 10-+ 5 500±50 1400±20D 75±15* 275±25* 20±10 6D±200 700±1500 3500±200 445±50 0 550±50 0 500±30 100±200 90d:20* 1350±150

1.31 1.61* 5.26 21-25 0.86 17.05 1.84* 12.060 ISAO 1.57 2.13 1.06 2.77 1.990 1.98 0.37 0.46 0.54 4,88* 0.12 5.77 15.06 0.79* 2.71 0.19 0.55* 6.450 28.25 3.52 4.13 0 3.58 0.690 0.60* 8.92

1±0.5* I:LO.5* 6± 30 weak weak weak 2d: 1* 8± 40 25±10 weak weak 30±10* 25=000 16± 5* wtak 15 :1: 50 15 :h 5* weak 25±10 weak 50±15* 75±25 25±100 10± 50 weak 20±100 150+50* weak 150±25 0 75±20 150±250 21±100 10-+ 50 250±50

1.59 4.84

448 OA8

1.26

0.82 7.31 11 .21

J-*

G-) J-*

11-

1-0

G-) 1J-

G-)

#

00M

10.36

y, ,.I(r _ J)1) OWV)

10.12 7.47

2-95 1.51 5.03

2.59

1.49

e.03

3.56

0.36 0.77

5.40 7.62 1.66 0.97

0.49

1.05 11 .57

0.28 0.00 6.02 0.39 0.02

L55 4.03 1.39 0.59 042 10.74

those AsterisIrs Ondico cbuws in values from of Mom et al. 7) . JU Most Significant chnnees are the six spin roa*pinmmtL 8) The numbers for the resonances coffespond to those ass4ped in fig. 3. 6) Reduced widths are calculated fi-omy2 - r12P, whecePis the Coulomb penchability evaluated at R - 1.25(l+Al/s)fta. Forthe *- resoneawes, only thef - j component adds. For mionances 3 and 17. the p' and y-ray angWer distribution led to inconsistent results.

For sixteen I- resonances mixing ratios were determined as weighted avera8es of the two experimental values. These final values of 6 in both the mpin andfspin representations are listed in table 3 and are shown graphically in fig. 4. The elastic and inelastic excitation functions were fit with the A-matrix computer prograin MULTI 11). In general the elastic widths agreed reasonably well with those

438

T. R. DITMCH et al. TAUB 2 Angular distribution results for I- resonances In 51Mn

Ru .

E, . . (MeV)

az

.

P, ly 02 2.0615 P, 01

2.0388

03

2.1077

07

2 .2972

09

2.3293

12

2.4539

13

2.4920

16

2.5495

17

2.6283

-0.80=LO.02 0.15 :LO.05 -0.22±0.04 0.43±0.05 0.07±0.04 0.40±0.05 -0.62±0.02 0.29~:0.05 -0.70+_0.02 0.22±0.05 -0.43±0.03 0.37±0.05 -0.37±0.03 0.40 :kO.05 -0.58±0.02 0.30 :LO.05 -0.04+0.04 0.43±0.05

v

P, 'Y P,

v

P,

y

P, 7

P,

v

P, 7

P,

v

Re§ . . E,

de

fflv)

0.00±0.14 -0.12±0.11 -1 .16 :LO.09 -0.88=LO.36 inconsistent

19 21 23

-0.46=LO.04 -O."±0.12 -0.34±0.04 -0.28±0.11 -0.76=LO.05 -0.65 :LO.18 -0.87±0.06 -0.75d:0.24 -0.52 :LO.04 -0.46+0.13 inconsistent

26

2.6946 P, 7 2.7490 P, 7 2.7921 P,

v

32

2.8549 P , 7 2.9325 P, 7 2.9599 P, 7 2.9854 P, 7 3.0021 P,

33

3 .0226 P,

29 30 31

v

v

a2

Ae

-0.43+0.03 O.W=LO.05 -0.26±0.03 0.02±0.05 0.01±0.04 0.14=LO.05 -0.01 ±0.04 0.14±0.05 -0.75 :LO.03 0.01 ±0.05 -0.61 ±0.02 0.00±0.05 -0.47=LO.03 0.43±0.05 -0.76±0.02 0.20=LO.05 -0.30+_0.03 0.01±0.05

0.76±0.05 0.50±0.13 1 .08±0-08 0.77±0.34 2.07±0.30 1 .60:LO.45 1 .94±0-25 1 .67±0-46 0.23 =j 0.05 0.33+-(L21 OA9±0.04 0.50±0 .13 -0-70±0-05 -0.86+0 .33 -0.21+0 .05 -0.24±0 .10 1 .01 ±O-06 0.74±0.35

TAKE 3 hfidnS ratios Reg.

4 fflv)

de

ai,

1 2 7 9 12 13 16 19 21 23 26 29 30 31 32 33

2.0388 2.0615 2.2972 2.3293 2A539 2.4920 2.5495 2.6946 2.7490 2.7921 2.8549 2.9325. 2.9599 2.9854 3 .0021 3 .0226

-0.06=LO .12 - 1 .02±0 .23 -0 .45 :LO.08 -0.31=LO.08 -0 .70±0.12 -0 .81±0.15 -0.49±0.08 0 .63±0.09 0 .92±0.21 1 .83±0.37 1 .80±0.36 0.28±0.13 0.49±0.08 -0.78±0.19 -0.22=LO.08 0.88±0 .21

1 .75±0.72 0.32±0.11 0.81 :L-0.11 1 .04±0.16 0.54±0.10 0.45±0.10 0.76=031 -large -3 .88±lA4 -1 .47±0.34 -1 .46±0.31 5 .54±2.53 larp 0.48±0.11 1 .22±0.22 -4.36±1 .74

600r+p

439

Fig. 4. The a2 coefficient varsns mixin ratio for the proton andy-rayaniplin distributions in both the channelspin and thetotal angula momentum representations-11w experimentallY datermineod mbft ratios are labelled by the resonance numbers (see fig. 3 and table 1).

of Moses et al. For the inelastic scattering from I- resonances the ratio of the widths in the two inelastic decay channels was held fixed at the value determined in the angular distribution analysis. The resulting fits to the inelastic data are excellent, and thus give additional credence to the mbdn ratio values . 17he elastic and inelastic widths are listed in table 1 ; the reduced widths are plotted in fig. 5.

440

T. R. DITTRICH et aL ~50cr(p.~)50W

95

JV~k

-20

-

4F

.

20

.

Ili

1

50cr

Il .,

il, . 11111

(p . p)5oCr

.

.

1

lr i .li

Il

5: Is 6

4.

7-

!î

eji

50cr (p, PP%re

15

C go ~~ 5

L

50or (P. P) 50cr

25

10

1.8

«

2:0 . '

2.2

2 .4 - ' ZO' ' E p (MéV)

ËZ

-5L-1

Fis. 5. Elastic and inelastic reduced widths for i- and I - resonances formed in 5 OCr+p.

5. Andynis Md

&mwm

5.1 . SPECTROSCOPIC FACTORS 11M Width of an analogue State appro3dn2aftly SatiSfLeS 19, 20) S.

rA - 2TO +l F(S.P.), where

(5.1)

r,, is the total lab width of the analogue state, r(s.p.) is the width of a single particle state of the appropriate spin and parity located at the energy of the analogue

5OCr+P

441

state, S. is the spectroscopic factor for the parent state [as observed in the (d, p) reaction] and To is the z-component of the isospin of the target. Ofthe four p-wave analogues observed ') in '*Cr +p, only two have appreciable inelastic strength : one is resonance number 9 (at E. - 2.329 MeV) and the other comprises resonance numbers 29, 30 and 31 (centered at E. - 2.967 MeV). Both analogues have P - J- . A computer program written by Harney 11 ) was used to calculate the elastic and inelastic single particle widths, both with theR-matrix method of Thompson, Adams and Robson22) (TI&.R) and the ShCU_Model method of 7'aidi and ])UModj o 23) and Ekmey "') (ZDH). The methods are compared by Harney and Weidennifiller 2 5). Our results on elastic analogue spectroscopic factors are discussed in ref. 6). Starting from the set of parameters used in the (d, p) analysis (with Ro - 1.25 fm and a - 0.67 fm) the well depth was adjusted to fit the parent state bindingenergy. The symmetry potential was estimated from V.y. = J(2TO+1)

125 MeV A

(5.2)

and added to the neutron potential to obtain the proton real well depth used in the determination of r(s.p.). The inelastic spectroscopic factors were calculated in the same manner, except that the single particle width was calculated at a lower energy (EA-E2 + - EA-0.782 MeV). The results are listed in table 4. The two mathods CM and ZDH) approtmately agree; only the ZDH results are listed in table 4. TA= 4

PwPortim of I - analosu mato fit 51 Mn F,Pm" (MeV)

JV" (MêV)

3.126 2.329

3.771 2.967

.r. (keV)

0.55

1.495

6.126

26.24

SM

0.09 0.17.0.19

0.06 0.06,0.08

rW(f - J) (keV) r,,,(r - J) OWV)

0.012 0.013

0.127 0.248

(.r - J) ftv) 2To+I IXS-P-) 1) (keV) iT-O-+I SPP-(r S,P, -

0.190

3.699

oln

3.796

0.05 0.05

0.03 0.07

2To+l

(keV)

SdP16b)

(r -

8) W. "). 6) Rd. 27).

(r

442

T.

PL

DrITRICH et aL

The present results for inelastic spectrosopic factors are consistent with ourprevious observations : in the (If, 2p) shell the inelastic spectroscopic factors for analogues of low-lying parent states are comparable to the elastic spectroscopic factors . In the simplest interpretation the inelastic amplitude corresponds to an excited core configuration in the parent state. The present results represent one step beyond our previous measurements, in that the amplitudes of the 2+ 0 P* and 2+ 0 pf configurations are separately determined 5.2. STRENGTH FUNCTIONS

Since the spin assignments for a number of p-wave resonances were changed, the p* and p* strength functions were recalculated . In each case a I- resonance had been incorrectly assigned J-; the present results thus increase the pf strength function and decrease the p* strength function. The measurement of the inelastic widths also provides now strength function information. The strength function is 2

<7 2>

Yi



AE

(5.3)

where analogue states are excluded.

For the I- elasticstrength function 14 resonances were included : 12 of the 1 . resonances listed in table 1, with the analogue state at Ep - 2.2335 MaY (resonance 6) excluded, and including two I- resonances observed by Moses et at. at 1.8916 and 1.9539 MeV. The value of s(I-) was 0.096, in good agreement with the previous value of Moses et al. The strength function results are summarized in table 5. TAM 5

Proton strength functions for -'OCr+p Resonance A

Eidt channel P PV - 1) P P'(total) P'V - D PV - 1)

a)

a (MOINY) 0.096 0.042 0.028 0.053 0.029 0.024

0.10 0.02

Ref. 7).

For the I- elastic strength function the resonances listed in table I were included with the exception of resonances 4, 9 and 29-3 1, which are associated with analogue states . The resulting value for s(I-) is 0.028. This value is somewhat higher.than that obtained by Moses et at. These results suggest that future spin reassignments for

5OCr + P

443

other nuclei in this region may change the detailed shape of the pi strength function, but will have little effect on the p* strength function. Information on strengt1i functions may also be obtained from die inelastic data. generally However, there are no accepted definitions, muchless an accepted notation . For the decay of the I- resonances only the J, - I component exists. We define a J1 - I strength function (associated with I- resonances) as S(f - 1, J" - I-) - 7, 7i2(j'

=

J, .r = J - )IAE .

(5.4)

The resulting value for the strength function is approximately0.04. For decay of the I- resonances bothj' = J andf I contribute. Strength functions for bothf - J andf - I decay associated with resonances were defined; the resulting values are listed in table 5. (Since inelastic scattering measurements led to inconsistent results for resonances 3 and 17, these two resonances were excluded.) 5.3 . AMPLJTUDES AND RELATIVE PILAMM

The reduced width amplitudes for the ordinary compound nuclear resonances should follow a Gaussian distribution and the (measurable) absolute values of the amplitudes should follow a. half-Gaussian. A detailed analysis is not appropriate for this limited number of I- resonances ; the results are in . qualitative agreement with the expected distribution. This method of determining the relative phase between the inelastic decay amplitudes appears suomssful: even in this first example a variety of useful spectroscopic information was obtained. However there are not suftient resonances for a serious statistical analysis, nor do the analogues have well-developed fine structure patterns . It is nevertheless interesting to examine the behavior of the relative phases. As listed in table 3, the sequence in theJ-spin representation is 7 positive, 4 negative, 4 positive and I negative . In the s-spin representation the sequence is 7 negative, 6 positive, 2 negative and 1 positive. The results are at the edge of statistical signifiall cance: four runs (defined as a sequence with the same sign) in sixteen events is at the 5 % significance level. N the ran of 7 at the beginning of the sequence is not a statistical accident, it is difficult to understand. The seven resonances whose decay amplitudes have the same relative phase cover an energy range of 500 keV. 6. Smnnisry The object of the present work was to illustrate a simple method of obtaining channel mixing ratios. This method can resolve ambiguities in resonance spin assignments and can yield detailed information about magnitudes and relative phases of decay amplitudes. Six resonances in "Mn which were assigned P = J - from elastic scattering studies have been reassigned P = J - . The magnitudes and relative phases ofthe inelastic amplitudes were obtained from the experimentaUy determined mixing ratios. The major limitation of the present results is the small number (16) of I- resonances analyzed. Experiments involving larger samples are now in progress .

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The authors would Wee to thainir Dr. A. M. Lane and Prof. H. A. Weidenmaller for valuable discussions. This manusmipt was prepared while one of us (G.ELM.) was at the Institut fdr Kernphysik, J. W. Goethe Universitift, Frankfurt am Main. He wouldlike tothan the members oftheIFKfor theirhospitality andtheAlexander von Humboldt Foundation for a Senior Scientist Award. References 1) R. L DehleUer and L J. M. van Gasterim. Nucl. Phys. A148 (IM) 62 2) R. IL Chrien. M. R. Bhat and 0. W. CWA Phys. Rev. CB (1970) 62 3) E. Albramson. R. A. Ebenstein. L Pima, 7- Vager and L P. Wurm . NUCL Phys. A144 (1970) 321 4) EL C3cmmt and G. Graw. Phys. Licit 57B (1975) 323 5) T. R. Dfttrich. C R. Gould, 0. E. Mitchell, E. 0. Bilpuch and K Stelzer, Phys. IAW. 59B (1975) 230 6) E. 0. Bilpuch, A. INC Lane, G. E. Mitchell and L D. Mons, Phys. Reports 28 (1976) 145 7) L D. Moses, E. 0. Bilpucb. H. W. Newson and 0. E. Mitchell . Nucl. Pbys. A175 (1972) 556 8) L M. Blatt and I- Q Diedenharn. Rev. Mod. Phys. 24 (1952) 249 9) L~ C. Bledenharn and M. IEL R=6 Rev. ModL Phys. 25 (1953) 729 10) U. Fano. Phys. Rm 90 (1952) 577 11) S. Dow= and 1. L 13. Goldfkt, Ekndbuch der Physik, vol. 42 (Springer. Berlin 19M p. 362 12) 1. J. B. Goldfarb, Nuclear reactions, voL 1. ad. P. K Eadt and M. Demwar (North-Holland, Amsterdam. 1959) p. 159 13) A. J. Ferguson. Angular correlation methods in gamma-raY SPOctroscOPY (North-Holland . Amstatam. 1965) 14) A. A. Kraus, Jr., L P. Schiffer, F. W. Prosser, Jr. and ]L~ Q Biedwharn. Ph3% Rev-104 (1956) 1667 15) P. B. Parks, H. W. Newson and R. INC Williamson. Rev. Sci. Instr. 29 (1958) 843 16) 1. F. WmqW, Ph. D. dissertation, North Carolina State Univasity. 1974~, unpublished 17) 0. C Kyker, Jr., IL G. Bilpuch and H. W. Newson, Ann. of Phys. 51 (1969) 124 18) D. L. Sellin. Ph. D. dissertati m Duke University, 1969, unpublished 19) Q Mahaux and H. A. Weidemnillier. Shell model approach to nuclear reactions (North-Holland, Amsterdam, 1969) 20) D. Robson. Imspin in nuclear physics6 edL D. EL Willinson, (North-Holland, Amsterdam. 1969) p. 461 21) H. L Harney, MPI filt Kernphysik. Heidelberg, unpublished 22) W. L Thompson, L I- Adsk and D. RobsoE6 Phys. Rev. 173 (1969) 975 23) S. A. S. Zaidl and S. Darmodjo. PUYL Rev. IAtt. 19 (1967) 1446 24) IL I- Harney, Nucl. Phys. AID (1968) 591 25) IL L. Harney and H. A. WisidenmUler, NucL Phys. A139 (1%9) 241 26) 0. Delic and B. A- Robson, Nucl. Phys. AILU (1969) 470 27) 1. E. Robertshaw and S. Mecca, Phys. Rev. 170 (1968) 1013