High-resolution proton scattering on 46Ti

Nuclear Physics A199 (1973) 571 --592; (~) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

H I G H - R E S O L U T I O N P R O T O N SCATTERING O N 46Ti N. H. PROCHNOW t, H. W. NEWSON and E. G. BILPUCH Duke University and Triangle Universities Nuclear Laboratory, Durham, North Carolina 27706 tt

and G. E. MITCHELL North Carolina State University, Raleigh, North Carolina 27607 and TUNL, Durham, North Carolina 27706 tt

Received 15 August 1972 Abstract: Differential cross sections were measured for 46Ti(p, p) and 46Ti(p, Pl) at four angles between Ep = 1.5 and 3.1 MeV, with an overall energy resolution of about 300 eV. Spins, parities, total and partial widths were extracted for 144 resonances. Six analogue states were identified. The s-wave states have expected spacing and width distributions, while the p~ states behave anomalously. The s½, p~ and P~r strength functions were determined.

E ..

NUCLEAR REACTIONS 46Ti(p,p), 46Ti(p, pl), Ep = 1.5-3.1 MeV; measured tr(E, 0). 47V deduced isobaric analogue resonances, J, x, F, Fp, Fpl, Coulomb energies, strength functions.

1. Introduction This p a p e r reports on one o f a series o f high-resolution m e a s u r e m e n t s o f p r o t o n i n d u c e d reactions in the m e d i u m - m a s s region. T h e two m a j o r p u r p o s e s o f these experiments are the study o f the fine structure o f a n a l o g u e states t - 4) a n d statistical studies o f the c o m p o u n d nuclear states. Earlier p a p e r s in this series covered elastic scattering 5 - 9) on the even Ni, F e a n d C r isotopes, o n 4STi, a n d n e u t r o n decay f r o m a n a l o g u e states to). P r e l i m i n a r y reports have been p u b l i s h e d o n statistical p r o p e r ties i t ) a n d on c h a n n e l - c o r r e l a t i o n p h e n o m e n a tz). F u t u r e p u b l i c a t i o n s will include, in a d d i t i o n to elastic scattering d a t a on other nuclei, m o r e general studies on aspects o f the fine-structure data, statistical studies, a n d experimental results on the (p, 7) r e a c t i o n t h r o u g h f r a g m e n t e d a n a l o g u e states. The present p a p e r describes the results o f elastic a n d inelastic scattering on 46Ti. T o place these results in perspective, it is helpful to discuss some o f the results f r o m the m a n y o t h e r nuclei studied by o u r high-resolution group. I n practice, w h a t is actually o b s e r v e d is d e t e r m i n e d by the level density. F o r a given p r o t o n lab b o m t Now at University of Wisconsin River Falls, River Falls, Wisconsin. Work at TUNL supported in part by the Research Corporation. *t Work supported in part by the US Atomic Energy Commission. 571

572

N.H. PROCHNOW

et aL

barding energy, the level density for different compound nuclei in this mass region varies over a large range. Thus the type of fine structure observed for the analogue states varies dramatically from nucleus to nucleus. For example, in S*Fe the level spacing is extremely large, the analogue states appear as single levels and the results are similar to those obtained for light nuclei. On the other hand, in SSFe the spacing is much smaller and a fine structure pattern is observed; there are literally no other neighboring p~ resonances observed (with our resolution) above or below the analogue region. Many examples close to these two extremes have been observed in other nuclei. In such cases the isobaric analogue states are usually very easy to identify. There are, however, regions of intermediate level density, where the background (7'<) strength is comparable to the analogue strength. In such cases analogue states may be extremely difficult, even impossible, to identify. 50Cr was such a nucleus; in some ways 46Ti resembles S°Cr. The present data were taken with excellent resolution (m300eV), most of the spin assignments (for s- and p-wave resonances) are quite reliable, and the fits to the data are very good, yet the density effect leads to some difficulties in positive identification of some of the analogue states. For 46Ti there are sufficient levels observed to perform qualitative statistical analyses, but not enough for detailed analysis. Possible non-statistical, non-analogue effects are observed. These are discussed in sects. 4 and 5. Sect. 2 describes the experimental procedure. The analysis was complicated by the presence of an isotopic contamination (4STi); the details of the point by point background subtraction procedure are briefly described. The data and the results of the resonance analysis are presented in sect. 3. In sect. 4 identification of the analogue states is discussed and spectroscopic factors and Coulomb energies obtained. Statistical aspects of these data are examined in sect. 5.

2. Experimental procedure and analysis 2.1. EQUIPMENT The experiment was performed using the high-resolution system of the TUNL 3 MV Van de Graaff accelerator. The experimental system has been described in earlier papers in this series. Targets were prepared by evaporation of titanium (crystal bar) onto carbon backings of thickness =
46Ti PROTON SCATTERING

573

as in previous papers, and will be omitted here. To summarise very briefly, penetrability effects limit the observed resonances to essentially s-, p - a n d d-wave resonances (six f-wave resonances were observed). On the basis of shape analysis of elasticscattering data alone, the/-value can be determined in essentially all cases; p½ and p~ resonances can normally be distinguished, but d~ and d~ resonances usually cannot be distinguished. The inelastic data helps in the j-value determination, but as in 48Ti, the d-wave resonances appear to decay by a mixture of orbital angular momental' = 0 and 2. This additional complexity usually makes the j-value determination for the d-wave resonances very difficult. Kyker 15) has previously studied the 46Ti(p, PiT) reaction with a resolution of about 2 keV. His measurements of the 7-ray angular distribution usually led to rather good j-values for the compound states, but rather

48Ti(p.p)48Ti

eL~

• 160"

I00

4

l

,

I 14.5%

~._ _~

i

.

46Ti(p,p)46Ti

o

I

200

.

I

2.69

,/'I

I

+

I

,

I

~I 'I J

14.5% OF 48Ti(p,li)48Ti

-#'I

46Ti(p,p146Ti --

2.71

,

OF 48"l'i(p.p)48"ri

,

I

/

I

I

,

i

2.96,

I

,

14.5% OF 4"8Ti(p,p)48Ti

//"2.92

I

2.94

F__.p (MeV) Fig. 1. Two sections of the 4aTi(p, p) and 46Ti(p, p) differential cross-section data at 160 °. The solid line represents a fit to the data. This figure illustrate the subtraction procedure used in the analysis of the 46Ti data. See text for discussion.

574

N.H.. PROCHNOW

et al.

poor determination of the/-values. Thus these two experiments compliment one another. The determination of j-values for the d-wave resonances are therefore somewhat better than in many of our previous experiments.

4Syi ( p,p )'~Yi 20C

~:-~;,~..L ~ i

tOO I .... 1 . 8 5

I 1530

.

I 1.95

__

I 2.00

I 2.10

2.~)5

~to. 20( c-}

E 10C

....

1

o

2~o

I

I

I

4~Ti (p.pl) 4s TI .

z25

:

~

~

Ep(MeV)

~

~

e~ ......

Fig. 2. T h e 46Ti(p, P) differential cross-section d a t a f r o m 1.80 to 2.50 M e V at 160 °. A l t h o u g h inelastic data were t a k e n f r o m 1.80 MeV, no resonances were observed until 2.29 MeV. T h e 46Ti(p, P 0 differential cross section is s h o w n f r o m 2.29 to 2.50 MeV. T h e solid line represents a fit to the data.

2.3. BACKGROUND SUBTRACTION The one practical difficulty which complicated the analysis of these data was the appreciable isotopic contamination present in the target-primarily 14.5 % 48Ti. The problem exists only in the elastic data. Since the energies of the first excited states are rather different in 46Ti and 48Ti, the inelastic groups could be easily separated. Above 2.5 MeV the 48Ti(p, P) data contain many closely spaced, large resonances and the resonance structure of the 46Ti(p, p) data also becomes increasingly complex. For this energy region many of the 48Ti (for simplicity we refer to the target in the following discussion) resonances occur very near the 46Ti resonances. Thus a subtraction of the cross section is required in order to perform an analysis of the 46TI data in this energy region. Fig. 1 illustrates the effect of the 48Ti resonances on the 46Ti data. The very large 48Ti resonances affect the cross-section normalization (this in turn may produce erroneous width assignments) as well as introducing the possibility of assigning some 4STi resonances as 46Ti resonances.

46Ti PROTON SCATTERING

575

In order to perform the subtraction the absolute energy and spacings of the 4aTi resonances observed in the 46Ti data must be the same (within < 100 eV) as the energy spacings in the 4aTi data. This requires that the energies and spacings of both isotopes be carefully checked. The contaminant in the 46Ti target consists of various components, which must be treated differently. That is, the contaminant background to be subtracted consists of: a 2-3 % general background, about 5 % from the various Ti

~500-

46Ti(p,p)46Ti

J6 o o

-

20C

IOC

46Ti(p,p)46Ti* 2.50

E

2.55

2.60

2.65

~.70

2.75

r

I

c

I

2.80

I

2.85

2.90

2.95

3.00

3.05

F-p (MeV) Fig. 3. The

46Ti(p,p)

and 46Ti(p, Pl) differential cross-section data from 2.50 to 3.07 MeV. The solid line represents a fit to the data.

isotopes other than *8Ti and *6Ti (resonance structure need not be considered) and about 15 % from the 4STi isotope (resonance structure must be considered). Although the procedure used to perform the cross section subtraction is involved, the subtraction is felt to be accurate to within 5 %. Fig. 1 shows a typical subtraction in two regions of the 46Ti(p, p) data. The normalization and fit is much improved after the subtraction, and the very obvious *STi(p, p) resonances disappear from the 46Ti(p,p) data, indicating the success of the subtraction procedure.

576

N.H. PROCHNOW et al. 3. Data

Figs. 2 and 3 show the elastic and inelastic excitation functions. Background has been subtracted from these and all further data shown. The solid lines are fits to the data. A measure of the quality of fit obtained is indicated in figs. 4 and 5, which show both elastic and inelastic data at several angles on an expanded energy scale. Overall results for 46Ti and 48Ti are shown for comparison in fig. 6. The decrease in the number of observed levels from 48Ti to 46Ti is obvious (about a factor of two).

.46Ti(p.p)46Ti

2oo~

.

<9,,,. = 160 °

15 I0( 5{ ¢J)

c

I

I

I

I

I

I

105"

E ' 20C

~

IC(

il 2,825

2.850

'

'

'

2.8?5

2.900

2,925

2.950

Ep (MeV) Fig. 4. This figure shows the elastic data at four angles on an expanded energy scale in the region of the analogue state at 2.90 MeV. The solid line represents a fit to the data. Resonance parameters were obtained for 144 resonances. The only previous work with which to compare is that of Kyker et al. 1~). They observed 45 resonances in inelastic scattering between Ep = 2.5 and 2.9 MeV. Nine of these resonances were not observed in the present experiment (this is expected, since in the present experiment thinner targets were used, the run times were shorter, etc.). For the resonances seen in both experiments, there were no serious discrepancies for the j- or/-values. In some cases Kyker had determined the j-value, while our experiment determined the/-value. In these cases Kyker's j-value was accepted. Table 1 lists the parameters of the 144 resonances analysed. Resonances whose j "

46Ti PROTON SCATI'ERING

577

value is in d o u b t are listed in parentheses. F o r d-wave resonances for which n o t even a m o s t p r o b a b l e assignment c o u l d be m a d e , a spin o f {+ was arbitrarily assigned. A l l ½+ resonances listed in parentheses were assigned in this m a n n e r . T h e errors in the elastic widths range f r o m 10 % for very strong resonances to as m u c h as 50 % for very w e a k resonances. The larger inelastic widths s h o u l d be accurate to 25 % o r better.

46Ti(p'P )46Ti

2~

@LAB= 160°

]

10(

I.D

.B E

2.825

2.850

2,ff/'5

2.900

Ep

~-'~5

~'o~40

(MeV)

Fig. 5. This figure shows the inelastic data on an expanded energy scale in the region of the analogue at 2.90 MeV. The solid line represents a fit to the data. The figure also illustrates the anisotropic angular distribution obtained for the inelastic scattering from most t - resonances observed. The 4very large inelastic resonances from 2.850 to 2.925 MeV are t - and clearly have anisotropic angular distributions. The comparison is further illustrated by the two p-wave resonances near 2.950 MeV. One is very narrow and has an anisotropic angular distribution ({- with a small width); the other is very broad and has an isotropic angular distribution (½- with a large width).

4. Analogue states 4. !. IDENTIFICATION Identification o f a n a l o g u e states is facilitated by p l o t t i n g the r e d u c e d widths separately for each spin a n d parity. T h e cumulative sums o f r e d u c e d widths for 46Ti are s h o w n in fig. 7. I n fig. 8 the r e d u c e d widths are plotted, with the results o f a (d, p )

578

N . H . P R O C H N O W et aL TABLE 1 47V resonance parameters

Eo a)

j . b)

(MeV) 1.5593 1.5647 1.6071 1.6133 1.6853 1.7713 1.8135 1.8218 1.8298 1.8498 1.8508 1.8870 1.9163 1.9631 1.9721 1.9939 2.0238 2.0269 2.0878 2.1035 2.1038 2.1515 2.1622 2.1808 2.1842 2.2002 2.2179 2.2381 2.2508 2.2817 2.2900

½+ (½-) (½-) (½-) (½-) (½-) ½½½½½]½½(½-) (½-) ~(½-) ½+ ½½(½-) ½+ ½½+ (½-) ½½+ 3½+ ]-

2.3051 2.3163 2.3271 2.3280 2.3475 2.3492 2.3720 2.3950 2.4257 2.4812 2.4867 2.4985 2.5044 2.5087 2.5151 2.5226 2.5297

½+ ~½+ (~+) (~+) ½(½-) ~½+ ½½+ ½(~+) ]½+ ~+ ~-

Fp

~,p~

(eV)

(keY)

90! 100-25! 10! 2042041554901 60455+ 50440440450410+ 5430t 154404325t 100451 54804165454120450i 404175-43301

15 10 10 5 10 10 25 10 10 20 15 15 10 5 5 3 5 5 5 50 25 3 3 10 20 3 10 5 5 20 60

12.28 35.35 7.13 2.76 3.88 2.65 16.96 9.54 6.10 5.24 4.74 3.30 2.95 3.09 0.60 0.28 1.49 0.74 0.67 12.38 3.81 0.16 0.06 2.41 2.09 0.14 3.24 0.55 0.98 1.71 7.27

404- 5 254-:[: 5 1751 25 8t 3 121 5 2 2 0 ! 20 10~- 5 504- 5 20~ 5 31001200 604- 10 !104- 15 104- 5 2 5 0 t 75 2 4 0 1 50 10! 5 354- 10

0.37 0.51 1.53 0.78 1.11 4.13 0.18 0.84 0.14 41.92 0.36 1.43 0.60 3.17 1.37 0.57 0.42

r o)

s" o)

1 1

~ ~

1

~

/'pl

;'p~

(eV)

(keV)

8 12

7.88 11.82

3

0.77

4~Ti PROTON SCATTERING

579

TABLE 1 (continued)

Eo ~)

j~r b)

(MeV)

Fp

yp2

(eV)

(keV)

2600±300 400± 75 5~ 3 2 0 1 10 11 1 8t 4 2 0 i 10 2 5 ~ 10

31.14 2.18 0.27 0.23 0.47 0.41 0.22 1.26

2.5333 2.5380 2.5391 2.5506 2.5539 2.5589 2.5680 2.5685

½½+ (~+) 8{(~+) ~8+

2.5787

~÷

4 0 ~ 15

1.97

2.5801 2.5929

½~-

525± 50 130± 15

5.66 1.36

2 5939 2.5994 2.5998 2.6068 2.6142

8+ ½+ 2-+ {+ {~"

3 0 ! 10 3 2 5 ! 60 5! 3 I0~ 5 2 0 1 10

I 42 1.56 0.23 0.46 0.90

2.6322 2.6368

88-

65! 60!

10 10

0.63 0.57

2.6529 2.6842

~+ ?.,-

3 5 ! 10 30~ 10

1.43 0.26

2.6899

~÷

15!

5

0.56

2.6953

~--

4t

2

1.24

2,6992

:}-

1450 ~ 150

12.15

2.7056

a-

1400~ 150

11.58

2.7096 2.7097 2.7190 2.7380 2.7411 2.7584

{.~-+ ½+ ½~½+

1 3 5 i 25 4 0 ± 15 1151 15 215~ 20 110± 15 11001200

1.11 1.43 0.44 1.67 0.85 3.95

2.7626

~-

2 5 ± 10

0.18

2.7670 2.7783 2.7850

?.,-+ ½+ ~-+

15~ I0 20± 5 10± 5

0.47 0.06 0.30

1" c)

s" ~)

Fot

yp 2

(eV)

(keV)

I

.~

1

0.24

0 2 2 0 2 2

8 8 ~,~ 8 ~

20 5 5 5 5 5

1.63 6.54 6.54 0.39 6.21 6.21

1 1 0

~ .~ 8

3 3 20

0.57 0.57 1.45

0 0 0 2 2

-?2 ~ ~ 8 ~

2 2 2 2 2

0.14 0.14 0.13 2.08 2.08

l 1 0 1 1 0 2 2 l 1 1 1 1 1

.~ ~ ~ ~ ~ ~{ ~ { ~ 8 g ~} .~

2 2 5 2 10 8 2 2 3 9 5 5 20 65

0.31 0.31 0.28 0.25 1.27 0.39 1.46 1.46 0.36 1.09

0

~

30

1.34

l

:~

20

2.03

2 2 1 1

.~ ~ .~ .~

15 15 12 8

8.09 8.09 1.10 0.74

0

{

2

0.06

0.60

0.60 2.32 7.54

N. H. P R O C H N O W et aL

580

TABLE 1 (continued)

Eo a)

j . b)

(MeV)

Fp

9,2

(eV)

(keY)

2.7891

~+

8004-100

2.73

2.7972 2.7990 2.8010

½~-÷ ~-

404- 10 304- 5 104- 5

0.28 0.87 0.06

2.8144 2.8206

]+ -~-

54- 3 354- 10

0.14 0.23

2.8284

]+

154-

5

0.41

2.8326

~-

554- 10

0.36

2.8344

~+

704- 10

1.89

2.8397

~-

104-

5

2.12

2.8414

½+

9004-100

2.82

2.8429 2.8456 2.8459

~÷ ½~-

154- 5 1200 4-150 254- 10

0.40 7.58 5.23

2.8557

~+

2.8638

~-

2.8643

204-

5

0.52

50

3.21

~-

254- 10

0.15

2,8658 2.8708

~-+ ~--

104154-

5 5

0.25 2.95

2.8732

~-

1504- 30

0.90

2.8736

~-

40-t- 20

0.24

2.8809

~+

404- 15

0.98

2.8811 2.8977 2.8981

½+ ~~--

304- 20 1254- 20 154- 10

0.08 0.72 0.08

2.9011 2.9055 2.9057

~+ (j+) ]-

84- 5 304- 15 280 4- 100

0.19 0.70 1.59

525 i

r c)

s' o)

F~

e~x2

(eV)

(keV)

2 2 1 0 1 1 0 1 1 0 2 2 i 1 0 2 2 1 1 2 2

~ ~ "~~ .]~ ~ .~ .~ ].~ ~ ~~ ~~ ~ ~~ ~ ~-

10 10 4 75 5 6 8 18 10 12 2 2 15 25 2 3 5 2 12 12 12

4.74 4.74 0.32 2.40 0.40 0.48 0.24 1.33 0.74 0.35 0.81 0.81 1.06 1.76 0.05 1.18 1.97 0.14 0.82 4.59 4.59

l 1 0 2 2 1 1 I 1 0 1 1 1 1 1 1 0 2 2

] ~ -~ ~, ~ ~ ~ ~~ ~ ~ ~ ~r ~~ ~ ~ ~] ~

3 5 1 I 1 160 25 10 5 2 15 20 90 10 15 5 5 2 2

0.20 0.34 0.02 0.36 0.36 10.05 1.57 0.63 0.31 0.05 0.92 1.23 5.47 0.61 0.91 0.30 0.12 0.65

1 1 1 0

~~ ~ ~

50 15 5 5

2.78 0.83 0.28 0.11

1 1

!~

50 30

2.71 1.63

0.65

46Ti PROTON SCATTERING

581

TABLE 1 (continued)

Eo a)

j~r b)

(MeV)

/'p

~p2

(eV)

(keV)

1500-4-300

8.51

5+ 3 5+ 3 254- 10 204- 10

0.11 0.11 0.06 0.11

2.9060

{-

2.9118 2.9232 2.9245 2.9307

6+ (6 + ) ½+ 3-

2.9312

½+

9005:100

2.45

2.9332 2.9350

[[+ ~-

55: 3 1504- 30

0.01 0.81

2.9389 2.9395

(6 + ) (6 +)

55:3 54- 3

0.11 0.11

2.9397 2.9412 2.9463

½(~+) (~--)

1400 + 200 455:10 55:3

7.49 0.97 0.82

2.9472 2.9526 2.9562 2.9607

(6 +) {-

55:3 505:15 18004-200 1105:15

0.11 0.26 9.36 0.57

2.9655 2.9836 2.9976 3.0047 3.0077 3.0212 3.0231 3.0279 3.0392 3.0476 3.0490 3.0524 3.0591 3.0605

½½(t +) ½(6 +) ½+ (6 +)

3.0654 3.0678 3.0691

½~-

(6 +) (~+) ½(6 +) (6 +) .{-

175+ 20 75+ 15 15 4- 5 190+ 25 354- 15 6505:75 255:10 205:10 305:15 124- 5 700± 75 3 4- 2 2+ 1 705:15

0.90 0.37 0.29 0.91 0.66 1.55 0.46 0.09 0.53 0.21 3.12 0.05 0.03 0.31

½½+ ({+)

550+ 75 3004- 45 3 5 ± 15

2.39 0.67 0.59

½-

I' c)

s' c)

Fp t

~:p12

(eV)

(keV)

1 1 0

~ ~ ~

150 90 3

8.11 4.87 0.06

1 1 2 2 0 !

{ ~ zz ~ -~ {

4 4 15 15 3 20

0.20 0.20 4.05 4.05 0.06 0.98

I

{

40

1.96

0 2 2 1 0 1 1 0 1 1 l 1

~ ~ ~ ~ ~ { ~ ~ .~ { ~ {

5

50 6 2 12 4 22 200 2 2

0.09 0.26 0.26 2.41 0.12 0.09 0.57 0.07 1.02 9.12 0.09 0.09

1

{

15

0.63

l 0

{ ~

100 75

3.89 1.21

0

~

1 0 0

~ ~ ~

15 20 30 10

0.23 0.72 0.44 0.14

! 1

{ ~

15 15

0.49 0.49

0

~

5

0.06

I I

a) Lab energies are quoted. Although the absolute energies are accurate only to ~ 3 keV, the relative energies over a small energy range should be reliable to ,,m 300 eV. b) Doubtful spin assignments are listed in parentheses. For d-wave resonances for which not even a most probable assignment could be made, a spin of j+ was arbitrarily assigned. All {~+ resonances listed in parentheses were assigned in this manner. c) Inelastic parameters are tabulated according to exit channel orbital angular momentum 1' and exit channel spin s'.

582

N.H.

PROCHNOW

e t al.

experiment 16) on 46Ti shown for comparison. The latter results are shown only in the energy region pertinent to this experiment ~2.50 to 4.0 MeV excitation energy (14th to 46th excited states). The excitation energies, (2J+ 1) times the spectroscopic factor, and the/-values for the stripping states are listed in table 2. Rapaport et al. 16)

3of

4SYi( p ,Pl) 4ayi ~

2c~t

6~LA8 = 160 ° !

; J i

i fO

!

o

L

4aTi (

P',

46Ti(

p, P, ) "6Ti

i

;.

,i

l

1

~i i~

I

'~;

! " ~

i ~.!.

''''

P )4aTi

2©C

..C)

AE • 300eV *

i

' 4~Ti ( p, p)4'~Ti

%0

260

2~o

2~,o ~.~o Ep (MeV)

~

2,80

3DO

Fig. 6. Summary of CSTi and 46Ti data. The solid line represents a fit to the data. The difference in

level density for the two compound systems agv and 47V is readily apparent.

assigned/-values; the spin assignments for the p-wave states (excluding a very weak state, stripping level no. 28 in table 2) are from a recent (d, p) polarization experiment by Kocher ~7). In fig. 8 the stripping states are indicated by the dark solid lines whose length is proportional to (2J+ 1)S, while the non-stripping states are indicated by dashed lines. Since the 1 = 3 penetrability is very small, the f-wave analogue is not expected to be observed. The two states which were observed to have rather small spectroscopic

46Ti P R O T O N S C A T T E R I N G

46Ti ( p,p)46Ti

j ~ = ,5/2+ 2C 0

583

32 RESONANCES

i ~= ~

I0

I0

J

1

I

I

i ~

i

I

'

'

i

,

I

i

i

,

,

i

i

f

'

,

,

i

RESONANCES

0

jrr = II~ 4C

23 RESONANCES

S

20 r-"

o 6C

'

~

'

'

1

i

jTt = ~/234 RESONANCES

4c ~qzt 20

z~ °,

,_ ,

I

[

i

,

,

,

I

Y

j'n", I/~ 200

/

39 RESONANCES

/

150

I00

50

0

, i

1.5

2.0

i

I

2.5 Ep(MeV)

i

L E I [ I

3.0

Fig. 7. Cumulative sums of reduced widths from the 46Ti elastic scattering data. The large anomalies at Ep = 2.70 a n d 2.90 M e V in the 3 - data, at E o = 1.56 a n d 1.81 M e V in the ½- d a t a a n d at Ep = 1.55 M e V in the ½+ d.ata indicate analogue states. The anomalies near Ep = 2.30 MeV (.:2d a t a ) a n d E , = 2.50 M e V (½- data) are not completely understood. See text for discussion.

factors (nos. 28 and 33 in table 2) are expected to have analogue strengths which are at most comparable to the typical T< strengths. It would be surprising if these states could be positively identified. These expectations hold true experimentally and further reference to these states is omitted. (The anomaly near Ep = 2.3 MeV in the ~-- data (figs. 7 and 9) possibly corresponds to the analogue state of stripping level no. 28 (table 2). However, the (p, p) and (p, Pl) data are inconclusive since this state is an unresolved doublet.)

584

N . H . PROCHNOW e t al.

47Ti : .LEVELS I ~(39

LEVELS)

46Ti (p,p)46Ti LEVELS ~'~(34 LEVELS) I/2+(23LEVELS) ALL

LEVELS (144]

-3.00 J-l

-2.75 ,t-I

b

~

-

-

O-

,t=l

Z-O .

. . . .

~

31

.__=-42

-2.50 ,r-,

r ' - - -

t,d

-22.5

I.

-2.00

1-3 2.75-

-I.75

341

2.50

t o

,

(2J + IIS

,~)

,o

"o

-,

ll0

1.50

~p2 {keV)

Fig. 8. Summary of the present 46Ti(p, p) results and the a6Ti(d, p)47Ti data of Rapaport et aL 16).

The six remaining states are have appreciable single-particle parentage and are reasonable candidates for observation as analogue states. The s, state near Ep = 1.6 MeV, two strong p, states near Ep = 1.8 MeV and the strong p~ states near Ep -2.7 MeV form the analogues o f the parent states at 2.570, 2.785 and 3.675 MeV, respectively. These spin assignments are in agreement with those o f ref. 17). On the basis o f ref. 17), the analogue states near Ep = 1.55 MeV, Ep = 2.55 MeV and Ep --2.95 MeV are expected to be p~, p~, and p~ states respectively.

a6Ti PROTON SCATTERING

585

TABLE 2 Stripping parameters for 47Ti Stripping a) level 15 16 21 22 28 33 34 37 43

E, (MeV)

1,

( 2 J + I)S

j r b)

2.545 2.570 2.785 2.835 3.276 3.514 3.544 3.675 3.913

1 0 1 3 1 0 1 1 1

0.32 0.09 0.25 0.89 0.02 0.003 0.20 0.48 0.82

9½+ ½6(6-) ½+ ½~.~-

") Ref. 16). ~) Spin assignments for the 1 = 1 states are from Kocher 17) with the exception of level no. 28.

The data are inconclusive with respect to p~ or p t for the state near Ep = 1.55 MeV. However, a P~r assignment is favored. Spectroscopic information is included in table 3 for a p~ spin assignment. In the region near Ep = 2.95 MeV two large p , states are located very near the expected analogue state energy as well as a small cluster of p~ states at a somewhat lower energy. Additional information regarding these states is available from the inelastic scattering data. Fig. 9 shows the sums of reduced widths for the p~ inelastic data. (Very few p~} states exhibit inelastic decay. The d~ results are also included in fig. 9 for completeness. No anomalies are apparent in the d-wave inelastic data.) There is a strong break in the p,~ inelastic strength near Ep = 2.90 MeV. The P,1 assignment of ref. xT) and the break in the p~ inelastic data are used to identify this analogue state. It is disturbing to note that the centroids of the anomalies in the elastic and inelastic scattering do not agree by g 30 keV. As noted below, there are further difficulties with the spectroscopic factors and Coulomb energies for this analogue. Difficulties also arise for the p , analogue state expected near Ep = 2.57 MeV. The two extremely large p~ states observed in this region have about 10 ~ of the singleparticle strength and would correspond to ( 2 J + I)S of about 0.6, as compared to the expected value of 0.2. These two states are about 50 keV apart and are located about 50 to 100 keV respectively, below the expected location for the analogue. The p~ state located almost exactly at the expected location for the analogue state would correspond to ( 2 J + 1)S of about 0.06, as compared to the expected value of 0.2. None of these states exhibit an inelastic decay. The large p½ state nearest to the expected location of the analogue state is therefore tentatively identified as the analogue state. The data in this region are discussed further in sect. 5.

586

N.H.

PROCHNOW

e t al.

30

4STi (P'P} 46Ti af =

46Ti (p,p)46T i 6(

J% 3/2

5/2"

32 RESONANCES

0

35RESONANCES

~

j. r~r,~

0 0

4(

~-~ 0

2c

~

i

E

--

I.

46Ti { P ' P~)46Ti .~%0 CHANNELSPIN=5/2.3/2

o

F-

, __Ff ~ -

I

rr

l

[

46Ti ( p, p,)46Ti

__

I;I CHANNELS.... 312

No.

~

I

t~ °

/

.,C=2

I

CHANNEL SPIN• 3/2

0

//

A" ~

[,q:

~ 40 I,,.,I::L

I

FI

I

I

40

I

l

40 3G

20 0

•

r--

2O 0

j~

2C 2!00

Ep(MeV)2"~0

3.~"

ic C

~-l-''J'Ep(MeV)

3.00

F i g . 9. Cumulative sums of reduced widths for inelastic scattering f r o m P k states and from d-wave states. Note the large anomaly in the 1' = l , s" = ~ data near Ep ~ 2.9 M e V (the anomaly near Ep = 2.3 M e V is o n l y tentatively identified as an analogue state).

4.2. SPECTROSCOPIC F A C T O R S

The spectroscopic factor for the parent state may be calculated from the analogue state data using the relation

Sop =

(2To +

1)to.Its.,

where T o is the z-component of the isospin of the target nucleus, /'pp is the total observed width. The single-particle width was calculated using a computer program written by Harney 18). The procedure is discussed in detail in previous publications in this series. Table 3 lists the results for the analogues observed in the present data. The two analogue states observed near Ep = 1.6 MeV and the analogue states at

46Ti PROTON SCATTERING

587

TABLE 3 Properties of observed analogue states 1st (½-) analogue Ex of parent (MeV) ~) 2.545(5) EpI'b (MeV) 1.565 Epc'~" (MeV) 1.531(2) /'pp (keV) 0.10 /'s.p. (keV) 2 Spp 0.15 Sap ¢) 0.16 B. ~) 8.880(3) AEc (MeV) 7.866(7) AE others (MeV) 7.867(4) a)

½+ analogue

2nd ½analogue

3rd ½analogue

1st ?2analogue

2nd ~analogue

2.570(5) 1.559 1.526(2) 0.10 5 0.06 0.05 8.880(3) 7.836(7)

2.785(5) 3.544(6) 3.675(6) 3.913(8) 1.816 2.533 2.702 2.894 1.777(3) 2.479(2) 2.644(3) 2.832(30) b) 0.25 2.60 2.98 2.66 6 45 75 110 0.12 0.17 0.12 0.07 0.13 0.10 0.12 0.20 8.880(3) 8.880(3) 8.880(3) 8.880(3) 7.872(7) 7.815(7) 7.849(7) 7.799(30)

~) Ref. 19). b) The number quoted is the centroid of the elastic widths, the centroid of the inelastic widths is 30 keV higher, in better agreement with the other Coulomb energy differences. c) Ref. 16). a) The Coulomb energy quoted is from Becchetti et al. 2o). They also quote several other measurements which yield somewhat lower Coulomb energies. Ep = 1.8 and 2.7 MeV yield very g o o d agreement with the (d, p) w o r k while the analogue states at Ep = 2.5 MeV and 2.9 MeV do not. The discrepancy for the Ep = 2.9 MeV state is rather striking for a state with such a large spectroscopic factor in the (d, p) experiment. 4.3. COULOMB ENERGIES The C o u l o m b energy difference between the parent and the analogue state is given by Ec=B,+E~'m'-Ex, where B n is the binding energy o f the last neutron in the parent system and E x is the excitation energy o f the parent state in the parent nucleus. Since the analogues observed in the present w o r k do not show a clear fine structure pattern, the analogue state energy is taken to be the centroid o f the observed states. The values for B, and Ex (and their uncertainties) are taken from Nucl. D a t a ' 9). The results are included in table 3. F o u r o f the analogues have C o u l o m b energies which agree reasonably well with previous results 20) while two analogue states do not agree. The expected Coulomb energy difference as calculated with Janecke's semi-empirical formula z,) is 7.90 MeV. Thus four o f the six strong states observed in the stripping reaction have easily identified analogue states whose spectroscopic factors and C o u l o m b energies have the expected values. The two analogue states near Ep = 2.5 and 2.9 MeV give inconsistent results for the spectroscopic factor and C o u l o m b energy. It should also be

588

N . H . P R O C H N O W et al.

noted that the two analogue states identified near Ep = 1.6 M e V are inverted with respect to energy as c o m p a r e d to the (d, p) results 16). T h a t is, the l = 1 state appears lower in excitation energy than the I = 0 state in the (d, p) experiment. While there is some question a b o u t the spin (½- or ~:-) for the l = 1 state, there is no d o u b t that the l = 0 state appears lower in energy than the 1 --- 1 state in the (p, p) experiment.

5. Statistical properties 5.1. GENERAL

In previous papers 9, 11) statistical properties o f the resonances observed in 48Ti + p reactions have been discussed. The present data are not as suitable for detailed statistical analysis, primarily due to the smaller n u m b e r o f levels observed. Therefore semiquantitative considerations are emphasised. It is apparent f r o m fig. 7 that s~r states are not being observed below Ep = 2.0 MeV (excluding the analogue state near Ep = 1.55 MeV) while p , states are observed. This is attributed to a difference in the strength function for s,~ and p½ in this region. Because o f this, the following discussion will be limited to data f r o m Ep = 2.0 to 3.1 MeV. TABLE 4

Summary of the observed resonance properties from Ep = 2.0 to 3.1 MeV J~

(~,p2) (eV)

Fp at Ep = 2.0 Fp at Ep = 3.0 (MeV) (MeV) (eV) ") (eV) a)

Number of resonances observed

Number of resonances expected for j>

½+ ½]~+ ~+ ~-

1300 4300 800 500 600 3200

60 80 12 2 2 1

500 900 180 30 35 25

22 25 33 10 32 6

½b)

40 40 50 50

a) Calculated lab widths using the observed average reduced width.

b) Assuming the number of J = ½ states to be the average number of ½+ and ½- states observed, and using a spin cut-off factor of a = 3. Table 4 summarizes the properties o f the levels observed in the region Ep = 2.0 to 3. I MeV. The lab widths quoted at Ep = 2.0 MeV (col. 3) and Ep = 3.0 MeV (col. 4) are calculated lab widths using the observed average reduced width (col. 2). Since it is possible to observe resonances whose lab widths are ~ 5 eV, it is clear that essentially all o f the J = ½ states should be observed and that m a n y (or most) of the d-wave resonances should be missed. Assuming that all J = ½ states are observed, the density o f states with angular m o m e n t u m J can be estimated (using p ( J ) ~ ( 2 J + 1)exp [ - ( J + ½)2/2tr2] and a cut-off factor 22) a = 3). These results are also listed in table 4.

46Ti PROTON SCATTERING

589

As expected many d-wave resonances are missed, as are almost all of the f-wave resonances. 5.2. s-WAVE SPACING A N D WIDTH DISTRIBUTIONS

Although the 22 s-wave resonances are not sufficient for any detailed statistical analysis, it is worthwhile to examine the spacing and width distributions. (In 4aTi an energy dependence of the level spacing was observed, and a correction was performed [refs. 9, ~~)] in order to compare directly with the Wigner distribution. In the 46Ti the sample size is too small to observe such detailed behaviour. For consistency the same correction was applied to the s-wave data in 46Ti as was used in 4STi; the corrected and uncorrected spacing distributions are not appreciably different.) The (corrected) spacing distribution is shown in fig. 1 0 - the results are quite consistent with the Wigner distribution, which is shown superimposed. For completeness the experimental width distribution is also shown in fig. 10, with a Porter-Thomas distribution superimposed. The agreement seems excellent. >'~'X t.L 0 2O p.

0

t-

(a)

oo

(b)

I

~d o~

-r-

el

I0 Z

C~ UJ ILl

0

a:

5

m Z

0 0.0

1.0

2.0

X~ S~/
3.0

4.0

I

b. 0 a-

iI

m 3E .-~ Z

0.II

i

I 0.0

I 1.0

2~.0

i 3.0

4.0

y. yz/
Fig. 10. Spacing and width distributions for the s-wave resonances in 46Ti. Wigner and PorterThomas distributions are superimposed on the spacing and width distributions, respectively. The experimental spacing distribution has been corrected for energy dependence (see text).

5.3. p-WAVE RESONANCES Since the s-wave resonances had quite reasonable spacing and width distributions, one might expect the same behaviour for the p½ resonances. This is not the case. The existence of analogue states tends to distort the width distribution. There is an even more serious problem in the region around Ep = 2.5 MeV. As can be seen from fig. 11 there is an anomaly in the reduced widths (as discussed earlier this anomaly is not an analogue state) near Ep = 2.5 MeV. The anomaly is one very large state at Ep = 2.481 MeV whose reduced width is ~ 10 times the average reduced width. If all

590

N.H. PROCHNOW et al.

o f the P~r levels are considered as originating from a Porter-Thomas distribution, then the probability o f a reduced width this large originating from a Porter-Thomas

distribution is only 360" 1

4C'Ti (p,p) I

>

:~6o

(0)

E

i/2-

LEVELS

~

<,./\

I

/./

4C

a

CALCULATED

i

121 3C

', ,

~ zc

I

m

i4 tt

II

I-0 F-

I,

I

1.5

(b)

~ ,c

he"

0

~50keV

I'

~' 2o

Z

.~NALOGUE STATES -

2.0

2.5

0

:3.0

Ep (MeV)

1.5

2'.o e:5 E p (M eV)

Fig. 11. Experimental level density (a) and reduced widths (b) for the ½- states in the a6Ti elastic scattering data. The experimental level density appears to behave anomalously. The solid curve is the expected level density using the semi-empirical formula of Gilbert and Cameron 22). The dashed histogram bars of (b) indicate the analogue state strengths.

Either this state is a part of the analogue state near Ep = 2.57 MeV (yielding an analogue state with a strength much greater than observed in the (d, p) experiment and an extremely low value for the Coulomb energy difference) or there is some other sort of non-statistical behaviour. Even if there is some sort of special state (for the sake of discussion, call the anomaly a doorway state) the spacing distribution is expected to display normal behaviour. This is again not the case. As fig. 11 shows very dramatically, the p~ density apparently has a deep valley in the vicinity of the anomaly. The solid curve indicates the expected level density as calculated from the semi-empirical formula of Gilbert and Cameron 22). 5.4. PROTON STRENGTH FUNCTIONS

Table 5 lists the proton strength functions obtained from these data for s~, p~ and p~ resonances. The strength functions were calculated from SF = E i

where the sum includes all T< levels observed in the interval A E . The analogue strengths have been removed. As is observed consistently in this mass region, the p~ strength is much larger than the p~ strength. That is, mass 46 is much closer to the 2p½ giant resonance than to the 2p~ giant resonance. The s~ strength is somewhat smaller than for nuclei with

*6Ti PROTON SCATTERING

591

higher mass numbers, however this is consistent with the overall trend for the strength functions in this mass region 23). TABLE 5

Proton strength functions for *6Ti+p J~

No. ofievels

El (MeV)

Er (MeV)

X(yp2)l(keV)

SF

1

½+ ½~-

22 35 21

2.088 1.607 1.887

3.067 3.065 3.060

27 150 19

0.03 0.10 0.02

A l t h o u g h detailed strength f u n c t i o n i n f o r m a t i o n has n o t been extracted f r o m the inelastic data, the results are qualitatively as expected. F o r example, as in 4STi, p~ resonances t e n d to have stronger inelastic decay t h a n do p~ resonances. This is att r i b u t e d to the fact the p~ resonances decay only by j , = ½, while the p~ resonances decay by b o t h jp = ½ a n d ~. Since the p~. strength f u n c t i o n is m u c h larger, the p~ resonances have stronger inelastic decay. As in *STi, the d-wave resonances have a surprising a m o u n t of l' = 2 decay mixed with 1' = 0, indicating that the d-wave strength f u n c t i o n must be rather large in this mass region.

The authors would like to acknowledge Dr. A. M. Lane for helpful correspondence and discussions and to thank the other members of our high-resolution group for advice and assistance. One of us (N. H. Prochnow) acknowledges the Research Corporation for a grant which enabled some of the measurements to be extended to lower energies. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

D. Robson, Phys. Rev. 137 (1965) B535 W. MacDonald and A. Mekjian, Phys. Rev. 160 (1967) 730 H. A. Weidenmiiller and C. Mahaux, Nucl. Phys. 89 (1966) 33 A. M. Lane, Isospin in nuclear physics, ed. D. H. Wilkinson (North-Holland, Amsterdam, 1969) p. 509 ft. C. Browne, H. W. Newson, E. G. Bilpuch and G. E. Mitchell, Nucl. Phys. A153 (1970) 481 D. P. Lindstrom, H. W. Newson, E. G. Bilpuch and G. E. Mitchell, Nucl. Phys. A168 (1971) 37 J. D. Moses, H. W. Newson, E. G. Bilpuch and G. E. Mitchell, Nucl. Phys. A175 (1971) 556 D. P. Lindstrom, H. W. Newson, E. G. Bilpuch and G. E. Mitchell, Nucl. Phys. A187 (1972) 481 N. I-L Prochnow, H. W. Newson, E. G. Bilpuch and G. E. Mitchell, to be published J. D. Moses, J. D. Browne, H. W. Newson, E. G. Bilpuch and G. E. Mitchell, Nucl. Phys. A168 (1971) 406 E. G. Bilpuch, N. H. Prochnow, R. Y. Cusson, H. W. Newson and G. E. Mitchell, Phys. Lett. 35B (1971) 303 G. E. Mitchell, E. G. Bilpuch, J. D. Moses, W. C. Peters and N. H. Prochnow, Statistical properties of nuclei, ed. J. B. Garg (Plenum Press, New York, 1972) p. 299 D. L. Sellin, Ph.D. dissertation, Duke University, 1968, unpublished

592 14) 15) 16) 17) 18) 19) 20) 21)

N . H . P R O C H N O W et aL

R. L. Auble, Nucl. Data 4, nos. 3-4 (1970) 269 G. C. Kyker, E. G. Bilpuch and H. W. Newson, Ann. of Phys. 51 (1969) 124 J. Rapaport, A. Sperduto and W. W. Buechner, Phys. Rev. 143 (1966) 808 D. C. Kocher, Ph.D. dissertation, University of Wisconsin, 1971, unpublished Coded by H. L. Harney, Max Planck Institut ftir Kernphysik, Heidelberg, unpublished M. B. Lewis, Nucl. Data 134 nos. 3, 4 (1970) 313 F. D. Becchetti, D. Dehnhard and T. G. Dzubay, Nucl. Phys. A165 (1971) 151 J. J~inecke, Isospin in nuclear physics, ed. D. H. Wilkinson (North-Holland, Amsterdam, 1969) p. 297 22) A. Gilbert and A. G. W. Cameron, Can. J. Phys. 43 (1965) 1446 23) E. G. Bilpuch, J. D. Moses, H. W. Newson and G. E. Mitchell, to be published