Study of structure in the 28Si(p, n)28P and 28Si(p, α)25Al excitation functions

Nuclear Physics A232 (1974) 176 - 188 ;

@ North-Holland

Publishing

Co., Amsterdam

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

STUDY OF STRUCTURE IN TIIE ‘*Si(p, n)28P AND 28Si(p, c~)~*AlEXCITATION FUNCTIONS G. D. GUNN f, K. W. KEMPER and J. D. FOX Department

of Physics,

The Florida State Tallahassee,

University,

Florida 32306 ‘ft

Received 26 June 1974 Abstract: The 28Si(p, n)28P and ?3i(p, ~r)*~Al reactions have been studied over the energy range of 16.0 to 18.2 MeV incident proton energy. Fluctuations appear in the excitation functions over the entire range with widths of 100 keV and 48 keV for the neutron and alpha channels, respectively. The energy averaged ?3(p, ~r)~~Alangular distributions are not reproduced by HauserFeshbach compound nucleus calculations but do resemble DWBA calculations. Because of the complex nature of the reaction mechanism in this energy range, it could not be concluded whether the structure in the excitation functions is due to doorway states or Ericson ~uctuations.

E

I

NUCLEAR REACTIONS 28Si(p, n), E = 15.8-18.2 MeV, measured cr,(E). %i (p, c(), E = 16.0-18.2 MeV; measured a(& E,, f3). 29P resonances deduced rn and r,

.

In a study of proton elastic and inelastic scattering on “Si by Kempar, Fox and Oliver (KFO) ‘), the presence of structure of an intermediate nature was observed in the excitation functions from 16.0 to 18.2 MeV (18.2-20.4 MeV in zgP). The width of the structure was estimated to be 300 keV, and the structure appeared to be somewhat correlated. However, it was not possible to determine if the structure was from doorway states or statistical in origin. To investigate the nature of the observed structure further, a study of the proton-induced neutron and alpha channels was undertaken. The ?Si(p, n)28P total cross section was measured from 15.8 to 18.2 MeV. ‘*Sifp, ~1)~‘Al excitation functions for a large angular range were measured from 16.0 to 18.2 MeV for the $* ground state, the 3’ 0.455 MeV level, and the +’ 0.949 MeV level. Fluctuation widths were extracted from the data. In addition, HauserFeshbach (HF) calculations were done for both the (p, II) and (p, E) reactions, and distorted-wave Born approximation (DWBA) calculations were done for the (p, a) reaction. i Present address: Nuclear Structure Research Laboratory, tt Supported in part by the National Science Foundation, GU-2612. 176

Univ. of Rochester, Rochester, NY. grants no. NSF-GP25974 and NSF-

177

28Sitp

2. Experimental procedure and discussion of data 2.1 THE ?iiCp, II)~~F EXCITATION

FUNCTION

In the reactions studied, protons originating from a direct-extraction negative ion source were injected into the Florida State University super FN tandem Van de Graaff accelerator. The neutron total reaction excitation function was measured over incident proton energies from 15.8 to 18.2 MeV in 50 keV steps. A large surface-area SiO, target, approximately 0.9 mgjcm” or 20 keV thick to an 18 MeVproton beam, was used; it was prepared as previously described in the article of KFO. All collimation before the target was removed to reduce the background. A leaky integrator with automatic fast beam stop operation “) was used in conjunction with a plastic scintillater to observe the decay of ‘*P via the 11.25 MeV p*. A thin aluminum window stopped the protons while allowing the high-energy positrons to reach the detector, which was placed at 90” to the incident beam. A low energy gate was placed on the energy spectrum to discriminate against the 3.8 MeV fi* from the “AI(p, n)27Si reaction. The data were then accumulated in the multiscaler mode so that the 270 msec half-life of the /3’ decay of “P could be monitored. The multiscaler was set to accumulate 10 msec per channel into a 256 channel analyzer. The multiscaler accumulated for 1.28 set after the beam was removed from the target by a fast beam stop, and after a six half-lives delay (1.7 set) for another 1.28 see to accumulate a

7 28

si(p,“128P

-

I.000

’

-

-

Houser-Feshboch

1

,

16.0

17.0

INCIDENT

calculation

I

1

16.0 MeV

PROTON ENERGY

Fig. 1. The 28Sifp, II)~*P excitation function from 15.8 to 18.2 MeV. The solid line is drawn to guide the eye. The dashed line is a Nauser-Feshbach compound nucleus calculation,

17s

G.

D. GUNN et al.

background spectrum. Two hundred cycles of beam on/off were run in this manner at each incident beam energy to acquire su@icient counting statistics. The background yield was subtracted from the data yield to arrive at a corrected yiefd. The excitation function for the 28Si(p, n)‘*P reaction is shown in fig. 1. No attempt was made to determine absolute cross sections. 2.2 THE 28SiCp, c#~AI EXCITATION

CURVES

The ?3(p, CC)‘~A~reaction excitation functions were initially studied over the incident energies of 16.0 to 18.2 MeV in 50 keV steps. The energy interval was chosen to coincide with the energy range covered by KFO. Thin SiO, targets, 50-100 .ug/cm2, were used and placed in a large volume scattering chamber “) containing six surface barrier detectors spaced 10” apart. The ground state reaction Q-value is - 7.70 MeV. The low energy of the emitted cz-particles allowed 100 pm detectors to be used. These detectors stopped the a-particles, but not the protons, thus yielding particle identification of the a-particles. A spectrum is shown in fig. 2. Three angle settings of the detector array were taken for each incident energy, so that an angular range from 40” to 170” (lab) was covered in 10” intervals together with overlap points.

800

2eSi(p,a)25Al Ep=l76MeV EiAB = 40”

CHANNEL Fig. 2. Spectrum for the ?3i(p, c@~AI reaction. Only lower levels are identified. Difficulties in data extraction due to impurities are illustrated by the spectrum.

Impurity peaks from ““Ot’p, a)13N and “C(‘p, a)‘B were present in the spectra at most energies and angles, as shown in fig. 2, requiring the use of peak fitting to extract peak yields for some of the data. Even so, it was not possible to extract some yields at all due to the impurities. Whenever possible, yields were found by simply adding the counts in the peaks of interest. Impurity peaks due to the “Si and 3oSi in the natural targets contributed to the under-lying background, and contributed to the uncertainty in the background subtraction. Due to the problems with the major

28Si+p

179

contaminants and the high background at lower energies from the proton energy losses in the counters, only the first three levels of 25A1 were included in this study. Biased amplifiers were used to cut down on the high count rate proton background and dead time corrections were made to the extracted yields whenever necessary. Excitation functions are shown in figs. 3-5. Fluctuations appear at all angles throughout the entire energy range for all three levels. Obvious correlation exists in the structure, especially from angle to angle within the same level. The fluctuations appear to be of an intermediate nature, i.e. the fluctuation widths can be estimated to be from 30 to 100 keV. This structure in the excitation curves resembles that observed in the proton and neutron channels, but is of a smaller fluctuation width.

28Si(p,cq,)

25AI

5/2’, 0.0 MeV

I’F,o

,

,

,

I70

,

/I!&

18.0

INCIDENT

PROTON

16.0

; IZO

18.0

ENERGY(MeV)

Fig. 3. The z8Si(p, c~o)~~Alexcitation functions. 20 keV and 50 keV data is shown. Error bars are statistical errors. When not shown, they are smaller than the data points as drawn. The line is drawn to guide the eye.

180

G. D. GUNN et al.

28Si(p,a,)25A/ l/2’ ,0.455

MeV

I

16.0

17.C

160 18.0 INCIDENT PROTON ENERGY

Fig. 4. The 2*Si(p, c#~AI

/

17.0

18.0

(MeV)

excitation functions.

Since the step size of the excitation function is of the same order as the estimated fluctuation width for the (p, CX) data, it is possible that finer structure in the excitation curves exists which is glossed over due to the energy step size. In addition, since a thin target was used, numerical averaging of the data is net essary so that comparisons can be made between the experimental cross sections and the Hauser-Feshbach “) compound nucleus model calculations ot the average cross section. This numerical averaging is perhaps inappropriate for the 50 keV excitation data, as it would involve either averaging over too few data points to be significant, or over too large an energy interval to use for comparison with theory. For these reasons a further study was undertaken, in which the incident proton energies cover the range from 17.5 to 18.02 MeV in 20 keV steps. The angular range from 30” to 170” was covered in 10” increments. The excitation curves are shown in figs. 3-5 along with the 50 keV excitation functions. More detailed structure is not observed. Proton elastic scattering data was taken simultaneously with the 20 keV (p, a) data. The broad structure seen previously “) is present, and again there is no indication of smaller fluctuations. Since the targets were natural SiOZ, the proton elastic scattering from I60 was used to find absolute cross sections by comparison with the tabulated data of Daehnick “). The natural abundance of ‘*Si, 92 %, was accounted for in the normalization.

zsSi+p

181

28Si(p,a,)25Af 3/z?.+,

16.0

17.0

18.0

INCIDENT

0.949 M&J

16.0

PROTON

ENERGY

17.0

18.0

(MeVV)

Fig. 5. The 28Si(p, E~)~~AI excitation functions.

Normalizations of various angle settings and small changes in the experimental arrangement from run to run, such as changes in detector collimation, were made through the various overlapping angles that were taken. Low energy a-particle and proton scattering were taken to check the relative solid angIes of the detector arrangement. The largest source of error in the extracted cross sections was due to the background subtraction and the statistical errors. Background subtraction errors were estimated to be about 5 % of the extracted yields. Statistical errors vary from 2 % to 15 %. A combination of background subtraction, statistical, beam integration, and relative solid angle deterlnination errors @ves a relative uncertainty in the data which varies between 5 and 1S %. The absolute error is 15 % and arises from the uncertainty in the determination of the target thickness-solid angle product. 3. Analysis To determine whether the observed (p, CZ)fluctuations might be statistical in nature, energy averaged angular distributions can be compared with calculations from the

182

G. D. GUNN

ei al.

Hauser-Feshbach compound nucleus model “). The averaging interval must contain several fluctuation widths, but must not be so large as to average over any broader underlying structure. This criterion is equivalent to that required to determine the fluctuation width itself. The following method, suggested by Pappalardo 6), was used to find the appropriate aveaging interval and hence the fluctuation width. The auto-correlation function over a finite range of data is given by

where A is the energy interval size used to find the average cross section (CJ) and E is the energy increment. Setting E = 0 and evaluating C(0, A) for various values of A, one encounters a range where C(A) is insensitive to A. A median value for A chosen from this range is appropriate for the averaging interval and for use in determining the fluctuation width. The averaging interval was determined to be 400-500 keV for the 20 keV (p, a) data. All of the fluctuation widths, r, were found by noting that the auto-correlation function can be approximated by a Lorentzian ‘), i.e.

so that

for each E,

The term T(E) was evaluated at the several central E where C(E) resembles the Lorentzian shape, and these values were then averaged. Table 1 is a tabulation of the fluctuation widths obtained from the 20 keV data using a 400 keV averaging range. The average value is 48 keV. This value corresponds to the normally quoted FWHM of the Lorentzian. The (KFO) estimate for the proton channel, 300 keV, is the FWHM estimate for a fluctuation of structure and is approximately twice as large as an estimate made from performing the autocorrelation analysis, 150 keV. The (p, cc) value of 48 keV is consistent with widths found previously in this mass and excitation energy range in the compound system “). A similar estimate made on the 50 keV data over a 500 keV range, shown in table 2, indicates an almost identical result for many of the angles for the various levels; the average value is also 48 keV. In the (p, n) channel the fluctuation width was found to be about 100 keV above 17.0 MeV. This figure is much less precise, as less data was available in this channel to be applied to the analysis, and the average cross section varies rapidly with energy after the reaction threshold at 15.7 MeV. Selected angular distributions of the ‘*Si(p, c~)‘~Al reactions are shown in fig. 6. Although there is a rather rapid change in the shapes of the angular distributions, the general shapes tend to persist over the range of energies studied.

average

011 a2

Cf-0

Angle

average

a2

a1

=0

Angle

30

22.6

20.2 25.1

51.4

51.4

50

27.9 31.0 45.0 34.6

50

40

70.9

70.9

69.9

69.9

40

30

TABLE 1

63.2 41.4 11.7 38.8

70

40.7 57.5 54.6 51.0

80

53.9 28.4 11.7 31.3

PO

TABLE 2

48.8 24.6 60.4 44.6

100

34.7 33.4 45.2 37.8

110

31.7 32.9 25.2 29.9

120

20.5 65.1 15.5 33.9

130

37.5 46.8

56.2

140

34.3 48.6

61.0

150

52.1

52.1

60

34.5

50.7 18.2

70

52.2

27.5 69.6 59.4

80

53.5

33.9 74.0

PO

44.2

46.6 11.6 74.6

100

36.8

27.5 68.8 14.2

110

40.6

40.6

120

34.9

.^~40.2 46.4 18.0

130

38.2

28.8

47.6

140

48.3

37.0

49.6

150

Widths, I’, extracted from 28Si(p, CC)~~AIexcitation functions taken in 50 keV steps

57.5 45.5 36.1 46.4

60

Widths, I: extracted from 28Si(p, CC)~~AIexcitation functions taken in 20 keV steps

80.8

85.2 24. I 133.0

.-.I.~-

160

93.6 39.5 121.1 84.7

160

68.3

89.1 41.6 74.3

170

92.9 74.6 89.6 85.7

170

48.0

51.8 47.4 54.9

Average r

54.9 43.1 45.2 48.3

Average r

zi

184

G. D. GUNN et ai.

The total cross sections wese found by performing the sum

The total cross-section excitation curves are shown in fig. 7. The (p, a,) and (p, az> excitation functions are rather smooth above 17 MeV, whiIe the (p, ccc) channel still has large ~u~tuat~ons. The structure below 17 MeV again appears to be correlated. Averaged total cross sections were generated by using a 500 keV averaging interval and are also shown in fig. 7. The averaged data indicates that there is no structure of larger width superimposed on the ~u~tuati~g data. The average angular distributions are shown in fig. 8. Averaging over various interval sizes up to the entire range of 2

ec.m, (degrees) Fig. 6. The ?3i(p, czfZSAlan&m distributions for the “*Si@, ~0, I, 2)25Al reactian. The rapid variation of the angular distributionswith incident energy is evident. Lines are drawn to guide the eye.

?Si+p

185

0

i I

1

I

16.0 INCIDENT

/

I

IZO PROTON

I

I

I

ENERGY

I

18.0 (MeV)

Fig. 7. The 2*Si(p, c~)~~Altotal cross-section excitation functions generated by a sum over angles. The solid line is an excitation curve averaged over 500 keV. Also shown are excitation curves generated from DWBA calculations and Hauser-Feshbach calculations.

MeV does not greatly affect the appearance of the angular distribution. By comparing figs. 6 and 8, it can be seen that the individual angular distributions are quite similar to the average angular distributions. The rather large difference in fluctuation widths obtained in the (p, p’), (p, n), and (p, X) studies is difficult to understand in terms of statistical model theories. The angular momentum dependence of the different exit channels is expected to not exceed 25 ‘A [ref. “)I and normally is about 10 %, which clearly cannot account for the difference. If, however, a large direct reaction contribution is present, then the extracted widths could be different, and it is not possible to use these widths as a measure of the properties of the compound system. To attempt to understand the reaction mechanism present, Hauser-Feshbach and DWBA calculations were performed. From the work of Shotter et al. lo), r/D is at least 2 in this energy range, and Hauser-Feshbach calculations should describe the energy averaged data if the reaction is purely statistical in nature. The statistical model calculations were made using the code HAUSER rl, “). HAUSER makes use of a sharp cutoff in the I of the transmission coefficients. Proton, neutron, and alpha channels are assumed to predominate in the evaporation of particles, and thus no other exit channels were considered in the calculations. Pairing energies from Cameron 13) were used. Optical model transmission coefficients were generated from subroutines of the code JIB I”). The optical model parameters used to calculate the transmission coefficients are listed in table 3 and discussed with the

G. D. GUNN

186

28Si(

et

af.

p,a)*%I

(Ep> =X7 MeV

5/2+,

O.OMeV

3/2+ ,0.949MeV

l/2+, 0.455MeV

I

_

\

! e lf

_---

3

Hauser -Feshbach DWBA + H-F

40

80

120

-

160

f&&h)

Oc,_kkg.)

Fig. 8. The 28Si(p, 0~)~~A.laveraged angular distributions. The angular distributions unaveraged angular distributions shown in fig. 6. Also shown are a Hauser-Feshbach tribution, a typical DWBA calculation, and a sum of these calculations.

resemble the angnlar dis-

DWBA analysis. A typical density of spin-zero states, p, was 135 MeV-’ using the constant temperature approximation to the Fermi gas model I’), with a spin cutoff parameter of 2 = 7.1. An excitation curve for the total 28Si(p, n)28P cross section generated with this code is shown in fig. 1 with the experimental excitation function. Normalization for the theory curve is an arbitrary factor since the data were not converted to absolute cross sections. The excitation function for the first MeV above the threshold is TABLE3 Ontical model narameters f0C

P,

n “1

w.Y t “1

42.8

165.9

YOI

@Or

@m>

(fm>

1.3 1.23 2.0

0.62 0.73 0.65

“) Ref. 16). *) Ref. l’). “) Adjusted to give the appropriate

used

separation

(fml 1.3 1.7 2.0

45.4 14.3

1.25 1.23

energies for the bound state channels.

28Si-l-p

187

somewhat reproduced by the calculations, but the calculations do not predict the total cross sections trend or magnitude thereafter. Calculations for the ‘*Sifp, CX)~~AI are shown in fig. 7. The,trends of the excitation curves are somewhat similar to the calculations for the 3’ and 3” levels, but not for the s* ground state. The magnitudes of the calculations were adjusted to match that of the 4+ level. Calculated angular distributions for the (p, E) channel using the Hauser-Feshbach model are shown in fig. 8 with the average angular distribution. The calculations do not resemble the experimental angular distributions. The backward peaking in the +* and 3’ levels is not well reproduced by the statistical model calculations. The large amount of structure evident in the energy averaged ‘%i(p, x)~~AI angular distributions indicates a large direct reaction contribution might be present. Consequently, zero-range DWBA calculations were carried out with the code DWUCK 15). Optical model parameters used are shown in table 3. The proton parameters are from a study by Crawley and Garvey ’ “). Alpha parameters are from a study of 27Al by Kemper, Obst, and White 17). Other a-parameter sets from studies on 2sSi and 24Mg [refs. I** ’ “)I were also used, but the resulting shapes of the angular distributions are generally similar to those resulting from the set in table 3. Bound state parameters are also shown in table 3. The Woods-Saxon well depth was varied to match the binding energy of the triton to “Al . The triton was treated as a cluster and a bound state radius parameter of 2.0 fm was used to simulate the large size of the triton, as suggested by Garrett et al. ‘O). No radial cutoff was used, nor was a spinorbit term included in the bound state. Because of the large uncertainties inherent in the (p, CX) calculations, extensive efforts to improve the fits by varying the optical parameters were not made. A DWBA excitation function for the (p, a> totai cross section is shown in 6g. 7. The trend of the data is fairly well reproduced for the -$+ and 3’ levels, but not as well as for the 2’ level. Both the DWBA and HF excitation functions are quite similar, and the total cross section data does not favor either reaction mechanism as predominant. As can be seen in fig. 8, the general trend of the angular distributions is reproduced by the DWBA calculations, especially for the 9’ level at 0.455 MeV indicating a large direct contribution. The backward peaking of the 3” level at 0.949 MeV is not predicted by the calculations. An incoherent sum of the DWBA and compound nucleus calculations might be expected to provide the best fit to the data. A CNiDWBA summed anguIar distribution is shown in fig. 8. Although some improvement is indicated, the backward peaking of the 3’ level is still not reproduced. 4. Conclusions Fluctuations similar to those observed at seIected angles in the ‘*Si(p, p’)%i reaction are also present in the “Si(p, n)‘$P and 28Si(p, E)~‘AI excitation functions. The trends of the averaged total cross section for the (p, a) channels are equally well

188

G. D. GUNN

et al.

described by either Hauser-Feshbach or DWBA calculations or a combination of the two. The (p, a) angular distributions are not reproduced by the statistical calculations but do resemble DWBA calculations, especially for the (p, q) group. A sum of the DWBA and Hauser-Feshbach angular distributions does not greatly improve the fit to the data. It would seem from the shapes of the angular distributions that the (p, a) reaction in this energy range is largely direct making a meaningful interpretation of the extracted fluctuation widths in terms of Ericson fluctuations or doorway states impossible. The authors wish to acknowledge A. Obst, S. Marsh, and R. L. White for their participation in the data taking, and M. Clark, K. Ford, and W. Thorner for helping in the preparation of the illustrations. We also wish to thank D. Robson for many informative talks. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20)

K. W. Kemper, J. D. Fox and D. W. Oliver, Phys. Rev. C5 (1972) 1257 D. T. Birch and J. W. Nelson, Nucl. Instr. 3.5 (1965) 293 G. D. Gunn, T. A. Schmick, J. D. Fox and L. Wright, Nucl. Instr. 113 (1973) 1 W. Hauser and H. Feshbach, Phys. Rev. 87 (1952) 366 W. W. Daehnick, Phys. Rev. 135 (1964) B1168 G. Pappalardo, Phys. Lett. 13 (1964) 320 T. Ericson, Adv. in Phys. 9 (1960) 425 T. Ericson and T. Mayer-Kuckuk, Ann. Rev. Nucl. Sci. 16 (1966) 183 D. Robson, A. Richter and H. L. Hamey, Phys. Rev. CS (1973) 153 A. C. Shotter, P. S. Fisher and D. K. Scott, Nucl. Phys. Al59 (1970) 577 A. W. Obst, Florida State University Internal Report, 1973, unpublished K. A. Eberhard, P. von Brentano, M. Bohning and R. 0. Stephen, Nucl. Phys. Al25 (1969) 673; K. A. Eberhard and C. Mayer-Bbricke, Nucl. Phys. Al42 (1970) 113 A. G. W. Cameron, Can J. Phys. 36 (1958) 1040; A. Gilbert and A. G. W. Cameron, Can J. Phys. 43 (1965) 1446 F. G. Perey, Phys. Rev. 131 (1963) 745 P. D. Kunz, University of Colorado, unpublished G. M. Crawley and G. T. Garvey, Phys. Rev. 160 (1967) 981 K. W. Kemper, A. W. Obst and R. L. White, Phys. Rev. C6 (1972) 2090 A. W. Obst and K. W. Kemper, Phys. Rev. C6 (1972) 1706 W. J. Thompson, G. E. Crawford and R. H. Davis, Nucl. Phys. A98 (1967) 228 3. D Garrett, H. G. Bingham, H. T. Fortune and R. Middleton, Phys. Rev. C5 (1972) 682