Structure in the 27Al(p, α)24Mg cross section between Ep = 4.0 and 5.5 MeV

Nuclear Physics

A138 (1969) 171-116;

Not to be reproduced

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CROSS SECTION

E, = 4.0 AND 5.5 MeV

M. K. MEHTA and A. S. DIVATIA Van de Graaff Laboratory,

Bhabha Atomic

Received

Research

Centre, Bombay-85

1 August 1969

Abstract: The excitation functions of the reactions 27Al(p, a,)*4Mg and “Al@, a1JZ4Mg* were measured in the proton energy range Ep = 4.0-5.5 MeV with an energy resolution of about 5 keV at lab angles of 60”, 90” and 165”. The excitation curves exhibit sharp maxima of widths between 10 and 50 keV superimposed on a broad 150-300 keV wide structure. The channel as well as angle cross correlation functions calculated with moving averages are high for all the cases. This as well as strong visual correlations of the sharp and the broad structure between various curves lead to the conclusion that the observed structure, both fine as well broad, is due to individual resonance effects and not to fluctuations. It is suggested that the fine structure is due to very slightly overlapping compound nuclear levels, while the broad structure may represent the “intermediate states” of the compound system. E

NUCLEAR REACTIONS 27Al(p, a& (p, aI), E = 4.0-5.5 MeV; measured a(& 0). ‘sSi resonances deduced r, autocorrelations, cross correlations.

1. Introduction As a continuation of our study of reactions induced by proton bombardment of “Al we have measured the excitation functions for the reactions 27Al(p, a,)24Mg and 27Al(p, u~)‘~M~* in the bombarding energy range 4.0-5.5 MeV [ref. ‘)I. This corresponds to an excitation energy ranging from 15.44 to 16.89 MeV in the nucleus 28Si. Recently these reactions have been studied by Put, Roeders and Van der Woude [ref. “)I in th; bombarding energy range 10.9-19.7 MeV. Elliott and Spear “) have studied the ’ 7Al(p, p)” 7A1 and ’ 7Al( p, p’)’ 7A1* reactions for proton bombarding energies from 3.5 to 11.3 MeV which overlaps with the energy range covered in the present work. Their energy resolution was 10 keV. The structure observed in these two experiments has been analysed in terms of the fluctuation theory of Ericson and others 4), however, Elliott and Spear “) have reservations about the applicability of the fluctuation theory to the lower part of their excitation functions. In our previous work ‘) it was established that an average width of about 18 keV can be attributed to the finer structure observed. It was also shown that fairly strong cross correlations existed between the a0 excitation curves at 90”(lab) and 150”(lab) as well as between the a0 at 90”(lab) and the p3 group (from the reaction 27Al(p, P~)~~AI*) at 90” when the averaging interval was properly chosen. It was concluded that this was due to the 171

F--%1

(P.C,)%ig*

INCIDENT

PROTON

fh,=t63

ENERGY

(MeV.LAB)--

Fig. 1. Excitation curves for the tcO and CQ groups resulting from proton bombardment of 27A1. The reaction and the laboratory angle are indicated on each curve. The vertical dashed lines are discussed in the text.

27Al(p,

173

cQz4Mg

apparent visual cross correlation between the gross structure which must then represent individual resonances. In the present work the excitation functions have been measured at three laboratory angles of 60”, 90” and 165” in steps of 5 keV, overall resolution being about 3 keV. The aim of the experiment was to study the cross correlation between the a, and GIN channels at the same angle as well as between two angles for the same channel, in order to establish the nature of the observed structure. 2. Experimental

technique

and results

The experimental arrangement was the same as that described in ref. ‘). Alpha particles were detected in three solid-state detectors placed at the lab angles of 60”, 90” and 150”. These detectors were operated in their partially depleted mode so that the elastically scattered protons from aluminium, as well as from oxygen and carbon contaminants, lost only a small part of their energy and did not stop within the depletion layer, while the alpha particles stopped completely. This resulted in a clean peak for the cl,-group which would otherwise have been masked between the peaks due to the scattered protons from carbon and oxygen. Self-supporting “Al targets were prepared having nearly the same thickness as the ones used in the previous experiment ‘) (x 3 keV for 2 MeV protons). The excitation curves were evaluated for the ~1~and a, groups at each of the three angles. The resulting excitation functions are shown in fig. 1. The curve for the a,,group at 90” is a very good reproduction of the same excitation function given in ref. ‘). Some of the sharp peaks rise higher in the present result indicating a slightly finer energy resolution. As the reproduction was good, no attempt was made to determine the absolute cross section, especially because it is not significant in the context of the present experiment. A quantitative measure of the reproduction was obtained by calculating the cross correlation coefficient between the ’ 'Al(p, a0)24Mg excitation curve at 90”(lab) in ref. ‘) and the curve B in fig. 1; the cross correlation coefficient is 0.93. 3. Analysis

and discussion

All six excitation functions exhibit fine and gross structure similar to that in ref. ‘). Hence a similar analysis of the data was undertaken, and the autocorrelation coefficients C(0) were calculated for various averaging intervals (the notation used here has been explained in ref. ‘)). Lorentzian fits to the autocorrelations coefficients C(E) for small incremental energies E, using properly selected values of the averaging interval result in a “coherence width” of about 18 keV. These results are not presented here in detail, since they are similar to those in ref. ‘). Labelling the curves in fig. 1 from bottom to top as A, B, C, D, E and F respectively, the angular cross correlation coefficients C,,(O), C,,(O), Cur(O), C,,(O), C&O) and &r(O) as well as channel cross correlation coefficients C,,(O), C&O) and

M. K.

174

MEHTA

AND A. S. DIVATIA

C&O) were calculated for various averaging intervals. These are shown in fig. 2. All of these display (to a varying degree) a peak with a maximum around 200-400 keV and a “width” of the same order. Ail the cross correlations are consistently high, the maximum values ranging between 0.45 and 0.52 for channel cross correlations and between 0.45 and 0.73 for the angular cross correlations. The maximum FRD error, estimated according to the expression given in ref. 3), is 25 y0 on all the cross correlation values. ANG. CROSS

ANG. CROSS

CORR. COEFFS.

0.4-1

,

CHANNEL

CORR. COEFFS.

,

CROSS

,

,

,

I--

CORR.COEFFS.

0.4 O.IIIIlIIIII’IbII 0 LOO 6 - AERAGING

800

1200

INreRvAL,kev-

s-

AVERAGING

INTERVAL,

kcv -c

Fig. 2. The variation in cross correlation functions for E = 0 (notation of ref. ‘)I with the averaging interval 6. The symbols CA, etc. are explained in the text.

To study whether the strong correlations are due to the fine or the gross structure, the excitation functions were carefully examined. The vertical lines drawn in fig. 1 illustrate the fact that most of the sharp peaks are correlated in all six excitation functions within t_ 5 keV. This difference of 5 keV is explainable as the energy steps are 5 keV while the resolution is less than that. On the other hand to check the correlation between the wider structure the 25 keV averaged data for all six excitation curves were plotted as shown in fig. 3, where the averaged excitation functions for a0 and 01~ are superposed at each angle. Again most of the peaks are correlated with a few remarkabIe exceptions, for example around EP x 4.3 MeV. It is inferred from this that

*‘Al(p,

175

a)24Mg

the wider structure also represents resonances due to some sort of levels in the compound system; an exception may then reflect the nature of the particular level giving rise to that resonance. Thus both the fine as well as the gross structure are strongly correlated between angles as well as channels. In view of this, good Lorentzian fits to the autocorrelation functions [fig. 4 of ref. ‘)I can be interpreted as giving an “average width” (r) of observed fine structure which represent individual, but slightly overlapping levels of

14 12

EXCITATION CURYES FOR do AND da GROUPS AVERAGED OVEFtFtZ~~e,V,o

10

INCIDENT

PROTON

ENERGY

(Me’4

LAB)

Fig. 3. The excitation curves of fig. 1 averaged over 25 keV interval. The CL,,curves and a1 curves are labelled respectively. The lab angle is indicated for each curve.

the compound nucleus and not the fluctuations predicted by the statistical theory. In other words the compound nucleus ‘*Si excited between 15 and 16 MeV does not show a continuous spectrum. However level density is high and is approaching a continuum to the extent that an “average width” for the levels does not have a meaning. Even estimates based on the statistical theory give a
176

M. K.

MEW-A

AND

A. S. DIVATIA

would range from 19 to 27 keV, again the range being slightly beyond the FRD error of &3 keV. An examination of fig. 3 indicates the presence of gross structures with widths varying from about 75 keV to 500 keV. These widths are much larger than the expected and observed compound nuclear level widths of 19 to 27 keV and much smaller than those for the single-particle giant resonances which would be of the order of an MeV. This, coupled with the fact that these peaks show high cross correlations between angles and channels lead us to conclude that they represent the “intermediate structure” arising from the excitation of simple configurations in the compound system. 4. Conclusion The nature of the fine structure observed in the excitation functions is established as the effect of discrete compound nuclear levels, which may be slightly overlapping, having average widths ranging from 19 to 27 keV at the excitation energy between 15.44 and 16.89 MeV in 2sSi. This conclusion is arrived at on the basis of the observed strong cross correlations observed in the present work and the Lorentzian fits to the autocorrelation functions reported in ref. ‘). The gross structure of widths ranging from 75 to 500 keV is interpreted as the intermediate structure representing excitation of levels of the compound system which have confi~ratio~s simpIer than the ones expected for the complex compound nuclear levels represented by the observed fine structure. These states could then be classified as the doorway states in a broad sense of the term “). We express our thanks to S. S. Kerekatte and K. K. Sekharan for their help in data taking and the operation crew of the Van de Graaff accelerator for the smooth operation of the machine during the experimental runs. References 1) M. K. Mehta et al., Nucl. Phys. 89 (1966) 22 2) L. W. Put, J. D. A. Roeders and A. van der Woude, Nucl. Phys. A112 (1968) 561 3) R. V. Elliott and R. H. Spear, Nucl. Phys. 84 (1966) 209 4) T. Eriscon, AM. of Phys. 23 (1963) 390; Phys. I.&t. 4 (1966) 258; D. hf. Brink and R. 0. Stephen, Phys. Lett. 5 (1963) 77; D. M. Brink, R. 0. Stephen and N. W. Tanner, Nud. Phys. 34 (1964) 577 5) P. P. Singh et aZ., Nucl. Phys. 65 (1965) 577 6) H. Feshbach, Rev. Mod. Phys. 36 (1964) 1076; R. A. Ferrel and W. M. MacDonald, Phys. Rev. Lett. 16 (1966) 187