Differential cross sections for radiative capture of energetic protons by 110Cd and 115In

Nuclear Physics A326 (1979) 26-36 ; © North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfiLn without written permission from the publisher

DIFFERENTIAL CROSS SECTIONS FOR RADIATIVE CAPTURE OF ENERGETIC PROTONS BY t t °Cd AND t ' .In F. RIGAUD, G. Y. PETIT and J. DALMAS Centre d'Etudfs Nucléaires de Bordeaux-Gradignan, Le Haut-Vigneau, 33170 Gradignan, France J. L. IRIGARAY Laboratoire de PhYsiyue Corpusculaire, Université de Clermont-Ferrand, 63170 Aubière, France M .SUFFERTI Basses Energies, Centre de Recherches Nucléaires et Université Louis Pasteur, 67037 Strasbourg Cedex, France F. SAPORETTI and G. LONGO Comitato Nazionale Energia Nucleare, Centro di Calcolo, 40138 Bologna, Italy and R. GUIDOTTI

Facoltddi Ingegneria dell'Unn;ersitd, Bologna, Italy Received 30 March 1979 Abstract : Spectra of high-energy photons following the radiative capture of 11-22 MeV protons in " °Cd and "' In are measured . The (p, ;) differential cross sections at 90° with respect to the beam axis is deduced from the integration of measured spectra. The photon angular distribution is measured for the 'Cd(p, ~0) reaction, too, at 13 MeV incident energy . Satisfactory agreement between theory and experiment is obtained by using the direct-semidirect model for dipole and quadrupole fast nucleon radiative capture. E

NUCLEAR REACTIONS "°Cd, "'In(p,1), E = 1-22 MeV; measured a(EP, 0.). Enriched . ..Cd and natural "In targets.

1 . Introduetion During the last decade great interest has been devoted to the measurement of nuclear excitations in the 5-30 MeV energy interval in order to locate and characterize the giant multipole resonances . This study has been carried out through different kinds of experiments ; in particular, nucleon radiative capture measurements have f

Present address : CERN - EP, 1211 Genève 23, Switzerland . 26

"'Cd

12s1 n( p,

,)

27

provided information (mainly on dominant electric dipole excitation) either by the activation method or by the integration of high-energy y-ray spectra'). In the present paper we show the results of measurements of prompt 7-rays emitted in the " °Cd(p, y) and `In(p, y) reactions. The 90° differential cross sections have been determined from 8-22 MeV, and the y-ray angular distribution at five angles with respect to the incident beam has been measured for 13 MeV protons captured in "°Cd . The results are compared with the predictions of the direct-semidirect model 2 .3), which is known to be a reasonably good means of analysis for fast nucleon radiative capture data (see, e.g., ref. a )) . The excitation function of the "°Cd(p, yo) reaction is well reproduced by model calculations and the observed y-ray angular distribution seems to indicate the presence of a quadrupole collective excitation induced by the capture process. 2. Experimental arrangement The beam of8-22 MeV protons was provided by the Strasbourg CRN MP tandem accelerator. In order to minimize the neutron background it was required that the direct proton beam hit nothing but the self-supporting target and that the protons scattered by the target could only strike graphite, the threshold of the '2 C(p, n) '2N reaction being 19.76 MeV. To realize these conditions'), the beam passed first through a graphite collimator (0 - 5 mm) placed before the target . The current measured on this collimator was maintained smaller than about 0.1 nA. Any increase in collimator current produced by beam position instability, for example, automatically stopped data acquisition. After the target, several graphite collimators prevented the protons scattered by the target from reaching the stainless steel walls of the beam pipe . Finally, the proton beam was dumped on a graphite disk placed inside a concrete pit 8 m from the target . The target thicknesses were 0.9±0.08 mg/cm2 for " °Cd (98 % enriched) and 4.5±0 .5 mg/cm2 for " Sin (natural). They were self-supporting and their thickness was measured by using proton backscattering techniques . The target holder connected to the beam dump constituted a good Faraday cup. Typical proton intensities ranged from 50 nA to 100 nA. The y-rays were detected at 90° to the proton beam with a y-ray spectrometer S) (fig . 1) which consisted of a 25 cm-x 30 cm Nal(TI) crystal surrounded by a plastic scintillator. The photons emitted by the target were concentrated by a conical lead collimator (AQ = 115 msr) into the inner region of the NaI crystal, thus reducing energy leakage. This collimator was filled with paraffin in order to reduce the fast neutron flux . An additional 20 cm of paraffin was placed between the target and the collimator. The spectrometer was shielded by 10-20 cm of lead. The response curves of the spectrometer to y-rays ranging from 11 MeV to 30 MeV .

28

F. RIGAUD et al.

Fig. 1 . The physical layout of the Nal(TI) crystal y-ray spectrometer .

was determined using the "Al(p, y)"Si, 12C(p, p, 7)12 C and t t B(p, 7)12 C reactions. The response curve consisted of a full energy peak and a low energy tail due to radiations escaping from the crystal and not detected by the plastic sinctillator . This tail was extrapolated linearily to zero for zero energy in accordance with Monte Carlo calculation results. The energy resolution (FWHM) was about 4 %. The absolute efficiency of the spectrometer was determined using the accepted and rejected spectra. Fast electronics was used in order to reduce pulse pileup effects. We have verified that the studied reaction yields are unchanged when half the target current is used . The raw spectra were stored in the computer memory and transferred to magnetic tapes for data analysis. 3. Experimental results

Fig. 2 shows a typical spectrum measured at EP = 8 MeV for the t" S ln(p, y)' t 6Sn reaction . The open circles correspond to the spectrum with a lead plug inserted in the detector collimator. This plug absorbs 96 % of the incident y-rays, with negligible influence on the spectrum produced in the NaI crystal by fast neutrons . As can be seen from the figure, the intensity of the latter is negligible in the energy region of interest . The arrows labelled y o and y, indicated, respectively, the transitions to the ground state and the first excited state (E. = 1 .293 MeV) of the final nucleus. The excited states above Ei x 2-MeV are closely spaced and the transitions to these states could not be resolved by the spectrometer. This spectrum shape agrees with the deuteron spectrum for ' t5 In(3He, d) 1t6Sn measured in

"'Cd, 0)

125 1n(p

29

y)

2000

Z O U

1500

1000

500

80

100 CHANNEL NUMBER

Fig. 2. The high-energy part of the ,,-ray spectra measured in the 115 1n(p,7) reaction. The arrows correspond to yo and y, transitions . The open circles correspond to the spectrum measured with the lead plug .

b)

â 0.15 a

1151n(p .Td 116 Sn

.05 0

10

14

la

115

L---1-10 Ep(M"v )

1

In

(',r1 ) 116

1

14

1

1

Sa

la

1

Fig. 3. Excitation curves for the 1151n(p, yo) (a) and 1151n(p, y,) (b) reactions measured at 90'.

F. RIGAUD et al .

30

ref. 6) at 25 .3 MeV incident energy . This reaction weakly excites the first excited states . For excitation energies higher than 3.7 MeV, strong transitions were observed . These spectra show that the first excited states of 116 Sn are rather poor single particle states . The y-ray yields were obtained from a computer analysis 7) which fitted the highenergy portion of the y-ray spectra by introducing simultaneously the response curve of the y-ray spectrometer for the yo and y t transitions. Fig. 3 shows the excitation curves for y o and yt measured at 90° to the incident beam . Fig. 4 shows a typical spectrum measured at EP = 10 MeV for the t t'Cd(p, y) t ' t In reaction . The open circles correspond to the spectrum measured with a lead plug as in fig. 2 . The arrow labelled y o indicates the transition leading to the ground state of the . . .In nucleus. The strong peak labelled "y3" indicates transitions to the first seven excited states of the 1 "In In nucleus . These levels are too close to each other to be resolved experimentally. 300

h F2 O

200

100

60

90

100 CHANNEL NUMBER

Fig. 4. The high-energy part of the y-ray spectra measured in the " ° Cd(p, y) reaction. The arrows correspond to the yo transition and ~i_iyi transitions. The open circles correspond to the spectrum measured with the lead plug .

Fig. 5 shows the excitation curves for y o and E;= t y i ) measured at 90° with respect to the incident beam . These curves were obtained from the y-ray spectra computer analysis 7) taking into account the response curves of the y-ray spectrometer for the MeV) and y 7 yo , yt (E. = 0.536 MeV), y2 (Ex = 0.804 MeV), y3 (Ex = 1 .101 .Cd(p, tt transitions. The insert of fig. 5a shows the y o) tt . In (Ex = 1 .348 MeV) photon angular distribution measured at EP = 13 MeV.

"OCd "sln(p ~,, ) ~1 .5 í }

31

E'=13AW

jw É

3

ó

t+ f

5!

v

C

0.5 +

0

1

110 1

10

ili

Cd (p,Y.) ~

1

14

1

In 1

18

i

f

7 110 Cd (p, E 1

L- . 1

22 10 Ep(MeV)

1

14

y

i)

0

+ 1111n

L. 1

18

1

22

0

Fig. 5. Excitation curves for the "°Cd(p, yu) (a) and "°Cd(p, 2] ;-, y;) (b) reactions measured at 90°. The "°Cd(p, ;'u) angular distribution measured at EP = 13 MeV is shown in the insert .

The errors of the differential cross sections depend on two kinds of uncertainties. The first is due to statistics and to the y-ray spectra analysis error (1 to 5 % for the different reactions) . The second corresponds to a systematic error in the absolute yield. The different non-correlated source for this type of error (target thickness, incident charge and charge collection, geometry of the detection solid angle, y-ray attenuation coefficients and y-ray spectrometer response curve extrapolation) give a systematic error of about ± 12 %. In figs . 3 and 5 only the first kind of uncertainty is shown by vertical error bars . At some energies, independent measurements were plotted instead of averaged values in order to give an idea of the dispersion of the data . 4. Comparison between experiment and theory The differential cross sections are investigated by means of the direct-semidirect model' , ') for dipole and quadrupole fast nucleon radiative capture 4). Starting from the radial matrix elements ML1. for an EL transition from an initial state (1Ï') to a bound state (1, j) (see ref. 8)) the cross section for (E1 +E2) capture to a given final state is written as 4 da ao(E) [1 í»2 ~AL"(LJXL"(61 + a )P(cos B)], I (1) däl 4n L" R=I where A L" are the electric dipole and quadrupole amplitudes A

-

4n

Me z

L+1

kzL+i

t

(jL921-144U1fi)Z(ltj'lj ;iL)ML1'1

F . RIGAUD

32

e1

ul.

XLu (0, 4s) are the vector spherical harmonics, ao the cross section integrated over the 47r solid angle, and the a coefficients are combinations of the amplitudes ALu : a, 3 = Y-fl . 3(,u)Re(A,,,A2*,,), u

a2 .4 =

E12 . 4(L, LM

h)I A LU l 2 .

The relative weight of the interference between dipole and quadrupole radiations is expressed through the interference factor I(E, 0) which can be measured by the ratio between the difference and the sum of the y-yields at angles 0Ï and n-OY, namely I(E, 0) =

a(E)P, (cos 0)+a3(E)P3(cos0) _ Y(E, 0)-Y(E, n-0) Y(E, 0)+Y(E, n-0) 1+a 2 (E)P2 (cos0)+a4(E)P4 (cos0)

(2)

Calculations are performed using the optical parameters 9) which were independently determined by simultaneously fitting a considerable amount of experimental data to nucleon-mucleus elastic scattering, reaction cross-section and polarization data . The potential is assumed to have a Woods-Saxon form with surface absorption, a spin-orbit term of the Thomas type and the Coulomb potential. of â uniformly charged sphere, U(r) = - Vf(r) - iWg(r) - Veh(r)c - I, with form factors f(r)

=

C1

+exp

r-R

( a »

-1

,

h(r)

g(r) = -4b -

12

X

d (r-R»-1 +exp dr C1 b

1 df(r) r dr '

where R = ro A}, a, b are the nuclear radius, the diffuseness and width parameters, and A x is the pion Compton wavelength . The usual Coulomb phase shift is taken into account in calculating the incident proton wave functions . lo) The single-particle state wave function is calculated by using the potential whose depth is adjusted by the computer programme to give the experimentally known proton binding energy . "'Cd are taken The excitation energy and the width of the giant dipole state in from ref. l") as equal to 15 .8 MeV and 6.2 MeV, respectively . Information on quadrupole giant states in "OCd is rather poor . On the basis of the investigation of ref. 12) the excitation energies and widths of the giant quadrupole states are

. . .Cd

. 125 1n( p . -,,)

33

considered equal to 12.5 MeV and 4 MeV for dT = 0 and to 28 MeV and 4 MeV ford T = 1 . The matrix element between the ground and dipole states is calculated by using the energy-weighted sum rule with the exchange force factor equal to 0.5. To calculate the semidirect quadrupole transitions the reduced electric transition strengths are assumed to be 1800 fm" and 1200 fm4 for isoscalar and isovector capture, respectively . The comparison between experiment and theory is here confined to the "oCd(p, yo) reaction leading to the single particle state Ig s . A first estimate, taking into account only direct E1+E2 capture, showed that the shape of the excitation function cannot be reproduced without introducing semidirect capture going through giant multipole states . From that calculation it was also clear that a magnitude agreement between experimental points and calculations can be obtained only by using a spectroscopic factor with a value of about 0.4-0.6. To our knowledge no information is available about the spectroscopic factors for the proton states of "' In. In this final nucleus we have an unfilled shell with 49 protons, so that a spectroscopic factor equal to 0.5 for the ground state seems reasonable and is used in the foregoing calculations which include both direct and semidirect processes. This value could be compared with the ground-state spectroscopic factor (S = 0.59) recently measured "a ) for the nearby " 0Cd nucleus. The volume form of the particle-vibration coupling (see ref. e )) is less adequate than the surface form for reproducing the experimental points of fig. 5 in the high-energy range. The use of a real or complex surface interaction ' 4) is equivalent as is shown by calculations in which the strengths of the particle-vibration coupling are given the values L', = 135 MeV, co = 50 MeV for the real interaction and v, = 120 MeV, vo = iro = it-, = 50 MeV for the complex interaction. The energy dependence of the a coefficients, in the 810 MeV energy range, is plotted in fig. 6a with curves calculated by using the complex interaction. Calculations show that direct as well as semidirect quadrupole cross sections have their peaks in the 22-27 MeV energy region . This leads to a maximum relative strength of quadrupole compared with dipole radiation at about 21-23 MeV. As can be seen from fig. 6a, peaks are obtained in correspondence with this energy both for the a4 coefficient, which is related to pure E2 transitions, and for the odd a-coefficients, which are due to the interference between dipole and quadrupole radiations. Examination of fig. 6a confirms that at 14 MeV proton energy, where the a2 and a4 coefficients are approximately equal to zero, the "OCd(p, y() cross section integrated over the 4n solid angle can be obtained multiplying by 4n the value of da/dQ for 0,, = 90°. This is not true for higher energies : at 25 MeV, for example, this procedure should produce an underestimate of the total cross section of more than 20 %. By using the a coefficients shown in fig. 6a, the interference factor I(E, 0) (see formula 2) is calculated for some forward angles and plotted in fig. 6b . Obviously

m

W v

0L5

0

10

20

30

40

EP(MrH)

Fig. 6. Calculated a, coefficients (a) interference factor /(E, 0) (b) for the II °Cd(p, ~°) reaction .

the same trends with opposite signs would be obtained for the backward angles 7z-O,,, while for ©., = 90° the interference vanishes . This factor, being essentially related to the odd a coefficients, has an energy trend similar to that of at . The curves shown in fig. 6b indicate that in the whole energy range considered a forward peaking in angular distributions of the emitted photons should be obtained. A comparison between the present experimental points for the "°Cd(p, y°) reaction and the results of calculations is shown in fig. 7. The dot-dashed curve of fig. 7a, obtained for E2 capture corresponding to the direct process alone (S = 1) clearly disagrees with the experimental points. The continuous and dashed curves, calculated with the direct-semidirect model (S = 0.5) by using a complex and real interaction respectively, are practically equivalent in fitting the data. In agreement with the theoretical predictions illustrated by fig. 6, the calculated angular distribution of fig. 7b shows a forward peaking. This asymmetry indicates the presence ofquadrupole capture. However, the 13 MeV proton energy considered, being in the neighbourhood of the E1 giant resonance, is not the most appropriate

. ..Cd 125 1n(p, -)

35

Fig. 7. (a) Comparison between theory and experiment for the "°Cd(p, ~0) differential cross section at 0.. = 90°. The dot-dashed curve is calculated for E2 capture going through the direct process alone (S = 1) . (b) Comparison between theory and experiment for the "°Cd(p, -0) differential cross section at EP = 13 MeV. In (a) and (b) the solid and dashed curves correspond to a complex and real interaction respectively (S = 0.5) by taking into account direct as well as semidirect isoscalar and isovector E2 contributions.

for studying quadrupole contributions which are masked by dipole strength . This prevents us from distinguishing whether E2 contributions aredue to direct transitions or to induced collective isovector or isoscalar excitations. Calculations carried out with different interpretations of quadrupole capture give curves similar to those plotted in fig. 7. For a more detailed investigation of the El-E2 interference in the reaction studied, angular distribution data at about 22 MeV proton incident energy and excitation functions for small forward (or great backward) angles would be very useful . Thanks are due to Dr. F. Fabbri for performing the required computations . References I) 2) 3) 4)

F. Rigaud, Thèse d'État, Université de Bordeaux 1 (1978), unpublished G. E. Brown, Nucl . Phys . 57 (1964) 339 C. F. Clement, A. M. Lane and J. R. Rook, Nucl . Phys . 66 (1965) 273, 293 F. Saporetti, G. Longo and R. Guidotti, Phys. Lett . 768 (1978) 15 ; G. Longo, F. Saporetti and R. Guidotti, Nuovo Cim. 46A (1978) 509 5) M . Suffert, A. Degre, R. Fischer and P. Jean, J. de Phys . 32 (1971) C 5b-261 ; M. Suffert, Proc . Int. Conf. on photonuclear reactions and applications, Asilomar, 1973, ed . B. Berman, vol. 2, p. 741 6) R. Shoup and J. D. Fox and G. Vourvopoulos, Nucl . Phys . A135 (1969) 689

36 7) 8) 9) 10) 11) 12) 13)

F. RIGAUD et al .

M. Schaeeffer, thèse d'état, Université de Strasbourg (1975) G. Longo and F. Saporetti, Nucl . Phys . A199 (1973) 530, Phys. Lett . 65B (1976) 15 F. D. Becchetti Jr . and G. W. Greenless, Phys . Rev . 182 (1969) 1190 A. Bohr and B. R. Mottelson, Nuclear structure, vol. 1 (Benjamin, New York, 1969) p. 239 A. Leprétre, H. Beil, R. Bergère, P. Carlos, A. De Miniac and A. Veyssière, Nucl . Phys. A219 (1974) 39 T. Walcher, Proc. Int. Conf. on nuclear physics, Múnich, Aug. 27-Sept. l, 1973, vol. 2, p. 510 F. Soga, Y. Hashimoto, N. Takahashi, Y. Iwasaki, K. Sakurai, S. Kohmoto and Y. Nogami, Nucl . Phys . A288 (1977) 504 14) G. Longo and F. Saporetti, Nucl . Sci. and Eng. 61 (1976) 40