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The (γ, α) reaction in Cu, Ag, In and Au
Nuclear Physics 61 (1965) 316--320; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher
THE (7, at) REACTION IN Cu, Ag, in and Au L. MENEGHETTI and S. VITALE l.N.F.N.-Istituto di Fisica dell'Universitti di Genooa and
Gruppo EURATOM-C.N.E.N. Received 9 June 1964 Abstract: Alpha particles photoproduced at 90 ° from Cu, Ag, In and Au were detected by silieork junction counters. Yields and spectra were obtained at 35 MeV maximum bremsstrahlung e n e r g y . A comparison with the statistical model suggests the presence of direct effects in alpha photoproduction from In and Au. El
I
N U C L E A R REACTIONS Cu, Ag, In, Au(7, '0, E <: 35 MeV; measured o(E~), deduced or. Natural t a r g e t s .
[
t
1. Introduction The understanding of the 7 ray nuclear absorption and of the photodisintegration processes, in the region of the giant resonance, is quite satisfactory for the more important phenomena. However several details are still to be clarified, and in particular, the ~ photoproduction processes were not studied in sufficient detail. The aim of this research was first to identify direct processes among the dominant evaporative processes in (7, ~) reactions. Evaporative (V, ~) production processes are not negligible in spite of the high Coulomb barrier, as the binding energy of particles is rather low. The presence of direct effects is connected with nucleon clusters on the nuclear surface. This last problem, which was investigated in recent years using several different approaches (hyperfragment production, (p, ~) reactions, etc.) had a positive solutiorL in the experiment of Igo et al. 1) on quasi-elastic (~, 2c¢) reactions at high energy.
2. Experimental System The experimental apparatus is shown in fig. 1. The particles were detected by two silicon counters operating simultaneously. The two counters (I00 mm 2 sensitive area) were placed at 20 mm from the targets in order to collect ~ particles photoproduced at 90°+ 15° from the beam axis. The counter pulses passed through two separated channels, each comprising a transistor charge316
THE 0), ~) REACTION
317
sensitive preamplifier, a fast-rise-time ( 1 0 - s sec) main amplifier and an output pulse lengthener, and then were fed to the two imputs of a 200-channel analyser which was separated into two sections of 100 channels each. A gating pulse from a scintillation counter in the beam, opened the analyser gate during the v-ray pulse.
Fig. 1. Block diagram of the experimental apparatus. Cx and C2- detectors, PAx and. PA~ charge-sensitive preamplifiers, AI and. A2 - fast-rise-time main amplifiers, SS1 and SS2 - step subtractors, PLx and. PL2 - Pulse lengtheners, S. C. - Scintillation counter monitor, (3. (3. - Gate pulse generator. -
In order to minimize pile-up effects the pulses at the input o f the main amplifier were clipped at 5- 10-8 sec by means of a delay line. Moreover at the output of the amplifiers a constant step was subtracted to eliminate pulses due to electrons and then the pulses were lengthened and fed to the analyser. The amplification and linearity of the electronic apparatus was frequently tested by recording the Ra spectrum. The targets were metallic sheets mounted at 70 ° to the beam axis. The target thicknesses were 11.52, 7.15, 5.06 and 5.6 mg/cm z for Cu, Ag, In and Au, respectively. The evacuated chamber with target and counters was mounted inside the body of the betatron to reduce the distance between the targets and the betatron anticathode to 60 era. The background measurements were made by interposing A1 filters of proper thickness, in front of the counters to stop the most energetic particles. Other background measurements were made without targets and filters. The effective thickness of the counters was experimentally deduced by measuring the end-points of the photoproton spectra. For each element the counter thicknesses were properly adjusted, varying the applied bias voltage, in order to have linear response to 0t with m a x i m u m energy and photoproton minimum background. The m a x i m u m energy of our betatron which was automatically controlled by a Katz circuit was 35 MeV. For V ray intensity control we used a thick-waUed Kernst type ionization chamber. This chamber was calibrated against a Victoreen dosemeter with a 3 m m lead cap and also by a yield determination of the reaction Cu65(V, n)Cu 64.
318
L.
MENEGHETTI
AND
S. V I T A L E
3. Results The ~ spectra obtained from the disintegration o f Cu, Ag, In and A u are shown in fig. 2. The corresponding yields, calculated from the data at 90 ° in the h y p o t h e s i s o f isotropical angular distribution, are given in table 1. (a)
(b)
~ ~
8
Copper
Silver
Zd
z~
10
I 6 8.6 11.312,9
Ec~ MeY
. 1214416819. ,%-L,T-h l..B.7..2.96 22t6,24Ec~MeV
(c)
Indium
Gold
(d)
..Q
z 1
1
4.8 ~2 9.6 ~2 ]4/, 168 19.2 21.6 24 263 E ~ MeV
48 72 9.6 1214./-, 16 819.2 21,6 24 26.3 E ~ MeV
Fig. 2. The histograms show the experimental ~-spectra. The solid lines are the calculated evaporative spectra corrected for target self-absorption and normalized to the maximum of the experimental spectra. TABLE 1 yields from the 90 ° data. Yield (per mole R) Elements Experimental Calculated evaporative Cu Ag In Au
(1 4-0.1)105 (2.8 ~0.3)104 (1.05-4-0.1)10 ~
3.1 104 3.4 l0 s 3.05 10~
(1.7 4-0.2)10 3
8.7
Errors in experimental yields are compounded of statistical errors and errors in the absolute calibration of the beam. These results are compared with those expected f r o m statistical calculations. The photo-alpha cross section yield, and spectrum in this m o d e l are defined as:
a,,(E,) =
~,(E,)F~(E,)
rJE,)+ r,(E,) '
f ]'max~,~(ee)N(Ee,Eemax)dee r(ee max) = e(Ee)N(Ee, Eemax)dee
~ E~ max
THE (F, cQ REACTION
319
where av(Ev) is the cross-section for compound nucleus production by rays with energy Ev; N(E~, Evmax) is the bremsstrahlung spectrum for maximum energy Ev max and the total alpha, proton and neutron widths F~, Fp and F , are defined as
r,
=
r, =
~0 max
-e)de,
flm"o,(*)*, CO(E--
--e)de,
:irna~ rn =
A -.)d.,
where ~r~(8), Crn(~) and ~p(8) is the cross-section for compound nucleus formation by e; n and p collision on the residual nucleus. The quantity c o ( E - Q - A - ~ ) is the level density of the target nucleus. We have approximated the cross-section of the inverse reactions as
er~(e)=yl~(l-?)q-y2~(l-?), % = yp(I-~),
O'n: ~)n(I----~)
with the parameters y and V fitted with data of Huizenga and Igo 1) and Dostrovsky et al. 2) and co(E) as e 2"t"~-a-~-~) with a = ~oA MeV -1. The gap energy A is calculated from Cameron's pairing energies 3). The Q values were taken from Wapstra 4). In our calculation for Cu and Ag nuclei, an average on isotope abundance was performed. The calculated yields are strongly dependent on Q , - Q~ and on the parameter a of the level density and so, for the uncertainty on the values of these data, the cross-sections and the yields calculated are no more than an indication of the order of magnitude. Anyway, the spectrum shape is less sensitive to these parameters. Taking into account the inaccuracy of calculation, the agreement on photo-alpha yields from Cu and Ag between experimental results and the theoretical ones is rather good. Also the values of (?, 00 cross-sections for these nuclei, reported in refs. s, 6) agree with our calculations if the contribution of the reaction (~, n~) is taken into account. If the results on In and Au are considered, a net disagreement is evident. For these nuclei the calculated yields are particularly low in In for the rather high value o f Q~ and in Au for the height of the Coulomb barrier. These data seem to indicate the existence of direct effects on the (?, or) reactions; effects that become observable as the evaporative mechanism is quenched. We have made an attempt to evaluate the weight of direct contributions in a rather arbitrary manner. The maximum of calculated evaporative spectra was normalized to the maximum of the experimental ones. It is evident that there is an excess of energetic alphas, especially in In and Au, which we have attributed to direct effects.
320
L. MENEGHETTI AND S. VITALE
A comparison was made between these extrapolated contributions and the predictions of a very simple model for direct effects in the (~, a) reaction, first proposed by Carver 7). According to this model, ct particles preformed at the nuclear surface are photo-ejected by electric dipole interactions. Carver gives a rough evaluation of the cross-sections ratio for direct alpha to direct photon production ad(%a) _ 4 ad(?, p)
v~ T, Z ½rp'
where 4(N-Z)2/N 2 is the ratio of squared electric dipole effective charges of particles and protons in a nucleus with electric charge Z and mass number A = N + Z; v, is the number of preformed alpha particles and TJTpis the ratio for the escape probabilities from a nucleus for an a particle and a proton. The data on (% p) yields are deduced from ref. s). The escape probability was evaluated by supposing that only • particles emitted in the outward direction may escape and by using semi-empirical data for barrier penetrabilities from Dostrowsky and Franzkel 2). The number of preformed ~ required to get an agreement is about 4-5. This figure is affected by very large errors, but anyway seems to us rather high when compared with results of Igo 1). We would like to thank Professor R. Malvano for his encouragement and suggestions. References 1) G. I. Igo, L. F. Hansen and T. J. Goording, Phys. Rev. 131 (1963) 337; J. R. Huizenga and G. I. Igo, Argonne National Laboratory Report N. 6373 (1961) 2) I. Dostrovsky, Z. Fraenkel and G. Friedlander, Phys. Rev. 116 (1959) 683 3) A. G. W. Cameron, Can. J. Phys. 36 (1958) 1040 4) A. H. Wapstra, F. Everling L. A. Koening and J. H. E. Mattauch, Nuclear data tables (United States Atomic Energy Commission, Washington, 1953) 5) F. Heenrich, H. Waffter and I. Walter, Helv. Phys. Acta 29 (1956) 6) S. P. Roalsvig, R. N. H. Hasman, L. D. Skarsgard and E. E. Wuschke, Can. J. 37 Phys. (1959) 722 7) F. H. Carver, Proc. Phys. Soc. 77 (1961) 417 8) V. G. Shevchenko and B. A. Jurev, Nuclear Physics 37 (1962) 495 9) R. M. Osokina, Direct interactions and nuclear reaction mechanisms, ed. by E. Clementel and C. Villi (Gordon and Breach, New York, 1963)
THE (7, at) REACTION IN Cu, Ag, in and Au L. MENEGHETTI and S. VITALE l.N.F.N.-Istituto di Fisica dell'Universitti di Genooa and
Gruppo EURATOM-C.N.E.N. Received 9 June 1964 Abstract: Alpha particles photoproduced at 90 ° from Cu, Ag, In and Au were detected by silieork junction counters. Yields and spectra were obtained at 35 MeV maximum bremsstrahlung e n e r g y . A comparison with the statistical model suggests the presence of direct effects in alpha photoproduction from In and Au. El
I
N U C L E A R REACTIONS Cu, Ag, In, Au(7, '0, E <: 35 MeV; measured o(E~), deduced or. Natural t a r g e t s .
[
t
1. Introduction The understanding of the 7 ray nuclear absorption and of the photodisintegration processes, in the region of the giant resonance, is quite satisfactory for the more important phenomena. However several details are still to be clarified, and in particular, the ~ photoproduction processes were not studied in sufficient detail. The aim of this research was first to identify direct processes among the dominant evaporative processes in (7, ~) reactions. Evaporative (V, ~) production processes are not negligible in spite of the high Coulomb barrier, as the binding energy of particles is rather low. The presence of direct effects is connected with nucleon clusters on the nuclear surface. This last problem, which was investigated in recent years using several different approaches (hyperfragment production, (p, ~) reactions, etc.) had a positive solutiorL in the experiment of Igo et al. 1) on quasi-elastic (~, 2c¢) reactions at high energy.
2. Experimental System The experimental apparatus is shown in fig. 1. The particles were detected by two silicon counters operating simultaneously. The two counters (I00 mm 2 sensitive area) were placed at 20 mm from the targets in order to collect ~ particles photoproduced at 90°+ 15° from the beam axis. The counter pulses passed through two separated channels, each comprising a transistor charge316
THE 0), ~) REACTION
317
sensitive preamplifier, a fast-rise-time ( 1 0 - s sec) main amplifier and an output pulse lengthener, and then were fed to the two imputs of a 200-channel analyser which was separated into two sections of 100 channels each. A gating pulse from a scintillation counter in the beam, opened the analyser gate during the v-ray pulse.
Fig. 1. Block diagram of the experimental apparatus. Cx and C2- detectors, PAx and. PA~ charge-sensitive preamplifiers, AI and. A2 - fast-rise-time main amplifiers, SS1 and SS2 - step subtractors, PLx and. PL2 - Pulse lengtheners, S. C. - Scintillation counter monitor, (3. (3. - Gate pulse generator. -
In order to minimize pile-up effects the pulses at the input o f the main amplifier were clipped at 5- 10-8 sec by means of a delay line. Moreover at the output of the amplifiers a constant step was subtracted to eliminate pulses due to electrons and then the pulses were lengthened and fed to the analyser. The amplification and linearity of the electronic apparatus was frequently tested by recording the Ra spectrum. The targets were metallic sheets mounted at 70 ° to the beam axis. The target thicknesses were 11.52, 7.15, 5.06 and 5.6 mg/cm z for Cu, Ag, In and Au, respectively. The evacuated chamber with target and counters was mounted inside the body of the betatron to reduce the distance between the targets and the betatron anticathode to 60 era. The background measurements were made by interposing A1 filters of proper thickness, in front of the counters to stop the most energetic particles. Other background measurements were made without targets and filters. The effective thickness of the counters was experimentally deduced by measuring the end-points of the photoproton spectra. For each element the counter thicknesses were properly adjusted, varying the applied bias voltage, in order to have linear response to 0t with m a x i m u m energy and photoproton minimum background. The m a x i m u m energy of our betatron which was automatically controlled by a Katz circuit was 35 MeV. For V ray intensity control we used a thick-waUed Kernst type ionization chamber. This chamber was calibrated against a Victoreen dosemeter with a 3 m m lead cap and also by a yield determination of the reaction Cu65(V, n)Cu 64.
318
L.
MENEGHETTI
AND
S. V I T A L E
3. Results The ~ spectra obtained from the disintegration o f Cu, Ag, In and A u are shown in fig. 2. The corresponding yields, calculated from the data at 90 ° in the h y p o t h e s i s o f isotropical angular distribution, are given in table 1. (a)
(b)
~ ~
8
Copper
Silver
Zd
z~
10
I 6 8.6 11.312,9
Ec~ MeY
. 1214416819. ,%-L,T-h l..B.7..2.96 22t6,24Ec~MeV
(c)
Indium
Gold
(d)
..Q
z 1
1
4.8 ~2 9.6 ~2 ]4/, 168 19.2 21.6 24 263 E ~ MeV
48 72 9.6 1214./-, 16 819.2 21,6 24 26.3 E ~ MeV
Fig. 2. The histograms show the experimental ~-spectra. The solid lines are the calculated evaporative spectra corrected for target self-absorption and normalized to the maximum of the experimental spectra. TABLE 1 yields from the 90 ° data. Yield (per mole R) Elements Experimental Calculated evaporative Cu Ag In Au
(1 4-0.1)105 (2.8 ~0.3)104 (1.05-4-0.1)10 ~
3.1 104 3.4 l0 s 3.05 10~
(1.7 4-0.2)10 3
8.7
Errors in experimental yields are compounded of statistical errors and errors in the absolute calibration of the beam. These results are compared with those expected f r o m statistical calculations. The photo-alpha cross section yield, and spectrum in this m o d e l are defined as:
a,,(E,) =
~,(E,)F~(E,)
rJE,)+ r,(E,) '
f ]'max~,~(ee)N(Ee,Eemax)dee r(ee max) = e(Ee)N(Ee, Eemax)dee
~ E~ max
THE (F, cQ REACTION
319
where av(Ev) is the cross-section for compound nucleus production by rays with energy Ev; N(E~, Evmax) is the bremsstrahlung spectrum for maximum energy Ev max and the total alpha, proton and neutron widths F~, Fp and F , are defined as
r,
=
r, =
~0 max
-e)de,
flm"o,(*)*, CO(E--
--e)de,
:irna~ rn =
A -.)d.,
where ~r~(8), Crn(~) and ~p(8) is the cross-section for compound nucleus formation by e; n and p collision on the residual nucleus. The quantity c o ( E - Q - A - ~ ) is the level density of the target nucleus. We have approximated the cross-section of the inverse reactions as
er~(e)=yl~(l-?)q-y2~(l-?), % = yp(I-~),
O'n: ~)n(I----~)
with the parameters y and V fitted with data of Huizenga and Igo 1) and Dostrovsky et al. 2) and co(E) as e 2"t"~-a-~-~) with a = ~oA MeV -1. The gap energy A is calculated from Cameron's pairing energies 3). The Q values were taken from Wapstra 4). In our calculation for Cu and Ag nuclei, an average on isotope abundance was performed. The calculated yields are strongly dependent on Q , - Q~ and on the parameter a of the level density and so, for the uncertainty on the values of these data, the cross-sections and the yields calculated are no more than an indication of the order of magnitude. Anyway, the spectrum shape is less sensitive to these parameters. Taking into account the inaccuracy of calculation, the agreement on photo-alpha yields from Cu and Ag between experimental results and the theoretical ones is rather good. Also the values of (?, 00 cross-sections for these nuclei, reported in refs. s, 6) agree with our calculations if the contribution of the reaction (~, n~) is taken into account. If the results on In and Au are considered, a net disagreement is evident. For these nuclei the calculated yields are particularly low in In for the rather high value o f Q~ and in Au for the height of the Coulomb barrier. These data seem to indicate the existence of direct effects on the (?, or) reactions; effects that become observable as the evaporative mechanism is quenched. We have made an attempt to evaluate the weight of direct contributions in a rather arbitrary manner. The maximum of calculated evaporative spectra was normalized to the maximum of the experimental ones. It is evident that there is an excess of energetic alphas, especially in In and Au, which we have attributed to direct effects.
320
L. MENEGHETTI AND S. VITALE
A comparison was made between these extrapolated contributions and the predictions of a very simple model for direct effects in the (~, a) reaction, first proposed by Carver 7). According to this model, ct particles preformed at the nuclear surface are photo-ejected by electric dipole interactions. Carver gives a rough evaluation of the cross-sections ratio for direct alpha to direct photon production ad(%a) _ 4 ad(?, p)
v~ T, Z ½rp'
where 4(N-Z)2/N 2 is the ratio of squared electric dipole effective charges of particles and protons in a nucleus with electric charge Z and mass number A = N + Z; v, is the number of preformed alpha particles and TJTpis the ratio for the escape probabilities from a nucleus for an a particle and a proton. The data on (% p) yields are deduced from ref. s). The escape probability was evaluated by supposing that only • particles emitted in the outward direction may escape and by using semi-empirical data for barrier penetrabilities from Dostrowsky and Franzkel 2). The number of preformed ~ required to get an agreement is about 4-5. This figure is affected by very large errors, but anyway seems to us rather high when compared with results of Igo 1). We would like to thank Professor R. Malvano for his encouragement and suggestions. References 1) G. I. Igo, L. F. Hansen and T. J. Goording, Phys. Rev. 131 (1963) 337; J. R. Huizenga and G. I. Igo, Argonne National Laboratory Report N. 6373 (1961) 2) I. Dostrovsky, Z. Fraenkel and G. Friedlander, Phys. Rev. 116 (1959) 683 3) A. G. W. Cameron, Can. J. Phys. 36 (1958) 1040 4) A. H. Wapstra, F. Everling L. A. Koening and J. H. E. Mattauch, Nuclear data tables (United States Atomic Energy Commission, Washington, 1953) 5) F. Heenrich, H. Waffter and I. Walter, Helv. Phys. Acta 29 (1956) 6) S. P. Roalsvig, R. N. H. Hasman, L. D. Skarsgard and E. E. Wuschke, Can. J. 37 Phys. (1959) 722 7) F. H. Carver, Proc. Phys. Soc. 77 (1961) 417 8) V. G. Shevchenko and B. A. Jurev, Nuclear Physics 37 (1962) 495 9) R. M. Osokina, Direct interactions and nuclear reaction mechanisms, ed. by E. Clementel and C. Villi (Gordon and Breach, New York, 1963)