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Nuclear gamma absorption cross section for magnesium in the energy region 10–30 MeV
2.I
I
Nuclear Physics 72 (1965) 137--144; ( ~ North-Holland Publishing Co., Amsterdam blot to be reproduced by photoprint or m i c r o f i l m without written permission from the publisher
NUCLEAR GAMMA ABSORPTION CROSS SECTION F O R M A G N E S I U M I N T H E E N E R G Y R E G I O N 10-30 M e V B. S. DOLBILKIN, V. I. KORIN, L. E. LAZAREVA, F. A. NIKOLAEV and V. A. ZAPEVALOV P. N. Lebedev Physical Institute, USSR Academy of Sciences, Moscow Received 25 December 1964 Abstract: The absorption cross section of y-quanta by Mg nuclei in the energy range 11-30 MeV has been measured by the absorption method on the 260 MeV synchrotron of the Lebedev Physical Institute. A nine channel pair magnetic y-spectrometer was used as a detector. The cross section obtained has a resonance structure and can be represented as a superposition of several partially overlapping peaks. Comparison with the resonances observed in the partial reaction cross sections shows that these peaks are probably separate groups of unresolved transitions. The shape and integrated cross section of the experimental curve in the 11-30 MeV range do not agree with the results of the available theoretical calculations for Mg. i
EI
I
NUCLEAR REACTION Mg(y), E = 11-30 MeV; measured try(E). Deduced resonance parameters. Natural target.
3
]
J
1. Experimental Procedure The 260 MeV Lebedev Physical Institute synchrotron has previously been used to study 160 and 12C by means o f the absorption method. The applicability o f this m e t h o d as a means of investigating the structure o f the nuclear absorption cross section of light nuclei is discussed in detail in refs. 1, 2). W h e n working with continuous bremsstrahlung radiation, the main difficulty in using the m e t h o d for this purpose is that two contradictory conditions have to be fulfilled: (i) the ~-ray detector should be capable o f a high resolution with (inevitably) a very low efficiency; (ii) the performance o f measurements with a high statistical accuracy (not worse than a few tenths o f one percent) over small energy intervals ( < 100 keV). To increase the efficiency o f the method, a nine-channel pair magnetic spectrometer was used instead o f the one-channel pair magnetic spectrometer which had been employed previously 1, z). Fig. 1 shows the design o f the spectrometer chamber. The slits o f the spectrometer, lying in the plane o f the radiator (the three slits on each side), are situated symmetrically with respect to the centre o f the radiator and at equal distances f r o m one another (r 1 : r2 : r3 = 19 : 20 : 21 cm). In this way, measurements were performed simultaneously for five values o f the energy (coincidences - 1 + 1 - ; 1+2-+2+1-; 1+3-+3+1-+2+2-; 2+3-_t_3+2-; 3+3-). 137
138
B.s. DOLBILK1Net al.
The main parameters of the spectrometer for these measurements were the following: 12.9 mg/cm2; 60 x 50 ram; 4 mm; 10 mm; 70 ram; 5 x 6 x 7 0 mm; 38, 39, 40, 41, 42 cm, 0.01 ~ ; at 10 MeV ~ 120 keV at 20 MeV ~ 220 keV.
thickness of radiator (gold) effective radiator area width of slits (lead) thickness of slits height of slits dimensions of plastic scintillators distances between the inner edges of the slits magnetic field stability spectrometer resolution
4.
~
2
~-
............... Lo j
.~
t I ~-
I ql
"~__~,q~
Fig. 1. Spectrometer chamber: 1-radiator, 2-system of slits, 3-scintillators, 4-light guides, 5FEU-36 photomultipliers, 6-three layer magnetic shielding, 7-region of the homogeneous magnetic field, 8-magnetometer coil (stabilization by the nuclear proton resonance method), 9-input and output windows for X-ray beam, 10--lead shielding, ll-pump-out tube.
Pulses from the photomultipliers (FEU-36) were passed through pulse shapers and into a matrix of coincidence circuits (resolving time of 3 nsec). Thereafter the pulses were amplified, discriminated by amplitude and fed into the recording system. Data processing was carried out by computer. A block of metallic magnesium (Mg > 99.9 ~ ) with a 70 x 70 mm cross section and 650 mm long was used as an absorber. After passing through this absorber (112.4 g/cm 2) the y-ray flux in the investigated energy region (10-30 MeV) was reduced by a
139
ABSORPTION CROSS SECTION
factor of ,~ 10. The ratio of the number of ?-quanta detected in the absence of the absorber in the beam of X-rays (No) to that with the absorber (N) was measured for each given energy (No/N = exp(a,u:l + apalr pr + a~omptonseat)nt; n is the number of nuclei in cm 3; t is the thickness of the absorber). These two quantities were measured alternately and were normalized to the same X-ray flux, which was measured by means of a thin walled integrating ionization chamber (monitor) situated between the lead collimator and the absorber. The measurements were made at maximum X-ray energy E~m~x = 260 MeV. To reduce the number of accidental coincidences the ?-ray pulses from the accelerator were extended in time up to 3000 #see. Accidental coincidences were registered throughout the period of measurements by a second set of coincidence circuits connected in parallel to the main ones via time delay lines. The percentage of accidental coincidences with the absorber in the X-ray beam was ~ 2 % and without the absorber it was ~ 20 %.
2. Experimental Results The absorption curve No/N(hv) was measured in the energy range hv = 11-30 MeV. In fig. 2 are given the nuclear absorption cross section values obtained from the
r,'l 9. 5C
4Q
l
~0 20 I0 0
Fig. 2. The nuclear absorption cross section.
ratios No/N after subtracting the "non-nuclear" part of the cross section (pair production process and Compton scattering) from the total absorption cross section. The measurements were performed with energy step ~ 40 keV, the data were then averaged over a range of 200 keV. Each point is the result of the averaging of 20-30
B. S. DOLBILKIN et al.
140
independent No/N ratio measurements. The errors given are root-mean-square. The energy scale is corrected for the finite resolution of the spectrometer. As was pointed out in ref. 1), there are two difficulties in separating the part of the cross section due to nuclear interaction. The first is a wide range of theoretical values for the cross section for pair production in the field of an electron. The second is the impossibility of estimating accurately the correction for "pumping over" of photons into the investigated energy range from the more energetic part of the spectrum (30 MeV < hv < 260 MeV) when an absorber is placed in the X-ray beam. In order to avoid these difficulties and to establish the zero of the nuclear absorption cross section scale, one must normalize the curve of the non-nuclear part of the cross section in the energy range around 10 MeV, where the relative contribution of the nuclear cross section is minimum. In the present case the normalization was carried out in the energy interval hv = 14.5-16 MeV. A detailed analysis of the cross sections for all possible reactions in this energy range 3-7) gives a mean value of the total cross section for these reactions in the range 14.5-16 MeV equal to 3_+12mb. In accordance with the indicated errors, the zero of the nuclear absorption cross section scale was determined with the accuracy ( + 1; - 2) mb. The nuclear cross section obtained for magnesium has a resonance structure, Representing the whole cross section as a superposition of the actually resolved peaks corresponding to the separate transitions or groups of unresolved transitions, it is possible to obtain an estimate of the main parameters for these peaks: the position hv.... the maximum cross section O-. . . . the half-width F and the integrated cross section (proportional to the oscillator strength of the corresponding transition). The solid curve in fig. 2 drawn through the experimental points was calculated by the: least-squares method for the case in which the shape of separate peaks can be described by the Breit-Wigner formula. This assumption is not self-evident, thus the calculation is of a qualitative nature only. In table 1 are listed the separate peak parameters obtained in this manner. The quantities O'max and F characterizing the shape o f the peaks are not corrected for the finite resolution of the spectrometer. TABLE 1 P a r a m e t e r s o f resonance p e a k s observed in the nuclear absorption cross section
hvres (MeV)
11.2
13.8
17.1
18.9
20.4
22.9
24.9
27.0
Crmnx (mb)
21
13
20
37
29
26
20
19
Half-width / ' (MeV)
fa(hv) d (hv) ( M e V - m b )
1.5 48
0.3 7
0.4 14
0.8 44
1.3 57
2.6 106
0.6 18
4.9 146
The following integral quantities were calculated fol the nuclear absorption cross section curve in the 11-30 MeV range: the integrated cross section - O-o=J" O-(hv)d(hv),
ABSORPTION CROSS SECTION
141
the arithmetic mean energy E = 1/0-0 S Ea(hv)d(hv), and the moments a - 1 = .[ 0-(hv)/(hv)d(hv) and 0-2 = S 0-(hv)/(hv)2d(hv) • The integrated absorption cross section ao in the interval 11-30 MeV is (365_2o)MeV +,o +xx o% of • mb. This equals (72_5.5) the value of the integrated cross section for electric dipole transitions obtained from the sum rule (60(NZ/A)(1 +0.4x) = 511 MeV. mb). The mean energy E for the given energy range is 21.6 MeV. Since an appreciable part of the integrated cross section is situated above 30 MeV, the obtained value of the mean energy must be several MeV below the true position of the centre of gravity of electric dipole transitions. The relative importance of transitions above 30 MeV for 0--1 and 0--2 is considerably less. The errors due to the restriction upon the upper limit of integration should here not exceed 15-20% for a - 1 and ,~ 10% for 0"_2. The values 0--1 and 0--2 obtained in the 11-30 MeV range are 17.9 mb and 0.95 mb/MeV, respectively. 3. Discussion of Results A resonance structure has also been observed in the partial cross sections for separate reactions in magnesium. The relevant experimental data are listed in table 2. TABLE 2 Positions of resonance peak maxima observed in the absorption cross section and partial cross sections of some reactions Absorption cross section (present work)
Photoneutron cross section a) trn = a(7, n ) + a(y, np)+2tr(?, 2n)
Cross section of the inverse reaction 9) 23Na(p, yo)2~Mg
11.2 13.8 16.0) 17.1
~17
6°1
Mg(?, p) reaction cross section calculated from the proton spectrum x0)
14.3 ,~16
17.6/ 18.9
18.9
20.4
~ 20.5
18.5/
18.6
19.2~ 19.7/
19.1 19.7
20.7| 21.2} 22.0 22.4 22.9 24.9 27.0
~21.0
~ 23 ~ 25
In samples with the natural isotope abundance (78.6 % 24Mg, 10.1% 2SMg and 11.3 ~o 2 6 M g ) the observed peaks are obviously due to the isotope 2 4 M g .
142
B . S . DOLBILKIN et al.
In column 2 are given the positions of the maxima in the cross section a, = a(y, n) + a(y, n p ) + 2a(y, 2 n ) + . . . measured by Miller, Schuhl, Tamas and Tzara s) on a linear accelerator with "monochromatic" y-ray beams. The spectral y-quantum distribution had a half-width of ~ 2 7oo.The cross section was measured in the interval 16.4-26.2 MeV. Taking into account a difference in the energy resolution the general shape of the curve a, is in good agreement with the absorption cross section curve obtained in this work. In column 3 are shown the results obtained by Gove 9) for the cross section of the reaction 23Na(p, yo)Z4Mg which is an inverse one to the reaction 24Mg(y, Po)- The work was carried out with a tandem generator with good energy resolution. The proton energy was varied from 4 MeV to 11.5 MeV, which corresponds to the excitation energy of the 24Mg nucleus from 15.5 up to 22.5 MeV. The energy resolution, determined by the thickness of the sample used, was ~ 0.6 ~ at excitation energies 16 MeV and ~ 0.25 7ooat energies 20-22 MeV. The considerably larger number of resonance peaks obtained by Gove in the cross section of the (p, Yo) reaction apparently indicates that the wide peaks observed in the nuclear absorption cross section are groups of narrower, partly overlapping resonances. The groups of peaks, which at lowest resolution appear to be observed as a single maximum, are bracketed in column 3. An analysis of the curve of the 23Na(p, yo)Z4Mg reaction cross section shows that the centre of gravity of each of these groups approximately coincides with the position of the peak maximum observed in the absorption cross section in the same range. Resonance peaks in the cross section of the Mgfy, p) reaction were also obtained by Yamamuro 10) who measured the energy spectrum of photoprotons from a magnesium sample irradiated by X-rays at Emax = 21.5 MeV. The measurements were carried out by a photoemulsion method. The cross section of the (y, p) reaction was calculated from the energy distribution of protons with the assumption that in each case the residual sodium nucleus was produced in its ground state after the emission of the proton, i.e. a(y, p) ~ a(7, Po). The results are given in column 4. The resonance structure in the cross section of the reaction Mg(y, p) obtained by Yamamuro is in satisfactory agreement with the peaks observed in the cross section of the inverse reaction 2aNa(p, yo)24Mg. Due, apparently, to the poorer resolution of the photoemulsion method, some resonances seem to be unresolved, and one broader maximum instead of two separate peaks was observed in the proton spectrum. The absence of additional peaks in the (y, p) cross section, calculated from the proton spectrum, due to the production of the residual nucleus in excited states, seems to confirm that the probability of these transitions is relatively small in the energy range below ~ 20 MeV. Electric dipole absorption by magnesium nuclei in the giant resonance region have been considered theoretically by Neudachin and 0rlin 11) (for 24Mg and 2SMg) and by Nilsson, Sawicki and Glendenning 12) (for Z4Mg). The magnesium nucleus is strongly deformed. From Coulomb excitation data la) the deformations of nuclei of
ABSORPTION CROSS SECTION
143
various magnesium isotopes are the following: 24Mg-0.49-0.68; 2SMg-0.39; 2 6 M g 0.47. In both calculations the Nilsson model was used. In the work of Neudachin and Orlin, the effect of residual interactions was calculated in the so-caned diagonal approximation without taking into account configuration mixing. The corresponding matrix elements were determined from spectroscopic data. Nilsson, Sawicki and Glendenning considered the effects of residual interactions including the effects of configuration mixing. The calculations were carried out for two types of nuclaer force, FerrellVisscher and Wigner. In each case calculations were made both taking into account ground state correlations by the Sawada method and ignoring them. In fig. 3 are illustrated: a) the nuclear absorption cross section obtained by Neu-
Neudachin,0rlin (absorption curve) b)
Ferre tL-Visscher i shell model
II I
I
FerreiI-Visscher
II
correlations
Ill.
included
wig.o.
~ . hi_ ,o~
I
shell model ~'~ i ~o~
~
II
[
. . . . .
J
z~.. correlations
nmn
m
I ni-
included
t?
The experirnen'~a [
~
absorption curvecross sec~'i0n
5
Io
~
15
!,il
£o
25
50
Fig. 3. a) The absorption cross section calculated in ref. xx).b) The transition energies hvre 8 and corresponding oscillator strength fen from the data of ref. 1~).The solid rectangles denote the group of transitions connected with the oscillations along the nuclear deformation axis; the open rectangles denote the group of transitions connected with the oscillations normal to the nuclear deformation The experimental absorption cross section curve obtained in the present
axis. c)
paper.
dachin and Odin for 24Mg(as was shown by these workers, the results for 25Mg do not differ significantly); b) the E1 transition energy and corresponding oscillator strength obtained for 2¢Mg in the work of Nilsson, Sawicki and Glendenning; c) the
144
B.S. DOLB1LKIN et al.
experimental absorption cross section curve obtained for magnesium from the present work. For all the various calculations carried out in ref. 12) the transitions separate into two distinct groups. The group of transitions connected with the oscillations along the axis of deformation ~11 is almost completely concentrated in the energy range 1618.5 MeV. The group of transitions connected with oscillations in the plane perpendicular to the axis of deformation col - in the range 21.5-26.0 MeV. The sum of the oscillator strengths for the transitions e)± is twice that for the transitions colt. As is seen in fig. 3, this does not agree with the experimental curve of the absorption cross section. The assumption that the 18.9 and 20.3 MeV peaks observed in the energy range 18.5-21.5 MeV are not due to the transition E1 is unlikely, as the integrated cross section in this energy range is ~ 30 ~ of the whole integrated cross section in the range from 11-30 MeV. The energy dependence of the absorption cross section given in ref. 11) also disagrees with experiment. The relatively very large value of the integrated cross section in the interval 13-17 MeV and the sharp decrease of the cross section above 23 MeV obtained theoretically does not correspond at all to the shape of the experimental curve. A further fundamental disagreement with the results of the theoretical calculations is as follows: The integrated absorption cross section in the region 11-30 MeV is about 70 ~ of the total value of the integrated cross section a o obtained from the sum rule. It follows that a certain number of dipole transitions must occur at energies higher than 30 MeV. In refs. 11, 12) all transition energies are below 27 MeV, i.e. the whole sum of oscillator strengths for electric dipole transitions is exhausted by the transitions in the energy region below 26-27 MeV. These discrepancies between the theoretical and experimental results can hardly be explained by the roughness of the calculations alone. In consequence, further theoretical consideration of the process of ?-quantum absorption by magnesium nuclei would appear to be desirable. The authors would like to thank N. S. Kozhevnikov for his assistance with the measurements and Dr. B. A. Tulupov for helpful discussions of the results. The authors take the opportunity to express their deep gratitude to Dr. A. N. Gorbunov and Professor P. A. Cerenkov for providing facilities on the 260 MeV synchrotron. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)
N. A. Burgov et al., JETP 43 (1962) 70 N. A. Burgov et al., JETP 45 (1963) 1693 B. M. Spicer, F. R. Allum, J. E. E. Baglin and H. H. Thies, Austr. J. Phys. 11 (1958) 273 K. Shoda et al., J. Phys. Soc. Japan 17 (1962) 735 B. S. Ishkhanov, I. M. Kapitonov, V. G. Shevchenko and B. A. Yuryev, Phys. Lett. 9 (1964) 162 E. G+ Fuller and E. Hayward, Phys. Rev. 101 (1956) 692 F. Bobard, G. Boul6gue and P. Chanson, Compt. Rend. 244 (1957) 1761 J. Miller, C. Schuhl, G. Tamas and C. Tzara, preprint H. E. Gove, Nuclear Physics 49 (1963) 279 N. Yamamuro, J. Phys. Soc. Japan 18 (1963) 11 V. G. Neudachin and V. N. Orlin, Nuclear Physics 31 (1962) 338 S. G. Nilsson, J. Sawicki and N. K. Glendenning, Nuclear Physics 33 (1962) 239 S. F. Semenko, P. N. Lebedev Physical Institute, preprint A31 (1963)
I
Nuclear Physics 72 (1965) 137--144; ( ~ North-Holland Publishing Co., Amsterdam blot to be reproduced by photoprint or m i c r o f i l m without written permission from the publisher
NUCLEAR GAMMA ABSORPTION CROSS SECTION F O R M A G N E S I U M I N T H E E N E R G Y R E G I O N 10-30 M e V B. S. DOLBILKIN, V. I. KORIN, L. E. LAZAREVA, F. A. NIKOLAEV and V. A. ZAPEVALOV P. N. Lebedev Physical Institute, USSR Academy of Sciences, Moscow Received 25 December 1964 Abstract: The absorption cross section of y-quanta by Mg nuclei in the energy range 11-30 MeV has been measured by the absorption method on the 260 MeV synchrotron of the Lebedev Physical Institute. A nine channel pair magnetic y-spectrometer was used as a detector. The cross section obtained has a resonance structure and can be represented as a superposition of several partially overlapping peaks. Comparison with the resonances observed in the partial reaction cross sections shows that these peaks are probably separate groups of unresolved transitions. The shape and integrated cross section of the experimental curve in the 11-30 MeV range do not agree with the results of the available theoretical calculations for Mg. i
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NUCLEAR REACTION Mg(y), E = 11-30 MeV; measured try(E). Deduced resonance parameters. Natural target.
3
]
J
1. Experimental Procedure The 260 MeV Lebedev Physical Institute synchrotron has previously been used to study 160 and 12C by means o f the absorption method. The applicability o f this m e t h o d as a means of investigating the structure o f the nuclear absorption cross section of light nuclei is discussed in detail in refs. 1, 2). W h e n working with continuous bremsstrahlung radiation, the main difficulty in using the m e t h o d for this purpose is that two contradictory conditions have to be fulfilled: (i) the ~-ray detector should be capable o f a high resolution with (inevitably) a very low efficiency; (ii) the performance o f measurements with a high statistical accuracy (not worse than a few tenths o f one percent) over small energy intervals ( < 100 keV). To increase the efficiency o f the method, a nine-channel pair magnetic spectrometer was used instead o f the one-channel pair magnetic spectrometer which had been employed previously 1, z). Fig. 1 shows the design o f the spectrometer chamber. The slits o f the spectrometer, lying in the plane o f the radiator (the three slits on each side), are situated symmetrically with respect to the centre o f the radiator and at equal distances f r o m one another (r 1 : r2 : r3 = 19 : 20 : 21 cm). In this way, measurements were performed simultaneously for five values o f the energy (coincidences - 1 + 1 - ; 1+2-+2+1-; 1+3-+3+1-+2+2-; 2+3-_t_3+2-; 3+3-). 137
138
B.s. DOLBILK1Net al.
The main parameters of the spectrometer for these measurements were the following: 12.9 mg/cm2; 60 x 50 ram; 4 mm; 10 mm; 70 ram; 5 x 6 x 7 0 mm; 38, 39, 40, 41, 42 cm, 0.01 ~ ; at 10 MeV ~ 120 keV at 20 MeV ~ 220 keV.
thickness of radiator (gold) effective radiator area width of slits (lead) thickness of slits height of slits dimensions of plastic scintillators distances between the inner edges of the slits magnetic field stability spectrometer resolution
4.
~
2
~-
............... Lo j
.~
t I ~-
I ql
"~__~,q~
Fig. 1. Spectrometer chamber: 1-radiator, 2-system of slits, 3-scintillators, 4-light guides, 5FEU-36 photomultipliers, 6-three layer magnetic shielding, 7-region of the homogeneous magnetic field, 8-magnetometer coil (stabilization by the nuclear proton resonance method), 9-input and output windows for X-ray beam, 10--lead shielding, ll-pump-out tube.
Pulses from the photomultipliers (FEU-36) were passed through pulse shapers and into a matrix of coincidence circuits (resolving time of 3 nsec). Thereafter the pulses were amplified, discriminated by amplitude and fed into the recording system. Data processing was carried out by computer. A block of metallic magnesium (Mg > 99.9 ~ ) with a 70 x 70 mm cross section and 650 mm long was used as an absorber. After passing through this absorber (112.4 g/cm 2) the y-ray flux in the investigated energy region (10-30 MeV) was reduced by a
139
ABSORPTION CROSS SECTION
factor of ,~ 10. The ratio of the number of ?-quanta detected in the absence of the absorber in the beam of X-rays (No) to that with the absorber (N) was measured for each given energy (No/N = exp(a,u:l + apalr pr + a~omptonseat)nt; n is the number of nuclei in cm 3; t is the thickness of the absorber). These two quantities were measured alternately and were normalized to the same X-ray flux, which was measured by means of a thin walled integrating ionization chamber (monitor) situated between the lead collimator and the absorber. The measurements were made at maximum X-ray energy E~m~x = 260 MeV. To reduce the number of accidental coincidences the ?-ray pulses from the accelerator were extended in time up to 3000 #see. Accidental coincidences were registered throughout the period of measurements by a second set of coincidence circuits connected in parallel to the main ones via time delay lines. The percentage of accidental coincidences with the absorber in the X-ray beam was ~ 2 % and without the absorber it was ~ 20 %.
2. Experimental Results The absorption curve No/N(hv) was measured in the energy range hv = 11-30 MeV. In fig. 2 are given the nuclear absorption cross section values obtained from the
r,'l 9. 5C
4Q
l
~0 20 I0 0
Fig. 2. The nuclear absorption cross section.
ratios No/N after subtracting the "non-nuclear" part of the cross section (pair production process and Compton scattering) from the total absorption cross section. The measurements were performed with energy step ~ 40 keV, the data were then averaged over a range of 200 keV. Each point is the result of the averaging of 20-30
B. S. DOLBILKIN et al.
140
independent No/N ratio measurements. The errors given are root-mean-square. The energy scale is corrected for the finite resolution of the spectrometer. As was pointed out in ref. 1), there are two difficulties in separating the part of the cross section due to nuclear interaction. The first is a wide range of theoretical values for the cross section for pair production in the field of an electron. The second is the impossibility of estimating accurately the correction for "pumping over" of photons into the investigated energy range from the more energetic part of the spectrum (30 MeV < hv < 260 MeV) when an absorber is placed in the X-ray beam. In order to avoid these difficulties and to establish the zero of the nuclear absorption cross section scale, one must normalize the curve of the non-nuclear part of the cross section in the energy range around 10 MeV, where the relative contribution of the nuclear cross section is minimum. In the present case the normalization was carried out in the energy interval hv = 14.5-16 MeV. A detailed analysis of the cross sections for all possible reactions in this energy range 3-7) gives a mean value of the total cross section for these reactions in the range 14.5-16 MeV equal to 3_+12mb. In accordance with the indicated errors, the zero of the nuclear absorption cross section scale was determined with the accuracy ( + 1; - 2) mb. The nuclear cross section obtained for magnesium has a resonance structure, Representing the whole cross section as a superposition of the actually resolved peaks corresponding to the separate transitions or groups of unresolved transitions, it is possible to obtain an estimate of the main parameters for these peaks: the position hv.... the maximum cross section O-. . . . the half-width F and the integrated cross section (proportional to the oscillator strength of the corresponding transition). The solid curve in fig. 2 drawn through the experimental points was calculated by the: least-squares method for the case in which the shape of separate peaks can be described by the Breit-Wigner formula. This assumption is not self-evident, thus the calculation is of a qualitative nature only. In table 1 are listed the separate peak parameters obtained in this manner. The quantities O'max and F characterizing the shape o f the peaks are not corrected for the finite resolution of the spectrometer. TABLE 1 P a r a m e t e r s o f resonance p e a k s observed in the nuclear absorption cross section
hvres (MeV)
11.2
13.8
17.1
18.9
20.4
22.9
24.9
27.0
Crmnx (mb)
21
13
20
37
29
26
20
19
Half-width / ' (MeV)
fa(hv) d (hv) ( M e V - m b )
1.5 48
0.3 7
0.4 14
0.8 44
1.3 57
2.6 106
0.6 18
4.9 146
The following integral quantities were calculated fol the nuclear absorption cross section curve in the 11-30 MeV range: the integrated cross section - O-o=J" O-(hv)d(hv),
ABSORPTION CROSS SECTION
141
the arithmetic mean energy E = 1/0-0 S Ea(hv)d(hv), and the moments a - 1 = .[ 0-(hv)/(hv)d(hv) and 0-2 = S 0-(hv)/(hv)2d(hv) • The integrated absorption cross section ao in the interval 11-30 MeV is (365_2o)MeV +,o +xx o% of • mb. This equals (72_5.5) the value of the integrated cross section for electric dipole transitions obtained from the sum rule (60(NZ/A)(1 +0.4x) = 511 MeV. mb). The mean energy E for the given energy range is 21.6 MeV. Since an appreciable part of the integrated cross section is situated above 30 MeV, the obtained value of the mean energy must be several MeV below the true position of the centre of gravity of electric dipole transitions. The relative importance of transitions above 30 MeV for 0--1 and 0--2 is considerably less. The errors due to the restriction upon the upper limit of integration should here not exceed 15-20% for a - 1 and ,~ 10% for 0"_2. The values 0--1 and 0--2 obtained in the 11-30 MeV range are 17.9 mb and 0.95 mb/MeV, respectively. 3. Discussion of Results A resonance structure has also been observed in the partial cross sections for separate reactions in magnesium. The relevant experimental data are listed in table 2. TABLE 2 Positions of resonance peak maxima observed in the absorption cross section and partial cross sections of some reactions Absorption cross section (present work)
Photoneutron cross section a) trn = a(7, n ) + a(y, np)+2tr(?, 2n)
Cross section of the inverse reaction 9) 23Na(p, yo)2~Mg
11.2 13.8 16.0) 17.1
~17
6°1
Mg(?, p) reaction cross section calculated from the proton spectrum x0)
14.3 ,~16
17.6/ 18.9
18.9
20.4
~ 20.5
18.5/
18.6
19.2~ 19.7/
19.1 19.7
20.7| 21.2} 22.0 22.4 22.9 24.9 27.0
~21.0
~ 23 ~ 25
In samples with the natural isotope abundance (78.6 % 24Mg, 10.1% 2SMg and 11.3 ~o 2 6 M g ) the observed peaks are obviously due to the isotope 2 4 M g .
142
B . S . DOLBILKIN et al.
In column 2 are given the positions of the maxima in the cross section a, = a(y, n) + a(y, n p ) + 2a(y, 2 n ) + . . . measured by Miller, Schuhl, Tamas and Tzara s) on a linear accelerator with "monochromatic" y-ray beams. The spectral y-quantum distribution had a half-width of ~ 2 7oo.The cross section was measured in the interval 16.4-26.2 MeV. Taking into account a difference in the energy resolution the general shape of the curve a, is in good agreement with the absorption cross section curve obtained in this work. In column 3 are shown the results obtained by Gove 9) for the cross section of the reaction 23Na(p, yo)Z4Mg which is an inverse one to the reaction 24Mg(y, Po)- The work was carried out with a tandem generator with good energy resolution. The proton energy was varied from 4 MeV to 11.5 MeV, which corresponds to the excitation energy of the 24Mg nucleus from 15.5 up to 22.5 MeV. The energy resolution, determined by the thickness of the sample used, was ~ 0.6 ~ at excitation energies 16 MeV and ~ 0.25 7ooat energies 20-22 MeV. The considerably larger number of resonance peaks obtained by Gove in the cross section of the (p, Yo) reaction apparently indicates that the wide peaks observed in the nuclear absorption cross section are groups of narrower, partly overlapping resonances. The groups of peaks, which at lowest resolution appear to be observed as a single maximum, are bracketed in column 3. An analysis of the curve of the 23Na(p, yo)Z4Mg reaction cross section shows that the centre of gravity of each of these groups approximately coincides with the position of the peak maximum observed in the absorption cross section in the same range. Resonance peaks in the cross section of the Mgfy, p) reaction were also obtained by Yamamuro 10) who measured the energy spectrum of photoprotons from a magnesium sample irradiated by X-rays at Emax = 21.5 MeV. The measurements were carried out by a photoemulsion method. The cross section of the (y, p) reaction was calculated from the energy distribution of protons with the assumption that in each case the residual sodium nucleus was produced in its ground state after the emission of the proton, i.e. a(y, p) ~ a(7, Po). The results are given in column 4. The resonance structure in the cross section of the reaction Mg(y, p) obtained by Yamamuro is in satisfactory agreement with the peaks observed in the cross section of the inverse reaction 2aNa(p, yo)24Mg. Due, apparently, to the poorer resolution of the photoemulsion method, some resonances seem to be unresolved, and one broader maximum instead of two separate peaks was observed in the proton spectrum. The absence of additional peaks in the (y, p) cross section, calculated from the proton spectrum, due to the production of the residual nucleus in excited states, seems to confirm that the probability of these transitions is relatively small in the energy range below ~ 20 MeV. Electric dipole absorption by magnesium nuclei in the giant resonance region have been considered theoretically by Neudachin and 0rlin 11) (for 24Mg and 2SMg) and by Nilsson, Sawicki and Glendenning 12) (for Z4Mg). The magnesium nucleus is strongly deformed. From Coulomb excitation data la) the deformations of nuclei of
ABSORPTION CROSS SECTION
143
various magnesium isotopes are the following: 24Mg-0.49-0.68; 2SMg-0.39; 2 6 M g 0.47. In both calculations the Nilsson model was used. In the work of Neudachin and Orlin, the effect of residual interactions was calculated in the so-caned diagonal approximation without taking into account configuration mixing. The corresponding matrix elements were determined from spectroscopic data. Nilsson, Sawicki and Glendenning considered the effects of residual interactions including the effects of configuration mixing. The calculations were carried out for two types of nuclaer force, FerrellVisscher and Wigner. In each case calculations were made both taking into account ground state correlations by the Sawada method and ignoring them. In fig. 3 are illustrated: a) the nuclear absorption cross section obtained by Neu-
Neudachin,0rlin (absorption curve) b)
Ferre tL-Visscher i shell model
II I
I
FerreiI-Visscher
II
correlations
Ill.
included
wig.o.
~ . hi_ ,o~
I
shell model ~'~ i ~o~
~
II
[
. . . . .
J
z~.. correlations
nmn
m
I ni-
included
t?
The experirnen'~a [
~
absorption curvecross sec~'i0n
5
Io
~
15
!,il
£o
25
50
Fig. 3. a) The absorption cross section calculated in ref. xx).b) The transition energies hvre 8 and corresponding oscillator strength fen from the data of ref. 1~).The solid rectangles denote the group of transitions connected with the oscillations along the nuclear deformation axis; the open rectangles denote the group of transitions connected with the oscillations normal to the nuclear deformation The experimental absorption cross section curve obtained in the present
axis. c)
paper.
dachin and Odin for 24Mg(as was shown by these workers, the results for 25Mg do not differ significantly); b) the E1 transition energy and corresponding oscillator strength obtained for 2¢Mg in the work of Nilsson, Sawicki and Glendenning; c) the
144
B.S. DOLB1LKIN et al.
experimental absorption cross section curve obtained for magnesium from the present work. For all the various calculations carried out in ref. 12) the transitions separate into two distinct groups. The group of transitions connected with the oscillations along the axis of deformation ~11 is almost completely concentrated in the energy range 1618.5 MeV. The group of transitions connected with oscillations in the plane perpendicular to the axis of deformation col - in the range 21.5-26.0 MeV. The sum of the oscillator strengths for the transitions e)± is twice that for the transitions colt. As is seen in fig. 3, this does not agree with the experimental curve of the absorption cross section. The assumption that the 18.9 and 20.3 MeV peaks observed in the energy range 18.5-21.5 MeV are not due to the transition E1 is unlikely, as the integrated cross section in this energy range is ~ 30 ~ of the whole integrated cross section in the range from 11-30 MeV. The energy dependence of the absorption cross section given in ref. 11) also disagrees with experiment. The relatively very large value of the integrated cross section in the interval 13-17 MeV and the sharp decrease of the cross section above 23 MeV obtained theoretically does not correspond at all to the shape of the experimental curve. A further fundamental disagreement with the results of the theoretical calculations is as follows: The integrated absorption cross section in the region 11-30 MeV is about 70 ~ of the total value of the integrated cross section a o obtained from the sum rule. It follows that a certain number of dipole transitions must occur at energies higher than 30 MeV. In refs. 11, 12) all transition energies are below 27 MeV, i.e. the whole sum of oscillator strengths for electric dipole transitions is exhausted by the transitions in the energy region below 26-27 MeV. These discrepancies between the theoretical and experimental results can hardly be explained by the roughness of the calculations alone. In consequence, further theoretical consideration of the process of ?-quantum absorption by magnesium nuclei would appear to be desirable. The authors would like to thank N. S. Kozhevnikov for his assistance with the measurements and Dr. B. A. Tulupov for helpful discussions of the results. The authors take the opportunity to express their deep gratitude to Dr. A. N. Gorbunov and Professor P. A. Cerenkov for providing facilities on the 260 MeV synchrotron. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)
N. A. Burgov et al., JETP 43 (1962) 70 N. A. Burgov et al., JETP 45 (1963) 1693 B. M. Spicer, F. R. Allum, J. E. E. Baglin and H. H. Thies, Austr. J. Phys. 11 (1958) 273 K. Shoda et al., J. Phys. Soc. Japan 17 (1962) 735 B. S. Ishkhanov, I. M. Kapitonov, V. G. Shevchenko and B. A. Yuryev, Phys. Lett. 9 (1964) 162 E. G+ Fuller and E. Hayward, Phys. Rev. 101 (1956) 692 F. Bobard, G. Boul6gue and P. Chanson, Compt. Rend. 244 (1957) 1761 J. Miller, C. Schuhl, G. Tamas and C. Tzara, preprint H. E. Gove, Nuclear Physics 49 (1963) 279 N. Yamamuro, J. Phys. Soc. Japan 18 (1963) 11 V. G. Neudachin and V. N. Orlin, Nuclear Physics 31 (1962) 338 S. G. Nilsson, J. Sawicki and N. K. Glendenning, Nuclear Physics 33 (1962) 239 S. F. Semenko, P. N. Lebedev Physical Institute, preprint A31 (1963)