ON THE RELATION BETWEEN THE WIDTH OF THE GIANT RESONANCE OF THE \((\gamma, n)\) REACTION AND THE FILLING OF NUCLEAR ENERGY LEVELS

A. K. BERZIN, R. P. MESHCHERYAKOV, S. I. SHORNIKOV, B. M. YAKOVLEV

It has previously been shown [1, 2, 3] that the widths of the giant resonance of the \((\gamma, n)\) reaction are closely connected with the magnitudes of the quadrupole moments of nuclei. The more deformed the nucleus, the greater the width of the giant resonance, and conversely. The smallest widths are found in nuclei with a filled neutron shell [4, 5, 6, 7, 8, 9]. In this connection one may suppose that the width of the giant resonance will also reflect the degree of filling of individual energy levels. Moreover, the resonance width will apparently be somewhat smaller for nuclei with filled levels. At present the shell model cannot predict with certainty at which isotope the filling of a given level is completed. Information on this question can evidently be obtained from an analysis of certain experimental data. Among the latter, apparently, are the values of the threshold energies of \((\gamma, n)\) reactions, since it is known, for example [10, 11, 12, 13], that all isotopes with a filled neutron shell have a threshold considerably higher than might have been expected. A similar effect was found by us [12] also for the isotopes Mo\(^{100}\) and Nd\(^{150}\). The first of these isotopes contains \(50+8\), and the second \(82+8\) neutrons.

To confirm this effect, a more careful measurement was made of the threshold-energy values for certain isotopes of molybdenum and neodymium. The thresholds of the isotopes Mo\(^{92}\), Mo\(^{94}\), Mo\(^{100}\), Nd\(^{142}\), and Nd\(^{150}\) were determined by the induced-activity method, while the thresholds of Mo\(^{97}\) and Nd\(^{146}\) were determined by the “direct” method of neutron registration. The threshold values for the remaining isotopes were determined in the processing of the total yield curve, which is the summed yield of photoneutrons from all isotopes of the given element. The threshold energies given in Table 1 are in most cases in good agreement with those obtained earlier [12]. However, there are also discrepancies, relating to thresholds calculated in processing the total yield curve and caused chiefly by the arbitrariness allowed in the course of the processing. The newly obtained results indicate a somewhat different character in the relation between threshold-energy values for the isotopes of a given element. However, as in the previous measurements, here too somewhat overestimated threshold values are clearly observed for isotopes containing 8 neutrons beyond a filled shell, which, possibly, is due to the filling of the corresponding energy levels or the completion of some other configuration.

Table 1

Note. \({}^{*}\) Threshold-energy values calculated in processing the overall yield curve.

In the present work, which is the first stage in the investigations being carried out on the problem indicated above, cross sections were studied for the isotopes La, Ce, Pr\(^{141}\), Nd, Nd\(^{142}\), and Nd\(^{150}\). Most of these objects had been studied previously; however, the results obtained in different works sometimes differ so greatly that it does not seem possible to use them in a comparative analysis with the available and newly obtained data.

Measurement Method

Betatrons at 25 MeV were used as the source of bremsstrahlung.

The measurement of the photoneutron yield as a function of the maximum \(\gamma\)-ray energy, when using the induced-activity method, was carried out by measuring \(\beta\)- and \(\gamma\)-activities. In the first case end-window counters in \(4\pi\) geometry were used; in the second, a scintillation \(\gamma\)-spectrometer with an NaJ(Tl) crystal. The resolution of the spectrometer was \(8\text{–}9\%\) for the 662 keV line of Cs\(^{137}\).

The molybdenum samples under investigation were made in the form of metal plates with a thickness of \(700 \ \mathrm{mg/cm^{2}}\). The samples intended for carrying out studies with rare earths were prepared in the form of powders of oxides of the elements under study, \(500 \ \mathrm{mg/cm^{2}}\) thick, loaded into thin-walled aluminum containers.

In measurements by induced activity, the irradiated samples were placed at a distance of 40 cm from the betatron target. An exception was made for the samples intended for taking the yield curve from the isotope Mo\(^{100}\). These samples were placed directly in the betatron chamber; however, it was not possible to obtain a sufficiently large count even with this geometry.

In measuring threshold energies by the method of “direct” neutron registration, the apparatus described by us earlier [11, 12] was used. The taking of yield curves intended for conversion into cross-section curves was carried out on the same apparatus, but

with a different detector arrangement. The detector was placed at such a distance from the sample that it had the same sensitivity to neutrons of all energies [14].

The photoneutron yield curves for determining thresholds were taken every 0.1–0.2 MeV. The upper boundary of the bremsstrahlung $\gamma$-radiation was established with the aid of a monitoring circuit providing an accuracy of $\pm 15$ keV [15]. The circuit was checked by the method of “ratios of induced activities” on a copper–silver pair [16].

When recording yield curves for the study of cross sections, the neutron yield from each sample was calibrated against the neutron yield from copper at an energy of 22 MeV. The yield for the natural mixture of copper isotopes at this energy was taken to be

$$ 2.7 \cdot 10^{6}\ \frac{\text{neutrons}}{\text{mole-roentgen}} $$

[8].

The dose of $\gamma$-radiation received by each sample was recorded with a thin-walled chamber. The chamber was periodically calibrated.

The background introduced by the aluminum containers was determined by irradiating them in the absence of the object under study. The maximum background value was less than 4% of the neutron yield of any sample. The magnitude of the contribution made by neutrons produced in the interaction of $\gamma$-radiation with the oxygen nuclei of the oxides under study was estimated from results obtained by irradiating water samples of corresponding weight. The magnitude of this contribution did not exceed 3%.

The statistical error of the measurements was no more than 0.4% for all the isotopes studied, except for the isotope Mo$^{100}$. In the latter case the statistical error was considerably larger.

Results of the Measurements

The yield curves obtained by using the method of “direct” registration include neutrons from all types of reactions possible at a given X-ray energy. Among such reactions in the energy region in which the cross-section studies were carried out are the reactions $(\gamma,n)$, $(\gamma,2n)$, and $(\gamma,np)$. As a result of the large Coulomb barrier, the proton yield in the last reaction will be extremely hindered, and the contribution of this reaction may be neglected. The magnitude of the contribution to the cross-section curve from the $(\gamma,2n)$ reaction was estimated in the same way as in [8].

The conversion of yield curves into cross sections was carried out by the method proposed in [17].

The cross sections for the isotopes of lanthanum (La), cerium (Ce), and neodymium (Nd) were calculated from the yield curve measured by the method of “direct” neutron registration. The isotope La$^{138}$ is present in the natural mixture of isotopes in an amount of $\sim 0.09\%$; therefore the contribution of neutrons from all reactions occurring on this isotope will be very small, and consequently the calculated cross section may be attributed entirely to the isotope La$^{139}$.

The estimate of the magnitude of the contribution of the $(\gamma,2n)$ reaction for Nd and Ce was made under the assumption that the nuclear temperature $\Theta$ and the reaction threshold are the same for all isotopes and have an average value. Such an estimate is, of course, very crude.

The cross sections of the isotopes Pr$^{141}$, Nd$^{142}$, and Nd$^{150}$ were calculated from yield curves measured by the induced-activity method. The period

the half-life of \(Pr^{140}\) (3.4 min) differs significantly from the half-life of \(Pr^{139}\) (4.5 hours), which makes it comparatively easy to separate the contribution of the \((\gamma,n)\) reaction from the contribution of the \((\gamma,2n)\) reaction. Separation of the activation curve corresponding to the isotope \(Nd^{141}\), whose half-life is close to the half-life of \(Nd^{149}\), was carried out in the same way as was done in [7]. It was not possible to determine exactly the magnitude of the contribution due to the \((\gamma,2n)\) reaction on the isotope \(Nd^{143}\). The threshold of this reaction, calculated from isotope masses [18], is 15.8 MeV. A rough estimate of the contribution gives a value of 3% at an energy of 24 MeV.

Table 2 gives the widths of the giant resonance for the objects studied. The results of other works are also given in the same table.

Table 2

The small width of the giant resonance in Ce evidently indicates that the main contribution to the yield curve is made by the isotope \(Ce^{142}\) (88.5% in the natural mixture), which has a filled shell of 82 neutrons. In addition, it may be assumed that the maxima of the cross sections of the isotopes \(Ce^{140}\) and \(Ce^{142}\) (11%) are located close to one another.

The small difference in the resonance widths for the isotope \(Nd^{150}\) and for nuclei having a filled neutron shell evidently indicates a small deformation of the \(Nd^{150}\) nucleus. This circumstance, together with the threshold data, makes it possible to suppose that in the isotope \(Nd^{150}\) the filling of the \(2f_{7/2}\) level is completed, or that some other configuration is completed.

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