Studies of some isomeric yield ratios produced with bremsstrahlung

PII:

Appl. Radiat. Isot. Vol. 49, No. 8, pp. 989±995, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0969-8043(97)10094-X 1350-4487/98 $19.00 + 0.00

Studies of some Isomeric Yield Ratios Produced with Bremsstrahlung DIMITAR KOLEV* Department of Atomic Physics, Faculty of Physics, University of So®a, 5 James Bourchier Blvd, 1164 So®a, Bulgaria (Received 26 April 1997) The experimental isomeric ratios for 52mg Mn, 86mg Y, 87mg Y, 89mg Zr, 110mg In, 111mg In, 112mg In, 152m1g Pm, 152m2m1 Eu, 162mg Ho, 164mg Ho and 178mg Lu measured by the activation technique from di€erent targets in (g, xnp) reactions (x R3) at the bremsstrahlung end-point energy of 43 MeV are presented. The predictions of calculations performed by means of compound nucleus particle evaporation and ®nal g-deexcitation were critically discussed. The importance of inclusion in the calculations of nonequilibrium particle emission and an adequate g-decay mode of isomeric nuclei was considered for some of the reactions investigated. # 1998 Elsevier Science Ltd. All rights reserved

Introduction

nucleus. When the IR is known, or can be calculated theoretically, additional information can be obtained, directed to the creation of measurable activity of only one isomeric state at least. Thereby, the irradiation and measurement conditions can be optimized. The IRs reported in the present work have been obtained with bremsstrahlung photons with maximal energy Egmax=43 MeV. The dominant reaction cross section at this energy is caused by interactions corresponding to the giant dipole resonance (GDR), whose highly collective structure predetermines weak non-equilibrium particle emission. The pre-equilibrium processes are stronger for the photon energies above GDR where, however, the reaction cross section decreases drastically. Thus, the equilibrium statistical model of nuclear reactions should be suitable enough as a ®rst order approximation for the mechanism of photonuclear reactions studied in this work. The model, frequently used for the calculation of neutron evaporation processes and subsequent g-ray deexcitation, has been developed by Huizenga and Vandenbosch (Huizenga and Vandenbosch, 1960; Vandenbosch and Huizenga, 1960). In order to apply that model (HVM) to our experimental data the emission of charged particles (Kolev and Bratovanov, 1995) has been added. The model has also been improved by including a more detailed deexcitation calculation of the particle emission process.

Activation by gamma irradiation can be used for di€erent practical purposes like activation analysis, production of isotopes for medical use, material science investigations, biological studies, etc. Usually, activation experiments are performed on small electron accelerators, like microtrons, with a typical bremsstrahlung end-point energy Egmax up to about 25 MeV or, rarely, on other type accelerators with Egmax around or less than 50 MeV. In this energy region valuable information concerning the photonuclear reactions mechanism can also be extracted. Successful application of the g-activation technique requires the existence of correct photonuclear data. The reaction excitation functions are essential among these data, together with the excitation functions. The data for isomeric yield ratios (IRs) and their properties are also of great importance, because in 40% of the possible reactions at the above photon energies isomeric nuclei occur in the exit reaction channel (Davidov et al., 1985). Therefore, the measured isomeric ratios together with a simple model, describing the population of isomeric pair, would be very helpful when activation experiment has to be planned. Combining the experimental data with an appropriate model, one can estimate the expected total activity of the sample and the partial activity of the speci®ed *To whom all correspondence should be addressed. 989

990

D. Kolev

The Experiment General presentation The following de®nition of the experimental isomeric ratios (IRs) was accepted: IR ˆ where Y i ˆ Nt

… Egmax Ethr

Yhigh , Ylow

si …Eg †f…Eg † dEg ,

i ˆ high, low:

…1†

The notations high, low signify the high and low spin states of the isomeric pair. Yi are the yields, Nt is the number of target nuclei, s(Ei) is the cross section for producing nucleus in state i, f(Eg) is the function representing the bremsstrahlung spectrum and Ethr is the reaction threshold. The irradiations were performed in the bremsstrahlung beam of the betatron of the Medical Academy of Bulgaria. The distance between samples and the internal converting Pt target of the accelerator was ®xed at 40 cm. Usually the target material was in powder form and its amount was less than 0.5 g. Thus, the targets used were highly homogeneous and thin, which led to a strongly reduced or negligible e€ect of self absorption of the g-rays measured. The samples were put in cylindrical PVC capsules with an external diameter of 10 mm and a wall thickness of 0.5 mm. Against the neutron interactions the capsules were shielded with a 1 mm thick cadmium foil and placed inside another plexiglass container with 6 mm thick walls. The irradiation duration varied from 12 to 30 min with the bremsstrahlung beam kept constant. The created activity was measured with di€erent highresolution g-spectrometers having FWHM < 3 keV at 1.332 MeV line of Co and maximal photopeak eciency 3±6%. For the measurement of lowenergy g-rays a ``thin'' detector was used. Induced activity was suciently low to avoid dead time corrections but the measurements had to be performed at small distances, or even zero, between the sample and the detector. At this ``bad'' measurement geometry a signi®cant e€ect of summing of cascade grays occurred. The collected g-rays spectra were processed precisely with appropriate routines (Gadjokov, 1979; Gopin et al., 1982). The areas of g-lines extracted were corrected, where necessary, for cascade g-rays summing according to Andreev et al. (1972) and self absorption following Proykova et al. (1991). It should be mentioned that the e€ect of self absorption reduces the number of cascade quanta reaching the detector volume and thereby decreases the probability for their summing. In order to calculate the IRs using the measured peak areas, two methods are developed (Kolev et al., 1995), which are based on solutions of the decay law equations. The ®rst (A1), uses the photo-

peak areas of two di€erent and independent g-transitions in the decay of the metastable and ground state nucleus of the isomeric pair. The second (A2), allows the calculation of the IR from the time variation of the photopeak area of one and the same gtransition, existing in the decay chain of both isomeric nuclei. It is proven (Kolev et al., 1995), that A2 gives an IR with the smallest possible uncertainties, determined only by the statistical errors. An approach, devoted to estimation of the contributions of the di€erent possible reactions to the measured IR in the case of experiments with a natural material target can be found in Kolev et al. (1994). Weighting coecients are introduced for the reactions obtained with target composed of natural isotopic mixture. They take into account the relative abundance of the isotope speci®ed and the total cross section of the corresponding reaction yielding the isomeric nucleus observed. The values of the coecients de®ne the contributions of possible reactions to the IR obtained at a speci®ed Egmax. The spectroscopic data used for IRs determination are taken from Lederer and Shirley (1978) and listed in Table 1. Results and comments The IRs obtained in the reactions studied together with the available data from other authors are summarized in Table 2. Speci®c details of the IR determinations are given below. 55 Mn(g, x3n)52m,g Mn. The area of the 377.7 keV g-line was slightly (1 3%) increased to compensate for the self absorption in the sample. In several measurements within a short time after the end of irradiation T1/2=21.9 20.9 min was determined for the 1434.1 keV activity, which therefore was ascribed to 52m Mn. The area of the 744.2 keV g-line was increased with 12.5% to correct the loss due to the summing of the 744.2, 935.5 and 1434.1 keV cascade g-rays. The IR presented in Table 2 was obtained as a weighted mean value of the IRs derived from the di€erent spectra measured. It was con®rmed numerically that the di€erence between the present IR and the reported values (Walters and Hummel, 1966) results only from the di€erences in the nuclear data used. The most probable reason for the smaller IR from VoÈlpel (1972) is that the summing of cascade g-rays was not taken into account for the 1434.1 keV g-line. Such a correction increases the value of the IR. 89 Y(g, 2n)87m,g Y and 89 Y(g, 3n)86m,g Y. The IRs were previously reported in our work (Abazov et al., 1980). Thus, the values included in Table 2 were newly calculated with the actual spectroscopic data. Additionally, the area of the 627.7 keV g-line was increased by a factor of 2.1 accounting for the summing e€ect of the twelve most intensive cascade transitions. A 6% loss due to the self absorption was estimated for the area of the 208 keV g-line.

Isomeric yield ratios with Bremsstrahlung

eral behavior of the IRs, seems to be quite arti®cial. Hence, the IR measured from thenat Zr target has to be related to the 90 Zr(g, n) reaction. A great number of IRs in this reaction, for bremsstrahlung photon energies around the GDR region, have been measured by many authors. The values obtained are quite di€erent. It was suggested by Davidov et al. (1987a) that probably in some investigations incorrect decay schemes had been used. Nevertheless, the disagreements remained, even for the results, which were considered as accurate enough (Davidov et al., 1987a). Taking into account the discussion by Davidov et al. (1987b) and our result, it seems, that the data reported by Huizenga and Vandenbosch (1960), Davidov et al. (1987b), as well as some IRs referred to by Davidov et al. (1987a) can be considered the most trustworthy. 113 In(g, 3n)110m,g In. In all experiments with a In target only the nat In was used. The 110m,g In cannot be created in the 115 In(g, n) reaction due to the reaction threshold, which is higher than the Egmax. The value of the IR has been already reported (Kolev et al., 1995) as a demonstration of a successful application of the method A2, mentioned above. nat In(g, xn)112m,g In and nat In(g, xn)111m,g In, x = 1 6 4. The weighting coecients for both 113 In(g, n) and 115 In(g, 3n) producing 112m,g In, are found to be 0.46 and 0.54, i.e. both reactions make a nearly equal contribution to the IR measured. The same holds for 111m,g In produced in the 113m,g In(g, 2n) and 115m,g In(g, 4n), where the weights are 0.47 and 0.53, respectively.

Table 1. Nuclear data for the isomeric nuclei observed: T1/2 is the decay half-life, Eg and Ig are the energy and abundance of g-lines and IIT is the intensity of isomeric transition, when it exists T1/2

Eg (keV)

Ig (%)

IIT (%)

21.1 min 5.59 d 48.0 min 14.74 h 13.2 h 80.3 h 4.18 min 3.27 d 4.9 h 69.1 min 7.6 min 2.83 d 20.9 min 14.4 min 4.1 min 7.52 min 1.60 h 9.30 h 68.0 m 15.0 m 37.5 m 29.0 m 22.9 m 28.1 m

1434.1 744.2 208.0 627.7 381.1 484.8 587.8 909.2 657.7 657.7 537.0 171.3 155.0 617.2 841.5 1097.0 89.8 841.6, 963.4 80.7 80.7 37.3 73.4, 91.4 426.4 1340.8

98.22 90.0 94.0 32.6 78.0 92.0 89.5 99.0 98.5 97.9 87.0 87.6 13.0 6.0 4.85 22.2 72.0 12.7, 12.0 11.5 7.8 11.4 1.78, 2.48 96.9 4.74

1.75

Nuclide 52m

Mn Mn Y 86g Y 87m Y 87g Y 89m Zr 89g Zr 110m In 110g In 111m In 111g In 112m In 112g In 152g Pm 152m1 Pm 152m2 Eu 152m1 Eu 162m Ho 162g Ho 164m Ho 164g Ho 178m Lu 178g Lu 52g

86m

991

99.31 98.0 93.8 ÿ 100 100 ÿ ÿ 61 100 ÿ

90

Zr(g, n) 89m,g Zr. When a nat Zr target is irradiated the possible reactions and the corresponding weighting coecients, calculated according to Kolev et al. (1994) are as follows: 90 Zr(g, n) with weight 0.94, 91 Zr(g, 2n) with weight 0.04 and 92 Zr(g, 3n) with weight 0.02. An observable contribution of the last two reactions to the IR can be expected in the case of di€erences in the individual IRs with more than one order of magnitude. Such an assumption, confronted with the knowledge of gen-

Table 2. The symbols Itarp, Im.s.p and Ig.s.p denote spins and parities of the targets, metastable and ground states of the isomeric nuclei respectively. Egmax is in units of MeV Reaction 55

89

Mn(g, 3n)

Egmax 52m,g

Mn

Y(g, 2n)87m,g Y

89

Y(g, 3n)86m,g Y Zr(g, xn)89m,g Zr, 1 Rx R3 90 Zr(g, n)89m,g Zr nat

nat

In(g, xn)112m,g In, x = 1, 3 In(g, n)112m,g In nat In(g, 2n)111m,g In, x = 2, 4 113 In(g, 3n)110m,g In 154 Sm(g, pn)152m1,g Pm 153 Eu(g, n)152m2,m1 Eu 165 Ho(g, n)164m,g Ho 165 Ho(g, 3n)162m,g Ho 179 Hf(g, p)178m,g Lu 180 Hf(g, pn)178m,g Lu nat Hf(g, pxn)178m,g Lu, xR 1 113

43 49 100 150 225 300 43 150±280 43 43 13 15 17 22 22.8 30 43 30 43 43 43 43 43 43 43 43 43

Itarp ÿ

5/2

Im.s.p 2

+

Ig.s.p +

6

1/2ÿ

9/2+

1/2ÿ

1/2ÿ 0+

8+ 1/2ÿ

4ÿ 9/2+

9/2+ 9/2+ 9/2+ 9/2+ 0+ 5/2+ 7/2ÿ

4+

1+

1/2+ 7+ (4) 8ÿ 6(ÿ) 6ÿ (9)ÿ

9/2+ 2+ (1+) 0ÿ 1+ 1+ 1+

9/2+ 0+

IR 0.452 0.04 0.412 0.02 0.792 0.07 0.922 0.04 0.892 0.04 0.892 0.04 0.592 0.04 0.722 0.05 0.132 0.02 0.312 0.01 0.29 0.63 0.77 0.872 0.03 0.632 0.04 0.502 0.15 3.4 2 0.3 4.0 2 0.5 6.1 2 0.4 0.752 0.03 0.372 0.11 0.011 2 0.002 0.332 0.03 1.792 0.04 0.692 0.07 0.162 0.03 0.422 0.09

Refs. VoÈlpel (1972) Walters and Hummel Walters and Hummel Walters and Hummel Walters and Hummel

(1966) (1966) (1966) (1966)

Walters and Hummel (1966) Davidov Davidov Davidov Davidov Davidov Davidov

et et et et et et

al. al. al. al. al. al.

(1987a) (1987a) (1987a) (1987b) (1987a) (1987a)

Davidov et al. (1987a)

Kolev et al. (1995) Kolev et al. (1995)

992 154

D. Kolev

Sm(g, np)152m,g Pm. There is some ambiguity related to the isomeric states of 152m,g Pm. The probable existence of an isomer with half-life of 15 min is mentioned in Lederer and Shirley (1978). Such activity was not observed in our measurements. The summing of cascade g-rays for the 841.5 keV g-line was corrected with an increase of 65.1%. Due to the poor spectroscopic data (Lederer and Shirley, 1978) for the 1097.0 keV transition, which is in cascade with the 341, 244.7 and 121.8 keV two additional uncertain transitions in the decay scheme were ignored. The abundance normalization of the 121.8 keV transition, presented by Lederer and Shirley (1978) is enough to apply the algorithm for summing corrections proposed by Andreev et al. (1972). Thereby, an increment of 38% was introduced in the measured area of the 1097.0 keV photopeak. 153 Eu(g, n)152m1,m2 Eu. The natural target material was used in this experiment. Summing corrections for the 89.9 and 963.4 keV g-lines were not introduced due to the low intensity of the other transitions in their cascades. It was shown numerically that the summing e€ect for 841.6 keV was also negligible. 165 Ho(g, n)164m,g Ho. The IR determined has been already reported (Kolev et al., 1995). Both isomers of 164 Ho decay through the low energy g-cascade. In order to avoid all corrections for summing and self absorption and thereby to reduce the uncertainties of the calculated IR the preference was given to the method A2. More details can be found in Kolev et al. (1995). 165 Ho(g, 3n)162m,g Ho. The situation with the IR in this reaction is identical to the case of 165 Ho(g, n) reaction. The results of application of A2 method to this reaction have been also described by Kolev et al. (1995). 179 Hf(g, p)178m,g Lu. The target thickness in this experiment was 0.1 cm. A cadmium absorber of 1 mm thickness was placed between the sample and the detector with the aim to reduce the summing of the low energy cascade g-rays in the decay of 178m,g Lu. The cascade of highly intensive transitions includes the 331.6, 216.7, 88.9, 426.4, 325.6, 213.4 and 93.2 keV g-rays. Accounting for the self absorption in the sample and in Cd-absorber the correction coecient for summing of the 426.4 keV g-line was found to be equal to 1.449. The summing correction for the 1340.8 keV g-line was shown to be negligible. 180 Hf(g, np)178m,g Lu. Exactly the same target as in the above experiment was used and the measurements were made with the same detector and in the same geometry, but without a Cd-absorber. The summing correction coecient for the 426.4 keV gline was estimated to be 1.438, which is practically equal to the value obtained with the Cd-absorber. This result con®rms that in the measurements discussed the low energy g-rays are absorbed mainly in

the sample and in the nonsensitive detector material and, hence, not detected. nat Hf(g, xnp)178m,g Lu, x = 1, 2. The target thickness in this experiment was 0.3 cm, which led to the summing correction coecient of 1.202 for the 426.4 keV g-line. The lower summing e€ect, in comparison with both preceding experiments with Hf target, is due to higher self-absorption of the low energy quanta in the target with higher thickness.

Interpretation and Discussion According to the model of Kolev and Bratovanov (1995) an excited composite system is created by the absorption of the E1 incident quanta with a certain energy. The formation cross section of the composite system is assumed to be equal to the photoneutron cross section (Berman, 1975; Dietrich and Berman, 1988). The composite system decays emitting neutrons, protons, alpha particles and deuterons. The number of particles emitted is limited to four. In the excitation energy calculation corrections for rotational and pairing energies are introduced. The binding energies of the particles to be emitted are calculated from the experimental masses (Wapstra and Bos, 1977a,b). The kinetic energies reachable by evaporated particles are determined from the corresponding di€erential evaporation spectra. These energies are involved in the calculations in opposite to the widely accepted approach where mean kinetic energies of the evaporated particles are used. The evaporation spectra are calculated with the Weisskopf±Ewing evaporation formula (Blann, 1967). The particle transmission coecients are calculated according to the optical model with parameters taken from (Perey and Perey, 1976; Ernst, 1995). The probability for the emission of a particle with a ®xed kinetic energy is determined from the evaporation spectra with account for all other competing channels. Thereby, the weights of the intermediate states account for the process of multiple emission of particles of di€erent type. Each excited state at the end of particle evaporation is used as the initial one for the ®nal g-emission, which is calculated with the HVM. In the HVM only a dipole radiation in the g-cascades is assumed, while the ®nal ``deciding'' quanta, populating either the high spin or the low spin state can be with an arbitrary multipolarity. Thus, for each incident energy the probabilities for a population of the isomeric states of the isomeric pair are obtained. Their ratios, averaged over corresponding reaction cross sections and bremsstrahlung intensities, give the mean value, which has to be compared with the experimental IR (see [1]) at the Egmax speci®ed. The level densities are calculated with the Ericson formula (Ericson, 1960) where the level density parameter is de®ned as a = A/k for each nuclide (A is the mass number) in the decay chain. In the present

Isomeric yield ratios with Bremsstrahlung

calculation we take k = 8 MeV which corresponds to its mean value in the mass region of the reactions studied (von Egidy et al., 1988). It was found that the variation of k between 7 and 10 MeV causes negligible changes in the predicted IR values. The most important parameter in the Ericson's formula is the well known spin-cut-o€ parameter SCOP, which limits the spin distribution for certain excitations. The IRs are strongly dependent on the angular momentum e€ects in the excited nucleus decay and therefore, the IRs are very sensitive to the SCOP values. Thus, the model is designed with the presumption that only the SCOP will be varied. The reason is that all other parameters used in the calculation, are either determined in agreement with well de®ned physical conditions, e.g. optical model parameters, or taken form experimental data, e.g. experimental masses, or do not in¯uence the model predictions as in the case with the speci®c parameters for the HVM calculation (Bartsch et al., 1976). Therefore, it was assumed that if the experimental IR cannot be reproduced by an acceptable value of SCOP, the inconsistency of the model has to be considered. The SCOP values for the best ®t to the experimental IRs are listed in Table 3. The results listed in Table 3 are ordered according to the number of particles emitted. For the reactions with emission of neutrons and protons the calculations are done for both the available channels. The low error values of the ®tting SCOPs are determined by the relatively small uncertainties of the measured IR. On the other hand an approxi-

993

mation to the mass dependence of SCOP, as obtained by von Egidy et al. (1988): SCOP = (0.98 2 0.23)A(0.26 2 0.06) produces SCOPs, but with rather large uncertainties and thereby is not suitable for calculation of referable SCOPR. Nevertheless, our results are comparable with SCOPs evaluated by this formula, despite the considerable di€erences in the approaches used. Whereas in our study each SCOP ®ts a single experimental IR according to certain reaction mechanism, in the work of von Egidy et al. (1988) a suggested mathematical function is used to ®t large number of discrete level data for various nuclei with ``strongly correlated'' errors, causing the substantial increase of the uncertainties in the derived formula. However, the approximate values of SCOP, typical for the nuclei produced, are taken from Gilbert and Cameron (1965) and shown in the column marked by SCOPR. The additional parameter ``center of spins'' COS = 1/2(Ig.s.+Im.s.) is also given (Bartsch et al., 1976). In the HVM calculation COS presents the spin value responsible for population either the high or the low spin state of the isomeric pair. Each exited state, which can emit the ``deciding'' quanta populates the higher spin isomeric state if the emitting state spin is higher than COS and vice versa. Furthermore, the statement of Bartsch et al. (1978), that the equilibrium calculations with the ®nal g-deexcitation according to HVM, applied to photonuclear reactions gives SCOP1 COS can be checked.

Table 3. Most important parameters related to the model calculations. SCOPR, SCOP and COS are in units of h Reaction 90

Zr(g, n)

113

153

89m,g

In(g, n)

Zr

112m,g

In

152m2,m1

Eu(g, n) Eu Ho(g, n)164m,g Ho 178m,g Hf(g, p) Lu 89 Y(g, 2n)87m,g Y 165 179

113

In(g, 2n)111m,g In Sm(g, np)152m1,g Pm 154 Sm(g, pn)152m1,g Pm 154 Sm4152m1,g Pm 180 Hf(g, np)178m,g Lu 180 Hf(g, pn)178m,g Lu 179 Hf, 180 Hf 4178m,g Lu 55 Mn(g, 3n)52m,g Mn 154

89

Y(g, 3n)86m,g Y In(g, 3n)110m,g In 115 In(g, 3n)112m,g In 165 Ho(g, 3n)162m,g Ho 115 In(g, xn)111m,g In 113

a

Egmax

SCOPR

SCOP

COS

43 30 30 43 30 30 43 43 43 43 150±280 43 43

3.3 3.3 3.3 4.0 4.0 4.0 4.8 4.8 4.5 3.5 3.5 4.0 4.8 4.8 4.8 4.5 4.5 4.5 2.6 2.6 3.5 4.0 4.0 4.8 4.0

2.32 20.04 2.8 20.7 2.91 20.54 3.452 0.05a 3.1 20.7 3.21 20.13 1.72 20.05 2.73 20.02 5.00 20.47 2.36 20.05 2.33 20.05 4.4b 2.11 20.18 2.07 20.16 2.082 0.11c 4.34 20.31 3.78 20.19 4.13 2 0.16c 3.46 20.09 3.56 20.09 4.32 20.12 4.34 20.05 3.452 0.05a 4.35 20.03 4.4b

2.5 2.5 2.5 2.5 2.5 2.5 4.0 3.5 5.0 2.5 2.5 2.5 2.5 2.5 2.5 5.0 5.0 5.0 4.0 4.0 6.0 4.5 2.5 3.5 2.5

43 43 43 43 43 49 43 43 43 43 43

Refs Carver et al. (1962) Bartsch et al. (1978) Carver et al. (1962) Bartsch et al. (1978)

Bartsch et al. (1978)

VoÈlpel (1972)

A value used in the model prediction for 113 In(g, n) and 115 In(g, 3n) reactions. The calculated IRs are averaged with the weights estimated in Section 2 for the nat In(g, xn)112mg In reaction (x = 1, 3). The mean value obtained ®ts the experimental IR with high accuracy. b The same as in a but for the nat In(g, xn)111mg In reaction (x = 2, 4). c Weighted mean value obtained from the data for the channels shown.

994

D. Kolev

As can be seen in Table 3 a trend exists for better agreement between the ®tting SCOP and those SCOPR, taken from the literature, if the number of emitted particles increases. The e€ect is due to the fact that for the ®rst particle emission the nonequilibrium reaction mechanism is quite strong, while all next particles are emitted by a composite system at higher equilibrium. In general, when unrealistic SCOPs occur, the model disadvantages could be related to: (i) the lack of nonequilibrium calculation and (ii) the divergence between the real low energy g-decay of the isomeric nucleus and the simple assumptions of the HVM. The detailed analysis, based on the nuclear structure and decay data, shows that these considerations, more or less, are important in all cases of problematic SCOPs, mentioned in the following discussion. Abnormally small SCOP ®ts to the experimental IRs obtained in the 90 Zr(g, n)89m,g Zr and 153 En(g, n)152m1,m2 Eu reactions. In the decay scheme of 89m,g Zr a non-negligible quadruple decay exists, which mode is not treated in the HVM at all. The g-decay of the 152m1,m2 Eu also does not correspond to the HVM assumptions, because of the presence of two competing levels with spins 5+ and 4+ located between the m1 and m2 states. The 4+ level feeds the ground state in the 152 Eu, which decay mode is not taken into account in the HVM. The 152 Eu is a deformed nucleus and therefore a quadruple radiation could be expected from the highly excited states. Two competing levels with spins 3+ and 2+ between the isomeric and the ground state present also in the decay scheme of the 164m,g Ho

and correspondingly, the ®tting SCOP is also quite di€erent from the expected SCOPR again due to the discrepancies between the real and the model decays. The data available from Lederer and Shirley (1978) for the decay of 87m,g Y, produced in the 89 Y(g, 2n) reaction are relatively poor and thereby it is not possible exactly to show the in¯uence of the properties of the real decay on the model predictions. On the other hand the 89 Y is neutron magic nucleus and therefore a strong nonequilibrium contribution has to be expected to the reaction mechanism. It is not reasonable to comment the unrealistic low SCOP in the reaction 154 Sm(g, np)152m1,g Pm, when the decay scheme of the 152m1,g Pm is uncertain which can cause even an incorrect experimental IR. The reason for the di€erence in the SCOP and SCOP values for the 55 Mn(g, 3n)52m,g Mn reaction can be searched in the relatively strong admixture of quanta with multipolarity higher than E1 in the real decay of 52m,g Mn. It is dicult to estimate the in¯uence of the possible discrepancy of the model and the real decay for the 86m,g Y on the SCOP value used, because of insucient spectroscopic data. On the other hand this nucleus as well as the above discussed 87m,g Y is obtained from the neutron magic target and thereby high nonequilibrium emission should be expected. In order to clarify the problem about the correlation of COS and spin-cut-o€ parameters, all SCOPs from Table 3 are drawn versus the corresponding COSs on Fig. 1. They are weightily approximated by straight line: SCOP = A1
COS + B1

Fig. 1. Spin-cut-o€-parameters as a function of COS.

Isomeric yield ratios with Bremsstrahlung

(solid line on Fig. 1), A1=0.52 2 0.13 and B1=1.69 2 0.46 h and the linear correlation coecient, LCC = 0.87. Ignoring the dependence of spin-cut-o€ parameters on the nuclear structure the same interpolation is applied to the SCOPRs (long-dashed line). The coecients are  which conA0=0.047 2 0.16 and B0=3.86 2 0.13 h, ®rm that the real SCOPRs do not correlate with COSs. The short-dashed line presents again the weighted approximation of the SCOPs, but all abnormal SCOPs discussed above (marked by empty circles) are excluded. The coecients in this case are: A2=0.22 20.11, B2=3.45 2 0.38 h and LCC = 0.77. It can be accepted that A2 and B2 are equal to A0 and B0 within the errors, i.e. when the model is adequate to the reaction mechanism of the reactions studied the necessary SCOPs are independent of COSs. Although the data used include a limited and not large number of reactions this statement contradicts the observation SCOP 1 COS, obtained by Bartsch et al. (1978). The compiled SCOPR values have to be considered mainly as tentative ones. They are obtained by the much stronger de®ned neutron capture measurements in the relatively low energy range. The SCOPs depend on the excitation energy. Thereby, the SCOPs values shown in Table 2 should be assumed as mean values obtained from the individual SCOPs of large number of states with excitation energy which can di€er with more than one order of magnitude. Therefore, the ®tting SCOPs could not be certainly equal to the SCOPR. Taking into account the results presented in Table 3 and the discussion above, it can be claimed, that the statistical model, combined with HVM, gives successful description of the reaction mechanism at least in 50% of the reactions discussed in the present study. Thus, it can be used as initial theoretical approximation to the solution of di€erent applied and fundamental problems. AcknowledgementsÐThe author would like thank Dr N. Nenov and Dr V. Todorov for their help during the measurements and for critical remarks in the course of the data evaluation.

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