PHOTONUCLEAR REACTIONS: MODERN STATUS OF THE DATA
© 2004 B. S. Ishkhanov1)'2), V. V. Varlamov2>*
Received January 21, 2004
Photonuclear reaction data play an important role in basic and applied researches. A radiation shielding design, a radiation transport analysis, an activation analysis, astrophysical nucleosynthesis, safeguards and inspection technologies, human body radiotherapy absorbed dose calculations, beam monitoring in heavy ion dissociation research at ultrarelativistic energies etc. could be mentioned. However, there exist quite evident systematical discrepancies both in shapes and magnitudes between photonuclear cross sections measured in various laboratories. These discrepancies noticeably reduce accuracy and reliability of data. A systematical overview of various types of the data contained in the international database is given. The modern status of the data is discussed. The reasons of significant discrepancies between various photonuclear data are analyzed and methods to reduce them are suggested.
INTRODUCTION
The absolute majority of the data on photonuclear reaction cross sections in the energy range of Giant Dipole Resonance (GDR) have been obtained [1 — 5] in experiments with bremsstrahlung (BR) and quasimonoenergetic photons produced by annihilation in flight of relativistic positrons (QMA). There are evident systematical discrepancies both in shapes and magnitudes between the data obtained not only in experiments of different types, but in experiments of the same type as well. The discrepancies are larger than statistical uncertainties and obviously depend on the experimental method explored. Though the majority of cross section data has been obtained quite long ago they are included into the contemporary large database [6] and extensively used till now. So the current status of photonuclear researches on a whole as well as an accuracy and reliability of each set of the data become understandable only after a careful analysis of existed systematical disagreements and of the ways to take them into account. Large databases give a good possibility for such an analysis.
section is not possible with them but only a reaction yield Y(Ejm). The latter is a cross section a(k) with a threshold Eth depended on a photon energy k and folded with the photon spectrum W(Ejm, k) with the end-point energy Ejm:
Y (Ejm) =
N(Ejm) eD(Ejm)
Ej.
a
W (E.
Eth
jm, k)a(k)dk.
(1)
Reaction cross section a can be obtained from the experimental yield Y using one of well-known mathematical methods (Penfold—Leiss, Tikhonov regu-larization, etc.). All of them have been developed especially to produce the effective photon spectrum (the apparatus function) that looks like (Fig. 16) an sufficiently narrow line. However, a constructed apparatus function has a complex shape, which can produce additional uncertainties in a shape, magnitude, and position of a cross section.
1. TWO MAIN TYPES OF PHOTONUCLEAR EXPERIMENTS
1.1. Experiments with Electron Bremsstrahlung Photons
Bremsstrahlung spectrum is a continuous one and therefore a direct measurement of a reaction cross
^Physics Faculty, Lomonosov Moscow State University, Russia.
2)Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Russia. E-mail: varlamov@depni.sinp.msu.ru
1.2. Experiments with Quasimonoenergetic Annihilation Photons
As an alternative to procedure of solving inverse ill-post problem (1) QMA experiments have been developed [5] (the majority of data has been obtained at Livermore (USA) and Saclay (France)). They consist of producing annihilation photons with the energy Ey = Ee+ +0.511 MeV by fast positrons. Since annihilation photons always are accompanied by positron bremsstrahlung a QMA experiment is carried out by three steps (Fig. 1 — 63Cu(7, n)62Cu reaction [7]): 1) measurements of the yield Ye+ (Ej)
1691
Photon energy, MeV
Fig. 1. Experimental yields [7] of 63Cu(y,n) 62Cu reaction (x), appropriate effective photon spectra (solid curves) and the apparatus function obtained by the reduction method (dashed curves): (a) the yield difference Ye+ (Ej) — Ye- (Ej) = Y(Ej) « « a(k) (2), i.e., the difference between spectra of photons produced by positrons and electrons, correspondingly; (b) the yield Ye- (Ej) and the electron bremsstrahlung spectrum (the apparatus function obtained by the Penfold—Leiss method is also presented (+)); (c) the yield Ye+ (Ej) and the spectrum of photons produced by positrons (the sum of bremsstrahlung and annihilation processes).
of reaction induced by photons from both the annihilation and bremsstrahlung of e+; 2) measurements of the yield Ye- (Ej) of reaction induced by photons from the e- bremsstrahlung; 3) the subtraction (the bremsstrahlung spectra supposed to be identical for e- and e+)
Ye+ (Ej) - Ye- (Ej) = Y(Ej) » a(k). (2)
The difference (2) is interpreted as a reaction cross section "measured directly".
It has to be pointed out that: 1) there is no a beam of QMA photons in reality: the QMA photons arise only as a difference of two real spectra; 2) the apparatus function (Fig. 1a) of an experiment is obtained individually because it depends on conditions of both the measurements (i.e., on yields — Ye+, Ye-); 3) a production of positron annihilation Y quanta is a result of few successive processes (a bremsstrahlung production (e- + A — A + e- + + y); a production of pairs (y + A — A + e- + e+); a positron annihilation (e+ + e- — 2y)). Due to this a number of quasimonoenergetic photons appears to be small and hence a statistical accuracy of measured yields as well as their normalizations are also low; 4) an apparatus function has a complex shape and is spread over a wide energy range, so the result of (2) is not a cross section really but a yield again.
2. MAIN DISCREPANCIES BETWEEN REACTION CROSS SECTIONS OBTAINED WITH BR AND QMA PHOTONS
As it follows from the above discussion, conditions of these two types of experiments are different and this is the reason of a significant disagreement in their results.
2.1. Total Photoneutron Reaction (Y,xn) Cross Sections Shape (Structure, Resolution)
As a typical example of well-known discrepancies under discussion photoneutron reaction 16O(y, xn) total cross sections obtained in BR [8] and QMA experiments [9, 10] can be pointed out. There are well-separated resonances in all the three cross sections obtained with a high enough energy resolution (200 [8], 180-200 [9], and 200-300 keV [10]). However, all the QMA resonances have larger widths and smaller amplitudes than the appropriate BR ones. The QMA data look like smoothed versions of the BR data. Absolute values of the BR data [8] and the Saclay QMA data [9] are close: integrated cross sections for the same integration limits are 36.90 and 34.52 MeV mb, respectively, but the Livermore QMA data [10] ((1.12-1.20) • 27.64 MeV mb) became
close enough to the two others only after additional normalization (the factor 1.12 will be discussed later).
An additional example of discrepancies concerned is a detailed comparison [11] of resonances in the 18O(y, xn) reaction cross section obtained with BR [11] and QMA photons [12]: all the resonances have larger amplitudes ((ABR/Aqma) = 1.17) and smaller widths ((rQMA/rBR) = 1.35) in the BR cross sections than in the QMA cross sections. Integrated cross sections for the energy range 8-28 MeV are also different: agR = 187.12 MeV mb and ctqma = = 167.33 MeV mb (the ratio is again -1.12).
The general systematics3) [13] of the disagreements is shown in Fig. 2 for a special parameter named "structureness" that describes as a whole the deviation of each reaction cross section from its significantly smoothed value (with a smearing parameter A about 1 MeV) for the whole energy range D:
N
i=1
(i*))2
(3)
where
Ei+A/2
(<n) = \ f <r(k)dk, ((a)) = 1 J a(k)dk
D
Ei-A/2
are averaged cross sections.
In Fig. 2, the ratios S/SL are presented, where S values are calculated for data from various laboratories whereas SL - for the Livermore QMA data (some other QMA data are used also). Data clearly separate into two groups: BR ((S/SL) = 4.35) and QMA ((S/SL) = 1.22). This means that in all the QMA laboratories an estimation of energy resolution using a width of the annihilation line (in many cases 250-400, sometimes 500, more rarely 150-300 keV) does not give a real resolution: the QMA cross sections are over-smoothed. This is confirmed by the value (S/SL) = 4.22 for data obtained in [14] using a tagged photon (TP) technique (the TP apparatus function is close to the Gauss shape).
Since in reality a QMA cross section (2) is only a yield (1), a real cross section can be obtained [15-18] only after an additional processing by the use of a real apparatus function and the reduction method [19, 20]. Actually, this is not a method of solving an inverse ill-posed problem (1) to unfold a cross section from a yield. The reduction method transforms data obtained with some experimental apparatus function (Fig. 1)
3)It contains more than 500 total photoneutron (y, xn) cross sections for nuclei from 3H to 238U.
S/SL, arb. units
6,7Li 160
102
101
63,65Cu
141
Pr
M
208
Pb
4.35 BR
M
4.22 TP M
1.22 QMA
U
100
tjpï
40
80
120
160
200
Mass number A
Fig. 2. The systematics of ratios S/SL (see text) obtained for the total photoneutron reaction cross section data: BR data ( ® — Moscow, ® — Melbourne (Australia), ® — other); QMA data (x — Saclay (France), +— Giessen (Germany), x — other); TP data ( n - Illinois (USA)).
0
into those, which would have being measured by means of an apparatus function of other quality (the better, e.g., is the Gauss line with the exactly known energy resolution). As a result one gets the most reasonably achievable monoenergetic representation of a reaction cross section from a reaction yield.
A reaction yield (1) measured using an apparatus function A and written in an operator form reads
y = Aa + v. (4)
T
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