Production cross-section

In Section 8.5 we gave results for the differential cross-section for e e — ff including — 7 interference and higher order corrections. 

The QED corrections are very important (see Kiihn and Zerwas, 1990) and give substantial contributions to cross-sections around the peak. Their effects, however, largely cancel when ratios are taken. This can be seen from Table 13.5 where the Bom cross-sections for fiji and 66 at the peak are compared with initial state radiative corrections calculated to order 0 a) and to order O(a ) [in the latter, an attempt is made to estimate higher orders by exponentiation (Berends et al., 1987, 1988b)]. 

The s dependence around the Z mass of the various cross-sections, 66, cc and their ratios) is shown in Fig. 13.20. 

The detailed results from box amplitudes and interference between initial and final state emissions calculated at the parton level can be foimd in Kiihn and Zerwas (1990) together with the original references. 

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A tabulation of the ECPSSR cross sections for proton and helium-ion ionization of Kand L levels in atoms can be used for calculations related to PIXE measurements. Some representative X-ray production cross sections, which are the product of the ionization cross sections and the fluorescence yields, are displayed in Figure 1. Although these A shell cross sections have been found to agree with available experimental values within 10%, which is adequate for standardless PKE, the accuracy of the i-shell cross sections is limited mainly by the uncertainties in the various Zrshell fluorescence yields. Knowledge of these yields is necessary to conven X-ray ionization cross sections to production cross sections. Of course, these same uncertainties apply to the EMPA, EDS, and XRF techniques. The Af-shell situation is even more complicated. 

Figura 1 Calculated K X-ray production cross sections for protons using the tabulated ECPSSR Ionization cross sections of Cohen end Harrigan, and the fluorescence yields calculated es In Johansson et al. (1 barn h IIT cm l.

Figure 2 Experimental and calculated background radiation production cross sections for (a) 360 g/cm plastic foil and (b) 200 fig/cm Al foil. ...

The height of a given X-ray peak is a measure of the amount of the corresponding element in the sample. The X-ray production cross-sections are known with good accuracy, the beam current can be measured by, for example, a Faraday cup (Figure 4.1) and the parameters of the experimental set-up are easily determined so that the sample composition can be determined in absolute terms. 

Computer software codes are available to deconvolute PIXE spectra and to calculate peak areas with accuracy, so that absolute amounts of elements present in the specimen may be derived. With a beam of 5 mm diameter incident on a thin organic specimen on a thin backing foil, trace elements can be detected at picogram levels. The x-ray production cross-sections, absorption coefficients and the various... 

In order to measure cross sections, a beam of electrons of known energy is directed through a gas sample of known pressure and the resulting ion and electron currents measured.63 If mass selective ion detection is used, then partial ionization cross sections oz may be determined. These cross sections correspond to the production of z electrons and an ion or ions having total charge +ze. Some instruments allow the counting cross section oc, also known as the ion production cross section, to be determined ... 

In general, however, the measured quantity is the total, gross, or electron production cross section ot ... 

Since the summation method allows absolute partial ionization cross sections to be determined, it is straightforward to extract the counting or ion production cross section from the data. Since this is the quantity which is given by many of the current... 

Figure 7 The ratio of measured single differential secondary electron production cross sections to the corresponding Rutherford cross sections for ionization of water vapor by electrons. (From Ref 38.)...

To give one a feel for the magnitude of the quantities involved, we outline below a very simple schematic method for estimating heavy-element production cross sections. It is intended to show the relevant factors and should not be taken too seriously, except to indicate the order of magnitude of a particular formation cross section. 

This nuclide was identified by genetic links to its daughters 258Db, 254Lr, 250Md, 250Fm, and 246Cf. The cross section reported for this reaction was 200 pb (approximately 1/5,000,000 of the production cross section assumed in the discovery of Md). This element was named bohrium (chemical symbol Bh) in honor of Niels Bohr. 

In 1982, Munzenberg et al. (1982, 1984) reported the observation of one atom of element 109 formed in the reaction 209Bi(58Fe, n). The decay of this atom was weakly correlated to its daughters 262Bh, 258Db, and 258Rf. The production cross section was 10 pb. This discovery was confirmed by the later observation of more... 

In 2004, Morita et al. reported the synthesis of a single atom of element 113 in the 70Zn + 209Bi reaction. The production cross section was 55 fb, a remarkably small value requiring several months of bombardment. 

Suppose you want to synthesize the nucleus 271Mt using the 37C1 + 238U reaction. Estimate the production cross section for this reaction. What is the expected half-life of this nucleus What is the expected decay mode ... 

Fig. 5.5. Inelastic scattering cross sections for positron-02 collisions. Key ,

To define more accurately the boundaries of the mass regions that could be accessed with the proposed He-jet coupled mass separator system, production cross sections for both neutron-deficient and neutron-rich nuclei far from stability have been estimated for 800-MeV proton reactions. The spallation-product cross sections were estimated through use of the Rudstam systemstics [RUD66]. For estimation of the fission-product cross sections, however, there is no established, similar approach. Thus, an empirical approach was taken in... 

We quote here only the latest value obtained from the measured hadronic production cross section in e+e- collisions as well as the information obtained from the analysis of hadronic tau decay data [29] ... 

The half-lives deduced from the 106 a singles, 15 a-a correlations and 109 SF decays were all compatible with the 34-s half-life of 262Db and the 4.3-s half-life of 258Lr. The total production cross section of 262Db at 99 MeV was 8.3 2.4 nb. 

Fig. 11. Search for superheavy nuclides in the reaction of 48Ca with 248Cm upper limits of production cross sections plotted versus half-life. The curves refer to different separation techniques (see text) recoil-fragment separators (curves 1, 2), fast on-line chemistry (3-5), and off-line chemistry with low-background counting (6-8). From P. Armbruster et al. [100].

The 48Ca+248Cm system has recently been reinvestigated at Dubna [103], now with positive evidence for the formation of 292116 (see Ch. 1). The half-lives in the postulated decay chain - milliseconds to seconds - fall into the region covered in Figure 11. But the production cross section is two orders of magnitude below the level reached in the previous studies. If these results can further be substantiated, they would give a hint why so many attempts to make superheavy elements by complete fusion failed. Over the years, the question was Is production the problem or is it survival - nuclear reaction or nuclear stability Are the cross sections too low or the half-lives too short These recent results would point to the production as the key problem. 

A radiochemical study [104] of the element distribution in the 238U+238U reaction at the unilac revealed the expected broad distribution of reaction products. Below uranium, where losses by sequential fission of transfer products are not significant, the observed yields decreased exponentially from Z=92 down to Z= 73. This trend was well reproduced [105] by a theoretical model treating nucleon transfer in the intermediate collision complex as a diffusion process. By extrapolation of the model to Z=70 nuclei about 100 microbam total production cross section resulted, associated with broad distributions of neutron numbers and excitation energies. 

Fig. 12. Production cross sections of transuranium nuclides in the interaction of 238U with 238U (solid lines) plotted versus mass number. Also shown are data for the l36Xe+238U interaction (dashed lines). FromM. Schadel et al. [104],...

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