Total Hadronic Photoabsorption cross sections on Hydrogen, Deuteron and Carbon Nuclei from 6 to 5 GeV

Fig.3. Total yield from the ¹²C target

(open circles- upper curve), empty

target (full triangles – down curve)

and their difference (full squares – average

curve).

Total cross section is the difference between two total hadron yields from full and empty target normalized on the corresponding fluxes. Taking into account the target thickness, we obtain the total cross section in absolute scale.

4. 
   SUMMING METHOD
   

Summing method supposes measurement of partial meson photoproduction cross section which contribute significantly to the total photoabsorption one. Similarly to the total hadron yield the partial reaction one (integrated over the solid angle) is determined by the equation:

, (2)
where is the partial cross section. Other parameters are the same as described in the subtraction method presented above.

A partial reaction yield was separated from the total one by means of the kinematics relations (energy and momentum conservation laws). The number of partial channels which contribute significantly to the total photoabsorption cross sections at E_< 1 GeV on the proton and neutron is limited by the following reactions:

p ->
n ->

Other reactions including tripple pion production, kaons photoproduction and Compton scattering contribute less than 2% in this energy region.

Evaluation algorithm for these partial channels was described elsewhere [1]. The result is available due to almost  solid angle and low background conditions of the GRAAL experiment. At first, here we took into account the single and double  mesons and meson photo-production on the proton and neutron using the deuteron target. The products of ⁰ decay (2) were detected in BGO-detector, nucleons and charged mesons were measured in both BGO and front scintillation wall detectors. Time of flight measurement for the forward detector was applied to separate nucleons and charged mesons. Simulation was done for each partial reaction providing the algorithm for data analysis. The contribution of neighbor channels to the any selected yield does not exceed 1%.

An example of the proton and pion selection for the reaction n=>p^ using two-dimension distributions is shown in fig.4.

Fig.4.

Selection of a proton and charged pion

in BGO detector

There where four criteria of event selection for the reactions p=>p⁰ and n=>n,^invariant mass of two -quanta, missing mass of the nucleon, difference between calculated and measured angles of nucleon and difference between calculated energy of nucleon and its energy measured by TOF.

Selection of events for -meson photo production was done practically by the same way as for ⁰ photo production, but the cuts on the invariant mass (only 2 gammas of decaywere considered) were applied corresponding to the mass of -meson.

Selection of events for double ⁰ photo production was done similarly to the single ⁰ photo production. The only difference was to use the two dimension distributions of invariant masses of two pars of -quanta corresponding to two ⁰.

Events with one neutral and one charged meson were selected using the invariant masses of ⁰ , at first. Then the energy and momentum of the missing mass were calculated. Energy of charged meson was measured, so the missing mass for the neutral and charged meson was equal to the mass of nucleon. Then the angle and energy of the nucleon was evaluated and compared with the measured values.

The most difficult case was to separate the reaction of two charged mesons photo production. If nucleon hits the BGO detector we can’t measure the energies of all three particles. Therefore, in order to decrease background, the events with nucleon, coming in forward direction where taken into account. Energy and momentum of the nucleon and its missing mass were calculated. Energy of one charged meson was evaluated, so the nucleon missing mass and this meson was equal to the mass of second meson. Then angle of second meson was calculated and compared with the measured value.

Principal problem of present analysis is determination of the measurement efficiency for all partial reactions which was done by simulations. This is based on the computer program chain which includes LAGGEN (LAGrange GENerator), LAGDIG (LAGrange DIGitation) and PREAN (PRE-Analysis). LAGGEN contains the event generator to extract the energy and angular distributions for reaction products taking into account the results of multi-pole analysis and previous experimental data. It would be emphasized that necessary literature data for all partial channels which contribute noticeably to the total absorption cross section are available. Differential cross sections for reactions with two particles in final state can be extracted with a high accuracy from literature; for three particle production they were supposed isotropic in accordance with existing experimental and multi-pole analysis data. The goal of this work was to use these data and to obtain the reliable results for absolute values of the partial and total cross sections. So, the first step of simulations was to get the geometrical efficiencies which are defined by the probability of the reaction product particle to reach the detector.

On the second stage the simulation was done using LAGGEN again which includes the MAID [9] and GEANT3.21 package [10], and to evaluate the probability for the particle which touches the detector to be measured, taking into account the ionization, energy losses, size of the cluster etc. Then, the code LAGDIG was used to provide the conversion of the traces of particles in detectors to the digital outputs (QDC, TDS), taking into account the thresholds of the detectors. After this procedure, the outputs were calibrated by means of the PREAN code, exactly in the same way as corresponding experimental data, and respective cuts were identical.

Finally, the measurement efficiency for any partial reaction was calculated as ratio of simulated events (obtained in accordance with the described above algorithm) to the total number of events simulated for selected reaction using the event generator.

The result of simulations is shown in table 2. Some multiple meson and kaon production processes above 1.0 GeV can contribute to the yield, but they were ignored. The BGO crystal threshold is equal to 10 MeV. The geometry partial efficiencies shown in parentheses are defined as the probability of all the particles to reach the detector and provide a total energy release greater than the BGO threshold of 160 MeV. It would mentioned that the data presented in table 2 are related to almost 4detector and can be useful for another such kind facilities.

Table 2.

Simulated BGO efficiency for selected partial channels on the proton and neutron..

In parentheses the geometry efficiency is shown (see text).

.

EGeVp > n	p > p	p > p	p > n	p > p	p > p
0.550.12(0.68)	0.44(0.72)	0.13(0.33)	0.031(0.29)	0.13(0.24)
0.650.13(0.64)	0.42(0.71)	0.15(0.34)	0.037(0.29)	0.13(0.24)
0.750.12(0.59)	0.35(0.64)	0.16(0.34)	0.038(0.29)	0.12(0.23)	0.008(0.00)
0.850.11(0.55)	0.25(0.56)	0.17(0.33)	0.034(0.28)	0.12(0.23)	0.052(0.10)
0.950.11(0.54)	0.19(0.52)	0.15(0.31)	0.031(0.26)	0.11(0.22)	0.069(0.14)
1.050.10(0.49)	0.13(0.50)	0.15(0.29)	0.027(0.25)	0.11(0.22)	0.066(0.14
1.150.09(0.44)	0.09(0.46)	0.16(0.28)	0.022(0.23)	0.10(0.21)	0.062(0.14)
1.250.08(0.41)	0.06(0.41)	0.17(0.26)	0.019(0.21)	0.10(0.21)	0.059(0.13)
1.350.07(0.40)	0.05(0.38)	0.17(0.24)	0.017(0.19)	0.10(0.20)	0.049(0.12)
1.450.06(0.38)	0.04(0.36)	0.17(0.22)	0.016(0.17)	0.10(0.18)	0.041(0.11)
n > p	n > n	n > n	n > p	n > n	n > n
0.65				
0.75					
0.85					
0.95					
1.05					
1.15					
1.25					
1.35					
1.45					

Outputs for each of twelve mentioned above reactions were collected in several dozen million events. For the same runs the corresponding fluxes were evaluated as was described in [1].

Naturally, the simulation results depend on different specialized experimental problems which were solved for different reactions. For example, for ^production channels, we took into account the overlapping neutral clusters from the ^ decay. For partial channels with a recoil neutron in the final state, we have to take into account the scattering neutrons in the BGO detector and to select the primary scattering events. Neutral clusters corresponding to the primary scattered neutron events were identified by the complanarity condition.

We would note that energy scale in presentation of all cross section has a bin of 20 MeV whereas the energy resolution of the tagging system is equal to 16 MeV at 1 GeV. This was done to avoid artificial wrong resonant structure which appears usually in the initial stage of analysis when the energy bin and microstrip energy width are identical. Of course, it is possible to check the number of events carefully by hand in any energy bin to avoid the artificcial structure. Here we prefered to use the energy bin of 20 MeV which seems to be optimal because it very slightly decreases the energy resolution but improves significantly the systematic errors.

5. EXPERIMENTAL RESULTS
FREE PROTON

GRAAL results on the total photoabsorption cross section for the free proton obtained by two independent methods are shown in fig.5. There is no visible difference between these two results in the energy region up to 1 GeV. It is seen also that above 1 GeV, the subtraction method gives an excess in comparison with the summing method and this difference is increasing with the photon energy. This means evidently that other reactions except mentioned in the present analysis (mostly triple meson production) contribute significantly at high energies (above 1 GeV). This result confirms high quality of the data obtained by the subtraction method which will be presented as the final GRAAL result on the total photoabsorption cross section on the free proton. Total error bars evaluated by the comparison of two methods results do not exceed 5%.

Fig.5.

Total photoabsorption cross section for

the free proton obtained at GRAAL by

the subtraction method (open points) and

summing method (black points).

Comparison of the GRAAL results (subtraction method) with available literature data is shown in fig.6. One can see a good agreement between different results in all energy regions.

Fig.6.
Total photoabsorption cross section for

the free proton obtained by GRAAL ,

Armstrong [3] and Mainz [6] are

represented by full, open points and

triangles, respectively.

It would be noticed that Armstrong data for the free proton photoabsorption cross section are widely used as reference ones for comparison with nuclear photoabsorption cross sections. In such case they are usually presented by the approximation curve basing on the multi-pole fit which takes into account nucleon resonances and non resonance background [7].. In fig.7 one can see a good agreement of the GRAAL and Armstrong approximation data for the free proton except some points on the left edge of the D13 resonance.

Fig.7

Total photoabsorption for the free

proton. Points correspond to

GRAAL data, curve is the result

of approximation [7] of the

Armstrong data.

NEUTRON
Situation with the neutron photoabsorption cross section is much more difficult because we have no free neutron target. But basing on the summing method we could evaluate the total photoabsorption for the bound neutron (deuteron target) and compare it with a bound proton cross section obtained with the same target under the same conditions (tagging and detector efficiency etc). Unexpectedly, the result was quite surprising as compared with an existing knowledge.

But first of all we see in fig.8 that subtraction and summing method gives the identical values (within 5% of error bars) at E< 1 GeV for the neutron cross section, as it was found for the free proton. Subtraction method was applied to the deuteron target, than cross section was normalized on factor 2 (number of nucleons in the deuteron). Summing method was done taking into account 12 partial channels (these results are presented below in fig.9).

In fig.8 one can see a noticeable difference with the Armstrong data [4] for the deuteron target. Unfortunately, all the GRAAL beam measurements with the deuteron target were performed with the UV laser only, so the energy range was a little bit less than for the free proton runs but it is enough to conclude that F15 resonance is clearly seen in both cross sections (proton an neutron). Also, we would mention that absolute values would be significantly corrected as the reference ones in accordance with the new GRAAL data.
Fig.8
Open and full points correspond to

the summing and subtraction method,

respectively. Triangles represent to the

Armstrong data [3] (deuteron target).

Fig.9 shows the partial cross sections which were measured as contributions to the total photo-absorption cross section on the proton and neutron (deuteron target).

Fig.9.
Partial cross sections f meson

photo-production on bound proton

(open dots) and neutron (stars)

measured with deuteron target.

Free proton data are shown for

comparison (open dots).

Now it is interesting to compare results obtained by the summing method for bound proton and neutron (deuteron target). In fig.10 one can see that both cross sections are coincide in limits of 5% error bars in spite of the fact that partial cross section for proton and neutron are different. Probably, this indicates the existence of so called “door-way” states which are identical for the proton and neutron in spite of the difference in electric charge (terminology is taken from the nuclear giant resonance physics). Indeed, such hypothesis produced many questions immediately about quantum numbers etc. How the partial channels including non resonant contribution are follows? Nevertheless, it is difficult to assume that equality for total proton and neutron cross sections could be originated by chance.

Also, one can expect now with a high reliability that total photoabsorption cross section for the free neutron and for the free proton are identical because they are identical for the bound nucleons in the deuteron target. If we assume this statement we can compare the free neutron cross section which is equal to the free proton cross section (see fig.11).

Fig.10.

Total photo-absorption cross section

for the bound proton (open points) and

neutron (full points) obtained by the

summing method (deuteron target).

We would note that correction on Fermi motion is not applied for the deuteron target here. Armstrong did such correction obtaining the neutron cross section by subtraction of the proton cross section from the deuteron one. The Armstrong result for the neutron is not in a agreement with new GRAAL result (see fig.11) and this disagreement is large..

Fig.11.
Total photoabsorption for the

neutron. Points – GRAAL data.

Curve is the Armstrong approximated

result obtained from the deuteron cross

section by subtraction of the proton one.

Total error bars are presented.

CARBON
Total photo-absorption cross section for the ¹²C nuclei is shown in Fig.12. GRAAL results were obtained by the subtraction method only. Good agreement with earlier published results and the “universal curve” is seen. Error bars are not shown here but we would remember about 5% systematic accuracy for the GRAAL data for hydrogen and deuterium.

Fig.11.

Total photo-absorption cross section

for ¹²С. Crosses correspond to

GRAAL data, full and open points

taken from Bianchi [4] e. a. and

Mirazita [5] e. a.data, respectively.

“Universal curve” is marked by the

full line.

One can see that F15 resonance is smeared completely as compared with the deuteron target. This result was found earlier [ 4,5] but we would pay attention on very strong difference in absolute values (about 30%) for carbon and deuteron and proton cross sections(see fig.12). Evidently this can be explained by Fermi motion effects and indicate probably an in important role of intra nuclear interactions in the final state.

Fig.12.

Comparison of the total photo-absorption

cross sections for the proton (open points), deuteron

(full triangles) and carbon (full points).

ACTINIDE NUCLEI

New GRAAL results for the proton and neutron allow to revise the existing data for heavy actinide nuclei where some interesting effects have been evidenced earlier [12, 13]. Now we can specify the features looking in the fig.13 as following. In the resonance region the total photoabsorption cross section of fissioning actinide nuclei exceeds the “universal curve” on 20%,. This effect was found for the first time in Novosibirsk [12] and was confirmed with higher precision and larger energy range at JLAB [13]. It indicates probably the contribution of high order electrodynamics excitation mechanisms for heavy (high Z) nuclei. At E_ > 1 GeV one can see the opposite picture, namely the free nucleon cross section exceeds the “universal curve” and fissioning nuclei one more than in 30%.

Fig.13.

Total photoabsorption cross section for the

actinide nuclei (CEBAF data [13])is shown

by solid line. Dotted line corresponds to the

free proton (Armstrong [ 2 ]), experimental

points are the results for different nuclei

with A = 7 – 240 (universal curve).

This figure is taken from paper [ 13 ] ; the only difference is related to the dotted line. In paper [13 ] it was calculated taking into account the difference between proton and neutron photoabsorption cross section. Now, in accordance with new GRAAL results, there is no difference between proton and neutron, so the free nucleon cross section is used for comparison.

High experimental accuracy for actinide nuclei and reference nucleon cross sections allow to conclude that experimental data can not be explained in frame of the traditional knowledge. Namely, in Delta resonance region it is seen that actinide cross section exceeds the nucleon reference one in 20%, about. This means, probably, that photoabsorption of actinide nuclei is not exhausted by the meson production mechanism only, or there contribute significantly non linear quantum electrodynamics effects like inelastic e+e- pair production etc. At first, indication on low energy and momentum transfer nuclear excitations at intermediate photon energies was done in [ 12 ]. Now it can be studied in details in closed future basing on modern high quality photonuclear facilities.

As seen in fig.13, above the Delta resonance region, situation is contrary. Here the nucleon cross section exceeds the actinide one in 30%, about. This effect also can not be explained by the existing knowledge and contradicts with the well known vector dominance model At first, the photon energy of 1 GeV is too small to produce significantly vector meson (,  etc) to provide the shadowing due to harmonization of photons. At second, the A dependence would be seen but all nuclear cross section normalized on the number of nucleons are rge same in this energy region in accordance with the experiment.

So, new results open new fundamental questions which would be interesting to study.
CONCLUSIONS
Now, we summarize new results on the total photoabsorption cross sections which are important for future developments, including sum rules, nucleon modifications in nuclear media, new mechanisms of nuclear excitations at intermediate energies etc. They are the following:

- total photoabsorption cross sections for proton and neutron (deuteron target) are identical within 5%of systematic error bars. F15 resonance near 1 GeV is seen in both cross sections. This means, probably that the free neutron cross section is equal to the free proton one. Also this indicates existence of the door-way states in the first step of photon – nucleon interaction which is the sane for the proton and neutron.

- Carbon photoabsorption cross section normalized on the number of nucleons is in 30% less then the free nucleon one in studied energy region. Fermi correction is not sufficient to explain modification of cross sections in nuclear medium. In this sense special attention would be paid to the heavy (actinide) nuclei.

Author thanks

This work is supported by RFBR, grant 08-02-00648-а
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