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GAMMA Experiment

GAMMA Experiment. Mutually compensative pseudo solutions of the primary energy spectra in the knee region. Samvel Ter-Antonyan. Yerevan Physics Institute. Astroparticle Physics 28 , 3 (2007) 321. EAS Inverse Problem. Detected EAS size spectra X = d 2 F/dN e dN m.

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GAMMA Experiment

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  1. GAMMA Experiment Mutually compensative pseudo solutions of the primary energy spectra in the knee region Samvel Ter-Antonyan Yerevan Physics Institute Astroparticle Physics 28, 3 (2007) 321

  2. EAS Inverse Problem Detected EAS size spectra X=d2F/dNedNm Unknown primary energy spectra; A  H, He,…,Fe Kernel function {A,E}  X The problem of uniqueness Let NA=1 andf(E)is a solution. Then f(E)+g(E) is also a solution if onlyW(E,X) g(E) dE << F(X) g(E) - oscillating functions

  3. Problem of uniqueness for NA>1 and Mutually compensative pseudo solutions forNA > 1 the pseudo solutions fA(E)+gA(E) exist if only WA(E,X) gA(E) dE =0(F) A - WA(E,X) gA(E) dE =  WA(E,X) gA(E) dE + 0(F) k mk NA nc=C NA number of possible combinations of pseudo functions: j j=2 at NA=5, nc=26

  4. How can we find the domains of pseudo solutions ? WA(E,X) gA(E) dE =0(F) A 1.In general, it is an open question for mathematicians. 2.Our approach: a) Computationof WA(E,X) b) for given fA(E)   F(X) c) Quest for | gA(,, | E) | 0from Using 2-minimization

  5. Simulation of KASCADE EAS spectra Reconstructed EAS size spectra EAS spectra atobservation level 2D Log-normal probability density funct. CORSIKA, NKG, SIBYLL2.1 e(A,E)=<Ln(Ne)> (A,E)=<Ln(N)> e(A,E), (A,E) (Ne,N|A,E) E  1, 3.16, 10, 31.6, 100 PeV; A  p,He,O,Fe n  5000, 3000, 2000, 1500, 1000 2/n.d.f.  0.4-1.4;2/n.d.f. <1.2 (E|LnNe,LnN)=0.97; (LnA|LnNe,LnN)=0.71

  6. Quest for pseudo solutions Monte-Carlo method Abundance of nuclei: 0.35; 0.4; 0.15; 0.1 WA(E,X) gA(E) dE = 0(F) A i=1,…60; j=1,…45 Ne,min=4103, N,min =6.4 104

  7. Examples of pseudo solutions, 1 WA(E,X) gA(E) dE = 0(F) N=7105, Em=1 PeV, 2=1.08

  8. Examples of pseudo solutions, 2 WA(E,X) gA(E) dE = 0(F) N=7105, Em=1 PeV, 2=1.1

  9. Examples of pseudo solutions, 3 WA(E,X) gA(E) dE = 0(F) P=3 PeV =1 at E < A =5 at E > A N=7106 ; 2=2.01 N=7105 ;2=0.25

  10. Domain of pseudo solutions and KASCADE spectral errors

  11. Examples of pseudo solutions, 4: Light and Heavy components  WLight(E,X) gLight(E) dE = WHeavy(E,X) gHeavy(E) dE 0(F) A p, He ( Light ) A O, Fe ( Heavy ) N=7105, Em=1 PeV, 2=1.0

  12. CONCLUSION GAMMA Experiment • The results show that the pseudo solutions with mutually compensative effects exist and belong to all families – linear, non-linear and even singular in logarithmic scale. • The mutually compensative pseudo solutions is practically impossible to avoid at NA>1. The significance of the pseudo solutions in mostcases exceeds the significance of the evaluatedprimary energyspectra. • All-particle energy spectrum are indifferent toward the pseudo solutions of elemental spectra. To decrease the contributions of the mutually compensative pseudo solutions one may apply a parameterization of EAS inverse problem using a priori (expected from theories)known primary energy spectra with a set of free spectralparameters. Just this approach was used in the GAMMA experiment.

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