On influence of p t (x Lab ) dependence in h-ah interactions on lateral features of most energetic particles in young EAS cores

On influence of p t (x Lab ) dependence in h-ah interactions on lateral features of most energetic particles in young EAS cores Rauf Mukhamedshin Institute for Nuclear Research, Moscow, Russia Masanobu Tamada Kinki University, Osaka, Japan Janusz Kempa Warsaw University of Technology

Introduction All the ground-based astrophysical experiments must simulate air cascade development. 2

Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air air nucleus interactions with different features were proposed. 3

Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models 4

Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition 5

Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition The most adequate model is not chosen yet 6

Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition The most adequate model is not chosen yet. Why? 7

Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition The most adequate model is not chosen yet. Why? Models are tuned on basis of sea-level EAS data 8

Introduction All the ground-based astrophysical experiments must simulate air cascade development. A number of models of hadron-air nucleus interactions with different features were proposed. CORSIKA includes QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 and EPOS 2.1, NEXUS and other models Different models give different PCR mass composition The most adequate model is not chosen yet. Why? Models are tuned on basis of sea-level EAS data high-mountain EAS data and X-ray X emulsion chamber (XREC) results are not taken into account 9

XREC experiments High-altitude PAMIR s X-ray emulsion chambers 10

XREC experiments X-ray Emulsion Chamber s s observables Spectra of single gamma-rays (γ/e( ± ) & hadrons (h) γ-h family = bundle of most high-energy correlated particles (γ,(, e ±, h) in young-eas core Particle energies E γ, E hγ > 4 TeV Energy & number of particles p per γ- h family Particle parameters Parameters of single γ-h families Parameters of fam families N fam Measurement accuracy ΣE tot =ΣE γ +ΣE hγ ~30 2000 000 TэВT n γ,n 4 x i, y i = coordinates R i = distance from center E i = single particle energy X 0, Y 0 = center coordinates R = ΣR i / n γ,h ; ER = Σ(E i R i )/ n γ,h Anisotropy parameters: λ n etc R = Σ R / N fam ; ER = ΣER/ N fam Anisotropy parameters, intensity, energy spectra of families x, y ~ 10 µm, θ < 3, 3 ϕ < 15 σ E /E ~ 0.2 0.3 Examples of γ -families 15.08.2011 R.Mukhamedshin,, Moscow, Russia 11

XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the PCR mass composition are decreased 15.08.2011 R.Mukhamedshin,, Moscow, Russia 12

XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the PCR mass composition are decreased γ-ray families are sensitive to the kinematic fragmentation range (x( Lab > 0.01 ) 15.08.2011 R.Mukhamedshin,, Moscow, Russia 13

XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the PCR mass composition are decreased γ-ray families are sensitive to the kinematic fragmentation range (x Lab >0.01 ) XREC γ-ray families are actually more model-sensitive than EAS 15.08.2011 R.Mukhamedshin,, Moscow, Russia 14

XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the vague PCR mass composition are decreased γ-ray families are sensitive to the kinematic fragmentation range (x Lab >0.01 ) XREC γ-ray families are actually more model-sensitive than EAS Data on γ-ray families can give some information being useful to test fragmentation-range range parameters of models 15.08.2011 R.Mukhamedshin,, Moscow, Russia 15

XREC experiments Important: Dominant part of γ-ray families is produced by PCR protons uncertainties related to the vague PCR mass composition are decreased γ-ray families are sensitive to the kinematic fragmentation range (x Lab >0.01 ) XREC γ-ray families are actually more model-sensitive than EAS Data on γ-ray families can give some information being useful to test fragmentation-range parameters of models The talk considers correlations between p t (x Lab ) behavior at x Lab 0.01 and lateral size of γ-ray families 15.08.2011 R.Mukhamedshin,, Moscow, Russia 16

XREC experiments Important: average energy of primary protons initiating γ-ray families with ΣE γ = 100 400 TeV is E 0 p 10 PeV = 101 16 ev at any more or less rational PCR composition 15.08.2011 R.Mukhamedshin,, Moscow, Russia 17

XREC experiments Important: average energy of primary protons initiating γ-ray families with ΣE γ = 100 400 TeV is E 0 p 10 PeV = 10 16 ev at any more or less rational PCR composition Assumption: main features of γ-families are determined by first interaction (as in the EAS case) 15.08.2011 R.Mukhamedshin,, Moscow, Russia 18

XREC experiments Important: average energy of primary protons initiating γ-ray families with ΣE γ = 100 400 TeV is E 0 p 10 PeV = 10 16 ev at any more or less rational PCR composition Assumption: main features of γ-families are determined by first interaction (as in the EAS case) Aim: Search for p-airp air-interaction interaction p t -dependent parameters P(p t ) giving most adequate correlation at E 0 =10 16 ev with R γ p of proton-initiated γ-ray families 15.08.2011 R.Mukhamedshin,, Moscow, Russia 19

XREC experiments Correlation between R γ and p t doubly averaged radius of γ-families, R γ,, is easily measured R γ is sensitive to variations of transversal momentum p t : the higher p t, the larger R γ mass of PCR particle: the larger mass (p He, e.g.), the larger R γ Double averaging of radius means that at first stage averaging is made over particles of each separate event. At the second stage, the required values are averaged over all events. 15.08.2011 R.Mukhamedshin,, Moscow, Russia 20

XREC experiments Correlation between R γ and p t doubly averaged radius of γ-families, R γ, is easily measured R γ is sensitive to variations of transversal momentum p t : the higher p t, the larger R γ mass of PCR particle: the larger mass (p He, e.g.), the larger R γ Double averaging of radius means that at first stage averaging is made over particles of each separate event. At the second stage, the required values are averaged over all events. 15.08.2011 R.Mukhamedshin,, Moscow, Russia 21

XREC experiments Correlation between R γ and p t doubly averaged radius of γ-families, R γ, is easily measured R γ is sensitive to variations of transversal momentum p t : the higher p t, the larger R γ mass of PCR particle: the larger mass (p He, e.g.),, the larger R γ Double averaging of radius means that at first stage averaging is made over particles of each separate event. At the second stage, the required values are averaged over all events. 15.08.2011 R.Mukhamedshin,, Moscow, Russia 22

XREC experiments Correlation between R γ and p t doubly averaged radius of γ-families, R γ, is easily measured R γ is sensitive to variations of transversal momentum p t : the higher p t, the larger R γ mass of PCR particle: the larger mass (p He, e.g.), the larger R γ Double averaging of radius means that at first stage averaging is made over particles of each separate event. At the second stage, the required values are averaged over all events. How strong and in what way does R γ depend on р t? 15.08.2011 R.Mukhamedshin,, Moscow, Russia 23

p t -dependent parameters P(p t ) of p-air interactions 1.5 pt, GeV/c 1.0 p-air charged E 0 =10 16 ev p t (X Lab ) dependence (X Lab QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ X Lab E/E 0 the higher E, E the larger XLab 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 X Lab Contribution of large-x Lab particles into family s s transverse features is higher than that of low-x Lab particles 15.08.2011 R.Mukhamedshin,, Moscow, Russia 24

p t -dependent parameters P(p t ) of p-air interactions 1.5 pt, GeV/c 1.0 p-air charged E 0 =10 16 ev p t (X Lab ) dependence (X Lab QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ X Lab E/E 0 the higher E, E the larger XLab 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 X Lab Contribution of large-x Lab particles into family s transverse features is higher than that of low-x Lab particles Search for desired parameters as X Lab - and X 2 Lab -weighted p t - dependent parameters 15.08.2011 R.Mukhamedshin,, Moscow, Russia 25

p t -dependent parameters P(p t ) of p-air interactions P 1 (p t ) P 2 (p t ) P 3 (p t ) P 4 (p t ) P 1 (p t ) = standard p t P 2 (p t ), P 4 (p t ), P 6 (p t ) = x Lab -weighted parameters P 3 (p t ), P 5 (p t ), P 7 (p t ) = x 2 Lab -weighted parameters P 4 (p t ) and P 5 (p t )= partly «truncated» parameters P 5 (p t ) X min X Lab X max X min X Lab X max P 6 (p t ) P 7 (p t ) P 6 (p t ) and P 7 (p t )= completely «truncated» parameters 26

Correlation of p t - dependent parameters and γ-ray families R γ p R γ p is simulated for PCR proton spectrum 27

Correlation of p t - dependent parameters and γ-ray families R γ p R γ p is simulated for PCR proton spectrum Models are tested as follows QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 (CORSIKA package) 28

Correlation of p t - dependent parameters and γ-ray families R γ p R γ p is simulated for PCR proton spectrum Models are tested as follows QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 (CORSIKA package) MC0 (R.M., ~1990) 29

Correlation of p t - dependent parameters and γ-ray families R γ p R γ p is simulated for PCR proton spectrum Models are tested as follows QGSJET 01, QGSJET II, SYBILL 2.1, EPOS 1.99 (CORSIKA package) MC0 (R.M., ~1990) FANSY 1.0 и FANSY 1.01 (R.M., 2006) are designed to analyze problems of γ-ray family alignment differs only in one parameter: p t (x Lab ) dependence at ~0.01 < x Lab < 0.5 and show clear influence of this x Lab range on R γ 30

Correlation of p t - dependent parameters and γ-ray families R γ p Search for correlations between R γ values and p t -dependent x Lab - & x 2 Lab -weighted parameters P(p t ) in whole x Lab interval at 0 X Lab 1 (all particles are included) 31

Correlation of p t - dependent parameters and γ-ray families R γ p Search for correlations between R γ values and p t -dependent x Lab - & x 2 Lab -weighted parameters P(p t ) in whole x Lab interval at 0 X Lab 1(all particles are included) in truncated x Lab intervals at X min X Lab X max (no low- and high-energy particles) max #) #) X min min = 0.01, 0.02, 0.03, 0.04, 0.05 (no low-energy particles) X max = 0.20, 0.25, 0.30, 0.40, 0.50 (no most energetic particle) 32

Correlation of p t - dependent parameters and γ-ray families R γ p Search for correlations between R γ values and p t -dependent x Lab - & x 2 Lab -weighted parameters P(p t ) in whole x Lab interval at 0 X Lab 1(all particles are included) in truncated x Lab intervals at X min X Lab X #) max (no low- and high-energy particles) as Y = m X m X + const $) #) X min = 0.01, 0.02, 0.03, 0.04, 0.05 (no low-energy particles) X max = 0.20, 0.25, 0.30, 0.40, 0.50 (no most energetic particle) $) X = P i (p t )/P FANSY 1.01 (p t ), Y = R= γ / R γ FANSY 1.01 33

Correlation of p t - dependent parameters and γ-ray families R γ p Search for correlations between R γ values and p t -dependent x Lab - & x 2 Lab -weighted parameters P(p t ) in whole x Lab interval at 0 X Lab 1(all particles are included) in truncated x Lab intervals at X min X Lab X #) max (no low- and high-energy particles) as Y = m X + const $) with m 1.25 (found by least-squares squares method) at r 2 0.96 (determinancy coefficient) ) (for all the models excluding QGSJET II) #) X min = 0.01, 0.02, 0.03, 0.04, 0.05 (no low-energy particles) X max = 0.20, 0.25, 0.30, 0.40, 0.50 (no most energetic particle) $) X = P i (p t )/P FANSY 1.01 (p t ), Y = R γ / R γ FANSY 1.01 ) Ideal case: m = 1 at r 2 = 1 34

Correlation of p t - dependent parameters and γ-ray families R γ p Definitions: m m All for all models m mq1sefmf for all models excluding QGSJET II 35

Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 1 (p t ) 20 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY 1.01 0 X Lab 1 m All = 1.99 ± 1.26 r 2 All= 0.33 10 0.3 0.4 0.5 0.6 0.7 p0.8 t, GeV/c 0.9 no correlation of R γ & p t (small r 2 ) scatter in R γ values is much more than that in p t values 36

Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 2 (p t ) 20 15 10 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY 1.01 0.3 0.4 0.5 0.6 0.7 p0.8 t x, GeV/c 0.9 0 X Lab 1 m All = 2.03 ± 1.05 r 2 All= 0.43 25 P 3 (p t ) 20 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY 1.01 10 0.3 0.4 0.5 0.6 0.7 p t 0.8 x 2, GeV/c 0.9 m All = 0.05 ± 0.97 r 2 All= 0.001 no correlation of R γ & P 2,3 (p t ) (r 2 is extremely small); scatter in R γ and P 3 ( p t ) values is large 37

Correlation of p t - dependent parameters and γ-ray families R γ p 25 a) P 4 (p t ) 20 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY 1.01 0 X Lab 0.5 m All = 0.62 ± 0.29 r 2 All= 0.47 10 0.3 0.4 0.5 0.6 0.7 p t x(<0.5) 0.8, GeV/c 0.9 25 P 5 (p t ) 20 15 10 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 MC0 FANSY 1.01 0.3 0.4 0.5 0.6 0.7 p t x 2 (<0.5), 0.8 GeV/c 0.9 m All = 0.72 ± 0.96 r 2 All= 0.10 no correlation between R γ & P 4,5 (p t ) (r 2 is small); scatter in R γ and P 4,5 (p t values is too large 38

Correlation of p t - dependent parameters and γ-ray families R γ p No real correlation between R γ and p t -dependent parameters P 1 (p t ) P 5 (p t ) Analysis of «truncated» parameters for different x min and x max There are different results for «truncated» intervals with different x min and x max Best results are shown below 39

Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 6 (p t ) 20 15 25 20 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch 0.4 0.5 0.6 0.7 p 0.8 t x tr.06-.25 0.9,GeV/c 1 0.06 X Lab 0.25 m Q1SEFMF= 1.24 ± 0.11 r 2 Q1SEFMF= 0.97 0.06 X Lab 0.20 m Q1SEFMF= 1.17 ± 0.10 r 2 Q1SEFMF= 0.97 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 0.3 15.08.2011 0.4 0.5 0.6 0.7 p t x tr.06-.2 0.8,GeV/c 0.9 ch R.Mukhamedshin, Moscow, Russia 40

Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 6 (p t ) 20 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch 0.3 0.4 0.5 0.6 0.7 p t x tr.07-.2 0.8,GeV/c 0.9 0.07 X Lab 0.20 m Q1SEFMF= 1.14 ± 0.09 r 2 Q1SEFMF= 0.97 41

Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 7 (p (7) t ) 20 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch 0.3 0.4 0.5 0.6 p 0.7 t x 2 tr.02-.2,gev/c 0.8 0.9 0.02 X Lab 0.20 m Q1SEFMF = 1.23 ± 0.12 r 2 Q1SEFMF= 0.96 25 20 15 a) QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 0.3 0.4 0.5 0.6 p 0.7 t x 2 tr.03-.2,gev/c 0.8 0.9 0.03 X Lab 0.20 m Q1SEFMF = 1.20 ± 0.11 r 2 Q1SEFMF= 0.97 ch 42

Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 7 (p t ) 20 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch 0.3 0.4 0.5 0.6 p 0.7 t x 2 tr.04-.2,gev/c 0.8 0.9 0.04 X Lab 0.20 m Q1SEFMF = 1.19 ± 0.10 r 2 Q1SEFMF= 0.97 25 20 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 0.3 0.4 0.5 0.6 p 0.7 t x 2 tr.05-.2,gev/c 0.8 0.9 ch 0.05 X Lab 0.20 m Q1SEFMF = 1.17 ± 0.09 r 2 Q1SEFMF= 0.97 43

Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 7 (p t ) 20 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch 0.3 0.4 0.5 0.6 p 0.7 t x 2 tr.06-.2,gev/c 0.8 0.9 0.06 X Lab 0.20 m Q1SEFMF = 1.15 ± 0.10 r 2 Q1SEFMF= 0.97 Clear linear dependence of R γ p on x Lab - and x 2 Lab -weighted «truncated» parameters (6) & (7) for QGSJET 01, EPOS 1.99, SYBILL 2.1, FANSY 1.0, MC0, FANSY 1.01 at ~0.02 02 < X Lab < ~0.25 QGSJET II deviates from general trend 44

Correlation of p t - dependent parameters and γ-ray families R γ p 25 P 7 (p t ) 20 15 QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 QGSJ 10 ch 0.3 0.4 0.5 0.6 p 0.7 t x 2 tr.06-.2,gev/c 0.8 0.9 0.06 X Lab 0.20 m Q1SEFMF = 1.15 ± 0.10 r 2 Q1SEFMF= 0.97 Clear linear dependence of R γ p on x Lab - and x 2 Lab -weighted «truncated» parameters (6) & (7) for QGSJET 01, EPOS 1.99, SYBILL 2.1, FANSY 1.0, MC0, FANSY 1.01 at ~0.02 < X Lab < ~0.25 QGSJET II deviates from general trend 45

Experiment and simulation 35 30 25 20 15 PAMIR experiment data and simulation results acceptable R γ too large R γ Pamir QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 0.4 0.5 0.6 0.7 0.8 p t x tr.05-.5 0.9, GeV/c 1 сh Simulation: complex composition of PCR spectrum (p,(, He, Fe) with XREC response 0.05 X Lab 0.5 P 6 (p t ) FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data 46

Experiment and simulation 35 30 25 20 15 PAMIR experiment data and simulation results acceptable R γ too large R γ Pamir QGSJET 01 QGSJET II SYBILL 2.1 EPOS 1.99 FANSY 1.0 QGSJ MC0 FANSY 1.01 0.4 0.5 0.6 0.7 0.8 p t x tr.05-.5 0.9, GeV/c 1 сh Simulation: complex composition of PCR spectrum (p,(, He, Fe) with XREC response 0.05 X Lab 0.5 P 6 (p t ) FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 contradict to «Pamir» data 47

Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data 48

Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 results contradict to «Pamir» data 49

Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 results contradict to «Pamir» data All models (excluding QGSJET II) ) show understandable dependence of γ-ray family size on p t -dependent parameters by P 6 (p t ) and P 7 (p t ) at X Lab 0.02 0.25 50

Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 results contradict to «Pamir» data All models (excluding QGSJET II) show understandable dependence of γ-ray family size on p t -dependent parameters by P 6 (p t ) and P 7 (p t )at X Lab 0.02 0.25 QGSJET II shows deviation from general trend 51

Conclusion FANSY 1.01, MC0, QGSJET 01 & EPOS 1.99 results are more or less close to «Pamir» experimental data QGSJET II, SYBILL 2.1 & FANSY 1.0 results contradict to «Pamir» data All models (excluding QGSJET II) show understandable dependence of γ-ray family size on p t -dependent parameters by P 6 (p t ) and P 7 (p t )at X Lab 0.02 0.25 QGSJET II shows deviation from general trend The wider EAS core, the stronger imitation of more heavy nuclei: p He, p He Li etc. QGSJET II, SYBILL 2.1 & FANSY 1.0 can imitate more heavy nuclei 52

Conclusion p t is not related to transversal size of γ-ray families 53

Conclusion p t is not related to transversal size of γ-ray families Just p t (x Lab ) dependence at X Lab 0.02 0.25 determines lateral divergence of beam of young EAS-core high-energy particles at initial stage 54

Conclusion p t is not related to transversal size of γ-ray families Just p t (x Lab ) dependence at X Lab 0.02 0.25 determines lateral divergence of beam of young EAS-core high-energy particles at initial stage Optimum p t (X Lab ) 0.5 GeV/c at X Lab 0.02 0.25 (E 0 10 16 ev) 55

Conclusion p t is not related to transversal size of γ-ray families Just p t (x Lab ) dependence at X Lab 0.02 0.25 determines lateral divergence of beam of young EAS-core high-energy particles at initial stage Optimum p t (X Lab ) 0.5 GeV/c at X Lab 0.02 0.25 (E 0 10 16 ev) X Lab - and/or X 2 Lab -weighted p t -dependent parameters defined in «truncated» x Lab ranges seem to be most adequate 56

Conclusion p t is not related to transversal size of γ-ray families Just p t (x Lab ) dependence at X Lab 0.02 0.25 determines lateral divergence of beam of young EAS-core high-energy particles at initial stage Optimum p t (X Lab ) 0.5 GeV/c at X Lab 0.02 0.25 (E 0 10 16 ev) X Lab - and/or X 2 Lab-weighted p t -dependent parameters defined in «truncated» x Lab ranges seem to be most adequate XREC high-altitude high-threshold data give a good chance to test models of hadron-nucleus nucleus interactions at superhigh energies 57