Albedo from cascades induced in iron by high energy gamma quanta were Monte Carlo simulated. Thereafter the albedo electromagnetic component from proton induced cascades were calculated analytically. The calculations showed that the albedo electromagnetic component increases more rapidly than the nuclear active component and will dominate at sufficiently high energies

Golynskaya, R. M.

Hein, L. A.

Plyasheshnikov, A. V.

Vorobyev, K. V.

English

NASA Technical Reports Server

380 HE 3.5.-.11
THE ELECTRONAGNETIC COMPONENT OF ALBEDO FROM
SUPERHIGH ENERGY CASCADES IN DENSE MEDIA ....
Golymskaya R.M., Hein L.A., Plyasheshnikov A.V., Vorobyev K.V.
Institute of NuclearPhysics, Moscow State University,
Moscow 119899, USSR ....
Albedo from cascades induced in iron byhigh-energy gam-
ma-quanta were Monte-Carlo simulated. Thereafter the albedo
electromagnetic component fromprQ_Dn'inducedcascades were
calculated analytically. The calculations showed that _ the
albedo electromagnetic componentlincreasesmore rapidly than
the nuclear-active component and will dominate at sufficient-
ly high energies.
I. Introduction. When a calorimetric installation is used
to detec_high energy particles esSential methodlCaldiffi-
culties are caused by albedo from absorber. Experlmentshows
that at energies of several TeV thenuclear-aCtive component
contributes the most into the albedo effect, and the depen-
dence of albedo onprimary energy is rather weak, i.e. loga-
rithmic. Calculations of the albedofrom electron-photon
cascades so far performed toenergies of 100 GeVshow that
the albedo electromagnetic component increases more rapidly,
according to a power law. It indicates that further rapid
increase being present, the electromagnetic component will
dominate and provide a rapid increase with energy of the
overall albedo flux.
A semi-analytical Monte-Carlomethod described in /I/
allowed calculations of albedO from the electronTphoton
showers to highest energies of interest now, In/2/, the re-
sults for lead have been reported. Wepresent here the re-
sults on t_e albedo from iron. The results obtained were
used to calculate the electromagnetic component of albedo
froma primary proton-induced caScade. Since, according to
the calculations, the albedo electron flux is 2-3orders _
less%hanthe gamma-quantum flux, results on the gamma-quan T
rum albedo only are presented. ....
2. Results for primary Eamma-quantum. Fig.1 shows the @nergy
dep_hdence of the albedo gamma-quantum flux for three angles
of incidence of a primary gamma-quantum, One can see that
this dependence is, with a high accuracy, a pure power law
• Fig.2 presents the albedo gamma-quantum fluxversus cas-
cede production depth. The results are for twoprimary ener-
gies and two incidences(producti?n depth is measured along
the normal to the entrance plane). It can be noted that i)
the exponent N_(t)_ e-_t provides a good description; ii)
the rate 6f albedo attenuation somewhat increases wlth
energy, e.g.j u (3 GeV)=.92, /_(I03 GeV)=.71, ....
iii) the results for various incidence angles demon_ra_ea
very high similarity. In Fig.3 the dependence of the mean
https://ntrs.nasa.gov/search.jsp?R=19850027635 2020-03-20T17:20:18+00:00Z
381 HE 3.5-11
energy of albedogamma-quamtaontheprimarygamma-quant_un
energy is shown for three inctdenceaz_Ies. The-mean energy
can be seen to somewhat increasewith_p_imaryenergy.
InPig,4, the ener_Spec_rum of' albedogamma-quanta_is
presented for a primry energyof 103 GeVand-an0rmal inCi-
dence. Itcanbe noted that about90%of the photons are
confined within the energy interval tolMeV,
Fig.5 showstherme radius versus primaryenergy, We pre -
sent the results for a normal inCidenceand-two production
depths t=O and t=2, Withan increase of priory energy the
area of albedo emissionfirstapparentlybr0adens, but at
higher energies one could supposesOme narroWing. In Pig.6,
the albedo gamma-quanta radial distribution is shown for
energy 3 GeV and anormal incidence. .............
The angular distributlonof albedo ganmm-quanta is prac-
tically izotropic in the an_lar range from30o t0 70@, the
meancoslne being equal to_=.7 and independent of both
energy and shower incidence angle, ....
3, Discussionofresu!tsforprimarY ga_-qugntum. We make
here an attempt to obtain the general features of the albedo
behaviour by constructing a rather simple modelof its pro-
duotion and applying the results of cascade theury. It proV-
ed to be feasible to deduce a simple formula which represents
a good reflection of the dependence of albedo on energy and
incidence angle _,C_,ti__C_S_-_t./._AC. 0 ....
where _ Is the critical energy,'_i(s) being the known cas-
cade theory function, and s is found from the equation
This formula canbethoUghtto be approximating over E,
t, and oose, i.e. the Values of N andj_ being once taken
from calculations for one energy, the albedo values can be
found for all energiesand incidenceg. The agreement with
calculations is demonstrated b_the follow_gcomparison: if
the value^of _ at E=3 GeV is taken, N _E. '°/Calculation_^
_ield E.4_/ is obtained6_or 8 normal incld@nce and N_E o_/calculated value is E 3/ forthe incidence angle _se=,6.
4. Prima roton. _he above discUSsed features of the beha-
viour O-falbedo---fromaprimarygamma-quant_unalloWed analyti-
cal going over to the albedo f_m a primary proton. The ex-
pression for the mean albedo value reads _
in the h,lA=h_+x _eaction, whereah;, hadro_ iseither nuc-
leon or _ion,_ibeing the nucleon o_3pionlnteraction
length. The abo?e expression showsthat the contribution of
the secondary interactions £sabout 25%, i.e. the albedo is
mainly determined by the flrstinteractioncharacteristics
and primary proton path, Only the variationof these charac-
terlsticsand _withenergyproVides a weakenergydepen _
dence of the expression in the figure brackets, i.e. theal -
bedo energy dependence maintains to be apower lawwith abo-
ut the same exponent S. _or %he inclusive distributions and .......
LHE 3._-Ii
382
interaction lengths corresponding to the modern accelerator
data the calculated values for the coefficient of transition
from a primary _amms-quantum to a proton/expression in the
figure brackets/ are the following
5.Conclusion. The gamma-quantum albedo indicates a rapid po-
wer law increase of N-~ES, where s _0°5_ to the highest
energies for which the calculation was performed. The mean
energy of albedo gamma-quant8 slightly _:v_eases with pri-
mary energy, the lateral distribution becomes broader, and
the angular distribution maintains its shape, being close
to the izotropic one. We should notice finally_our simula-
tions do not incorporate the Landau-_Pomeranchuk effect. The
effect should reveal itself _n Pe at energies >10J*eV, i.e.
providing far deeper cascade development the albedo should
sharply decrease with energy (see /2/).
References .
I. Plyasheshnikov A.V., Vorobyev K.V+ _ 1981_ Proc. 17th
ICRC, 5, 206.
2. Plyasheshnikov A.V., Vorobyev K+V., 1983, Proc. 18th
ICRC, 11, 73.
0.63 :i r+-+ ........ +.......-'- ....
° / _ -_0"
_,n_'403 _. _
/e _/-.o _" o COSe:_
/ .-_ o" • C_,_:O°G+ _& +'
IA '_0/ "_0 ...... ++'-........._........._ J -
_o _o_ _os to_ io_ _oo t
Pig+1.The dependence of Fig®2.The albedo atten_ation
the albedo flux on the with the shift of the cascade
energy of the primary generation point°
gamma-quantum. Lines are
for the power approxima- Crosses are for primar;y ,nergy
tion. _ = 3 GeV;
circles _+ 103 GeV+
HE 3.5 ii
883
I
IK
_.o t / i
0.5 °_" t :_
i
l_ig.4.The energy spectra
of the albedo quanta.
, , , ' ' ' ,,,The primary quantum ener-
: iO i tO i ._0i _.0_' iO _ iO G gy is '103 GeV, normal
E (G_v) incidence
Fig.3.Mean energy of the albedo
quanta Versus the primaru quan-
tum energy
0 t=O
! '
' ' ' ' b ' o e_ I0iO i _0t t0 _ _0s d s dO6 )(Gcv)
Pig.5.The albedo RNS radius Fig.6.The albedo quanta
vs primary energy, for two radlaldistribution.
depths of the cascade genera- Primary energy is 3 GeV,
tion, normal incidence normal incidence


The electromagnetic component of albedo from superhigh energy cascades in dense media

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