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Comparative Energy Dependence of Proton and Pion Degradation

in Diamond1


I.Lazanu and S.Lazanu+


University of Bucharest, Faculty of Physics, POBox MG-11, Bucharest, Romania
+National Institute of Materials Physics, POBox MG-7, Bucharest-Magurele, Romania




Abstract

A comparative theoretical study of the damages produced by protons and pions, in the energy
range 50 MeV  50 GeV, in diamond, is presented. The concentration of primary defects (CPD)
induced by hadron irradiation is used to describe material degradation. The CPD has very different
behaviours for protons and pions: the proton degradation is important at low energies and is higher
than the pion one in the whole energy range investigated, with the exception of the 33 resonance
region, where a large maximum of the degradation exists for pions.

In comparison with silicon, the most investigated and the most utilised semiconductor material
for detectors, diamond theoretically proves to be one order of magnitude more resistant both to
proton and to pion irradiation.





PACS codes: 61.80.Az; 61.82.-d


Keywords: Diamond; Detectors; Radiation damage; Proton; Pion






1 accepted for publication in Nuclear Instruments and Methods in Physics Research A (1999)

1


Comparative Energy Dependence of Proton and Pion Degradation
in Diamond

I.Lazanu and S.Lazanu*



1. Introduction

Diamond shown promising properties [1] for its use as a very fast position sensitive detector
for experiments in the highest radiation levels at the large hadron collider.
Up to now, the radiation resistance of diamond detectors has been demonstrated for photons
and electrons, and experimental studies for pion, proton and neutron fields are in progress [2].
The theoretical calculations of diamond damage by + and - mesons in the 33 resonance
energy range have been reported in reference [3], and the extension up to 50 GeV pion kinetic
energy in reference [4], respectively.
For proton irradiation, some results exist for silicon [5,6,7], GaAs [8,9], InP [9], Ge [10], and
also for diamond [11].
In this work, the theoretical estimation of the degradation of diamond in proton fields is
presented comparatively with the similar calculations for pions, in the energy range 50 MeV - 50
GeV.
The physical quantity relevant to characterise the material degradation in radiation fields is the
concentration of primary defects (CPD) produced by hadrons in the diamond lattice. For
monoelement materials, the CPD is proportional to the non-ionising energy loss (NIEL), historically
used to characterise the lattice degradation in particle fields. The CPD better correlates the damages
produced in different materials at the same kinetic energy of the incident hadron.


2. Model calculations for the degradation

The CPD has been calculated as:

(
n E )
CPD = (
E)
with:

( N d
n E ) = (
E)d i

(LERi)
2E
i d
d k



where: E is the kinetic energy of the incident hadron; N - atomic density of the target material; Ed -
threshold energy for displacements in the lattice; (E) - the pion fluence in the primary beam; ERi -
recoil energy of the residual nucleus form the interaction mechanism i, from the interaction k (k=
elastic, absorption and inelastic if the hadron is a pion, and k = elastic and inelastic if it is a nucleon,
respectively), having a d / d - differential cross section; L(E
i Ri) - Lindhard factor describing the
partition between ionisation and displacements. The energy channelled into displacements, for each
recoil (characterised by its charge and mass number), and for each energy, has been taken from
reference [3].

The contribution of each channel to the total concentration of defects depends on the
probability of interaction and on the kinematics of the process, reflected in the recoil energy of the
residual nucleus.


2


In an elastic scattering process of interaction, symbolically represented by:


h + Nucleus h + Nucleus

the hadron does not excite the target nucleus.

The inelastic hadron - nucleus scattering includes all reactions of the type:

h + Nucleus a1 + a2 + ... + an + Residual Nucleus

where the reaction products a1, a2,, ..., an can be pion, proton, neutron, deuteron, other particles or
light nuclei.

When the kinetic energy of the incident particle exceeds the threshold energy of 140 MeV,
secondary pions could also be produced.

If the inelastic process is produced by nucleons, the identity of the incoming projectile is lost,
and the creation of the secondary particles is associated with energy exchanges which are of the
order of MeV or larger.

For pion - nucleus processes, a characteristic interaction is possible: the absorption, the
process by which the pion disappear as a real particle within the nucleus. In these calculations, the
absorption is considered separately. Absorption on a single nucleon is kinematically prohibited, and
the simplest process is on two nucleons. Absorption on more nucleons is also possible.

The interaction of pions with nucleons and nuclei at kinetic energies comparable to the pion
rest mass is dominated by the delta resonance production, with spin and isospin 3/2. At higher
energies, other resonances could be produced, but with much less importance, and the pion
behaviour does not differ significantly by that of other hadrons.

The energy dependence of cross sections, for proton and pion interactions with the carbon
nucleus, present very different behaviours: the proton - nucleus cross section decreases with the
increase of the projectile energy, then has a minimum at relatively low energies, followed by a
smooth increase, while the pion - nucleus cross sections present for all processes a large maximum,
at about 160 MeV, and which reflects the resonant structure of the interaction.

Since the inelastic and absorption collisions are considerably more complex than elastic
scattering, special reaction models must be developed for their analysis.

For the concrete calculations, the available experimental data have been used, and also
different phenomenological approximations.

In Figures 1 and 2, the energy dependencies of the proton - carbon and pion - carbon cross
sections are shown, respectively.

For proton - carbon interactions, the elastic cross sections are from reference [12], the inelastic
ones (data) from reference [13], and the continuous curve represent the parametrisation from
reference [14].

For positive pions - carbon interactions, the data are from reference [15] for the elastic cross
sections, from [16,17,18] for reaction cross sections, and from [17,19] for absorption, respectively.
The continuous curves are best fits of the data, and have been used to extrapolate / interpolate the
values of the cross sections at energies of interest. The inelastic cross sections are obtained as
differences between reaction and absorption ones, and are represented as dashed lines in Fig. 2.

Elastic and Rutherford contributions to the CPD have been treated together, and the existent
data for differential cross sections have been extrapolated at other energies in the frame a simple
optical model.



3


The main difficulty is related to the inelastic interaction, due to the multitude of open channels,
corresponding to possible final states. Some simplifying assumptions concerning this interactions
have been made. Both for pions and protons, the knock-out interaction has been considered
separately, using the data from [17,20,21] for pions, and from [12] for protons, respectively. The
rest of the channels have been considered as equivalent to the interaction on an effective number of
nucleons. Particle generation has been neglected.

In the case of pions, in the energy range of the delta resonance, another important contribution
is given by absorption; above 1 GeV this process is negligible. Details about the contributions of
different absorption mechanisms could be found in [2].


3. Results and interpretation

The results obtained for the energy dependence of the CPD (and NIEL) produced by protons
and pions are represented on the same graph in Figure 3.

The CPD for protons present an abrupt decrease at low energies, followed by a minimum and,
at higher energies, by a plateau. For pions, there exists a large maximum in the region of the 33
resonance. The minimum for proton degradation and respectively the maximum for pion one are in
the same energetic range.

For both protons and pions, the energy dependence of the CPD follows mainly the energy
dependence of the cross sections. The value of CPD at minimum for protons and the corresponding
maximum for pions are in the ratio of approximately 0.47, while at the highest energies where
calculations were performed, the ratio is around 1.95.

In Figure 4, the ratio of CPD produced by protons and pions in diamond (continuous line) is
represented on the same graph with the corresponding ratio of the proton and pion total cross
sections in carbon (dashed line). The two curves have a similar shape: a decreasing dependence from
low energies up to the region corresponding to the delta resonance in the pion interaction, and a
smooth energy dependence at higher energies with a minimum around 1 GeV; at high energies, the
ratio of the CPD for protons and pions in diamond is proportional to the corresponding ratio of the
total cross sections. This behaviour is in agreement with the estimations of Tang [22] on the
distribution of secondary fragments resulting from the interaction.

For comparison, similar curves have been represented for silicon in Figure 5. There exist some
NIEL calculations for protons, reported in references [5] and [6], and for pions: [4,5] and [23]. For
the pion calculations, the results of Van Ginneken are accurate especially at high energies, because
the resonant behaviour has been considered only by an increase of the cross sections and not as a
specific mechanism of interaction. The Huhtinen and Aarnio calculations for pions are simple
estimations, obtained using a scaling procedure of the proton NIEL results. At low energies, the
ratio of the two degradations is estimated from references [6] and [4] (continuous line) and from
reference [5] (continuous line for the energies where the results are accurate and dash - dotted line
for the rest). The ratio of the total cross sections is represented with dashed line. The results suggest
the similarity between diamond and silicon from the point of view of the ratio of degradations
produced by protons and pions, and suggest also the possibility of applying a scaling procedure at
energies higher then the delta resonance.

As absolute values, from the comparison of the present results for proton and pion degradation
of diamond with the corresponding ones in silicon, the diamond proves to be one order of magnitude
more resistant both to proton and to pion irradiation.





4


4. Summary

A comparative theoretical study of the damages produced by protons and pions in diamond has
been done in the energy range between 50 MeV and 50 GeV. The concentration of primary defects
in the diamond lattice was used to describe the radiation effects.

The CPD produced by protons and pions have very different energy dependencies. The CPD
for protons presents an abrupt decrease at low energies, followed by a minimum and, at higher
energies, by a plateau. For pions, there exists a large maximum in the region of the 33 resonance.
The minimum for proton degradation and respectively the maximum for pion one are in the same
energetic range. For both protons and pions, the energy dependence of the CPD follows mainly the
energy dependence of the total cross sections.

In comparison with silicon, the most investigated and the most used semiconductor material
for detectors, diamond theoretically proves to be one order of magnitude more resistant to proton
and pion irradiation. Experimental studies are necessary to confirm these results.



References

1. A.Paoletti and A.Tucciatore, eds. "The physics of diamond"; Proc. Int. School of Physics
"Enrico Fermi", Course CXXXV, IOS Press, Amsterdam, Oxford, Tokyo, Washington (1997).

2. RD 42 Collaboration, see, e.g. D.Meier et al., CERN-EP/98-79 and W.Adam et al.,
CERN/LHCC 98-20 (1998).

3. I.Lazanu, S.Lazanu, E.Borchi and M.Bruzzi, Nucl. Instr. Meth. Phys. Res. A 406 (1998) 259.

4. S.Lazanu and I.Lazanu, Nucl. Instr. Meth. Phys. Res. A 419 (1998) 570.

5. A.Van Ginneken, Preprint Fermi National Accelerator Laboratory FN-522 (1989).

6. E.Burke, IEEE Trans. Nucl. Sci., NS-33 (1986) 1276.

7. G.P.Summers, E.A.Burke, C.J.Dale, E.A.Wolicki, P.W.Marshall and M.A.Gehlhausen, IEEE
Trans. Nucl. Sci. NS-34 (1987) 1134.

8. G.P.Summers, E.A.Burke, M.A.Xapsos, C.J.Dale, P.W.Marshall and E.L.Petersen, IEEE
Trans. Nucl. Sci. NS-35 (1988) 1221.

9. G.P.Summers, E.A.Burke, P.Shapiro, S.R.Messenger and R.J.Walters, IEEE Transactions
Nucl. Sci. NS-40 (1990) 1372.

10. P.W.Marshall, C.J.Dale, G.P.Summers, T.Palmer and R.Zuleeg, IEEE Trans. Nucl. Sci. NS-36
(1989) 1882.

11. S.Lazanu, I.Lazanu and E.Borchi, "Diamond degradation in hadron fields", (preliminary
results) presented at the 6-th Int. Conf. Advanced Technology and Particle Physics, Como,
1998, to be published in the Proceedings.

12. http://t2.lanl.gov.

13. V.S.Barashenkov, Preprint JINR Dubna P2-89-770 (1990) (in Russian).

14. C.Caso et al., "Review of Particle Properties", The European J. of Physics C 3 (1998).

15. M.Gmitro, S.S.Kamalov and R.Mach, Nucl. Phys. Inst. Rez, Czechoslovakia, UJF02/1986,
(1986).

16. V.S.Barashenkov, Preprint JINR Dubna P2-90-158 (1990) (in Russian).



5


17. D.Ashery, I.Navon, G.Azuelos, H.K.Walter, H.J.Pfeiffer and F.W.Schleputz, Phys.Rev. 23
(1981) 2173.

18. A.Mihul, T.Angelescu, R.Ionica, Yu.A.Scherbakov, I.Lazanu, T.Preda and R.Piragino, Il
Nuovo Cimento 105A (1992) 1637.

19. R.Tacik, E.T.Boschitz, W.Gyles, W.List, C.R.Ottermann, M.Webler, U.Wiedner, and R.R.
Johnson, Phys. Rev. C32 (1985) 1335.

20. G.D.Harp, K.Chen, G.Friedlander, Z.Frankel and J.M.Miller, Phys. Rev. C8 (1973) 581.

21. . D.Ashery and J.P.Schiffer, Ann. Rev. Nucl. Part. Sci. 36 (1986) 207.

22. H.H.K.Tang, IBM Journal of Research and Development, 40 (1996) 91.

23. M.Huhtinen and A.Aarnio, Nucl. Instr. Meth. Phys. Res. A 335 (1993) 580.

M.Huhtinen and A.Aarnio, Preprint, Helsinki University, HU SEFT R 1993-02 (1993).





6


Figure captions




Figure 1. Energy dependence of proton - carbon cross sections: total, elastic and inelastic. The
continuous curves represent parametrisations of the data.


Figure 2. Energy dependence of pion - carbon cross sections: up to down the curves represent total,
inelastic, elastic and absorption cross sections. The curves are the best fits of the data.


Figure 3. Concentration of radiation induced defects (left scale) and non-ionising energy loss (right
scale) produced by protons (dashed line) and pions (continuous line) in diamond.


Figure 4. Ratio of proton - carbon and pion - carbon total cross sections (dashed line) and ratio of
CPD produced by protons and pions in diamond (continuous line), versus particle kinetic energy.


Figure 5. Energy dependence of the ratio of proton to pion silicon total cross sections (dashed line)
and energy dependence of the ratio of the degradation produced by protons and pions in silicon as
follows:

- proton degradation from reference [6],and pion one from ref. [4] (continuous line);

- proton and pion calculation after reference [5]: dashed - dotted between 50 MeV and 1 GeV,
and continuous between 1 and 50 GeV.





7



