- Email: [email protected]
Ultraviolet Cherenkov-Channeling Radiation by Protons
Radiation Physics and Chemistry 171 (2020) 108719
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Ultraviolet Cherenkov-Channeling Radiation by Protons a,∗
a
b,c,d
K.B. Korotchenko , Yu. Eikhorn , S.B. Dabagov
T
a
National Research Tomsk Polytechnic University, 30 Lenin Ave., 634050 Tomsk, Russia INFN - Laboratori Nazionali di Frascati, Via E. Fermi 40, I-00044, Frascati (RM), Italy RAS - P.N. Lebedev Physical Institute, Leninsky Pr. 53, 119991, Moscow, Russia d National Research Nuclear University MEPhI, Kashirskoe Sh. 31, 115409, Moscow, Russia b c
ARTICLE INFO
ABSTRACT
Keywords: Cherenkov radiation Channeling radiation Electromagnetic radiation by protons Large-angle ultraviolet radiation Proton planar channeling
In present work we have theoretically studied some features for generation of principally new type of radiation, so-called mixed Cherenkov-Channeling Radiation (ChCR). The earlier developed theory for relativistic electrons have been presently applied to the radiation emission by protons at medical accelerators. This type of radiation can be observed at protons channeling in optically transparent crystals, which is accompanied by channeling radiation (CR), and can be proposed as alternative to conventional Cherenkov radiation (ChR). We demonstrate that, as expected, ChCR photons are emitted at large angles with respect to the projectile momentum and close to the Cherenkov ones as well. It is shown that the ChCR intensity can essentially exceed the ChR one. Applying the numerical methods, the quantitative characteristics of ChCR for selected crystals as well as their distinctive peculiarities are analysed.
1. Introduction The history of Cherenkov radiation (ChR) begins its report from 1934 when it was discovered by Cherenkov and Vavilov (see for some details in (Cherenkov, 1934; Afanasiev, 2017)). Presently, ChR is mostly recognised as powerful detection technique, while since relatively recent time ChR has been used in medicine for diagnostic imaging as well as for therapeutic treatment (Shaffer et al., 2016, 2017; Thorek et al., 2012; Glaser et al., 2015). The use of ChR for direct optical imaging by means of a CCD unit was first described by Cho and colleagues (Cho et al., 2009). Successfully, Cherenkov luminescence imaging was first introduced by Robertson and colleagues. (Robertson et al., 2009). All those and other similar studies utilise simplified features of ChR at optical frequencies for applied tasks. As known, in biomedical research the refractive index n is often assumed to be constant over the visible spectrum. However, its value, being the radiation frequency ω dependent, typically varies with photon energy n = n ( ) . The importance of this experience is clearly seen from the Frank-Tamm theory (Tamm and Frank, 1937; Bolotovsky, 2009). As stated by that theory, a charged particle moving in condensed matter emits ChR photons of optical frequencies. Typical number of Cherenkov photons emitted per 1 cm path and per 1 eV photon energy is a bit more than 300 (see, for instance, in (Jackson, 1998)). The ChR intensity becomes higher at the increase of the refractive index n
∗
revealing wherein a continuous ChR spectrum, ~ 2 , in the visible region (λ is the radiation wavelength). ChR is typically related to quasi-free charge particle motion in a crystal with optimised index of refraction. However, ChR photons can be also emitted by charged particles, the transverse motion of which is limited within well defined narrow channels. For instance, a crystalchanneled electron emits photons of optical or ultraviolet (UV) frequencies at large angles to its direction of motion, which is close to Cherenkov angle, under the condition that the crystal refractive index n > 1 (Beloshitsky and Kumakhov, 1978). On the other hand, channeling of a charged particle in a crystal is accompanied by electromagnetic radiation admitted as channeling radiation (CR). CR was first predicted theoretically by Kumakhov (1976). His prediction was based on classical electrodynamics. After several years of intense both studies and discussions it was registered at SLAC (Miroshnichenko et al., 1979). Successfully, the CR quantum theory was proposed by Beloshitsky and Kumakhov (1978) and later on developed in many other works (see for Refs. in the review paper Dabagov and Zhevago, 2008). According to these works CR photons generated by relativistic electrons (or positrons) are mostly emitted in the forward direction, while near Cherenkov angle the CR intensity is essentially smaller. This conclusion is also valid for heavy charged particles. Moreover, for heavy particles the radiation intensity, in general, independently on the emission angle, is much suppressed than for light
Corresponding author. E-mail addresses: [email protected] (K.B. Korotchenko), [email protected] (Y. Eikhorn), [email protected] (S.B. Dabagov).
https://doi.org/10.1016/j.radphyschem.2020.108719 Received 8 October 2019; Received in revised form 15 January 2020; Accepted 20 January 2020 Available online 24 January 2020 0969-806X/ © 2020 Elsevier Ltd. All rights reserved.
Radiation Physics and Chemistry 171 (2020) 108719
K.B. Korotchenko, et al.
particles due to the large mass factor. However, as predicted (Korotchenko and Pivovarov, 2016, 2018), the number of photons per unit path and per unit energy emitted by channeled electrons at close to ChR angles might significantly exceed the number of ordinary ChR-photons, which are emitted only by non channeled particles. It can be interpreted as a new type of large-angle CR, so-called mixed Cherenkov-Channeling Radiation (ChCR) (Korotchenko et al., 2019). Apart of basic research interests this type of radiation might be functional for medical applications based on the use of various accelerators as radiation sources. For instance, for typical clinical electron accelerators the electron energy is less than about 20 MeV (McLaughlin, 2013; Zhanget al., 2009). This electron energy is not enough to emit ChCR comparable by the intensity with that of ChR. In modern clinics the electron accelerators have been often substituted by the proton ones. However, for proton accelerators both ChR and CR intensities remain low, too. Fortunately, the proton, unlike the electron, is a positively charged particle that makes its averaged planar potential for the same crystallographic planes closer to the parabolic one. Accordingly, their wave functions as well as their energy levels at channeling differ essentially providing the advantage of protons for radiation emission. Thus, the energy of protons at clinical accelerators might be enough for intense emission of ChCR-photons on the contrary to classical ChR. This work aims in showing the feasibility of clinical proton accelerators to generate intense ChCR in both optical and ultraviolet frequency ranges at proton channeling in optically transparent crystals of a pronounced dispersion n = n ( ) function.
Fig. 2. Transmittance T = T ( ) for C (diamond) crystals for various thicknesses corresponding to experimental data (Polyanskiy).
range of CR-photon energies remains practically constant and just at the range edges smoothly changes being not over n 2 . On the contrary, the C crystal refractive index in the range (3, 10) eV shows an increase from n 2.4 up to n 3.6 that successfully followed by a sharp reduction. According to the theory (see in the following), the number of ChCR photons per unit path and per unit energy should grow for the energy ranges where the derivative of refractive index n ( )/ increases as defined by the function G ( ) . Thus, we can expect that the number of ChCR photons emitted by protons in a diamond C would be essentially higher than that in LiF. According to the data (Agafonov), in a LiF crystal of less than 1 mm thickness the transmittance equals to T 94% in the range of (0.225, 5.5) eV and then followed by a slow drop off to 60% at 10.8 eV 191nm) in 6.5 eV ( photon energy. For the photons with energy a C crystal of L 0.75 µm thickness the transmittance is not high, T 40% , the crystal becomes transparent at energies less than 6.5 eV (Polyanskiy) (see Fig. 2). The transmittance T ( ) versus the photon energy for a diamond crystal of various thicknesses is presented in Fig. 2 (the plots are related to experimental data (Polyanskiy)). As seen, the diamond crystal < 5.6 eV intransmits efficiently the photons with energies dependently on its thickness. This allows the limitation of our analysis = 5.6 eV (see in for the emission of ChCR to minimal photon energy Sect. 5).
2. Crystal optical behaviours According to the aim of our work, ChCR in different optically transparent crystals has been analysed. We have chosen two crystals, diamond (C) and LiF. Our choice for these crystals is defined by their high transmission ability at optical frequencies for C (the diamond of < 5.6 eV) (Polyanskiy)) any thickness is transparent at > 221nm ( and at UV frequencies for LiF (Agafonov). The experimentally revealed dependencies n = n ( ) for these crystals reproduced from the aforementioned papers are shown in Fig. 1. Evaluating the plots of Fig. 1 one can learn that the index of re(0.2, 3) fraction trends to be quasi unchanged at photon energies (0.3, 5) eV for LiF (these are the optical eV for C crystal and photon energies emitted at proton channeling, i.e. CR-photon energies). 10 eV the LiF refractive index Moreover, one can see that up to persists in being about 2 times less than that for C. This means, the Cherenkov angle for LiF is much smaller than for C that in specific cases may be a decisive constructive constraint. Additionally, the refractive index for a LiF crystal through the whole
3. Theoretical background Recently, well-known theory of CR was for the first time extended for the case when the crystal dispersion n ( ) is taken into account (Korotchenko and Pivovarov, 2018) resulting in the following exact expression for its spectral distribution dIif d
o
=
e 2x if2 if2
3n2 ( ) Pi ( 0 ) G (
4c3
)
(W ) (W0)×
2
×
+
1
2
G( ) = 1 +
Fig. 1. Index of refraction n = n ( (Agafonov) crystals.
m if
+
m if
n n( )
,
+ n2 ( )
m if
=
2
,
(1)
if
1
n2 ( )
2
This expression describes the radiation emitted by the projectile into the solid angle o , the frequencies of which if = i f are stipulated by the energies i and f of the initial i-th and the final f-th transverse quantum states of channeled electron, respectively. In Eq. (1) the matrix element of transition probability is defined by x if , = v/c , where v is the longitudinal electron velocity and c is the light velocity, Pi ( 0) is the function for initial population of the i-th transverse quantum state
) for both C (diamond) (Polyanskiy) and LiF
2
Radiation Physics and Chemistry 171 (2020) 108719
K.B. Korotchenko, et al.
that depends on the angle 0 = arctan[px / pz ] between the projectile momentum and the channeling crystallographic plane. The function n = n ( ) represents the real part of refractive index. Other denominations of Eq. (1) are determined by the following multiparameter expressions including the arguments for Heaviside functions (…) +
=( =(
W = W0 =
+ cos ( cos (
+ 2 ) sin + 2 ) sin
if
1
n ( ) cos ( +
), )
(2)
,
)
if
1
(3)
n ( ) cos
The physical meaning of Eq. (3) is determined by the fact that these expressions are the arguments of Heaviside functions ( ) . Thus, W and W0 must be positive, i.e. they simply limit the frequencies of radiated photons ω in dependence of the polar angle θ, at which the photons are emitted, as well as the collimation angle for a photon beam if
1
n ( ) cos ( +
)
>
>
if
1
n ( ) cos
(4)
4. Angular spread of radiation emission As seen from general expressions (1)–(4), CR for a fixed projectile energy is the frequency (energy) tunable radiation defined by the angle of emission. In other words, for any emission direction a we observe the radiation with a maximum at well-stated photon energy a , and vice versa. Hence, in order to optimise the CR use for medical appli( ) dependences for existing medical cations we have to draw the proton accelerators. According to (Sengbuscha et al., 2009) for a body treatment in mostly optimised case the accelerator should operate for protons of 250 MeV energy. The proton energy of most modern medical accelerators varies within the range 200 MeV, while for some specific cases 400 the proton energy can grow up to 800 MeV used for so-called π-therapy (Agafonov). Taking into account the features of above chosen crystals let us analyse the cases for two selected proton energies as follows:
Fig. 3. Dependences of polar angles θ vs ChCR-photon energies calculated for: a) a 200 MeV proton channeled in (110) C; b) a 600 MeV proton channeled in (111) LiF. The dashed lines present the emission angles for Cherenkov photons. The photons are emitted as a result of spontaneous transitions to the same energetic level of transverse quantum states for channeled protons.
Due to the fact that the parameters W0 and W of Eq. (1) are the arguments of Heaviside function, the angle of emission for ChCR photons is more than Cherenkov angle Ch (for photons of equal energy). Hence, the energy range for selected ChCR photon is always located upper the curve, which describes ChR. ChR in both a diamond C and a LiF crystals have been calculated according to the standard ChR expressions (Jackson, 1998; Beringeret al., 2012; Patrignaniet al., 2016) with n = n ( ) taken from the data of Fig. 1. Protons channeled in a (111) LiF crystal can emit > 0.1 eV only at proton energies not less than ChR-photons 500 MeV. We have chosen 600 MeV proton energy for our further calculations due to the fact that for less energetic channeled protons it becomes impossible getting measurable number of ChR photons per (0.3, 12.4) eV. unit path and per unit energy within the range Cherenkov angles as function of photon energies are shown by black dashed lines in both Fig. 3a and b. We would like to underline that the lowermost strip of finite width lines, the ones adjacent to the dashed i transitions. In other words, ChCRline, in Fig. 3 is due to the i photons suitable to this strip are emitted exceptionally at intraband transitions of channeled protons between transverse quantum states.
- 200 MeV for diamond (C) oriented for (110) planar channeling; - 600 MeV for LiF oriented for (111) planar channeling (due to low value of the refractive index). The results of our calculations based on the use of Eq. (3) at = 0.3 mrad collimation angle for a photon beam (a maximal value, at which we can get a contribution from the intraband transitions) are shown in Fig. 3 as contour maps.1 Separate stripes in the figures correspond to the photons emitted as a result of spontaneous transitions to the same energetic level of transverse quantum states for channeled protons. The lowest stripe (adjacent to dashed lines representing the emission angles for Cherenkov photons) corresponds to intraband transitions ((Korotchenko and Pivovarov, 2018; Korotchenko and Pivovarov, 2016; Korotchenko et al., 2019)). Taking into account that in Eq. (3) the index of refraction, the projectile velocity and Cherenkov angle are correlated within the expression 1/[n ( ) ] = cos Ch , it becomes easy to analyse the features of the plots presented in the figure. Each angle on the plot determines the energy range for ChCR photons , which is settled by two parameters, i.e. the energy if of ChCR photon emitted at spontaneous transition between transverse quantum states of a channeled proton and the collimation angle of radiation . 1
The spectral regions corresponding to the angle discussed below.
5. ChCR by planar channeled MeV protons The photon number emitted by channeled proton per unit path and per unit energy within a finite solid angle o can be calculated summing up Eq. (1) over allowed transitions between quantum states of a
70.65 in Fig. 3a are
3
Radiation Physics and Chemistry 171 (2020) 108719
K.B. Korotchenko, et al.
Fig. 5. Plots of the function G ( ) for C and LiF.
6.5 eV by Fig. 4. ChCR angular distributions for two selected cases: a) 10.8 eV by 600 MeV proton 200 MeV proton channeled in (110) C; b) channeled in (111) LiF.
channeled projectile
dN = i, f
1 1 c
dIif d
o
(5)
As aforementioned the ChCR radiation intensity is a function of two parameters, i.e. the polar emission angle θ and the energy of ChCR ) . In Figs. 4 and 6 we have presented the photons , dN = f ( , angular distributions of ChCR radiation for two selected photon fre6.5 eV by 200 MeV proton and 10.8 eV by 600 MeV quencies, proton. Each distribution corresponds to the transmittance cut-off for related crystals C (110) and LiF (111). = = 0.3 At the calculation results presented we have fixed mrad (a maximal allowed value for the intraband transitions). The polar angle θ is measured from the proton momentum, while the azimuthal angle ϕ from the perpendicular to the channeling plane (see in (Beloshitsky and Kumakhov, 1978; Korotchenko and Pivovarov, 2018; Korotchenko and Pivovarov, 2016; Korotchenko et al., 2019)). We can see from Fig. 4 (a, b) that the positions of intense peaks are at allowed emission angles in accordance with the data of Fig. 3. The positions of Cherenkov angles Ch 69.65 for C and Ch 38. 2 for LiF are indicated by the arrows. The numbers of Cherenkov photons per unit path and per unit energy are about 18 times for C and about 28 times for LiF less compared to ChCR photons. As seen from Eq. (1) the number of ChCR photons generated by protons in C should essentially exceed the one in LiF. The results of 6.5 Fig. 4 proves this fact, although for ChCR photons with energy eV (by 200 MeV protons) in C the factor G ( ) = 1.7 is comparable with = 10.8 eV by 600 MeV protons) (Fig. 5). G ( ) = 1.33 for LiF (ChCR Thus, in full agreement with our theory the intensity of ChCR emitted by protons in C is much higher than that in LiF. Indeed, we get the value
Fig. 6. Spectral distributions of ChCR emitted by channeled protons of: a) 69.75 in a C crystal; b) 200 MeV energy at the polar emission angle 38. 3 in a LiF crystal. 600 MeV energy at the polar emission angle
more than one order of magnitude, independently on the proton beam energy (note, the beam energy in LiF is 3 times over the one in C). Thereby, for higher intensity of ChCR the diamond crystal has an advantage, while for getting higher ChCR photon energy the preference is for the LiF crystal. The spectral distributions of ChCR emitted by 200 or 600 MeV protons planar channeled, correspondingly, at fixed polar angles 38. 3 for LiF are shown in Fig. 6. From these 69.75 for C and plots we can see that ChCR at frequencies corresponding to the transmittance cut-offs for related crystals (6.5 eV in C and 10.8 eV in LiF) are characterised by high monochromaticity, especially for a LiF crystal. 10.8 eV in LiF Before we have noted that for the photon energy 6.5 eV the transmittance is T 60%, while for the photon energy 4
Radiation Physics and Chemistry 171 (2020) 108719
K.B. Korotchenko, et al.
5.6 eV (a), and Fig. 7. Angular distribution of ChCR at photon energy spectral distribution of ChCR emitted at angle 70. 7 (b) by 200 MeV proton channeled in a C crystal.
Fig. 8. Angular distribution of ChCR at energy distribution of ChCR photons emitted at angle tons channeled in a C crystal.
in C of L 0.75 µm thickness the transmittance is T 40% . Both values are rather high. However, it means that at the crystal exit the number of ChCR photons per unit path and per unit energy at these fixed energies should be 1.7 (LiF) and 2.5 (C) times less. According to the data of Fig. 2, the diamond crystal is transparent at 5.6 eV for practically any crystal thickness. Then, photon energy 5.6 eV up to at the energy increase for a ChCR photon from 6.5 eV the transmittance is decreased. For instance, for ultrathin diamond (C) crystal we obtain the following data:
3.22 eV emitted by The angular distribution of ChCR at energy 200 MeV protons channeled in a diamond (C) crystal is presented in Fig. 8a. The number of ChCR photons dN 1.05 ph/(eV cm) is rather low but over the number of ChR photons ( Ch 65. 4 ) in about 7 times. The results presented in Figs. 7b and 8b are in good agreement with the plot of ChCR for allowed polar angles as defined in Fig. 3a by the scenario for extra lines, i.e. the horizontal line corresponds to the emission 70.67 and intersects the second strip of lines at two quantum angle (2.4, 3.9) eV and (4.95, 6.1) eV. energy ranges of ChCR Such peculiarity of ChCR spectrum suggests the solution for essential extend of the range for continuous ChCR. Namely, it takes place if we chose the angle of emission to be less than 70.65 , i.e. on the plot of Fig. 3a the horizontal line to be drawn at 70. 0 . 70 is The spectral distribution of ChCR-photons emitted at shown in Fig. 9. In this case the horizontal line in Fig. 3a corresponding to this angle should cross off the widest energy range of ChCR-photons (2.7, 5.6) eV on the second strip of lines. The maximal Cherenkov photons number in this region is dN 0.15 ph/(eV cm). Therefore, in (3.6, 5.6) eV the ChCR-photons number per unit path the interval and per unit energy emitted by protons channeled in (110) C would be not less than Cherenkov one.
T (6.5 eV ) = 55%, - L = 0.5 µ m T (6.5 eV ) = 40%, - L = 0.75 µ m T (6.5 eV ) = 30%. - L = 1 µm In order to explore the possibility of obtaining soft UV-radiation from 200 MeV protons channeled in (110) C crystal we calculate both 5.6 spectral and angular characteristics of ChCR for two energies: 3.22 eV (the threshold for visible light (Lawrenceet al., eV and 1272)). 5.6 eV. Fig. 7a shows the ChCR angular distribution at energy The maximal number dN 8.35 ph/(eV cm) of ChCR photons are 70. 7 . Successfully, the spectral distribution of emitted at angle ChCR at maximal radiation flux (at fixed angle) has been drawn (Fig. 7b). Cherenkov angle Ch 67. 9 for these particle-crystal parameters is indicated in Fig. 7a. Comparing the data of Figs. 4a and 7a one can see that the path and energy normalised number of ChCR photons of energy 6.5 5.6 eV is slightly greater (about 3 times) than those of eV. It is notable here that the radiation flux of ChR (classical case) remains even less (in about 50 times) than the one for ChCR.
3.22 eV (a) and spectral 70.65 (b) by 200 MeV pro-
6. Conclusion In this report for the first time it was shown that optical channeling radiation (in this special case, ChCR) by protons might be of comparable intensity with optical channeling radiation by electrons (Korotchenko et al., 2019). This work aimed in studying principally new type of radiation by channeled protons, mixed Cherenkov-Channeling Radiation (ChCR), as 5
Radiation Physics and Chemistry 171 (2020) 108719
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CRediT authorship contribution statement K.B. Korotchenko: Methodology, Validation, Writing - original draft. Yu. Eikhorn: Investigation, Data curation, Software. S.B. Dabagov: Conceptualization, Supervision, Validation, Writing - review & editing. Acknowledgments This research is supported by the Competitiveness Programs of both the Tomsk Polytechnic University and the National Research Nuclear University MEPhI. References Afanasiev, G., 2017. Nat. Nanotechnol. 12 (2), 106–117. Agafonov, A.V. Accelerators in medicine. http://web.ihep.su/library/pubs/aconf96/ps/ c96-198.pdf (in Russian). Beloshitsky, V., Kumakhov, M., 1978. Sov. Phys. JETP 47 (4), 652–658. Beringer, J., et al., 2012. Particle data group. Phys. Rev. D 86 012029. Bolotovsky, B., 2009. Phys. Usp. 11, 1099. Cherenkov, P., 1934. Dokl. Akad. Nauk SSSR 2, 451. Cho, J.S., Taschereau, R., Olma, S., Liu, K., Chen, Y.C., Shen, C.K., van Dam, R.M., Chatziioannou, A.F., 2009. Phys. Med. Biol. 54 (22), 6757–6771. Dabagov, S., Zhevago, N., 2008. La Rivista del Nuovo Cimento 31 (9), 491. Glaser, A.K., Zhang, R., Andreozzi, J.M., Gladstone, D.J., Pogue, B.W., 2015. Phys. Med. Biol. 60, 6701–6718. Jackson, J., 1998. Classical Electrodynamics, third ed. John Wiley and Sons, New York. Korotchenko, K., Pivovarov, Yu, 2016. JETP Lett. (Engl. Transl.) 103 (2), 87–93. Korotchenko, K., Pivovarov, Yu, 2018. Phys. Lett. 382, 444–448. Korotchenko, K., Pivovarov, Yu, Takabayashi, Y., Dabagov, S., 2019. Phys. Lett. B 795, 592–598. Kumakhov, M., 1976. Phys. Lett. 57 (14), 17. K.P. Lawrence et al., Sci. Rep. 8:12722. doi:10.1038/s41598-018-30738-6. McLaughlin, D., 2013. Energy Spectra Comparisons for Matched Clinical Electron Beams on Elekta Linear Accelerators Using a Permanent Magnet Spectrometer. LSU Master’s Theses. . Miroshnichenko, I., Murray, J., Avakyan, R., Figut, T., 1979. JEPT Lett 29 (12), 722. Patrignani, C., et al., 2016. Particle data group. Chin. Phys. C 40, 100001. Polyanskiy, M.N. Refractive index database. http://refractiveindex.info. Robertson, R., Germanos, M., Li, C., Mitchell, G., Cherry, S., Silva, M., 2009. Phys. Med. Biol. 54 (16), N355–N365. Sengbuscha, E., Pérez-Andùjar, A., DeLuca, P., Mackie, T., 2009. Med. Phys. 36 (2), 364–372. Shaffer, T.M., Drain, C.M., Grimm, J., 2016. J. Nucl. Med. 57 (11), 1661–1666. Shaffer, T.M., Pratt, E.C., Grimm, J., 2017. Nat. Nanotechnol. 12 (2), 106–117. Tamm, I., Frank, I., 1937. Dokl. Akad. Nauk SSSR 14, 107. Thorek, D.L., Robertson, R., Bacchus, W.A., Hahn, J., Rothberg, J., Beattie, B.J., Grimm, J., 2012. Am J Nucl Med Mol Imaging 2 (2), 163–173. Zhang, S., et al., 2009. J. Appl. Clin. Med. Phys. 10 (4), 177–187.
Fig. 9. Dependence (with extra lines) of polar angles θ on ChCR-photon en(a) calculated for proton with energy 200 MeV channeled in (110) C ergies 70 by crystal. Spectral distributions (b) of ChCR-photons emitted at angle channeled protons with energy 200 MeV in diamond crystal.
alternative to Cherenkov radiation, which nowadays widely used in medical applications. Our investigations on various features of ChCR emission by protons channeled in optically transparent crystals of LiF and C (diamond) result in the following conclusions: - the intensity of ChCR by channeled protons (not only electrons (Korotchenko et al., 2019)) at optical frequencies might be much over the intensity of ordinary ChR at equal conditions; - ChCR photons are emitted by channeled protons at the angles close to Cherenkov ones but always at larger values (similar to channeled electrons (Korotchenko et al., 2019)); - for soft UV range the diamond (C) crystal is preferable; - the use of a LiF crystal is better for two cases: - for getting hard UV (~ 11 eV); - if due to specific construction behaviours it becomes difficult to get out radiation at large angles with respect to the direction of motion for channeled protons; - for soft UV range in a C crystal the choice of a polar angle allows obtaining the ChCR spectral distribution continuous for a wider frequency (energy) range. Finally, we can conclude that our studies suggest the use of Cherenkov radiation by channeled protons at modern medical accelerators without essential facility modifications.
6
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
Ultraviolet Cherenkov-Channeling Radiation by Protons a,∗
a
b,c,d
K.B. Korotchenko , Yu. Eikhorn , S.B. Dabagov
T
a
National Research Tomsk Polytechnic University, 30 Lenin Ave., 634050 Tomsk, Russia INFN - Laboratori Nazionali di Frascati, Via E. Fermi 40, I-00044, Frascati (RM), Italy RAS - P.N. Lebedev Physical Institute, Leninsky Pr. 53, 119991, Moscow, Russia d National Research Nuclear University MEPhI, Kashirskoe Sh. 31, 115409, Moscow, Russia b c
ARTICLE INFO
ABSTRACT
Keywords: Cherenkov radiation Channeling radiation Electromagnetic radiation by protons Large-angle ultraviolet radiation Proton planar channeling
In present work we have theoretically studied some features for generation of principally new type of radiation, so-called mixed Cherenkov-Channeling Radiation (ChCR). The earlier developed theory for relativistic electrons have been presently applied to the radiation emission by protons at medical accelerators. This type of radiation can be observed at protons channeling in optically transparent crystals, which is accompanied by channeling radiation (CR), and can be proposed as alternative to conventional Cherenkov radiation (ChR). We demonstrate that, as expected, ChCR photons are emitted at large angles with respect to the projectile momentum and close to the Cherenkov ones as well. It is shown that the ChCR intensity can essentially exceed the ChR one. Applying the numerical methods, the quantitative characteristics of ChCR for selected crystals as well as their distinctive peculiarities are analysed.
1. Introduction The history of Cherenkov radiation (ChR) begins its report from 1934 when it was discovered by Cherenkov and Vavilov (see for some details in (Cherenkov, 1934; Afanasiev, 2017)). Presently, ChR is mostly recognised as powerful detection technique, while since relatively recent time ChR has been used in medicine for diagnostic imaging as well as for therapeutic treatment (Shaffer et al., 2016, 2017; Thorek et al., 2012; Glaser et al., 2015). The use of ChR for direct optical imaging by means of a CCD unit was first described by Cho and colleagues (Cho et al., 2009). Successfully, Cherenkov luminescence imaging was first introduced by Robertson and colleagues. (Robertson et al., 2009). All those and other similar studies utilise simplified features of ChR at optical frequencies for applied tasks. As known, in biomedical research the refractive index n is often assumed to be constant over the visible spectrum. However, its value, being the radiation frequency ω dependent, typically varies with photon energy n = n ( ) . The importance of this experience is clearly seen from the Frank-Tamm theory (Tamm and Frank, 1937; Bolotovsky, 2009). As stated by that theory, a charged particle moving in condensed matter emits ChR photons of optical frequencies. Typical number of Cherenkov photons emitted per 1 cm path and per 1 eV photon energy is a bit more than 300 (see, for instance, in (Jackson, 1998)). The ChR intensity becomes higher at the increase of the refractive index n
∗
revealing wherein a continuous ChR spectrum, ~ 2 , in the visible region (λ is the radiation wavelength). ChR is typically related to quasi-free charge particle motion in a crystal with optimised index of refraction. However, ChR photons can be also emitted by charged particles, the transverse motion of which is limited within well defined narrow channels. For instance, a crystalchanneled electron emits photons of optical or ultraviolet (UV) frequencies at large angles to its direction of motion, which is close to Cherenkov angle, under the condition that the crystal refractive index n > 1 (Beloshitsky and Kumakhov, 1978). On the other hand, channeling of a charged particle in a crystal is accompanied by electromagnetic radiation admitted as channeling radiation (CR). CR was first predicted theoretically by Kumakhov (1976). His prediction was based on classical electrodynamics. After several years of intense both studies and discussions it was registered at SLAC (Miroshnichenko et al., 1979). Successfully, the CR quantum theory was proposed by Beloshitsky and Kumakhov (1978) and later on developed in many other works (see for Refs. in the review paper Dabagov and Zhevago, 2008). According to these works CR photons generated by relativistic electrons (or positrons) are mostly emitted in the forward direction, while near Cherenkov angle the CR intensity is essentially smaller. This conclusion is also valid for heavy charged particles. Moreover, for heavy particles the radiation intensity, in general, independently on the emission angle, is much suppressed than for light
Corresponding author. E-mail addresses: [email protected] (K.B. Korotchenko), [email protected] (Y. Eikhorn), [email protected] (S.B. Dabagov).
https://doi.org/10.1016/j.radphyschem.2020.108719 Received 8 October 2019; Received in revised form 15 January 2020; Accepted 20 January 2020 Available online 24 January 2020 0969-806X/ © 2020 Elsevier Ltd. All rights reserved.
Radiation Physics and Chemistry 171 (2020) 108719
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particles due to the large mass factor. However, as predicted (Korotchenko and Pivovarov, 2016, 2018), the number of photons per unit path and per unit energy emitted by channeled electrons at close to ChR angles might significantly exceed the number of ordinary ChR-photons, which are emitted only by non channeled particles. It can be interpreted as a new type of large-angle CR, so-called mixed Cherenkov-Channeling Radiation (ChCR) (Korotchenko et al., 2019). Apart of basic research interests this type of radiation might be functional for medical applications based on the use of various accelerators as radiation sources. For instance, for typical clinical electron accelerators the electron energy is less than about 20 MeV (McLaughlin, 2013; Zhanget al., 2009). This electron energy is not enough to emit ChCR comparable by the intensity with that of ChR. In modern clinics the electron accelerators have been often substituted by the proton ones. However, for proton accelerators both ChR and CR intensities remain low, too. Fortunately, the proton, unlike the electron, is a positively charged particle that makes its averaged planar potential for the same crystallographic planes closer to the parabolic one. Accordingly, their wave functions as well as their energy levels at channeling differ essentially providing the advantage of protons for radiation emission. Thus, the energy of protons at clinical accelerators might be enough for intense emission of ChCR-photons on the contrary to classical ChR. This work aims in showing the feasibility of clinical proton accelerators to generate intense ChCR in both optical and ultraviolet frequency ranges at proton channeling in optically transparent crystals of a pronounced dispersion n = n ( ) function.
Fig. 2. Transmittance T = T ( ) for C (diamond) crystals for various thicknesses corresponding to experimental data (Polyanskiy).
range of CR-photon energies remains practically constant and just at the range edges smoothly changes being not over n 2 . On the contrary, the C crystal refractive index in the range (3, 10) eV shows an increase from n 2.4 up to n 3.6 that successfully followed by a sharp reduction. According to the theory (see in the following), the number of ChCR photons per unit path and per unit energy should grow for the energy ranges where the derivative of refractive index n ( )/ increases as defined by the function G ( ) . Thus, we can expect that the number of ChCR photons emitted by protons in a diamond C would be essentially higher than that in LiF. According to the data (Agafonov), in a LiF crystal of less than 1 mm thickness the transmittance equals to T 94% in the range of (0.225, 5.5) eV and then followed by a slow drop off to 60% at 10.8 eV 191nm) in 6.5 eV ( photon energy. For the photons with energy a C crystal of L 0.75 µm thickness the transmittance is not high, T 40% , the crystal becomes transparent at energies less than 6.5 eV (Polyanskiy) (see Fig. 2). The transmittance T ( ) versus the photon energy for a diamond crystal of various thicknesses is presented in Fig. 2 (the plots are related to experimental data (Polyanskiy)). As seen, the diamond crystal < 5.6 eV intransmits efficiently the photons with energies dependently on its thickness. This allows the limitation of our analysis = 5.6 eV (see in for the emission of ChCR to minimal photon energy Sect. 5).
2. Crystal optical behaviours According to the aim of our work, ChCR in different optically transparent crystals has been analysed. We have chosen two crystals, diamond (C) and LiF. Our choice for these crystals is defined by their high transmission ability at optical frequencies for C (the diamond of < 5.6 eV) (Polyanskiy)) any thickness is transparent at > 221nm ( and at UV frequencies for LiF (Agafonov). The experimentally revealed dependencies n = n ( ) for these crystals reproduced from the aforementioned papers are shown in Fig. 1. Evaluating the plots of Fig. 1 one can learn that the index of re(0.2, 3) fraction trends to be quasi unchanged at photon energies (0.3, 5) eV for LiF (these are the optical eV for C crystal and photon energies emitted at proton channeling, i.e. CR-photon energies). 10 eV the LiF refractive index Moreover, one can see that up to persists in being about 2 times less than that for C. This means, the Cherenkov angle for LiF is much smaller than for C that in specific cases may be a decisive constructive constraint. Additionally, the refractive index for a LiF crystal through the whole
3. Theoretical background Recently, well-known theory of CR was for the first time extended for the case when the crystal dispersion n ( ) is taken into account (Korotchenko and Pivovarov, 2018) resulting in the following exact expression for its spectral distribution dIif d
o
=
e 2x if2 if2
3n2 ( ) Pi ( 0 ) G (
4c3
)
(W ) (W0)×
2
×
+
1
2
G( ) = 1 +
Fig. 1. Index of refraction n = n ( (Agafonov) crystals.
m if
+
m if
n n( )
,
+ n2 ( )
m if
=
2
,
(1)
if
1
n2 ( )
2
This expression describes the radiation emitted by the projectile into the solid angle o , the frequencies of which if = i f are stipulated by the energies i and f of the initial i-th and the final f-th transverse quantum states of channeled electron, respectively. In Eq. (1) the matrix element of transition probability is defined by x if , = v/c , where v is the longitudinal electron velocity and c is the light velocity, Pi ( 0) is the function for initial population of the i-th transverse quantum state
) for both C (diamond) (Polyanskiy) and LiF
2
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that depends on the angle 0 = arctan[px / pz ] between the projectile momentum and the channeling crystallographic plane. The function n = n ( ) represents the real part of refractive index. Other denominations of Eq. (1) are determined by the following multiparameter expressions including the arguments for Heaviside functions (…) +
=( =(
W = W0 =
+ cos ( cos (
+ 2 ) sin + 2 ) sin
if
1
n ( ) cos ( +
), )
(2)
,
)
if
1
(3)
n ( ) cos
The physical meaning of Eq. (3) is determined by the fact that these expressions are the arguments of Heaviside functions ( ) . Thus, W and W0 must be positive, i.e. they simply limit the frequencies of radiated photons ω in dependence of the polar angle θ, at which the photons are emitted, as well as the collimation angle for a photon beam if
1
n ( ) cos ( +
)
>
>
if
1
n ( ) cos
(4)
4. Angular spread of radiation emission As seen from general expressions (1)–(4), CR for a fixed projectile energy is the frequency (energy) tunable radiation defined by the angle of emission. In other words, for any emission direction a we observe the radiation with a maximum at well-stated photon energy a , and vice versa. Hence, in order to optimise the CR use for medical appli( ) dependences for existing medical cations we have to draw the proton accelerators. According to (Sengbuscha et al., 2009) for a body treatment in mostly optimised case the accelerator should operate for protons of 250 MeV energy. The proton energy of most modern medical accelerators varies within the range 200 MeV, while for some specific cases 400 the proton energy can grow up to 800 MeV used for so-called π-therapy (Agafonov). Taking into account the features of above chosen crystals let us analyse the cases for two selected proton energies as follows:
Fig. 3. Dependences of polar angles θ vs ChCR-photon energies calculated for: a) a 200 MeV proton channeled in (110) C; b) a 600 MeV proton channeled in (111) LiF. The dashed lines present the emission angles for Cherenkov photons. The photons are emitted as a result of spontaneous transitions to the same energetic level of transverse quantum states for channeled protons.
Due to the fact that the parameters W0 and W of Eq. (1) are the arguments of Heaviside function, the angle of emission for ChCR photons is more than Cherenkov angle Ch (for photons of equal energy). Hence, the energy range for selected ChCR photon is always located upper the curve, which describes ChR. ChR in both a diamond C and a LiF crystals have been calculated according to the standard ChR expressions (Jackson, 1998; Beringeret al., 2012; Patrignaniet al., 2016) with n = n ( ) taken from the data of Fig. 1. Protons channeled in a (111) LiF crystal can emit > 0.1 eV only at proton energies not less than ChR-photons 500 MeV. We have chosen 600 MeV proton energy for our further calculations due to the fact that for less energetic channeled protons it becomes impossible getting measurable number of ChR photons per (0.3, 12.4) eV. unit path and per unit energy within the range Cherenkov angles as function of photon energies are shown by black dashed lines in both Fig. 3a and b. We would like to underline that the lowermost strip of finite width lines, the ones adjacent to the dashed i transitions. In other words, ChCRline, in Fig. 3 is due to the i photons suitable to this strip are emitted exceptionally at intraband transitions of channeled protons between transverse quantum states.
- 200 MeV for diamond (C) oriented for (110) planar channeling; - 600 MeV for LiF oriented for (111) planar channeling (due to low value of the refractive index). The results of our calculations based on the use of Eq. (3) at = 0.3 mrad collimation angle for a photon beam (a maximal value, at which we can get a contribution from the intraband transitions) are shown in Fig. 3 as contour maps.1 Separate stripes in the figures correspond to the photons emitted as a result of spontaneous transitions to the same energetic level of transverse quantum states for channeled protons. The lowest stripe (adjacent to dashed lines representing the emission angles for Cherenkov photons) corresponds to intraband transitions ((Korotchenko and Pivovarov, 2018; Korotchenko and Pivovarov, 2016; Korotchenko et al., 2019)). Taking into account that in Eq. (3) the index of refraction, the projectile velocity and Cherenkov angle are correlated within the expression 1/[n ( ) ] = cos Ch , it becomes easy to analyse the features of the plots presented in the figure. Each angle on the plot determines the energy range for ChCR photons , which is settled by two parameters, i.e. the energy if of ChCR photon emitted at spontaneous transition between transverse quantum states of a channeled proton and the collimation angle of radiation . 1
The spectral regions corresponding to the angle discussed below.
5. ChCR by planar channeled MeV protons The photon number emitted by channeled proton per unit path and per unit energy within a finite solid angle o can be calculated summing up Eq. (1) over allowed transitions between quantum states of a
70.65 in Fig. 3a are
3
Radiation Physics and Chemistry 171 (2020) 108719
K.B. Korotchenko, et al.
Fig. 5. Plots of the function G ( ) for C and LiF.
6.5 eV by Fig. 4. ChCR angular distributions for two selected cases: a) 10.8 eV by 600 MeV proton 200 MeV proton channeled in (110) C; b) channeled in (111) LiF.
channeled projectile
dN = i, f
1 1 c
dIif d
o
(5)
As aforementioned the ChCR radiation intensity is a function of two parameters, i.e. the polar emission angle θ and the energy of ChCR ) . In Figs. 4 and 6 we have presented the photons , dN = f ( , angular distributions of ChCR radiation for two selected photon fre6.5 eV by 200 MeV proton and 10.8 eV by 600 MeV quencies, proton. Each distribution corresponds to the transmittance cut-off for related crystals C (110) and LiF (111). = = 0.3 At the calculation results presented we have fixed mrad (a maximal allowed value for the intraband transitions). The polar angle θ is measured from the proton momentum, while the azimuthal angle ϕ from the perpendicular to the channeling plane (see in (Beloshitsky and Kumakhov, 1978; Korotchenko and Pivovarov, 2018; Korotchenko and Pivovarov, 2016; Korotchenko et al., 2019)). We can see from Fig. 4 (a, b) that the positions of intense peaks are at allowed emission angles in accordance with the data of Fig. 3. The positions of Cherenkov angles Ch 69.65 for C and Ch 38. 2 for LiF are indicated by the arrows. The numbers of Cherenkov photons per unit path and per unit energy are about 18 times for C and about 28 times for LiF less compared to ChCR photons. As seen from Eq. (1) the number of ChCR photons generated by protons in C should essentially exceed the one in LiF. The results of 6.5 Fig. 4 proves this fact, although for ChCR photons with energy eV (by 200 MeV protons) in C the factor G ( ) = 1.7 is comparable with = 10.8 eV by 600 MeV protons) (Fig. 5). G ( ) = 1.33 for LiF (ChCR Thus, in full agreement with our theory the intensity of ChCR emitted by protons in C is much higher than that in LiF. Indeed, we get the value
Fig. 6. Spectral distributions of ChCR emitted by channeled protons of: a) 69.75 in a C crystal; b) 200 MeV energy at the polar emission angle 38. 3 in a LiF crystal. 600 MeV energy at the polar emission angle
more than one order of magnitude, independently on the proton beam energy (note, the beam energy in LiF is 3 times over the one in C). Thereby, for higher intensity of ChCR the diamond crystal has an advantage, while for getting higher ChCR photon energy the preference is for the LiF crystal. The spectral distributions of ChCR emitted by 200 or 600 MeV protons planar channeled, correspondingly, at fixed polar angles 38. 3 for LiF are shown in Fig. 6. From these 69.75 for C and plots we can see that ChCR at frequencies corresponding to the transmittance cut-offs for related crystals (6.5 eV in C and 10.8 eV in LiF) are characterised by high monochromaticity, especially for a LiF crystal. 10.8 eV in LiF Before we have noted that for the photon energy 6.5 eV the transmittance is T 60%, while for the photon energy 4
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5.6 eV (a), and Fig. 7. Angular distribution of ChCR at photon energy spectral distribution of ChCR emitted at angle 70. 7 (b) by 200 MeV proton channeled in a C crystal.
Fig. 8. Angular distribution of ChCR at energy distribution of ChCR photons emitted at angle tons channeled in a C crystal.
in C of L 0.75 µm thickness the transmittance is T 40% . Both values are rather high. However, it means that at the crystal exit the number of ChCR photons per unit path and per unit energy at these fixed energies should be 1.7 (LiF) and 2.5 (C) times less. According to the data of Fig. 2, the diamond crystal is transparent at 5.6 eV for practically any crystal thickness. Then, photon energy 5.6 eV up to at the energy increase for a ChCR photon from 6.5 eV the transmittance is decreased. For instance, for ultrathin diamond (C) crystal we obtain the following data:
3.22 eV emitted by The angular distribution of ChCR at energy 200 MeV protons channeled in a diamond (C) crystal is presented in Fig. 8a. The number of ChCR photons dN 1.05 ph/(eV cm) is rather low but over the number of ChR photons ( Ch 65. 4 ) in about 7 times. The results presented in Figs. 7b and 8b are in good agreement with the plot of ChCR for allowed polar angles as defined in Fig. 3a by the scenario for extra lines, i.e. the horizontal line corresponds to the emission 70.67 and intersects the second strip of lines at two quantum angle (2.4, 3.9) eV and (4.95, 6.1) eV. energy ranges of ChCR Such peculiarity of ChCR spectrum suggests the solution for essential extend of the range for continuous ChCR. Namely, it takes place if we chose the angle of emission to be less than 70.65 , i.e. on the plot of Fig. 3a the horizontal line to be drawn at 70. 0 . 70 is The spectral distribution of ChCR-photons emitted at shown in Fig. 9. In this case the horizontal line in Fig. 3a corresponding to this angle should cross off the widest energy range of ChCR-photons (2.7, 5.6) eV on the second strip of lines. The maximal Cherenkov photons number in this region is dN 0.15 ph/(eV cm). Therefore, in (3.6, 5.6) eV the ChCR-photons number per unit path the interval and per unit energy emitted by protons channeled in (110) C would be not less than Cherenkov one.
T (6.5 eV ) = 55%, - L = 0.5 µ m T (6.5 eV ) = 40%, - L = 0.75 µ m T (6.5 eV ) = 30%. - L = 1 µm In order to explore the possibility of obtaining soft UV-radiation from 200 MeV protons channeled in (110) C crystal we calculate both 5.6 spectral and angular characteristics of ChCR for two energies: 3.22 eV (the threshold for visible light (Lawrenceet al., eV and 1272)). 5.6 eV. Fig. 7a shows the ChCR angular distribution at energy The maximal number dN 8.35 ph/(eV cm) of ChCR photons are 70. 7 . Successfully, the spectral distribution of emitted at angle ChCR at maximal radiation flux (at fixed angle) has been drawn (Fig. 7b). Cherenkov angle Ch 67. 9 for these particle-crystal parameters is indicated in Fig. 7a. Comparing the data of Figs. 4a and 7a one can see that the path and energy normalised number of ChCR photons of energy 6.5 5.6 eV is slightly greater (about 3 times) than those of eV. It is notable here that the radiation flux of ChR (classical case) remains even less (in about 50 times) than the one for ChCR.
3.22 eV (a) and spectral 70.65 (b) by 200 MeV pro-
6. Conclusion In this report for the first time it was shown that optical channeling radiation (in this special case, ChCR) by protons might be of comparable intensity with optical channeling radiation by electrons (Korotchenko et al., 2019). This work aimed in studying principally new type of radiation by channeled protons, mixed Cherenkov-Channeling Radiation (ChCR), as 5
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CRediT authorship contribution statement K.B. Korotchenko: Methodology, Validation, Writing - original draft. Yu. Eikhorn: Investigation, Data curation, Software. S.B. Dabagov: Conceptualization, Supervision, Validation, Writing - review & editing. Acknowledgments This research is supported by the Competitiveness Programs of both the Tomsk Polytechnic University and the National Research Nuclear University MEPhI. References Afanasiev, G., 2017. Nat. Nanotechnol. 12 (2), 106–117. Agafonov, A.V. Accelerators in medicine. http://web.ihep.su/library/pubs/aconf96/ps/ c96-198.pdf (in Russian). Beloshitsky, V., Kumakhov, M., 1978. Sov. Phys. JETP 47 (4), 652–658. Beringer, J., et al., 2012. Particle data group. Phys. Rev. D 86 012029. Bolotovsky, B., 2009. Phys. Usp. 11, 1099. Cherenkov, P., 1934. Dokl. Akad. Nauk SSSR 2, 451. Cho, J.S., Taschereau, R., Olma, S., Liu, K., Chen, Y.C., Shen, C.K., van Dam, R.M., Chatziioannou, A.F., 2009. Phys. Med. Biol. 54 (22), 6757–6771. Dabagov, S., Zhevago, N., 2008. La Rivista del Nuovo Cimento 31 (9), 491. Glaser, A.K., Zhang, R., Andreozzi, J.M., Gladstone, D.J., Pogue, B.W., 2015. Phys. Med. Biol. 60, 6701–6718. Jackson, J., 1998. Classical Electrodynamics, third ed. John Wiley and Sons, New York. Korotchenko, K., Pivovarov, Yu, 2016. JETP Lett. (Engl. Transl.) 103 (2), 87–93. Korotchenko, K., Pivovarov, Yu, 2018. Phys. Lett. 382, 444–448. Korotchenko, K., Pivovarov, Yu, Takabayashi, Y., Dabagov, S., 2019. Phys. Lett. B 795, 592–598. Kumakhov, M., 1976. Phys. Lett. 57 (14), 17. K.P. Lawrence et al., Sci. Rep. 8:12722. doi:10.1038/s41598-018-30738-6. McLaughlin, D., 2013. Energy Spectra Comparisons for Matched Clinical Electron Beams on Elekta Linear Accelerators Using a Permanent Magnet Spectrometer. LSU Master’s Theses. . Miroshnichenko, I., Murray, J., Avakyan, R., Figut, T., 1979. JEPT Lett 29 (12), 722. Patrignani, C., et al., 2016. Particle data group. Chin. Phys. C 40, 100001. Polyanskiy, M.N. Refractive index database. http://refractiveindex.info. Robertson, R., Germanos, M., Li, C., Mitchell, G., Cherry, S., Silva, M., 2009. Phys. Med. Biol. 54 (16), N355–N365. Sengbuscha, E., Pérez-Andùjar, A., DeLuca, P., Mackie, T., 2009. Med. Phys. 36 (2), 364–372. Shaffer, T.M., Drain, C.M., Grimm, J., 2016. J. Nucl. Med. 57 (11), 1661–1666. Shaffer, T.M., Pratt, E.C., Grimm, J., 2017. Nat. Nanotechnol. 12 (2), 106–117. Tamm, I., Frank, I., 1937. Dokl. Akad. Nauk SSSR 14, 107. Thorek, D.L., Robertson, R., Bacchus, W.A., Hahn, J., Rothberg, J., Beattie, B.J., Grimm, J., 2012. Am J Nucl Med Mol Imaging 2 (2), 163–173. Zhang, S., et al., 2009. J. Appl. Clin. Med. Phys. 10 (4), 177–187.
Fig. 9. Dependence (with extra lines) of polar angles θ on ChCR-photon en(a) calculated for proton with energy 200 MeV channeled in (110) C ergies 70 by crystal. Spectral distributions (b) of ChCR-photons emitted at angle channeled protons with energy 200 MeV in diamond crystal.
alternative to Cherenkov radiation, which nowadays widely used in medical applications. Our investigations on various features of ChCR emission by protons channeled in optically transparent crystals of LiF and C (diamond) result in the following conclusions: - the intensity of ChCR by channeled protons (not only electrons (Korotchenko et al., 2019)) at optical frequencies might be much over the intensity of ordinary ChR at equal conditions; - ChCR photons are emitted by channeled protons at the angles close to Cherenkov ones but always at larger values (similar to channeled electrons (Korotchenko et al., 2019)); - for soft UV range the diamond (C) crystal is preferable; - the use of a LiF crystal is better for two cases: - for getting hard UV (~ 11 eV); - if due to specific construction behaviours it becomes difficult to get out radiation at large angles with respect to the direction of motion for channeled protons; - for soft UV range in a C crystal the choice of a polar angle allows obtaining the ChCR spectral distribution continuous for a wider frequency (energy) range. Finally, we can conclude that our studies suggest the use of Cherenkov radiation by channeled protons at modern medical accelerators without essential facility modifications.
6