what term is used to describe a linear sequence in which energy is transferred

Radiation Effects on Matter

Gregory Choppin , ... Christian Ekberg , in Radiochemistry and Nuclear Chemistry (Fourth Edition), 2013

8.1 Energy Transfer

The chemical effects of radiations depend on the composition of thing and the amount of free energy deposited past the radiation. In this department nosotros consider only the energy transfer. For this purpose it is practical to split up high energy radiation into (i) charged particles (eastward⁻, east⁺, α, etc) and (two) uncharged particles (northward) and electromagnetic radiations (γ). The latter produce recoil diminutive ions, products of nuclear reactions and electrons equally charged secondary ionizing particles. The terms straight and indirect ionizing radiations are oft used for (1) and (2) respectively.

The amount of energy imparted to thing in a given volume is

(8.1) $E_{\text{imp}}={\mathrm{Eastward}}_{\text{in}}+\Sigma Q-{\mathrm{Eastward}}_{\text{out}}$

where E _in is the free energy (excluding mass free energy) of the radiation entering the volume, E _out is the energy of the radiation leaving the volume, ΣQ is the sum of all Q-values for nuclear transformation that take occurred in the volume. For a axle of charged particles E _in  = E _kin; for γ-rays information technology is Due east _γ. If no nuclear transformations occur, ΣQ  =   0. For neutrons which are captured and for radionuclides which disuse in the absorber, ΣQ  >   0; in the case of radionuclides already present in the absorber, E _in  =   0.

viii.1.1 Charged particles

We learned in the previous chapter that the energy of charged particles is absorbed mainly through ionization and atomic excitation. For positrons the annihilation process (at Due east _kin ≈ 0) must exist considered. For electrons of high kinetic energy bremsstrahlung must be taken into business relationship. However, in the following text we simplify by neglecting annihilation and bremsstrahlung processes. The bremsstrahlung correction can be made with the assist of Figure 7.9 which gives the boilerplate specific free energy loss of electrons through ionization and bremsstrahlung.

It has been institute that the average free energy, w, for the formation of an ion pair in gaseous material by charged particles is between 25 and 40 eV. For the same absorbing material it is adequately independent of the type of radiation and the free energy. Table 8.i lists values of w in some gases. The ionization potentials j of the gases are lower than the typical w-values and thus the residue of the free energy, w−j, appears as excitation energy. Since the excitation energies per atom are ≤5 eV, several excited atoms are formed for each ion pair formed. While information technology is easy to measure w in a gas, information technology is more difficult to obtain reliable values for liquids and solids. They also differ more widely; e.k. w is 1300 eV per ion pair in hexane (for high energy electrons) while it is about v eV per ion pair in inorganic solids.

Table viii.1. Ion pair formation energies for charged particles. All values in eV

Cushion	w	j	west-j
He(k)	43	24.v	18.five
H2(g)	36	15.6	20.4
O2(m)	31.5	12.5	19
Air	34	fifteen	19
H2O(g or l)	38	thirteen	25
Ar(grand) five MeV α	26.4
Ar(thou) 340 MeV p+	25.5
Ar(k) ten keV e–	26.four
Ar(g) one MeV east–	25.5
Ar(thousand) average	26	15.7	10.3

The specific free energy loss of a particle in matter is chosen the stopping power $\widehat{\mathrm{South}}$ ,

(eight.2) $\hat{S}=\text{d}{E}_{\mathrm{loss}}/\text{d}x\left(\mathrm{J}/\mathrm{m}\right)$

where ten is the distance traversed by the particle. To a adept start approximation the stopping power of a material is determined past its atomic limerick and is almost independent of the chemical binding of the atoms. Stopping power is a part of the particle velocity and changes as the particle is slowed downward.

The specific ionization J is the number of ion pairs produced per unit path length

(8.3) $J=\text{d}{N}_{\mathrm{j}}/\text{d}\mathrm{ten}\left(\text{ion}\text{pairs/m}\right)$

The value of J depends on the particle and its energy as seen from Effigy 7.seven. The relation between $\widehat{\mathrm{South}}$ and J is

(8.4) $\widehat{\mathrm{Southward}}=\mathrm{due\; west}J\left(\text{J}/\text{m}\right)$

The mass stopping ability, Ŝ/ρ, is commonly expressed in units of MeV/g cm².

Another important concept is the linear energy transfer (abbreviated as Permit) of charged particles. It is defined equally the free energy absorbed in thing per unit path length travelled by a charged particle

(eight.5) $L\mathrm{East}T=\text{d}{E}_{\text{abs}}/\text{d}x$

Values of LET in h2o are given for diverse particles and energies in Table vii.two. For the aforementioned energy and the aforementioned absorbing material, the LET values increment in the order:

high energy electrons (also approximatively γ-rays

< β-particles (also approximately soft 10-rays)

< protons

< deuterons

< heavy ions (ions of N, O, etc.)

< fission fragments

The relationship between Allow, which refers to the energy absorbed in matter, and the stopping power, which refers to the energy loss of the particle, is

(8.half-dozen) $\text{d}{\mathrm{Eastward}}_{\text{loss}}/\text{d}x=\text{d}{E}_{\text{abs}}/\text{d}\mathrm{ten}+{\mathrm{Eastward}}_{\text{10}}$

The divergence East _x in these two energy terms is related to the energy loss past electromagnetic radiation (mainly bremsstrahlung).

8.1.2 Uncharged radiation

When neutrons or photons having the incident particle energy Eastward _in are absorbed, a certain fraction of energy East _tr is transferred into kinetic free energy of charged particles when traversing the altitude dx. We can ascertain an energy transfer coefficient every bit

(8.7) ${\mu }_{\text{tr}}=E_{\text{in}}^{-\mathrm{one}}\mathrm{d}{\mathrm{Eastward}}_{\text{tr}}/\text{d}x\left({\text{m}}^{-1}\right)$

If we fail the bremsstrahlung associated with the absorption of the secondary charged particles formed in the initial assimilation processes, E _tr is the energy absorbed (designated as Due east _abs), and we tin can write Eqn (eight.7) as

(8.8) ${\mu }_{\text{a}}={\mathrm{East}}_{\text{in}}^{-1}\text{d}{E}_{\text{abs}}/\text{d}\mathrm{ten}\left({\text{thou}}^{-1}\right)$

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The Resolution Revolution: Recent Advances In cryoEM

R.Thousand. Glaeser , in Methods in Enzymology, 2016

2.3 Values of the Linear Energy Transfer (Let) Can Be Used to Estimate the Energy Deposited

The term "linear energy transfer (LET)" is used to indicate the average amount of energy that is lost per unit path-length equally a charged particle travels through a given textile. The LET for electrons is traditionally expressed in units of MeV/cm, or, when divided by the mass density, in units of MeV-cm ²/thousand. Values of the LET for electrons have been tabulated for many materials and for a wide range of energies of the incident electrons (Berger & Selzer, 1964).

The average amount of energy deposited in a thin sample, per electron, can exist estimated by multiplying the Allow by the sample thickness, t. Similarly, the total energy deposited per gram of a specimen, following an exposure of N electrons/area, is

(1) $E=\frac{\mathrm{Allow}\cdot N}{\rho }$

where ρ is the mass density of the specimen material.

The energy deposited per gram is referred to every bit the radiation dose. Radiation doses are usually expressed in rads in the older literature, where 1   rad is equal to 100   erg/g. Alternatively the dose is expressed in the Standard International (SI) units of gray (Gy), where 1   Gy   =   1   J/kg, and thus 1   rad   =   0.01   Gy. Since the dose is proportional to the electron exposure, information technology is commonly used jargon to refer to the exposure as being the "dose." While this terminology is non strictly right, the intended significant becomes understandable in context.

Taking vitreous ice every bit an example, the LET for 300   keV electrons, divided past the mass density, is ~   two.iv   MeV   cm^two/one thousand. It follows that a dose of ~   three.8   ×   10⁹  rad is deposited in a cryo-EM specimen equally a result of an electron exposure of x   east/Ų. This estimate is too loftier, of course, because not all of the energy lost by incident electrons is really deposited in a sparse sample. Rather, as mentioned before, some of the free energy escapes in the form of kinetic energy of secondary electrons. Depending upon the thickness of the specimen, the actual dose has been estimated to exist reduced by one-half or more (Grubb, 1974). Unless one is concerned nearly making a very precise estimate of the radiation dose, withal, it is not important to brand a correction for this upshot.

To farther illustrate the linear human relationship expressed in Eq. (1), the rad dose is plotted in Fig. ii every bit a part of electron exposure. The specimen is again taken to be vitreous ice, and the energy of the electrons is assumed to be 300   keV. More than is said beneath about each of the arrows shown in Fig. 2.

Fig. 2. Graph showing the linear human relationship between electron exposure (300   keV electrons) and the rad dose deposited in a specimen. Five annotated arrows are included in the graph to indicate the full general region of electron exposure at which various landmarks of radiations damage are incurred. The notation D₃₇ indicates the dose/exposure at which the desired signal falls to 37% (e^{−   1}) of its initial value.

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PROTECTIVE Furnishings ON MICROORGANISMS IN RADIATION STERILISED TISSUES

Jolyon H. Hendry , in Sterilisation of Tissues Using Ionising Radiations, 2005

Radiation quality

Densely ionising radiation (high linear free energy transfer, LET) is more efficient in killing cells, by a gene of three or more in terms of lower sterilisation doses in the case of neutrons or hadrons. There is less indirect activeness, and hence the furnishings of changes in oxygen tension and temperature are less. There is as well less repair, because of increasing complexity of the principal lesions every bit the density of the ionisations increases. Hence procedures designed to achieve differential modifications to radio sensitivity through the indirect action pathway will exist less applicative in the case of loftier Allow radiations.

Some other characteristic of neutrons is the higher interaction cantankerous-section with hydrogenous materials, and then that tissues with low hydrogen content such as bone will exist relatively protected. Cortical os contains 5% hydrogen past weight, in contrast to various soft tissues that comprise around 10%. This is an aspect worthy of investigation for os sterilisation; because the differential can be as much as 40% less absorbed dose in cortical bone compared to soft tissue when using seven.five to 25 MeV neutrons ^[8] . Hence the bone would be protected compared to the soft tissues, which may harbour pathogens.

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Applications and perspectives of boron nitride nanotubes in cancer therapy

Tiago Hilario Ferreira , Edesia M.B. de Sousa , in Boron Nitride Nanotubes in Nanomedicine, 2016

6.vii Boron neutron capture therapy

Boron neutron capture therapy (BNCT) is a high-linear free energy transfer (LET) radiotherapy exploitable for cancer treatment, based on the nuclear capture and fission reactions that occur when ¹⁰B is irradiated with thermal neutrons to produce an alpha particle (⁴He) and a ⁷Li nucleus (Fig. 6.5 and Eq. 6.one) [74].

Figure six.5. Schematic representation of the boron neutron capture therapy

(6.1) ${}^{10}\text{B}+n\text{thursday}\to {}^{11}\text{B}*\to \alpha +{}^{\mathrm{vii}}\text{Li}+2.31\text{MeV}$

For BNCT to be successful, a sufficient number of ^tenB atoms (approximately 10^ix atoms/cell) should be selectively delivered to the tumor, and enough thermal neutrons must be absorbed by them to sustain a lethal ¹⁰B(n,α)^sevenLi-capture reaction. The subversive effects of these high-energy particles are limited to boron-containing cells, and having both particles a range comparable to the diameter of a jail cell, they can cause selective tumor cell decease without significant amercement to the surrounding normal tissues, provided that the boron-carrier compound accumulates preferentially in tumor cells [10]. In this context, BNCT is a potentially promising treatment for malignant brain tumors every bit well as for other cancers, despite the limitation due to a scarcity of neutron sources. Information technology is worth mentioning that dissimilar other elements used in radiotherapy, the ^tenB employed in BNCT treatment is nonradioactive [75].

Almost of the compounds that are usually exploited in BNCT can normally deliver merely one or ii boron atoms per molecule, and ofttimes without cancer cell specificity. In this sense, highly boron-enriched nanocomposites might permit a selective commitment of a consistent amount of boron to the tumor [76–78].

The utilise of BNNT in this therapy could let some important current limitations of BNCT to be solved [79]. Considering of their high boron amount, BNNTs can well-nigh deliver a significant number of boron atoms to the tumor. One time functionalized with targeting molecules, BNNTs tin can specifically achieve tumor cells, further improving B accumulation at the diseased site and thus enhancing the effectiveness of the BNCT while reducing the effects in the surrounding healthy tissues.

Apart from the earlier mentioned preliminary written report of Ciofani et al. [58], recently Nakamura and colleagues demonstrated for the first time the antitumor event of BNNTs in combination with thermal neutron irradiation on cancer cells [eighty]. It was observed that BNNT-DSPE-PEG2000 accrue in B16 cells approximately three times higher than sodium borocaptate (BSH, a typical drug used in BNCT) and that a higher BNCT antitumor effect was observed in the cells treated with BNNT–DSPE-PEG2000 compared to those treated with BSH, strongly supporting BNNTs equally possible B-carrier candidate in BNCT.

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Radiation Toxicology, Ionizing and Nonionizing

B.R. Scott , in Encyclopedia of Toxicology (Third Edition), 2014

Chromosome Disorders

Ii forms of genomic damage that depend on radiation quality (i.eastward., LET) are the induction of single-strand breaks (SSBs) and double-strand breaks (DSBs). The two types of damage are considered to exist important considering SSBs are more than easily and accurately repaired by the cell than DSBs. Thus, DSBs result in damage that is both more lethal and more than able to outcome in chromosome disorders. For low-Allow radiations, increased production of DSBs is a function of dose rate, equally single tracks are so sparsely ionizing that breaking more than than one chromosome with a single rail is unlikely, peculiarly at depression radiations doses; therefore, DSBs arise as a result of multiple tracks occurring sufficiently close in time and space. On the other hand, loftier-Permit radiations produces a high enough ionization density within its tracks that DSBs tin occur from unmarried traversals of a cell nucleus. This, in part, is responsible for the greater RBE for high-LET radiation for cell killing, mutation induction, cell transformation, and cancer induction.

Damage that is produced by radiation tin be chromosomal or chromatid, depending on whether the cell is in a pre- or postreplication state. In either case, sufficient energy is imparted to interruption a chromosome or chromatid, usually into a major and a pocket-size fragment. Once this has occurred: (1) the broken ends may rejoin to restore the chromosome'southward original configuration; (2) a fragment may fail to rejoin, resulting in a deletion, which is sometimes large enough to be scored every bit a micronucleus; or (3) broken ends may rejoin with other broken ends to yield abnormal forms that are after scored at the post-obit mitosis as rings, dicentrics, anaphase bridges, or symmetric and asymmetric translocations.

Chromosome anomalies and aberrations tin can influence heredity. Most somatic cells of humans contain 23 pairs of chromosomes, with i member of each pair contributed by the sperm and the other contributed by the egg. When the procedure of sperm or egg cell product goes awry as a result of radiation damage, abnormal chromosome numbers (aneuploidy) can arise. Aneuploidy is a class of genetic instability.

It has been estimated that in approximately ninety% of cases, aneuploidy will result in spontaneous loss of pregnancy. In the remaining 10% of cases, a severely affected child would be expected because of the inherited genomic instability. Conditions such equally Down syndrome and both Klinefelter and Turner anomalies are the result of genomic instability associated with aneuploidy. These defects are relatively severe, in terms of both life expectancy (∼45 years) and level of disability (∼50%). Persons born with aneuploidy unremarkably are physiologically and morphologically abnormal and do non have children. Thus, their genomic instability tends not to be passed on to other generations.

Chromosomes can be hands broken by radiation, which can lead to a structural rearrangement (called a translocation). Translocations are also a form of genomic instability. When translocations occur in germ cells, they tin be transmitted to the offspring. Translocations usually yield chromosomes with besides little or as well much genetic information. If a child is born with a balanced translocation (not too little or too much data) he or she would not commonly be affected just could pass on genomic instability to future generations. Those born with such genomic instability could suffer astringent physical and mental disabilities.

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Contemporary Aspects of Boron: Chemistry and Biological Applications

A.K. Azab , ... Yard. Srebnik , in Studies in Inorganic Chemistry, 2005

v. Summary

BNCT is based on capture reaction between the ^x B atom and a neutron to generate loftier linear energy transfer of α-particles and recoiling 7Li nuclei. Neither the boron nor the neutrons each lone can cause tissue damage; nonetheless, the neutron absorption past the boron provides the high energy to be constructive in the biological compartment. For this binary system (BNCT) to be successful, not but high energy neutron beams have to be employed, just also loftier tumor concentrations of ¹⁰B and high tumor: normal tissue ratio must be accomplished. BNCT was initially implemented in brain tumors and melanomas; however it seems that it will exist gradually expanded to other types of cancer in future. Several boronic entities have been used clinically with limited successful results; all the same, more than entities are existence investigated in laboratories with promising potentials. Today, simply few clinical trials on BNCT take been conducted around the world, i major reason for its limited use can be attributed to the neutron source, which is a nuclear reactor and its high costs. If the clinical results would justify the costs, BNCT may accept the opportunity to become a daily process in hospital all over the world. Withal, the results from the clinical trial of BNCT are not groundbreaking, and that is attributed, equally in other cancer therapies, to the lack of sufficient differentiation between tumor and normal cells. The research in the hereafter should be focused on studying and developing new boron entities with such biochemical and physicochemical backdrop to achieve tumor targeting in vivo, and to bring it to the clinical use.

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NUCLEAR RADIATION, ITS INTERACTION WITH MATTER AND RADIOISOTOPE DECAY

MICHAEL F. L'ANNUNZIATA , in Handbook of Radioactive decay Analysis (Second Edition), 2003

B. Linear Energy Transfer

The International Committee on Radiation Units and Measurements or ICRU (Taylor et al., 1970) defines linear energy transfer ( 50) of charged particles in a medium as

(ane.139) $L=\frac{\text{d}{E}_{\mathrm{Fifty}}}{\text{d}\mathrm{50}}$

where dEastward_L is the average energy locally imparted to the medium by a charged particle of specified free energy in traversing a altitude dl. The term "locally imparted" refers either to a maximum altitude from the particle runway or to a maximum value of discrete energy loss by the particle beyond which losses are no longer considered as local. Linear energy transfer or LET is mostly measured in units of keV μm⁻¹. The ICRU recommends when a restricted form of LET is desired, that the energy cutting-off course of Permit be practical because this tin can be evaluated using restricted stopping-power formulae (Taylor et al., 1970). The energy-restricted course of LET or L _Δ is therefore defined as that office of the total energy loss of a charged particle which is due to energy transfers up to a specified energy cutting-off value

(ane.140) $L_{\Delta }={\left(\frac{\text{d}E}{\text{d}l}\right)}_{\Delta }$

where the cut-off free energy (Δ) in eV units must be defined or stated. If no cutting-off energy is applied then the subscript ∞ is used in place of Δ, where L _∞ would signify the value of Allow, which includes all energy losses and would therefore be equal to the total mass stopping power.

Fig. 1.31 illustrates charged particle interactions within an absorber involved in the measurement of Allow. The possible types of energy loss, ΔEastward, of a charged particle of specified energy, East, traversing an absorber over a track length Δl is illustrated, where O represents a particle traversing the observer without any free energy loss, U is the free energy transferred to a localized interaction site, q is the free energy transferred to a short-range secondary particle when q ≤ Δ, and Δ is a selected cut-off free energy level (e.m., 100 eV), Q′ is the energy transferred to a long-range secondary particle (due east.g., germination of delta rays) for which Q′ > Δ, γ is the energy transferred to photons (e.g., excitation fluorescence, Cherenkov photons, etc.), r is a selected cut-off distance from the particle's initial trajectory or path of travel, and θ is the bending of particle scatter. The interactions q, Q, and γ are subdivided in Fig. 1.31 when these fall into different compartments of the cushion medium. Meet Taylor et al. (1970) for methods used for the precise calculations of LET. Some examples of LET in water for diverse radiations types are given in Table i.10. The table clearly illustrates that radiation of a given free energy with shorter range in a medium will yield higher values of Let than radiations of the same free energy with longer ranges in the aforementioned medium. This may be intuitively obvious, because the shorter the range of the radiation the greater is the energy dissipated per unit path length of travel. We can take this further and generalize that the post-obit radiation types will yield Allow values of decreasing orders of magnitude (the heavier charged particles are considered hither to be of the same energy for purposes of comparison) co-ordinate to the sequence:

FIGURE i.31. Diagram of the passage of particle of energy E through a thickness Δl of cloth illustrating the several types of energy loss that may occur.

(From Taylor et al., 1970.) Copyright © 1970

TABLE i.ten. Rails-average Values of LET $\left({\overline{\mathrm{Fifty}}}_{\Delta }\right)$ in Water Irradiated with Various Radiations ^a

Radiation	Cut-off Energy, Δ (eV)	${\overline{L}}_{\Delta }\left(\text{keV}\mu {\text{m}}^{-1}\right)$
60Co gamma rays	Unrestricted	0.239
	10,000	0.232
	ane,000	0.230
	100	0.229
22-MeV x-rays	100	0.19
2-MeV electrons (whole track)	100	0.xx
200-kV ten-rays	100	1.7
3H beta particles	100	4.seven
50-kV ten-rays	100	6.iii
v.three MeV blastoff particles (whole rail)	100	43

a

From Taylor et al. (1970).

(1.141) $\left[\begin{array}{l}\text{Decreasing Let:}\\ \text{FissionProducts}>\text{Alpha Particles}>\text{Deuterons}>\text{Protons}>\\ \text{Depression-energy x-Rays and Beta Particles}>\text{High-energy}\\ \text{ten-Rays and Beta Particles}>\\ \text{Gamma Radiation and High-energy Beta Particles}\end{array}\right]$

Although the electromagnetic x- and gamma radiations are not charged particles, these radiations practice take the characteristics of particles (photons), that produce ionization in matter. They are, therefore, included in the above sequence (1.141) and among the radiations listed in Table ane.10.

The term delta rays, referred to in the previous paragraph, is used to identify energetic electrons that produce secondary ionization. When a charged particle, such as an alpha particle, travels through matter ionization occurs principally through coulombic attraction of orbital electrons to the positive charge on the alpha particle with the ejection of electrons of such low free energy that these electrons do not produce farther ionization. However, direct head-on collisions of the primary ionizing particle with an electron does occur occasionally whereby a large amount of energy is transferred to the electron. The energetic electron volition so travel on in the absorbing matter to produce secondary ionization. These energetic electrons are referred to as delta rays. Delta rays class ionization tracks away from the runway produced past the primary ionizing particle. The occurrence and effects of delta rays in radiations absorption are applied to studies of radiations dosimetry (Casnati et al., 1998 and Cucinotta et al., 1998).

When we compare particles of similar energy, we can state that, the ranges of particles of greater mass and accuse will evidently be shorter and the magnitude of their LET values would exist consequently higher in any given medium. The relationship betwixt mass, charge, free energy, range of particles, and their respective LET values tin can be appreciated from Tabular array 1.eleven. The Allow values in Tabular array 1.11 are estimated by dividing the radiations energy by its range or path length in the medium. Such a calculation provides only an gauge of the LET, because the free energy dissipated past the radiation will vary along its path of travel, particularly in the case of charged particles, more energy is released when the particle slows downwards earlier it comes to a end as illustrated in Fig. ane.3, when free energy liberated in ion-pair formation is the highest. However, the LET values provided in Table 1.11 requite good orders of magnitude for comparative purposes.

TABLE 1.11. Range and LET Values for Diverse Charged-Particle Radiations in Water in Order of Decreasing Mass ^a

Nuclide	Radiation Energy (MeV)	Range in H2o (mm)	Average LET in Water (keV μm−1)
Thorium-232	α, iv.0	0.029 b	138
Americium-241	α, 5.5	0.048 b	114
Thorium-227	α, 6.0	0.055 b	109
Polonium-211	α, 7.4	0.075 b	98
—	d, 4.0	0.219 c	18.3
—	d, v.5	0.377 c	fourteen.six
—	d, vi.0	0.440 c	13.6
—	d, 7.iv	0.611 c	12.i
—	p, iv.0	0.355 d	11.3
—	p, 5.five	0.613 e	9.0
—	p, half-dozen.0	0.699 f	8.half-dozen
—	p, seven.4	1.009 g	seven.iii
Tritium	β−, 0.0186 (E max)	0.00575 h	iii.2 h
Carbon-fourteen	β−, 0.156 (E max)	0.280 h	0.56 h
Phosphorus-32	β−, ane.710 (E max)	7.92 h	0.22*
Yttrium-90	β−, two.280 (East max)	10.99 h	0.21 h

a

The deuteron (d) and proton (p) energies were arbitrarily selected to correspond to the blastoff particle (α) energies to facilitate the comparison of the furnishings of particle mass and charge on range and LET.

b

Calculated according to Eqs. 1.14 and 1.15.

c

The deuteron range is calculated from the equation R_Z,M,E = M/Z ² R_p,Eastward/M . The equation provides the range of a particle of charge Z, mass M, and energy E, where R_{p,Eastward/Yard} is the range in the same absorber of a proton of energy Due east/M (Friedlander et al., 1964).

d

Calculated co-ordinate to Eqs. 1.12, 1.14 and 1.15, R _air = 28.5 mg cm⁻² (Fig. B.i, Appendix B).

east

Calculated according to Eqs. 1.12, 1.14 and ane.15, R _air = 49.5 mg cm⁻² (Fig. B.3).

f

Calculated according to Eqs. 1.12, 1.xiv and 1.xv, R _air = 56.five mg cm⁻² (Fig. B.1).

g

Calculated according to Eqs. 1.12, i.14 and 1.15, R _air = 82.0 mg cm^−two (Fig. B.ane).

h

Calculations are based on the maximum energy (E _max) of the beta particles. When the lower value of average beta particle-free energy (Due east _av) is used, the calculated value of range would be shorter and LET higher. The range was calculated co-ordinate to the empirical formula R = 0.412E ^{1.27–0.0954lnE} available from the curve provided in Fig. B.iii, Appendix B.

The concept of LET and the calculated values of LET for dissimilar radiations types and energies tin help us translate and sometimes even predict the furnishings of ionizing radiation on matter. For example, we tin predict that heavy charged particles, such as blastoff radiation, will dissipate their energy at shorter distances within a given absorber trunk than the more penetrating beta- or gamma radiations. As well, low-energy x-radiations can produce a similar effect every bit certain beta radiations. The gild of magnitude of the LET will help us predict the penetration ability and caste of energy dissipation in an absorber torso, which is disquisitional information in studies of radiation chemistry, radiation therapy, and dosimetry, among others. For boosted information, the reader is referred to works by Ehman and Vance (1991), Farhataziz and Rodgers (1987), and Spinks and Woods (1990).

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Gas Ionization Detectors

Georg Steinhauser , Karl Buchtela , in Handbook of Radioactivity Analysis (Third Edition), 2012

F Liquid Ionization and Proportional Detectors

Detector materials of high density offering some advantages, particularly for the detection of radiation with depression linear energy transfer and loftier energy. Radiation spectroscopy in many cases can be carried out much more reliably using detector materials of higher density. Consequently, research related to liquid- and solid-state ionization detectors is carried out. Noble gases in the liquid or solid phase are dielectric materials where created electrons remain gratuitous if all electronegative impurities can be removed.

Among the noble gases, xenon has attracted much interest as a filling medium for ionization-type detectors, such every bit ion chambers and proportional counting systems. The start of the ion multiplication phenomenon is observed at a field strength of 10⁸  5/yard. At 10^five  V/yard, the electron drift velocity is about iii   ×   10³  chiliad/s. Main obstacles to the construction of such detectors are the requirements for performance at a low temperature and for extensive purification of the detector medium. Liquid xenon ionization chambers compared with sodium iodide (NaI) detectors have a similar gamma efficiency and a higher energy resolution (L'Annunziata, 1987). Of grade, the energy resolution of semiconductor gamma detectors is still better.

The size of useful liquid or solid noble-gas ionization detectors depends on the purity of the filling material. Position sensing by big detectors can be carried out by measuring the electron migrate time. Gridded versions of such ion chamber detectors have also been reported.

Liquid ionization chambers (Ar and Xe) are frequently used in basic nuclear physics, e.thou. for the search for weakly interacting massive particles (WIMPs), such as the neutrinos predicted by supersymmetric theories (Ovchinnikov and Parusov, 1999).

Some information is available related to nonpolar liquids equally ionization detectors at room temperature. Here, the purity that tin be achieved and maintained for the applied material is extremely important. Inquiry has been carried out using, for case, tetramethylsilane. This material was used for ion chambers working in pulse and current mode (Knoll, 2010).

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Gas ionization detectors

Georg Steinhauser , Karl Buchtela , in Handbook of Radioactivity Analysis (Quaternary Edition), 2020

F Liquid ionization and proportional detectors

Detector materials of high density offering some advantages, particularly for the detection of radiation with low Allow and high free energy. Radiation spectroscopy in many cases tin exist carried out much more reliably using detector materials of higher density. Consequently, inquiry related to liquid and solid-land ionization detectors is carried out. Noble gases in the liquid or solid phase are dielectric materials where created electrons remain gratuitous in one case all electronegative impurities accept been removed.

Among the noble gases, xenon has attracted much interest as a filling medium for ionization-blazon detectors (Incicchitti et al., 1990), such as ion chambers and PC systems. The start of the ion multiplication phenomenon is observed at a field force of 10⁸  V/m. At 10⁵  V/grand, the electron drift velocity is about 3   ×   ten³  g/s. Chief obstacles to the construction of such detectors are the requirements for operation at a depression temperature and for all-encompassing purification of the detector medium. Liquid xenon ionization chambers compared with sodium iodide (NaI) detectors take a similar gamma efficiency and a higher energy resolution (50'Annunziata, 1987). Of grade, the energy resolution of semiconductor gamma detectors is however meliorate.

The size of useful liquid or solid element of group 0 ionization detectors depends on the purity of the filling fabric. Position sensing by large detectors can exist carried out by measuring the electron drift fourth dimension. Gridded versions of such ion chamber detectors have too been reported.

Liquid ionization chambers (He, Ar, Xe) are ofttimes used in basic nuclear physics, for example, for the search for weakly interacting massive particles, such as the neutrinos predicted by supersymmetric theories (Ovchinnikov and Parusov, 1999; Masaoka et al., 2000).

Liquid xenon is also used in proportional scintillation detectors (Aprile et al., 2014), which finds awarding in the search for dark affair. Arazi et al. (2013) observed proportional luminescence (secondary scintillation) in the holes of a THGEM immersed in liquid xenon, when bombarded with 662   keV gamma photons or 4   MeV alpha particles. This brilliance was establish to be nigh linear to the practical voltage. The observation may result in novel detector systems.

Piddling data is available related to nonpolar liquids as ionization detectors at room temperature. Here, the purity that can be achieved and maintained for the applied material is extremely important. Research has been carried out using, for case, tetramethylsilane. This material was used for ion chambers working in pulse and current mode (Knoll, 1989).

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Theory of Heavy Ion Standoff Physics in Hadron Therapy

Roberto D. Rivarola , ... Christophe Champion , in Advances in Quantum Chemical science, 2013

five.ane Linear energy transfer

While mean stopping power refers to the energy lost by the particle beam traversing the surrounding media, linear free energy transfer (Let) refers to the energy absorbed by the media per unit of measurement of altitude travelled past the ionizing radiation. LET or restricted stopping power is defined as the ratio:

(56) $L_{\mathrm{\Delta }\epsilon }=\frac{\mathrm{d}{\mathrm{Due\; east}}_{\mathrm{\Delta }\epsilon }}{\mathrm{d}l}\text{,}$

where $\mathrm{d}{E}_{\mathrm{\Delta }\epsilon }$ is the local mean energy captivated by the media by means of collisions involving transfer energies lower than a specific value $\mathrm{\Delta }\epsilon$ (cut value) and $\mathrm{d}l$ is the altitude traversed by the projectile. We understand past "local" the consideration of absorbed energies limited up past the maximum value $\mathrm{\Delta }\epsilon$ . Thus, $L_{\mathrm{\Delta }\epsilon }$ is related to the role of the mean stopping power involving transfer energies smaller than the cutting value $\mathrm{\Delta }\epsilon$ . Information technology can besides be related to the maximum distance reached (range) past electrons from the projectile track.

Different cut levels are usually selected to dissever delta rays as they are appropriate for different reactions. $L_{\infty }$ is divers as the energy captivated by the media per unit of measurement of distance traversed past the projectile when all possible energy transfers are considered. This quantity coincides numerically with the stopping power.

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